2009 NEHRP Recommended Seismic Provisions
for New Buildings and Other Structures:
PART 3,
RESOURCE PAPERS (RP) ON SPECIAL
TOPICS IN SEISMIC DESIGN
This part of the 2009 NEHRP Recommended Seismic Provisions consists of a series of resource papers that include:
• Proposals for code and standard changes reflecting new and innovative concepts or technologies that are judged, at the
time of publication of this edition of the Provisions, to require additional exposure to those who use codes and standards
and to possibly require systematic trial use. Some of these potential future changes are formatted for direct adoption
while others discuss only the thrust of the proposed change.
• Discussions of topics that historically have been difficult to adequately codify. These papers provide background
information intended to stimulate further discussion and research and, eventually, code change proposals.
Like Parts 1 and 2 of this volume, these resource papers have been approved for inclusion in this volume by both the 2009
Provisions Update Committee and the BSSC membership.
Comments and questions about the topics treated in these Part 3 resource papers should be addressed to:
Building Seismic Safety Council
National Institute of Building Sciences
1090 Vermont Avenue, N.W., Suite 700
Washington, D.C. 20005
(202) 2897800, Fax: (202) 2891092, Email: bssc@nibs.org
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Resource Paper 1
ALTERNATE MATERIALS, DESIGN, AND METHODS OF
CONSTRUCTION
Early in its deliberations, the 2009 Provisions Update Committee (PUC) established Issue Team 1, Performance Criteria, to
develop a proposal that would encourage the development of construction equivalent to that provided by prescriptive
provisions but possibly offering economic, performance, or construction speed advantages. The PUC took this step in light
of an ongoing FEMAfunded project to develop a recommended methodology for reliably quantifying building system
performance and response parameters for use in seismic design, in response to growing interest in performancebased
design and its use to develop alternate designs equivalent to prescriptive code provisions, and in recognition of the fact that a
lack of guidance on methods of approval for such submittals might discourage the creation of needed review processes in
some jurisdictions.
This paper was initially prepared by BSSC 2009 Issue Team 1 as a proposal for a Provisions Part 1 modification to Section
11.1.4 of ASCE/SEI 705. The voting by the BSSC member organizations, however, resulted in many comments about: use
of the new methodology prior to completion of the FEMA project and/or prior to complete vetting of the project
recommendations, approval methods for components and products on a smaller scale than full building systems, and the lack
of specificity in the suggested approval processes. Although the issue team developed complete responses to these comments,
the majority of the team recommended interim placement in Part 3 of the Provisions. Due to the high interest and need for
guidance on approval of submittals under the Alternate Means section, it is recommended that this or a similar change be
considered for inclusion in ASCE/SEI 705 as soon as possible.
PROPOSED CHANGE
Rearrange ASCE/SEI 705 Section 11.1.4.1 and add new Sec 11.1.4.2 as shown below (additions underlined).
11.1.4 Alternate Materials, Design, and Methods of Construction.
11.1.4.1 General. The provisions of this standard are not intended to prevent the use of any material, alternate design
method, or alternate method of construction not specifically prescribed, provided that any such alternate has been approved
and its use authorized by the authority having jurisdiction. The authority having jurisdiction may approve any such alternate,
provided that the authority finds that the alternate is satisfactory and complies with the intent of the provisions of this
standard, and that the alternate is, for the purpose intended, at least the equivalent of that prescribed in this standard in
suitability, effectiveness, durability, and seismic resistance.
11.1.4.2 Approval of Proposals Under Sec 11.1.4. Nothing in this section shall limit the ability of the authority having
jurisdiction to develop or accept general requirements for proposals under Section 11.1.4 or specific requirements for
particular components or systems, such as acceptance of reports from evaluation services or other demonstration of
equivalence as specified in Section 11.1.4.1. In the absence of such criteria, the approval process shall include the following
elements:
11.1.4.2.1 Peer Review. Peer review of the preliminary submittal, final design, and/or construction documents.
11.1.4.2.2 Preliminary Submittal. A submittal of a detailed description and, if applicable, design criteria for the alternate
material or method, for approval by the authority having jurisdiction, prior to application for a building permit.
11.1.4.2.3 Structural Design Criteria. For submittals requesting use of alternate materials, alternate design methods or
alternate methods of construction for the complete seismicforceresisting system, a structural design criteria shall be
included based on the seismic performance for the Performance Category, as described in the 2006 International Code
Council Performance Code, that is equivalent to the Occupancy Category of the building.
The design criteria submittal shall demonstrate how the required seismic performance will be met by generally following one
of the two methods described below:
1. Nonlinear procedures described in ASCE/SEI 4106, Seismic Rehabilitation of Existing Buildings.
2. Probabilistic nonlinear analysis methods of Quantification of Building Seismic Performance Factor, FEMA P695.
Using these methods, it shall be demonstrated that for the required performance objectives there is an acceptably low
probability of not reaching the specified performance level, given the specified ground motion.
11.1.4.2.4 Nonstructural Design Criteria. For seismic protection of nonstructural components not part of a designated
seismic system, the design shall demonstrate that the components and systems are capable of remaining secured to the
structure and will not generate lifethreatening debris under the Design Earthquake Ground Motion. For designated seismic
systems and components of such systems, the design shall demonstrate that the components and systems will be capable of
remaining functional following design level shaking. The procedures of Section 13.2.5 and 13.2.6 may be applied as
satisfactory fulfillment of these requirements.
Resource Paper 2
NONLINEAR STATIC PROCEDURE
This resource paper was prepared by Technical Subcommittee 2, Design Criteria and Analysis and Advanced Technologies,
as a replacement for the Appendix to Chapter 5 of the 2003 edition of the NEHRP Recommended Provisions. It revises the
information on the nonlinear static procedure (NSP) to allow its use in design of regular buildings less than 40 feet in height.
The principal value of this approach as currently presented is for the design of buildings that are controlled by drift limits.
Such buildings can be designed to have sufficient stiffness without using the equivalent lateral force (ELF) procedure and to
have sufficient strength without conducting detailed member evaluations (Rd < R/O 0). In the future, the height limitation
may be relaxed if, for example, the NSP is used in conjunction with a nonlinear dynamic analysis.
Because requirements for the nonlinear static procedure are now specified in ASCE/SEI 4106, it is simpler to refer to that
document than to write applicable requirements into the Provisions. Modifications to the ASCE/SEI 705 requirements are
introduced here to maintain consistency with the nonlinear static procedure information presented in the 2003 Provisions.
The 40foot height limit was selected based on the accuracy of response quantities determined for a threestory momentframe
structure; no height limit was identified in the FEMAfunded Applied Technology Council project on the evaluation of
inelastic seismic analysis procedures (Improvement of Nonlinear Static Seismic Analysis Procedures, FEMA 440). Although
higher modes will have a similar influence on ELF quantities, the higher base shear strengths and story shears of the ELF
procedure will tend to result in smaller member ductility demands. Thus, precision in the NSP estimates is especially
important when system strengths are lower than those resulting from use of the ELF approach, which evaluates member
deformation demands in detail.
This resource paper simplifies the language used to establish whether lateral strength is nominally less than that required by
the ELF procedure. This is now stated succinctly as Rd > R/O o. Section references have been harmonized with ASCE/SEI 7
05 section numbers. If adopted for ASCE/SEI 710 or subsequent editions, the chapter number assigned to the requirements
portion of this paper will have to be substituted where “X” appears below.
REQUIREMENTS
X Nonlinear Static Procedure
X.1 Definitions
Target Displacement. An estimate of the maximum expected displacement of the control node, determined according to
Section 3.3.3.3.2 of ASCE/SEI 41 Supplement1 using Sa defined as a design earthquake spectral response acceleration
according to the 2009 NEHRP Recommended Seismic Provisions at the effective period.
X.2 Notation
QEi Force in ith member determined according to Section 12.15.8.
Rd The system strength ratio as determined by Equation X1.
Rmax The maximum strength ratio, defined by Equation 316 of ASCE/SEI 41 Supplement 1.
.i The deformations for member i.
O0 See Section 11.3.
X.3 Applicability. Regular structures less than 40 feet in height in Occupancy Categories I and II may be designed using
the nonlinear static procedure following the requirements of this chapter.
X.4 Seismicforceresisting System. The seismicforceresisting system shall conform to one of the types in Tables 12.21
and 15.41 and shall be in accordance with the seismic design category and height limitations indicated in these tables. The
appropriate response modification coefficient, R, and system overstrength factor, O0, identified in these tables shall be used,
subject to the additional requirements of this chapter.
X.5 Modeling and Analysis. Modeling and analysis shall conform to Section 3.3.3 of ASCE/SEI 41 Supplement 1 except
that: (a) Sa shall be defined as a design earthquake spectral response acceleration according to the NEHRP Recommended
Seismic Provisions at the effective period and (b) the analysis shall be conducted for seismic actions occurring
simultaneously with the effects of dead load in combination with not less than 25 percent of the required design live loads,
reduced as permitted for the area of a single floor. Pdelta effects shall be included in the analysis model, and dead and live
loads acting on the entire structure shall be represented in the model.
X.6 Maximum Strength Ratio. The system strength ratio, R
(X1)
where C
d, is given by Equation X1 as follows:
m, Vy, and W are as defined in Section 3.3.3.3.2 of ASCE/SEI 41 Supplement 1 and Sa is defined as a design
earthquake spectral response acceleration according to the 2009 NEHRP Recommended Seismic Provisions at the effective
period. Use of the nonlinear static procedure is not permitted when Rd exceeds Rmax.
X.7 Story Drift. The design story drift, ., taken as the value obtained for each story at the step at which the target
displacement is reached, shall not exceed the drift limit specified in Section 12.12.1 multiplied by 0.85R/Cd.
X.8 Member Strength. In addition to satisfying the requirements of Section 12.15.9, member strengths also shall satisfy the
requirements of Section 2.3 using E = 0, except that Section 12.4.3.2 shall apply when the effect of structural overstrength on
the design seismic force must be considered. When the effect of structural overstrength is considered, the value of the
individual member forces, QEi, obtained from the analysis at the target displacement shall be taken in place of the quantity
O0QE.
X.9 Detailed Evaluation. Detailed evaluation satisfying Sections X.9.1and X.9.2 is required if Rd exceeds R/O0.
X.9.1 Required Member Force and Deformation. For each nonlinear static analysis, the design response parameters,
including the individual member forces, QEi, and member deformations, .i, shall be taken as the values obtained from the
analysis at the step at which the target displacement is reached. Equation
/
a
d m
y
R S C
V W
=
X.9.2 Member Capacity. The adequacy of individual members and their connections to withstand the member forces, QEi,
and member deformations, .i, shall be evaluated based on laboratory test data for similar components. The effects of gravity
and other loads on member deformation capacity shall be considered in these evaluations. The deformation of a member
supporting gravity loads shall not exceed: (a) twothirds of the deformation that results in loss of ability to support gravity
loads and (b) twothirds of the deformation at which the member strength has deteriorated to less than the 70 percent of the
peak strength of the component model. The deformation of a member not required for gravity load support shall not exceed
twothirds of the value at which member strength has deteriorated to less than 70 percent of the peak strength of the
component model. Alternatively, it shall be permissible to deem member deformation to be acceptable if the deformation
does not exceed the value provided in ASCE/SEI 41 Supplement 1 for the Life Safety performance level.
Member forces shall be deemed acceptable if not in excess of expected capacities.
X.10 Design Review. A review of the design of the seismicforceresisting system and the supporting structural analyses
shall be performed by an independent team having experience in seismic analysis methods and the theory and application of
nonlinear seismic analysis and structural behavior under earthquake loading. The team shall be composed of at least two
members including at least one registered design professional. The design review shall include:
1. Review of any sitespecific seismic criteria employed in the analysis including the development of sitespecific spectra
and
2. Review of the determination of the target displacement and effective yield strength of the structure.
For those structures with Rd exceeding R/O0, the design review shall further include, but need not be limited to, the
following:
1. Review of acceptance criteria used to demonstrate the adequacy of structural elements and systems to withstand the
calculated force and deformation demands together with the laboratory and other data used to substantiate such criteria.
Review of the acceptance criteria for nonlinear procedures given in ASCE/SEI 41 Supplement 1 shall be at the discretion
of the design review team.
2. Review of the final design of the entire structural system and all supporting analyses.
The design review team shall issue a report that identifies, within the scope of the review, significant concerns and any
departures from general conformance with the NEHRP Recommended Provisions.
COMMENTARY
This resource paper presents proposed requirements for nonlinear static analysis, a seismic analysis procedure also sometimes
known as pushover analysis, for review and comment and for adoption into a subsequent edition of the NEHRP
Recommended Provisions.
Although nonlinear static analysis has only recently been included in design provisions for new building construction, the
procedure itself is not new and has been used for many years in both research and design applications. For example,
nonlinear static analysis has been used for many years as a standard methodology in the design of the offshore platform
structures for hydrodynamic effects and has been adopted recently in several standard methodologies for the seismic
evaluation and rehabilitation of building structures, including the Recommended Seismic Design Criteria for New Steel
MomentFrame Buildings (FEMA 350, 2000), Seismic Rehabilitation of Existing Buildings (ASCE/SEI 4106, 2007), and
Seismic Evaluation and Retrofit of Concrete Buildings (Applied Technology Council, 1996). Nonlinear static analysis also
forms the basis for earthquake loss estimation procedures contained in the earthquake module of the multihazard software
application HAZUSMH MR2 (FEMA, 2006) and its Advanced Engineering Building Module (FEMA, 2002). A critical
review of and improvement to nonlinear static analysis methods, Improvement of Nonlinear Static Seismic Analysis
Procedures, was published as FEMA 440 in 2005. Although it does not explicitly appear in the Provisions, the nonlinear
static analysis methodology also forms the basis for the equivalent lateral force procedures contained in the provisions for
baseisolated structures and structures with dampers.
One of the controversies surrounding the introduction of this methodology into the Provisions relates to the determination of
the limit deformation (sometimes called a target displacement). Several methodologies for estimating the amount of
deformation induced in a structure as a result of earthquake ground shaking have been proposed and are included in various
adoptions of the procedure. The approach presented in this paper is based on statistical correlations of the displacements
predicted by linear and nonlinear dynamic analyses of structures recommended in the FEMA 440 report (2005) on the
evaluation of inelastic seismic analysis procedures.
A second controversy relates to the limited availability of consensusbased acceptance criteria to be used to determine the
adequacy of a design once the forces and deformations produced by design earthquake ground shaking are estimated. It
should be noted that this limitation applies equally to the nonlinear response history approach, which already has been
adopted into building codes.
A third controversy relates to the effects of higher modes (or multidegreeoffreedom effects for structures responding
nonlinearly) on response quantities. FEMA 440 identifies significant disparities between response quantities determined by
nonlinear static analysis and those determined by nonlinear dynamic analysis for all but lowrise structures; therefore, use of
the nonlinear static procedure for the design of members proposed here is limited to structures 40 feet or less in height. This
limitation has resulted in the nonlinear static procedure being located in Part 3 of the Provisions. The nonlinear static
procedure may be used to ensure that structures designed according to the equivalent lateral force procedure achieve strengths
comparable to code expectations. Interstory drifts are compared with tabulated allowable story drifts to maintain consistency
with past practice, although it is recognized that larger interstory drifts should be anticipated due to higher mode or multidegree
offreedom effects.
Nonlinear static analysis provides a simplified method of directly evaluating nonlinear response of structures to strong
earthquake ground shaking that can be an attractive alternative to the more complex procedures of nonlinear response history
analysis. It may be useful for characterizing system strength and stiffness and for establishing that the structure develops a
desirable inelastic mechanism.
REFERENCES
American Society of Civil Engineers/Structural Engineering Institute. 2006. Seismic Rehabilitation of Existing Buildings,
ASCE/SEI 4106, with Supplement 1. American Society of Civil Engineers, Reston, Virginia.
Applied Technology Council. 1996. Seismic Evaluation and Retrofit of Concrete Buildings, SSC Report 9601. Seismic
Safety Commission, State of California, Sacramento, California.
Applied Technology Council. 2005. Improvement of Nonlinear Static Seismic Analysis Procedures, FEMA 440. FEMA,
Washington, D.C.
Building Seismic Safety Council. 2003. NEHRP Recommended Provisions for the Development of Seismic Regulations for
New Buildings and Other Structures, FEMA 450. FEMA, Washington, D.C.
Federal Emergency Management Agency. 2006. HAZUSMH MR2 Multihazard Loss Estimation Methodology, Earthquake
Model, Technical Manual. Prepared for FEMA by the National Institute of Building Sciences. FEMA, Washington, D.C.
Federal Emergency Management Agency. 2002. Earthquake Loss Estimation Methodology, HAZUS99SR2, Advanced
Engineering Building Module, Technical and User’s Manual. Prepared for FEMA by National Institute of Building
Sciences. FEMA, Washington, D.C.
Federal Emergency Management Agency. 2000. Recommended Seismic Design Criteria for New Steel MomentFrame
Buildings, FEMA 350. FEMA, Washington, D.C.
Resource Paper 3
SEISMICRESPONSEHISTORY ANALYSIS
This resource paper was developed by Technical Subcommittee 2, Design Criteria and Analysis and Advanced Technologies,
as a replacement for ASCE/SEI 705 Chapter 16, Seismic ResponseHistory Analysis. It reorganizes the chapter to eliminate
redundancy as well as inconsistencies and duplication of ASCE/SEI 705 Chapter 12 analysis requirements. When responsehistory
analyses (RHA) are used, they are commonly used as an maximum considered earthquake verification after a
preliminary design has been completed. This paper adds a number of important requirements for RHA conducted at the
risktargeted maximum considered earthquake level. Feedback will be appreciated.
PROPOSED REPLACEMENT FOR ASCE/SEI 705 CHAPTER 16,
SEISMICRESPONSEHISTORY ANALYSIS
16.1 GENERAL REQUIREMENTS
A responsehistory analysis (RHA) shall consist of an analysis of a mathematical model of the structure to determine, through
methods of numerical integration, its response to suites of ground motion acceleration histories. The analysis shall be
performed in accordance with the requirements of this chapter. Structures with elements of the seismicforceresisting
system responding significantly beyond their elastic limit shall satisfy Section 16.3.12. When the analysis is used to validate
a design that uses the exceptions in Section 16.1.1, the ground motions shall be scaled to the risktargeted maximum
considered earthquake (MCER) ground motion level in accordance with Section 16.2 and the acceptance criteria shall meet
Section 16.4.
16.1.1 Design Requirements. The design of the structure shall meet all requirements for equivalent lateral force or modal
response spectrum analysis in accordance with Section 12.6 except that specific exceptions to such requirements are
permitted to be taken, provided the exceptions are:
1. Identified clearly in the documentation submitted for design review and
2. Justified through rational application of the RHA.
16.1.2 Level of Ground Motion. The analysis shall be based on the MCER ground motions defined in Section 11.4.
16.1.3 Occupancy Categories III and IV. For Occupancy Categories III and IV, the ground motion is in accordance with
Section 16.1.2, but the acceptance criteria in accordance with Section 16.4 are more restrictive compared to values applicable
to Occupancy Categories I and II. When alternative acceptance criteria are used, they shall be demonstrated to be consistent
with the importance factor, I, in accordance with Section 11.5. Nonstructural elements shall be designed in accordance with
Chapter 13 using Ip as required by Section 13.1.3.
16.2 GROUND MOTION
A suite of not less than seven appropriate ground motions shall be used in the analysis.
Appropriate ground motion acceleration histories shall be obtained from records of events having magnitudes, fault distances,
and source mechanisms that are consistent with those that control the MCER. If a sufficient number of appropriate recorded
ground motion records is not available, appropriate simulated or modified ground motion records are permitted to be used to
as part of the total number required.
When applicable, the ground motion acceleration histories shall include near fault and directivity effects including direction
of fault rupture and velocity pulses as appropriate.
16.2.1 Duration. Each responsehistory analysis shall be run for the full duration of the ground motion except that the first
or last portion of the record is permitted to be truncated provided that the truncation does not significantly modify either the
frequency content or the number of cycles of ground motion with an amplitude sufficient to induce nonlinear response.
16.2.2 Twodimensional Analysis. When twodimensional analyses are performed, each ground motion shall consist of a
horizontal acceleration history. The ground motions shall be scaled such that the average value, over all ground motions, of
the 5percentdamped response spectra for the suite of motions is not less than the MCER response spectrum for the site for
periods ranging from 0.2T to 1.5T where T is the natural period of the structure in the fundamental mode for the direction of
response being analyzed.
16.2.3 Threedimensional Analysis. When threedimensional analysis is performed, ground motions shall consist of pairs
of appropriate horizontal ground motion acceleration components. For each pair of horizontal ground motion components, a
square root of the sum of the squares (SRSS) spectrum shall be constructed by taking the SRSS of the 5percentdamped
response spectra for the scaled components (for direct scaling, an identical scale factor is applied to both components of a
pair). Each pair of motions shall be scaled such that for each period between 0.2T and 1.5T, the average, over all component
pairs, of the SRSS spectra does not fall below 1.3 times the corresponding ordinate of the MCER response spectrum by more
than 10 percent.
16.3 MODELING AND ANALYSIS
Mathematical models shall conform to the requirements of Section 12.7. Design review requirements are described in
Section 16.5.
16.3.1 Interaction of Elements. The analysis shall consider the interaction of all structural and nonstructural elements that
can adversely affect the response of the structure to earthquake ground motions, including elements not designated as part of
the seismicforceresisting system.
16.3.2 Identification of Nonlinear Response. Documentation submitted for design review shall identify the elements in the
seismicforceresisting system (SFRS) designed for nonlinear seismic response. All other elements in the SFRS shall be
demonstrated by analysis to remain essentially elastic (refer to Section 16.4.3).
16.3.3 Twodimensional Analysis. A twodimensional analysis model is permitted to be used if Section 12.7.3 does not
require a threedimensional model or if documentation submitted for design review demonstrates that the twodimensional
analysis captures all significant threedimensional effects including plan torsion, nonorthogonal earthquake response,
engagement of overturning resistance through flange effects or transverse coupling, and nonorthogonal effects on strongcolumn
weakbeam behavior.
16.3.4 Direction of Loading. Twodimensional modeling shall account for direction of loading effects in accordance with
Section 12.5.
16.3.5 Diaphragm Modeling. Floor and roof diaphragms responding linearly shall be modeled according to Section 12.3.1.
Diaphragms responding beyond the linear range shall be modeled using nonlinear forcedeformation relationships if required
by Section 16.3.11
16.3.6 Seismic Mass. The masses used in the analytical model shall be as defined in Section 12.7.2. When modal
computation techniques are used for responsehistory computation, Section 12.9.1 shall be satisfied and the results shall be
multiplied by the ratio of the total mass to the mass participating in the modes included in the analysis.
16.3.7 Gravity Load. The modeling of and demands on elements in the analysis model shall be determined considering
earthquake effects acting in the presence of expected gravity loads. For building structures with ordinary occupancies,
expected gravity loads shall be taken as 1.0D + 0.5L
For live loads subject to reduction on the basis of area in accordance with Section 4.8, the tributary area shall be permitted to
be taken as the total floor area in the structure subject to that live load and KLL shall be set to 1.0.
For other occupancies or when the expected gravity load is not well represented by 1.0D + 0.5L or is highly variable, the
analysis shall be modified accordingly.
16.3.8 Pdelta Effects. Pdelta effects shall be included in the analysis using the gravity loads defined in Section 16.3.7.
16.3.9 Inherent Plan Torsion. Inherent plan torsion shall be included in accordance with Section 12.8.4.1.
16.3.10 Accidental Plan Torsion. If the accidental torsion requirements of Section 12.8.4.2 are included in the
determination of the strength of the nonlinear elements of the structure and in the analysis used to meet the requirements of
Section 16.1.1, inclusion of accidental torsion in the RHA is not required.
16.3.11 Nonlinear Modeling. The mathematical model shall directly account for the nonlinear hysteretic behavior of the
members and connections that comprise the structural elements.
The hysteretic forcedeformation behavior of elements shall be modeled consistent with applicable laboratory test data and
shall account for all significant yielding, strength degradation, stiffness degradation, hysteretic pinching, and interaction
effects indicated by such test data. Strength of elements shall be based on expected values considering material overstrength,
strain hardening, and hysteretic strength degradation at the expected range of deformation. The behavior model shall not be
extended to deformations beyond levels substantiated by test data.
Linear properties, consistent with the requirements of Section 12.7.3, are permitted to be used for those elements
demonstrated by the analysis to remain within their linear range of response.
16.3.12 Stiffness. To the extent that such effects are significant for the MCER response, element properties shall account for
the following:
1. Stiffness properties of reinforced concrete and reinforced masonry shall account for cracking and other phenomena that
affect effective initial stiffness including strain penetration, bond slip, joint and panel zone deformation, and tension shift
associated with shear cracking.
2. Stiffness properties of steel or other connected elements shall account for connection stiffness and, for moment frames,
the effect of panel zone (beamcolumn joint) deformations.
16.3.13 Damping. The equivalent viscous damping level shall not exceed 5 percent of critical damping for any mode
required to obtain the effective mass according to Section 12.7.2 unless substantiated. Documentation submitted for design
review shall identify how damping effects are included in the RHA to account for energy dissipation that is not considered
directly in the nonlinear analysis model.
16.4 ANALYSIS RESULTS
16.4.1 Design Values. The calculation of design values shall account for the signs of response parameters and the
combinations of response parameters (e.g., axial force and bending moment) that can govern the design.
16.4.2 Analysis Results. The response parameters of interest shall be calculated for each ground motion used for the RHA.
The peak value of each parameter shall be determined for each ground motion. The average of the peaks shall be used for
checking acceptance criteria. When a combination of response parameters is important (e.g., for elements resisting both
flexural and axial forces), these results shall be captured to be consistent with the acceptance criteria.
16.4.3 Acceptance Criteria for Ductile Behavior. Element response that satisfies the definition for deformationcontrolled
actions in Section 2.4.4.3 of ASCE/SEI 41 shall be evaluated on the basis of either nonlinear or linear behavior. If the
calculated force in an element does not exceed 1.5 times its nominal strength, that element is permitted to be considered
linear (essentially elastic).
16.4.3.1 Nonlinear Behavior of Ductile Elements. Member deformation shall not result in deterioration of its attainable
member strength to less than 80 percent of the peak resistance. Deformation capacities shall be based on values tabulated in
ASCE/SEI 41 or from laboratory test data for similar elements. When ASCE/SEI 41 is used, the following performance
levels are to be used:
1. Collapse prevention for Occupancy Categories I and II,
2. Life safety for Occupancy Category IV, and
3. 80 percent of collapse prevention but not less than life safety for Occupancy Category III.
Documentation shall be submitted for design review to substantiate the adequacy of individual elements and their
connections to withstand the deformation demands from the RHA.
16.4.3.2 Linear Behavior of Ductile Elements. Calculated force demands shall not exceed 150 percent of nominal
capacities divided by the importance factor, I.
16.4.4 Acceptance Criteria for Nonductile Behavior. Any type of element response that does not satisfy the definition for
deformationcontrolled actions in Section 2.4.4.3 of ASCE/SEI 41 shall be evaluated on a linear basis. The demands from
Section 16.4.2 shall not exceed the expected strength. Nominal strength is permitted to be used in lieu of expected strength.
16.4.5 Story Drift. The story drift ratio shall not exceed 1.5 times the limits of Section 12.12.1 for any story unless those
elements not designated as part of the seismicforceresisting system are capable of undergoing the calculated story drift for
each RHA without collapse of the portion of the structure supported by those elements.
16.4.6 Stability. The structure shall be shown to be stable for the MCER ground motions.
16.5 Design Review. A design review of the seismicforceresisting system, the structural analysis, and the documentation
shall be performed by an independent team of registered design professionals in the appropriate disciplines and others
experienced in seismic analysis methods and the theory and application of nonlinear seismic analysis and structural behavior
under extreme cyclic loads. The design review shall include, but need not be limited to, the following:
1. Review of any sitespecific seismic criteria employed in the analysis including the development of sitespecific spectra
and ground motion time histories.
2. Review of acceptance criteria used to demonstrate the adequacy of structural elements and systems to withstand the
calculated force and deformation demands and laboratory and other data that substantiate these criteria.
3. Review of the preliminary design including the selection of structural system and the configuration of structural
elements.
4. Review of the final design of the entire structural system and all supporting analyses.
Resource Paper 4
FOUNDATION GEOTECHNICAL ULTIMATE STRENGTH DESIGN
AND FOUNDATION LOADDEFORMATION MODELING
(2003 Provisions Appendix to Chapter 7, Foundation Design Requirements)
This resource paper originally appeared as the appendix to Chapter 7, Foundation Design Requirements, of the 2003
NEHRP Recommended Provisions. It includes ultimate strength design (USD) procedures for the geotechnical design of
foundations for trial use and evaluation by design professionals prior to adoption into a subsequent edition of the Provisions.
Similarly, the resource paper presents criteria for the modeling of loaddeformation characteristics of the foundationsoil
system (foundation stiffness) for those analysis procedures in Chapter 5 of the 2003 Provisions that permit use of realistic
assumptions for foundation stiffness rather than the assumption of a fixed base. Note that only format changes have been
made and Provisions section numbers cited refer to the 2003 edition of the Provisions.
Practice for geotechnical foundation design has been based on allowable stresses with allowable foundation load capacities
for dead plus live loads based on limiting longterm static settlements and providing a large factor of safety. In current
practice, allowable soil stresses for dead plus live loads are typically increased by onethird for load combinations that
include wind or seismic forces. The allowable stresses for dead plus live loads are often far below ultimate soil capacity.
This resource paper’s Provisions and the associated Commentary provide criteria and guidance for the direct use of ultimate
foundation load capacity for load combinations that include seismic forces. The acceptance criteria cover both the analyses
for fixedbase assumptions and analyses for linear and nonlinear modeling of foundation stiffness for flexiblebase
assumptions.
Although USD for foundations has not previously been included in design provisions for new buildings, the same basic
principles used in this resource paper have been adapted to generate guidelines for the seismic evaluation and retrofit design
of existing buildings (FEMA 273; FEMA 356; Applied Technology Council, 1996). The criteria and procedures presented
herein for the nonlinear modeling of foundation stiffness combine a linear or multilinear stiffness and a limiting load
capacity based on ultimate soil strength and are essentially the same as those presented in the publications cited above.
With respect to the adoption of USD procedures for geotechnical foundation design, the primary issue considered by the
2003 Provisions Update Committee and the BSSC member organizations was the impact of the proposed USD procedures on
the size of foundations and the consequent effect on the potential for foundation rocking and building performance. A
synopsis of two sets of design examples is presented at the end of this resource paper. The example results illustrate the
expected effects of the methodology in that relative foundation sizes from USD vs. ASD are related to the factor of safety on
load capacity under vertical dead plus live loads. When factors of safety are high, smaller foundations result from USD, but
when factors of safety are low, it is possible that foundations may be larger using USD. Additional examples, including
nonlinear dynamic analyses incorporating nonlinear loaddeformation models for foundation soil stiffness and capacity, are
warranted to further evaluate and possibly refine the methodologies and criteria presented in this paper. It is hoped that
trial usage of the methodologies presented herein will allow the necessary consensus to be developed to permit later
incorporation into the Provisions. Feedback will be appreciated.
APPENDIX TO 2003 PROVISIONS CHAPTER 7, FOUNDATION DESIGN REQUIREMENTS
A7.1 General
A7.1.1 Scope. This resource paper includes only those foundation requirements that are specifically related to seismic
resistant construction. It assumes compliance with all other basic requirements which include, but are not limited to,
requirements for the extent of the foundation investigation, fills to be present or to be placed in the area of the structure, slope
stability, subsurface drainage, settlement control, and soil bearing and lateral soil pressure recommendations for loads acting
without seismic forces.
A7.1.2 Definitions
Allowable foundation load capacity: See Section A7.2.2.
Ultimate foundation load capacity: See Section A7.2.2.
A7.1.3 Notation
Qas Allowable foundation load capacity.
Qus Ultimate foundation load capacity.
f The strength reduction, capacity reduction, or resistance factor.
A7.2 General Design Requirements
The resisting capacities of the foundations, subjected to the load combinations prescribed elsewhere in these Provisions, shall
meet the requirements of this resource paper.
A7.2.1 Foundation Components. The strength and detailing of foundation components under seismic loading conditions,
including foundation elements and attachments of the foundation elements to the superstructure, shall comply with the
requirements of Chapters 8, 9, 10, 11, or 12, unless otherwise specified in this chapter. The strength of foundation
components shall not be less than that required for load combinations that do not include seismic load effects.
A7.2.2 Foundation Load Capacities. The vertical capacity of foundations (footings, piles, piers, mats or caissons) as
limited by the soil shall be sufficient to support the structure for all prescribed load combinations without seismic forces,
taking into account the settlement that the structure can withstand while providing an adequate factor of safety against failure.
Such capacities are defined as allowable foundation load capacities, Qas. For load combinations including seismic load
effects as specified in Section 4.2.2, vertical, lateral, and rocking load capacities of foundations as limited by the soil shall be
sufficient to resist loads with acceptable deformations, considering the short duration of loading, the dynamic properties of
the soil, and the ultimate load capacities, Qus, of the foundations under vertical, lateral, and rocking loading.
A7.2.2.1 Determination of Ultimate Foundation Load Capacities. Ultimate foundation load capacities shall be
determined by a qualified geotechnical engineer based on geotechnical site investigations that include field and laboratory
testing to determine soil classification and soil strength parameters, and/or capacities based on insitu testing of prototype
foundations. For competent soils that do not undergo strength degradation under seismic loading, strength parameters for
static loading conditions shall be used to compute ultimate load capacities for seismic design. For sensitive cohesive soils or
saturated cohesionless soils, the potential for earthquake induced strength degradation shall be considered.
Ultimate foundation load capacities, Qus, under vertical, lateral, and rocking loading shall be determined using accepted
foundation design procedures and principles of plastic analysis. Calculated ultimate load capacities, Qus, shall be bestestimated
values using soil properties that are representative average values for individual foundations. Bestestimated
values of Qus shall be reduced by resistance factors (f) to reflect uncertainties in site conditions and in the reliability of
analysis methods. The factored foundation load capacity, fQus, shall then be used to check acceptance criteria, and as the
foundation capacity in foundation nonlinear loaddeformation models.
If ultimate foundation load capacities are determined based on geotechnical site investigations including laboratory or insitu
tests, f factors equal to 0.8 for cohesive soils and 0.7 for cohesionless soils shall be used for vertical, lateral, and rocking
resistance for all foundation types. If ultimate foundation load capacities are determined based on fullscale fieldtesting of
prototype foundations, f factors equal to 1.0 for cohesive soils and 0.9 for cohesionless soils are permitted.
A7.2.2.2 Acceptance Criteria. For linear analysis procedures (Sections 5.2, 5.3, and 5.4), factored foundation load
capacities, fQus, shall not be exceeded for load combinations that include seismic load effects.
For the nonlinear response history procedure (Section 5.5) and the nonlinear static procedure (Appendix to Chapter 5), if the
factored foundation load capacity, fQus, is reached during seismic loading, the potential significance of associated transient
and permanent foundation displacements shall be evaluated. Foundation displacements are acceptable if they do not impair
the continuing function of Seismic Use Group III structures or the life safety of any structure.
For nonlinear analysis procedures, an additional evaluation of structural behavior shall be performed to check potential
changes in structural ductility demands due to higher than anticipated foundation capacity. For this additional evaluation,
values of Qus shall be increased by the factor 1/f.
A7.2.3 Foundation Loaddeformation Modeling. When permitted for the analysis procedures in Chapter 5 and the
Appendix to Chapter 5, the loaddeformation characteristics of the foundationsoil system (foundation stiffness), if included
in the analysis, shall be modeled in accordance with the requirements of this section. For linear analysis methods, the linear
loaddeformation behavior of foundations shall be represented by an equivalent linear stiffness using soil properties that are
compatible with the soil strain levels associated with the design earthquake motion. The straincompatible shear modulus, G,
and the associated straincompatible shear wave velocity, vS, needed for the evaluation of equivalent linear stiffness shall be
determined using the criteria in Section 5.6.2.1.1 or based on a sitespecific study. Parametric variations of not less than 50
percent increase and decrease in stiffness shall be incorporated in dynamic analyses unless smaller variations can be justified
based on field measurements of dynamic soil properties or direct measurements of dynamic foundation stiffness.
For nonlinear analysis methods, the nonlinear loaddeformation behavior of the foundationsoil system may be represented
by a bilinear or multilinear curve having an initial equivalent linear stiffness and a limiting foundation capacity. The initial
equivalent linear stiffness shall be determined as described above for linear analysis methods. The limiting foundation
capacity shall be taken as the factored foundation load capacity, fQus. Parametric variations in analyses shall include: (1) a
reduction in stiffness of 50 percent combined with a limiting foundation capacity, fQus, and (2) an increase in stiffness of 50
percent combined with a limiting foundation capacity equal to Qus increased by a factor 1/f.
COMMENTARY
CA7.2 General Design Requirements
CA7.2.2 Foundation Load Capacities. In current geotechnical engineering practice, foundation design is based on
allowable stresses, with allowable foundation load capacities, Qas, for dead plus live loads based on limiting static settlements
and providing a large factor of safety against exceeding ultimate capacities. In current practice, allowable soil stresses for
dead plus live loads are increased by onethird for load combinations that include wind or seismic forces. The onethird
increase is overly conservative if the allowable stresses for dead plus live loads are far below ultimate soil capacity. This
resource paper provides guidance for the direct use of ultimate foundation load capacity, Qus, for load combinations including
seismic effects. It is required that foundations be capable of resisting loads with acceptable deformations considering the
short duration of seismic loading, the dynamic properties of the soil, and the ultimate load capacities, Qus, of the foundations
under vertical, lateral, and rocking loading.
CA7.2.2.1. Determination of Ultimate Foundation Load Capacities. For competent soils that are not expected to
degrade in strength during seismic loading (e.g., due to partial or total liquefaction of cohesionless soils or strength reduction
of sensitive clays), use of static soil strengths is recommended for determining ultimate foundation load capacities, Qus. Use
of static strengths is somewhat conservative for such soils because rateofloading effects tend to increase soil strengths for
transient loading. Such rate effects are neglected because they may not result in significant strength increase for some soil
types and are difficult to confidently estimate without special dynamic testing programs. The assessment of the potential for
soil liquefaction or other mechanisms for reducing soil strengths is critical, because these effects may reduce soil strengths
greatly below static strengths in susceptible soils.
The bestestimated ultimate vertical load capacity of footings, Qus, should be determined using accepted foundation
engineering practice. In the absence of moment loading, the ultimate vertical load capacity of a rectangular footing of width
B and length L may be written as Qus = qcBL where qc = ultimate soil bearing pressure.
For rigid footings subject to moment and vertical load, contact stresses become concentrated at footing edges, particularly as
footing uplift occurs. The ultimate moment capacity, Mus, of the footing as limited by the soil is dependent upon the ratio of
the vertical load stress, q, to the ultimate soil bearing pressure qc. Assuming that contact stresses are proportional to vertical
displacements and remain elastic up to qc, it can be shown that uplift will occur prior to plastic yielding of the soils when q/qc
is less than 0.5. If q/ qc is greater than 0.5, then the soil at the toe will yield prior to uplift. This is illustrated in Figure CA7.2.2
1. In general the ultimate moment capacity of a rectangular footing may be expressed as:
where P = vertical load, q = P/BL, B = footing width, and L = footing length in direction of rotation.
The ultimate lateral load capacity of a footing may be assumed equal to the sum of the bestestimated ultimate soil passive
resistance against the vertical face of the footing plus the bestestimated ultimate soil friction force on the footing base. The
determination of ultimate passive resistance should consider the potential contribution of friction on the face of the footing on
the passive resistance.
For piles, the bestestimated ultimate vertical load capacity (for both axial compression and axial tensile loading) should be
determined using accepted foundation engineering practice. When evaluating axial tensile load capacity, consideration
should be given to the capability of pile cap and splice connections to take tensile loads. Equation
1
us 2
M LP q
qc
. .
= .  .
. .
The ultimate moment capacity of a pile group should be determined assuming a rigid pile cap, leading to an initial triangular
distribution of axial pile loading from applied overturning moments. However, full axial capacity of piles may be mobilized
when computing ultimate moment capacity, in a manner analogous to that described for a footing in Figure CA7.2.21. The
ultimate lateral capacity of a pile group may be assumed equal to the bestestimated ultimate passive resistance acting against
the edge of the pile cap and the additional passive resistance provided by piles.
Resistance factors, f, are provided to factor ultimate foundation load capacities, Qus, to reduced capacities, fQus, used to
check foundation acceptance criteria. The values of f recommended in the Provisions are higher than those recommended in
some codes and specifications for longterm static loading. The development of resistance factors for static loading has been
based on detailed reliability studies and on calibrations to give designs and factors of safety comparable to those given by
allowable stress design. As indicated in the first paragraph of this section, mobilized strengths for seismic loading conditions
are expected to be somewhat higher than the static strengths specified for use in obtaining values of Qus, especially for
cohesive soils. In the absence of any detailed reliability studies for seismic loading conditions, values of f equal to 0.8 and
0.7 were selected for cohesive and cohesionless soils, respectively, when geotechnical site investigations, including
laboratory or insitu tests, are conducted, and values of f equal to 1.0 and 0.9 were selected when fullscale field tests of
prototype foundations are conducted. These values are comparable to the values of 0.8 (for soil strengths determined based
on a comprehensive site soil investigation including soil sampling and testing) and 0.9 (for soil strengths determined by site
loading testing using plate bearing or near full scale foundation element testing) recommended by the SEAOC Seismology
Committee Ad Hoc Foundation Committee (2001).
CA7.2.2.2 Acceptance Criteria. The factored load capacity, fQus, provides the basis for the acceptance criteria,
particularly for the linear analysis procedures. The mobilization of ultimate capacity in the nonlinear analysis procedures
does not necessarily mean unacceptable performance as structural deformations due to foundation displacements may be
tolerable, as discussed by Martin and Lam (2000). For the nonlinear analysis procedures, it is also prudent to evaluate
structural behavior utilizing parametric increases in foundation load capacities above Qus by a factor of 1/f, to check potential
changes in structural ductility demands.
CA7.2.3 Foundation Loaddeformation Modeling. Analysis methods described in Section 5.3 (response spectrum
procedure) and Section 5.4 (linear response history procedure), permit the use of realistic assumptions for foundation
stiffness, as opposed to the assumption of a fixed base. In addition, the nonlinear response history procedure (Section 5.5)
and the nonlinear static procedure (Appendix to Chapter 5) permit the use of realistic assumptions for the stiffness and loadcarrying
characteristics of the foundations. Guidance for flexible foundation (nonfixed base) modeling for the above
analysis procedures are described herein.
Figure CA7.2.21.
Foundation loaddeformation behavior characterized by stiffness and load capacity may significantly influence the seismic
performance of a structure, with respect to both load demands and distribution among structural elements (ATC 1996,
NEHRP 1997a, 1997b). This is illustrated schematically in Figure CA 7.2.31. While it is recognized that the loaddeformation
behavior of foundations is nonlinear, an equivalent elastoplastic representation of loaddeformation behavior is
often assumed as illustrated in Figure CA 7.2.32. To allow for variability and uncertainty in the selection of soil parameters
Figure CA7.2.31 showing stiff/strong foundation and flexible/weak foundation and Figure CA7.2.32 showing loaddeformation
255
Figure CA7.2.32
and analysis methods used to determine stiffness and capacity, a range of parameters for foundation modeling should be used
to permit sensitivity evaluations.
Figure CA7.2.31
Figure CA7.2.32.
Consider the spread footing shown in Figure CA 7.2.33 with an applied vertical load (P), lateral load (H), and moment (M).
The soil characteristics might be modeled as two translational springs and a rotational spring, each characterized by a linear
elasticstiffness and a plastic capacity. The use of a Winkler spring model acting in conjunction with the foundation to
eliminate the rotational spring may also be used, as shown in Figure CA7.2.34. The Winkler model can capture more
accurately progressive mobilization of plastic capacity during rocking behavior. Note the lateral action is normally
uncoupled from the vertical and rotational action. Many foundation systems are relatively stiff and strong in the horizontal
direction, due to passive resistance against the face of footings or basement walls, and friction beneath footings and floor
slabs. Comparisons of horizontal stiffness of the foundation and the structure can provide guidance on the need to include
horizontal foundation stiffness in demand or capacity analyses. In general, foundation rocking has the most influence on
structural response. Slender shear wall structures founded on strip footings, in particular, are most sensitive to the effects of
foundation rocking.
Assuming a shallow footing foundation may be represented by an embedded rigid plate in an elastic halfspace, classical
elastic solutions may be used to compute the uncoupled elastic stiffness parameters. Representative solutions are described
in Commentary to Section 5.6. Solutions developed by Gazetas (1991) are also often used, as described in ATC (1996).
Dynamic soil properties (i.e. properties consistent with seismic wave velocities and associated moduli of the soils as opposed
to static soil moduli) should be used in dynamic soil solutions. The effects of nonlinearity on dynamic soil properties should
be incorporated using the reduction factors in Section 5.6.2.1.1 or based on a sitespecific study.
In the case of pile groups, the uncoupled spring model shown in Figure CA 7.2.33 also may be used, when the footing
represents the pile cap. In the case of the vertical and rotational springs, it can be assumed that the contribution of the pile
cap is relatively small compared to the contribution of the piles. In general, mobilization of passive pressures by either the
pile caps or basement walls will control lateral spring stiffness. Hence, estimates of lateral spring stiffness can be computed
using elastic solutions as for footings. In instances when piles may contribute significantly to lateral stiffness (i.e., very soft
soils, battered piles), solutions using beamcolumn pile models are recommended.
Axial pile group stiffness spring values, ksv, are generally in the range given by:
ksv = to
where A = crosssectional area of a pile, E = modulus of elasticity of piles, L = Length of piles, and N = number of piles in
group. Equation
0.5
1
N AE
n L
S
= Equation
2
1
N AE
n L
S
=
Values of axial stiffness depend on complex nonlinear interaction of the pile and soil (NEHRP, 1997b). For simplicity, best
estimate values of AE/L and 1.5 AE/L are recommended for piles when axial capacity is primarily controlled by end bearing
and side friction, respectively.
Figure CA7.2.33. Figure CA7.2.34.
The rocking spring stiffness values, ksr, about each horizontal pile cap axis may be computed by assuming each axial pile
spring acts as a discrete Winkler spring. The rotational spring constant (moment per unit rotation) is then given by:
where kvn = axial stiffness of the nth pile and Sn = distance between nth pile and axis of rotation. The effects of group action
and the influence of pile batter are not accounted for in the above equations. These effects should be evaluated if judged
significant.
Design Examples. In order to study and illustrate the effects of the change from allowable stress to ultimate strength design
of foundations a series of examples were generated. The examples compared the size of foundations resulting from ultimate
strength designs (USD) according to the new procedures with those that would be obtained from conventional allowable
stress designs (ASD). Equation
2
1 sr
N
k kvnSn n
= S
=
Figure CA7.2.35 Example building.
The examples were based upon a single sixstory reinforced concrete building with shear walls and gravity frame (see Figure
7.2.35). One set of examples was for a shallow spread footing design beneath a shear wall. The other set applied to deep
castindrilledhole (CIDH) piers placed beneath the same wall. For each set of examples, individual designs reflected a
range of soil strengths and ASD factors of safety. The vertical loads were not changed, but two levels of seismic overturning
demand were imposed.
While is not possible to generalize the results of these examples to apply universally, they are representative of the effects of
the change to USD for a realistic case study. For the spread footing foundation the area of the footing for USD compared to
that for ASD is controlled by the factor of safety applied to the soil strength for vertical loads. This reduction ranged from 0
to 20 percent for a low FOS (2) up to 25 to 40 percent for a high FOS (4). This is not surprising; when ASD uses a high
factor of safety and is thus most conservative, USD results in a smaller footing size. However, the footing size cannot be
smaller than that required for allowable stresses for static design under vertical dead plus live loads. For the pier example, the
required length for USD was actually about 50 percent greater than for ASD for a low FOS (1.5) and up to 40 percent less for
a high FOS (4).
Figure CA7.2.35 Example building.
REFERENCES
Applied Technology Council. 1996. Seismic Evaluation and Retrofit of Concrete Buildings, ATC 40, 2 volumes. Prepared
for the Seismic Safety Commission of the State of California. ATC, Redwood City, California.
Building Seismic Safety Council. 1997a and b. National Earthquake Hazard Reduction Program Guidelines and
Commentary for the Seismic Rehabilitation of Buildings, FEMA 273 and 274. Federal Emergency Management Agency,
Washington, D.C.
Gazetas, G. 1991. “Foundation Vibrations,” Foundation Engineering Handbook, 2nd Edition, Vas Nostrand Reinhold,
Edited by HsaiYang Fang.
Martin, G. R., and I. P. Lam. 2000. “Earthquake Resistant Design of Foundations: Retrofit of Existing Foundations,” in
GeoEng 2000, proceedings of the International Conference on Geological and Geotechnical Engineering, Melbourne,
Australia, November.
Structural Engineers Association of California, Seismology Committee, Ad Hoc Foundations Committee. 2001.
“USD/LRFD/Limit State Approach to Foundation Design,” in Proceedings of the 70th Annual SEAOC Convention, San
Diego, California.
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Resource Paper 5
ALTERNATIVE PROVISIONS
FOR THE DESIGN OF PIPING SYSTEMS
(2003 Provisions Appendix to Chapter 6, Architectural, Mechanical, and Electrical
Component Design Requirements)
Chapter 6, Architectural, Mechanical, and Electrical Component Design Requirements, of the 2003 NEHRP Recommended
Provisions did not recognize discrete levels of performance that may be relevant to the seismic design of piping systems,
particularly for essential facilities. This appendix was added to the 2003 Provisions to provide preliminary criteria for the
establishment of such performance criteria and their use in the assessment and design of piping systems. The situation has
not changed and this appendix and its commentary are reproduced here as a resource for use in the future. Note that only
format changes have been made and Provisions section numbers cited refer to the 2003 edition of the Provisions. The
performance criteria, from least restrictive to most severe, are: position retention, leak tightness, and operability. In
particular, the interaction of systems and interface with the relevant piping design standards is addressed.
PROVISIONS
A6.1 Definitions
Leak Tightness: The condition of a piping system characterized by containment of contents, or maintenance of a vacuum,
with no discernable leakage.
Operability: The condition of a piping system characterized by leak tightness as well as continued delivery, shutoff or
throttle of pipe contents flow by means of unimpaired operation of equipment and components such as pumps, compressors
and valves.
Position Retention: The condition of a piping system characterized by the absence of collapse or fall of any part of the
system.
A6.2 Design Approach
The seismic design of piping systems is determined on the basis of Seismic Design Category, Ip, and pipe size, as provided in
Table A6.21. For each case in Table A6.21, the procedure for seismic qualification is specified in Section A.6.5.
When IP = 1.0, the piping system is not critical and is required to maintain position retention.
When IP = 1.5, the piping system is critical and is required to exhibit leak tightness and may be required to maintain
operability.
Table A6.21 Seismic Design Requirements
IP = 1.0
IP = 1.5
Seismic
Design
Category
Pipe Size = 4 inch (SI:
102 mm)
Pipe Size > 4 inch (SI:
102 mm)
Pipe Size = 4 inch (SI:
102 mm)
Pipe Size > 4 inch (SI:
102 mm)
B
Interactions (A6.5.2.1)
Interactions (A6.5.2.1)
Bracing (A6.5.2.2)
Restraints (A6.5.2.3)
Operabilitya (A6.5.2.4)
Interactions (A6.5.2.1)
Bracing (A6.5.2.2)
Restraints (A6.5.2.3)
Operabilitya (A6.5.2.4)
Interactions (A6.5.2.1)
C or D
Interactions (A6.5.2.1)
Interactions (A6.5.2.1)
Bracing (A6.5.2.2)
Restraints (A6.5.2.3)
Operabilitya (A6.5.2.4)
Interactions (A6.5.4.2.1)
Analysis (A6.5.2.5)
Restraints (A6.5.2.3)
Operabilitya (A6.5.2.4)
Interactions (A6.5.2.1)
E or F
Bracing (A6.5.2.2)
Restraints (A6.5.2.3)
Interactions (A6.5.2.1)
Bracing (A6.5.2.2)
Restraints (A6.5.2.3)
Operabilitya (A6.5.2.4)
Interactions (A6.5.2.1)
Analysis (A6.5.2.5)
Restraints (A6.5.2.3)
Operabilitya (A6.5.2.4)
Interactions (A6.5.2.1)
Analysis (A6.5.2.5)
Restraints (A6.5.2.3)
Operabilitya (A6.5.2.4)
Interactions (A6.5.2.1)
a Leak tightness is the default requirement. Operability applies only when specified by design.
A6.3 System Coefficients
A6.3.1 Deformability. Piping systems shall be classified as either high, limited, or lowdeformability systems. All
materials in highdeformability piping systems shall have an elongation at rupture of at least 10 percent at the operating
temperature, and pipes and pipe components used in highdeformability systems shall be joined by welding or by bolted
flanges. Systems containing components with an elongation at rupture of less than 10 percent at the operating temperature,
or having joints that rely only on friction, shall be classified as lowdeformability systems. Systems that are neither high nor
lowdeformability systems shall be classified as limited deformability systems. Systems with threaded connections shall be
classified as limited or lowdeformability systems.
A6.3.2 Seismic Coefficients. The seismic coefficients aP and RP are specified in Table 6.4.1 for high, limited, and lowdeformability
piping systems.
A6.4 Seismic Demand
A6.4.1 Seismic demand on a piping system consists of applied forces and relative displacements.
A6.4.2 Seismic forces shall be determined as specified in Section 6.2.6.
A6.4.3 Seismic relative displacements at points of attachments of pipe restraints to the structure shall be determined as
specified in Section 6.2.7.
A6.5 Seismic Qualification
A6.5.1 Elevator system piping shall satisfy the provisions of Section 6.4.9. ASME B31 pressure piping systems shall satisfy
the provisions of the applicable ASME B31 code section. Fire sprinkler systems shall satisfy the provisions of Section
A6.5.2.6.
A6.5.2 The seismic qualification of piping systems depends on the Design Approach selected in Section A6.2.
A6.5.2.1 When interactions are specified they shall be evaluated in accordance with Section 6.2.3.
A6.5.2.2 When bracing is specified, the pipe must be seismically restrained. Lateral restraints shall be provided (a) to limit
the bending stress in the pipe to yield at the operating temperature and (b) to limit the rotations at articulated joints within the
manufacturer limits. Unlike analysis (Section A6.5.2.5), bracing does not require a detailed analysis of the piping system; the
distance between seismic restraints may be established based on beam approximations of the pipe spans. The effect of
seismic restraints on operating loads (thermal expansion and contraction and weight) shall be considered.
A6.5.2.3 When restraints are specified, the pipe seismic restraints as well as their welds and anchorage attachment to the
structure shall comply with the provisions of Chapters 8 to 12 of the 2003 Provisions. Supports shall be constructed so that
support engagement is maintained considering both lateral and vertical seismic forces.
A6.5.2.4 When operability is specified, the equipment and components that must perform an active function that involves
moving parts (such as pumps, compressors, fans and valve operators) shall comply with the requirements of Section2.4.5.
A6.5.2.5 When analysis is specified, the piping system shall be analyzed by static or dynamic methods. The maximum
calculated elastic stress due to the earthquake loads and concurrent weight and pressure shall be limited to 1.5SY (where SY is
the minimum specified material yield stress at normal operating temperature) and the rotations at articulated joints shall be
within the manufacturer limits. The analysis shall include the effects of stress intensification factors as determined in the
ASME B31 pressure piping code, and corrosion effects.
A6.5.2.6 Fire protection sprinkler systems shall meet the following requirements:
A6.5.2.6.1 Fire protection sprinkler systems in Seismic Design Categories A, B and C designed and constructed in
accordance with NFPA13 shall be deemed to satisfy the seismic force and relative displacement requirements of these
Provisions.
A6.5.2.6.2 In Seismic Design Categories D, E and F, fire protection sprinkler systems designed and constructed in
accordance with NFPA 13 shall also meet the following additional criteria:
1. The spacing of longitudinal sway bracing and transverse sway bracing specified in NFPA 13 Section 9.3.5 shall be
reduced by multiplying the maximum brace spacing permitted in NFPA 13 Section 9.3.5 by 0.8Wp/Fp.
2. The value of 0.8Wp/Fp shall not be taken as greater than 1.0.
COMMENTARY
CA6.1 Seismic Interaction. There are two types of seismic interactions: system interactions and spatial interactions. A
system interaction is a spurious or erroneous signal resulting in unanticipated operating conditions, such as the spurious startup
of a pump motor or the unintended closure of a valve. Spatial interactions are interactions caused by the failure of a
structure or component in close proximity. Spatial interactions can in turn be further divided into falling interactions, swing
interactions, and spray interactions. A falling interaction is an impact on a critical component due to the fall of overhead or
adjacent equipment or structure. A swing interaction is an impact due to the swing or rocking of adjacent component or
suspended system. A spray interaction is due to the leakage of overhead or adjacent piping or vessels.
Any interaction involves two components, a source, and a target. An interaction source is the component or structure that
could fail and interact with the seismically designed component. An interaction target is a seismically qualified component
that is being impacted, sprayed or spuriously activated. For an interaction to affect a seismically qualified component, it must
be credible and significant. A credible interaction is one that can take place. For example, the fall of a ceiling panel located
overhead from a motor control center is a credible interaction because the falling panel can reach and impact the motor
control center. The target (the MCC) is said to be within the zone of influence of the source (the ceiling panel). A significant
interaction is one that can result in damage to the target. For example, the fall of a light fixture on a 20inch steel pipe may
be credible (the light fixture being above the pipe) but may not be significant (the light fixture will not damage the steel
pipe). In contrast, the overturning of a rack on an instrument panel is a significant interaction.
The process of considering seismic interactions begins with a interaction review. For new structures, this involves
examination of the design drawings, to identify the interaction targets, and credible and significant sources of interaction. In
many cases, the design documents may only locate components and systems in schematic terms. The actual location of, for
example, piping and ductwork systems is determined in the field. In this case and when work is being performed on an
existing structure, it is necessary to begin the interaction review with a walkdown, typically with a photographic record.
Based on the assembled data, supporting calculations to document credible and significant sources of interactions can be
prepared.
In practice, it is only necessary to document credible and significant sources of interaction. It is not necessary to list and
evaluate every single overhead or adjacent component in the area around the target, only those that could interact and whose
interaction could damage the target. Because only credible and significant sources of interaction are documented, an
important aspect of the interaction review is engineering judgment. The spatial interaction review should therefore be
performed by experienced seismic design engineers.
When system interactions are of importance, the written input of a system engineer is in order.
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Resource Paper 6
OTHER NONBUILDING STRUCTURES
(2003 Provisions Appendix to Chapter 14, Nonbuilding Structure Design Requirements)
This appendix first appeared in the 2000 NEHRP Recommended Seismic Provisions and was revised for inclusion in the
2003 Provisions. It is intended to serve as a resource document for future voluntary standards and model code development
and to encourage development of uptodate consensus standards for electrical transmission, substation, and distribution
structures, telecommunications towers, and buried structures as well as performance criteria for tanks and vessels. The
guidance presented reflects current industry design practice for these types of nonbuilding structures. Feedback will be
appreciated. Note that only format changes have been made and Provisions section numbers cited refer to the 2003 edition
of the Provisions.
PROVISIONS
A14.1 General
A14.1.1 Scope. This paper includes design requirements for electrical transmission, substation, and distribution structures,
telecommunications towers, and buried structures and performance criteria for tanks and vessels.
A14.1.2 References
IEEE 693 Institute of Electrical and Electronics Engineers, Recommended Practices for Seismic Design of Substations,
Power Engineering Society, Piscataway, New Jersey, 1997.
A14.1.3 Definitions
Base shear: See Section 4.1.3.
Buried structures: Subgrade structures such as tanks, tunnels, and pipes.
Dead load: See Section 4.1.3.
Registered design professional: See Section 2.1.3.
Seismic Use Group: See Section 1.1.4.
Structure: See Section 1.1.4.
A14.1.4 Notation
Cd See Section 4.1.4.
CS See Section 5.1.3.
I See Section 1.1.5.
R See Section 4.1.4.
SD1 See Section 3.1.4.
SDS See Section 3.1.4.
T See Section 4.1.4.
V See Section 5.1.3.
W See Section 1.1.5.
O0
See Section 4.1.4.
A14.2 Design Requirements
A14.2.1 Buried Structures. Buried structures that are assigned to Seismic Use Group II or III, or warrant special seismic
design as determined by the registered design professional, shall be identified in the geotechnical report. Such buried
structures shall be designed to resist minimum seismic lateral forces and expected differential displacements determined from
a properly substantiated analysis using approved procedures.
A14.3 Performance Criteria for Tanks and Vessels
Tanks and vessels shall be designed to meet the minimum postearthquake performance criteria as specified in Table A14.3
1. These criteria depend on the Seismic Use Group and contentrelated hazards of the tanks and vessels being considered.
Table A14.31 Performance Criteria for Tanks and Vessels
Performance
Category a
Minimum Postearthquake Performance
I
The structure shall be permitted to fail if the resulting spill does not pose a threat to the public or to
adjoining Category I, II or III structures.
II
The structure shall be permitted to sustain localized damage, including minor leaks, if (a) such damage
remains localized and does not propagate; and (b) the resulting leakage does not pose a threat to the
public or to adjoining Category I, II or III structures.
III
The structure shall be permitted to sustain minor damage, and its operational systems or components
(valves and controls) shall be permitted to become inoperative, if (a) the structure retains its ability to
contain 100 percent of its contents; and (b) the damage is not accompanied by and does not lead to
leakage.
IVb
The structure shall be permitted to sustain minor damage provided that (a) it shall retain its ability to
contain 100 percent of its contents without leakage; and (b) its operational systems or components shall
remain fully operational.
a Performance Categories I, II, and III correspond to the Seismic Use Groups defined in Section 1.2 and tabulated in Table 14.21.
b For tanks and vessels in Performance Category IV, an Importance Factor, I, of 1.0 shall be used.
COMMENTARY
CA14.1 General
CA14.2.1 Buried Structures. This section is included for the following reasons:
1. The material may serve as a starting point for continued development.
2. The comments stimulated by consideration of this section will provide valuable input so that this section may be further
developed and then incorporated in the Provisions in the future.
3. It was determined by TS 13 and the Provisions Update Committee that it would be premature to incorporate this section
into the Provisions for the 2000 edition.
4. Accepted industry standards are in the process of incorporating seismic design methodology reflecting the Provisions.
It is not the intent of the Provisions Update Committee to discourage incorporation of this section into a building code or to
minimize the importance of this section. Placing this section in the appendix indicates only that this section requires further
development.
Seismic forces on buried structures may include forces due to: soil displacement, seismic lateral earth pressure, buoyant
forces related to liquefaction, permanent ground displacements from slope instability, lateral spread movement, fault
movement, or dynamic ground displacement caused by dynamic strains from wave propagation. Identification of appropriate
seismic loading conditions is dependent upon subsurface soil conditions and the configuration of the buried structure.
Conditions related to permanent ground movement can often be avoided by careful site selection for isolated buried
structures such as tanks and vaults. Relocation is often impractical for long buried structures such as tunnels and pipelines.
Wave propagation strains are a significant seismic force condition for buried structures if local site conditions (for instance,
deep surface soil deposits with low shear wave velocities) can support the propagation of large amplitude seismic waves.
Wave propagation strains tend to be most pronounced at the junctions of dissimilar buried structures (such as a pipeline
connecting with a building) or at the interfaces of different geologic materials (such as a pipeline passing from rock to soft
soil).
Loading conditions related to liquefaction require detailed subsurface information that can be used to assess the potential for
liquefaction and, for long buried structures, the length of structure exposed to liquefaction effects. In addition, the
assessment of liquefaction requires specifying an earthquake magnitude that is consistent with the definition of ground
shaking. It is recommended that one refer to Chapter 7 of this Commentary for additional guidance in determining
liquefaction potential and seismic magnitude. Providing detailed structural design procedures in this area is beyond the scope
of this document.
Loading conditions related to lateral spread movement and slope instability can be defined in terms of lateral soil pressures or
prescribed ground displacements. In both cases, sufficient subsurface investigation in the vicinity of the buried structure is
necessary to estimate the amount of movement, the direction of movement relative to the buried structure, and the portion of
the buried structure exposed to the loading conditions. Definition of lateral spread loading conditions requires special
geotechnical expertise and specific procedures in this area are beyond the scope of this document.
Defining the loading conditions for fault movement requires specific location of the fault and an estimate of the earthquake
magnitude on the fault that is consistent with the ground shaking hazard in the Provisions. Identification of the fault location
should be based on past earthquake movements, trenching studies, information from boring logs, or other accepted fault
identification techniques. Defining fault movement conditions requires special seismological expertise. Additional guidance
can be found in the Chapter 7 Commentary.
It may not be practically feasible to design a buried structure to resist the effects of permanent ground deformation.
Alternative approaches in such cases may include relocation to avoid the condition, ground improvements to reduce the
loads, or implementing special procedures or design features to minimize the impact of damage (such as remote controlled or
automatic isolation valves that provide the ability to rapidly bypass damage or postearthquake procedures to expedite
repair). The goal of providing procedures or design features as an alternative to designing for the seismic loadings is to
change the hazard and function classification of the buried structure such that it is not classified as Seismic Use Group II
or III.
It is recommended that one refer to the Chapter 7 Commentary for additional guidance in determining liquefaction potential
and determining seismic magnitude.
Buried structures are subgrade structures such as tanks, tunnels, and pipes. Buried structures that are designated as Seismic
Use Group II or III, or are of such a size or length to warrant special seismic design as determined by the registered design
professional, must be identified in the geotechnical report.
Buried structures must be designed to resist minimum seismic lateral forces determined from a substantiated analysis using
approved procedures. Flexible couplings must be provided for buried structures requiring special seismic considerations
when changes in the support system, configuration, or soil condition occur.
The requirement for and value of flexible couplings should be determined by the “properly substantiated analysis and
approved procedures.” It is assumed that the need for flexible couplings refers to buried piping or conduits. The prior
wording of Section A14.2.3 was far too broad in requiring flexible couplings when changes in the support system,
configuration or soil condition occur. These broad requirements could result in flexible couplings installed at locations where
permanent ground displacement is expected or at transitions between aboveground supported pipe and buried pipe. As
currently available flexible couplings are not generally designed to match the ultimate strength properties of the piping or
conduit, the prior requirements potentially introduce a weak point in the piping or conduit system. The original focus of the
prior requirements was penetrations of buried service lines into a building or other structure. Properly designed flexible
couplings can be an effective means to limit forces at connections to buried structures. However, special care is needed to
make sure the design loads and displacements are adequately specified. There are several other alternative to providing
sufficient flexibility at connections to buried structures that are more robust in terms of margin above their design levels.
REFERENCES
Agrawal, P. K., and J. M. Kramer. 1976. “Analysis of Transmission Structures and Substation Structures and Equipment for
Seismic Loading,” Sargent and Lundy Transmission and Substation Conference, December 2, 1976.
American Society of Civil Engineers (ASCE). 1997. Design of Latticed Transmission Structures, ANSI/ASCE/SEI 10.
ASCE. 1991. Tubular Pole Design Standard, ASCE/SEI Manual 72.
ASCE. 2000. Guidelines for Electrical Transmission Line Structural Loading, ASCE/SEI Manual 74.
ASCE. 1995. Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7.
ASCE. 1997. The Design of Guyed Electrical Transmission Structures, ASCE/SEI Manual 91.
ASCE. 2000. Substation Structure Design Guide.
Li, H.N., S. Wang, M. Lu, and Q. Wang. 1991. “Aseismic Calculations for Transmission Towers,” in ASCE/SEI Technical
Council on Lifeline Earthquake Engineering, Monograph No. 4, August 1991.
Steinhardt, O. W. 1981. “Low Cost Seismic Strengthening of Power Systems,” Journal of The Technical Councils of ASCE,
April.
Amiri, G. G., and G. G. McClure. 1996. “Seismic Response to Tall Guyed Telecommunication Towers,” Paper 1982, in
Proceedings of the Eleventh World Conference on Earthquake Engineering. Elsevier Science Ltd.
Australian Standards Association. 1994. Standard Design of Steel Lattice Towers and Masts, AS 3995.
Canadian Standards Association. 1994. Antennas, Towers, and Masts.
Li, H.N., L. E. Suarez, and M. P. Singh. 1994. “Seismic Effects on HighVoltage Transmission Tower and Cable Systems,”
Fifth U.S. National Conference on Earthquake Engineering.
Federal Emergency Management Agency. 1990. Earthquake Resistant Construction of Electric Transmission and
Telecommunication Facilities Serving the Federal Government, FEMA 202..
Galvez, C. A., and G. G. McClure. 1995. “A Simplified Method for Aseismic Design of SelfSupporting Latticed
Telecommunication Towers,” Seventh Canadian Conference on Earthquake Engineering, Montreal.
Institute of Electrical and Electronics Engineers (IEEE). 1997. National Electrical Safety Code, ANSI C2.
IEEE. 1997. Recommended Practices for Seismic Design of Substations. IEEE 693. Power Engineering Society,
Piscataway, New Jersey.
IEEE. 1991. TrialUse Design Guide for Wood Transmission Structures, IEEE 751. Power Engineering Society,
Piscataway, New Jersey.
Long, L.W. 1973. Analysis of Seismic Effects on Transmission Structures, IEEE Paper T 73 3266.
Lum, W. B., N. N. Nielson, R. Koyanagi, and A. N. L. Chui. 1984. “Damage Survey of the Kasiki, Hawaii Earthquake of
November 16, 1993,” Earthquake Spectra, November.
Lyver, T. D., W. H. Mueller, and L. Kempner, Jr. 1996. Response Modification Factor, Rw, for Transmission Towers.
Portland State University, Portland, Oregon.
National Center for Earthquake Engineering Research. 1995. The HanshinAwaji Earthquake of January 17,
1995CPerformance of Lifelines, Technical Report NCEER950015. State University of New York at Buffalo.
Rural Electrical Administration (REA). 1992. Design Manual for High Voltage Transmission Lines, Bulleton 1724E200.
REA. 1978. Design Guide for Rural Substations, Bulletin 651.
REA. 1982. Mechanical Design Manual for Overhead Distribution Lines, Bulletin 1602.
Telecommunications Industry Association (TIA). 1996. Structural Standards for Steel Antenna Towers and Antenna
Supporting Structures, TIA/EIA 222F.
Resource Paper 7
SPECIAL REQUIREMENTS FOR SEISMIC DESIGN OF
STRUCTURAL GLUED LAMINATED TIMBER (Glulam) ARCH
MEMBERS AND THEIR CONNECTIONS
IN THREEHINGE ARCH SYSTEMS
Glulam arch structures are used with some regularity in churches and other public buildings and assembly areas; however,
ASCE/SEI 705 does not provide guidance regarding the seismic design of these systems. The design recommendations
reflected in this resource paper were drafted by BSSC Technical Subcommittee 7, Design of Wood, with input from the
American Institute of Timber Construction (AITC). This paper provides seismic design coefficients for two classes of onestory
threehinge arch systems: a special glulam arch and a glulam arch not specifically detailed for seismic resistance.
For special glulam arch systems, required detailing enables limited inelastic behavior in connections through either wood
bearing or fastener yielding. This is accomplished by requiring design of wood members at connections for the lesser of
overstrength forces or the forces that can be developed in the connections. Use of glulam arch systems not specifically
detailed for seismic resistance is limited to Seismic Design Categories A, B, and C. This limit is analogous to the approach
taken for steel systems not specifically detailed for seismic resistance and wood shear wall systems with other than wood
structural panel. The value of R = 2.0 is based on a relative comparison of R for special systems. The assumed system
overstrength for both systems is O0=2.5.
To facilitate eventual code/standard adoption of the guidance provided in this paper, requirements are presented first
followed by a commentary section.
PROPOSED REQUIREMENTS FOR ONESTORY THREEHINGE ARCH SYSTEMS
1. Scope. These provisions are intended for use in the design and detailing of structural glued laminated timber (glulam)
arch members and connections that are part of the seismicforceresisting system in onestory threehinge arch systems.
Seismic design coefficients for these systems shall be as specified in the applicable building code or, in the absence of such
information, shall be as indicated in Table 1.
Glulam arch systems not specifically detailed for seismic resistance shall comply with recommended detailing in AITC 104
2003, Typical Construction Details and the requirements of the 2005 National Design Specification. for Wood Construction
(NDS.) including Appendix E, ASCE/SEI 705, Minimum Design Loads for Buildings and Other Structures and the
applicable building code.
Special glulam arch systems shall meet the requirements for glulam arch systems not specifically designed for seismic
resistance. In addition, special glulam arch systems shall meet the requirements of Sections 1.1 through 1.7 below.
Table 1 Seismic Design Coefficients for OneStory Glulam Arch Systems
SeismicForceResisting System
R
O0
Cd
Special glulam arch
2.5
2.5
2.5
Glulam arch not specifically detailed for seismic resistancea
2.0
2.5
2.0
a Limited to Seismic Design Categories A, B, and C only.
1.1 Connection Requirements. Connections that are part of the special glulam arch seismicforceresisting system shall be
in accordance with requirements of NDS Chapter 10 for mechanical connections and the additional requirements of this
section.
1.1.1 Arch Base. Arch base connections shall utilize a steel shoe assembly in accordance with AITC 104. Timber rivets or
doweltype fasteners such as thrubolts or lag screws shall attach the arch to the shoe. Doweltype fasteners shall be chosen
such that the expected yield mode is Mode III or Mode IV as defined in the NDS. Timber rivet connections shall be designed
to ensure that the expected strength limit state is characterized by rivet capacity.
1.1.2 Arch Peak. Connection of the arch at the peak shall utilize shear plates, bolts, steel dowels, or metal side plates or
combination thereof in accordance with AITC 104.
1.2 Nominal Connection Capacity. The nominal capacity of a connection shall be determined in accordance with the
following:
1. For dowel type fasteners  n x Z(KF)(.)(CM)(Ct)(Ceg) where n is the number of fasteners; Z is the reference lateral design
value for a single fastener; and KF, ., CM, Ct, and Ceg are adjustment factors specified in the NDS for format conversion,
time effect, wet service, temperature and end grain, respectively.
2. For timber rivets: (Pr or Qr) x (KF)(.)(CM)(Ct)(Cst) where Pr is parallel to grain reference rivet capacity; Qr is
perpendicular to grain reference rivet capacity; and KF, ., CM, Ct, and Cst are adjustment factors specified in the NDS for
format conversion, time effect, wet service, temperature and metal side plate, respectively.
3. For split ring and shear plate connectors  n x P x (KF)(.)(CM)(Ct)(Cd)(Cst) or n x Q x (KF)(l)(CM)(Ct)(Cd) where n is the
number of fasteners; P is the reference design value parallel to the grain for a single split ring connector unit or shear
plate unit; Q is the reference design value perpendicular to grain for a single split ring connector unit or shear plate unit;
and KF, ., CM, Ct, Cd , and Cst are adjustment factors specified in the NDS for format conversion, time effect, wet service,
temperature, penetration and metal side plate, respectively.
1.3 Member Requirements. Arch members that are part of the special glulam arch seismicforceresisting system shall
meet requirements of the NDS and the requirements of this section.
1.3.1 Slenderness. The ratio of tangent point depth to breadth (dt /b) shall not exceed 6 based on actual dimensions when
one edge of the arch is braced by decking fastened directly to the arch or braced at frequent intervals as by girts or roof
purlins. When such lateral bracing is not present, dt /b shall not exceed 5.
1.3.2 End Grain Bearing. At the arch base, end grain bearing shall be on a metal plate with sufficient strength and stiffness
to distribute the applied load. At moment splices, end grain bearing shall be on a metal plate when fc > (0.75)(Fc
*) as required
in accordance with NDS Section 3.10.1.3.
1.3.3 Compression Perpendicular to Grain. Compression perpendicular to grain induced at the arch base shall be by a
metal plate with sufficient strength and stiffness to distribute the applied load.
1.4 Member Resistance.
1.4.1 Moment, Tension, Compression, and Shear. The arch member for special glulam arch systems shall be designed to
resist moment, tension, compression, shear, and applicable combinations of these induced by seismic forces determined in
accordance with the load combinations of ASCE/SEI 705 Section 12.4.3.2 (load combinations with overstrength) but need
not exceed forces resulting from strength at connections determined in accordance with Section 1.4.2a.
1.4.2 Member Resistance at Connections. The arch member for special glulam arch systems shall be designed for limit
states of net section tension rupture, row tearout, group tearout as defined in NDS Appendix E, and shear in accordance
with NDS Section 3.4.3.3 due to the seismic forces as determined by the lesser of:
1. The nominal connection capacity determined in accordance with Section 1.2 for load resistance factor design (LRFD) or
the nominal connection capacity determined in accordance with Section 1.2 divided by 1.35 for allowable stress design
(ASD).
2. The required capacity resulting from load combinations of ASCE/SEI 705 Section 12.4.3.2 (load combinations with
overstrength).
1.5 Transfer of Forces to the Arch Members. The diaphragm, members, and connections shall be sized to transfer outofplane
wall and roof forces into the arch.
1.6 End Fixity. In accordance with assumed pinned behavior of a threehinge arch, determination of reaction and arch
member forces is based on assumed idealized pin behavior at the arch peak and base. Actual detailing may introduce partial
moment fixity at reactions, and consideration shall be given to the effect of such fixity on member and connection response.
1.7 Arch Moment Splice. Arch moment splices shall utilize a metal bearing plate (when required), metal side plates, shear
plates, bolts, steel dowels, timber rivets, or combination thereof in accordance with AITC 104. Design forces for determining
the size and number of fasteners shall be based on load combinations of ASCE/SEI 705 Section 12.4.3.2 (load combinations
with overstrength) but need not exceed the member design force based on forces resulting from strength at connections (see
Section 1.4.1 and 1.4.2a).
Figure C1.0 showing Threehinge arch configuration.
Figure C1.0 Showing Tudor arch configuration.
COMMENTARY FOR ONESTORY THREEHINGE ARCH SYSTEMS
C1 Scope. Special provisions are provided for the design of arch members and connections to resist seismic forces as part of
a threehinge arch system (see Figure C1.0). Such systems typically employ glued laminated timber Tudor arch members
and are commonly used in church construction and other facilities intended for public assembly. Common features of these
systems are the presence of 2x and 3x tongue and groove roof decking with wood structural panel overlay, longitudinal and
transverse walls of light frame construction, or longitudinal and transverse masonry walls. Transverse end walls may or may
not be designed as shear walls.
Special requirements apply to typical construction details used for over 50 years in threehinged arch systems as outlined in
AITC 104, Typical Construction Details. Typical arch base details in AITC 104 are generally expected to produce good
performance characteristics of connection yielding by either wood bearing or a combination of wood bearing and fastener
yielding and will limit occurrence strength limit states of row tearout, group tearout, and net section tension rupture prior to
connection yielding. The design requirements in this white paper utilize standard details that have been used successfully
and that encourages a combination of wood bearing and metal fastener yielding modes at the base.
Tudor Arch
Three Hinged
Figure C1.0 Threehinge arch and Tudor arch configurations.
C1.1 Connection Requirements for Special Glulam Arch Systems. The ordinary load combinations (load combinations
without overstrength) of ASCE/SEI 705 are used to determine the size and number of fasteners in arch member connections
at the base. Determination of the size and number of fasteners is not subject to special load combinations (load combinations
with overstrength forces) to enable limited inelastic behavior of doweltype fasteners (either by wood bearing or fastener
bending) when coupled with the wood member strength requirements of Section 1.4. This approach recognizes that wood
connection strength is typically governed by wood failure mechanisms, not failure of the metal fasteners. For a given wood
member crosssection, determination of the size and number of fasteners based on the overstrength load combinations may
not be beneficial to overall connection performance due to an increased number of fasteners and a reduction in wood member
net section to accommodate the fasteners.
C1.1.1 Arch Base. The connection at the arch base utilizes a metal shoe (see Figure C1.1.1) and typically employs a thrubolt
loaded in double shear. Placement of the bolt(s) is an important consideration. Inservice drying of the member causes
shrinkage which must be accounted for in the detailing of the connection to prevent splitting due to the development of
tension perpendicular to grain stresses.
It is recommended that the bolt(s) be placed within 6 inches of the back of the arch if standard size holes are used. Where
bolt(s) are placed farther than this from the back of the arch to resist the required loads, the designer should provide detailing
to allow the wood to shrink without pulling away from the bearing seat. This may be accomplished through the use of slotted
holes or oversized holes in the arch member. It is recognized that some movement of the arch at the base will occur before
the bolt is engaged. This practice is used to prevent wood splitting due to occurrence of dimensional change under gravity
loads. In some situations a bearing seat is also used at the inside face of the arch. In such a case, the bolt(s) is generally
placed at the geometric center of the section with the hole(s) detailed to accommodate shrinkage.
Timber rivets as well as lag screws installed at each side of the arch base are expected to produce comparable performance
provided that the controlling yield mechanism is based on dowel yielding or rivet capacity.
Under outward loads, the bending yield capacity of the plate at the back of the metal shoe will typically determine the size of
the bearing area (i.e., the plate will yield before the wood reaches its design compression perpendicular to grain stress).
Figure C1.1.1 (a) Typical arch base with thrubolt and (b) arch base with true hinge.
Bearing
plate
Anchor
bolts
Welded
assembly
Arch
Machine Bolt Figure C1.1.2 Showing Typical arch peak connection detail.
270
Figure C1.1.1 (b) arch base with true hinge.
(a)
(b)
Figure C1.1.1 (a) Typical arch base with thrubolt and (b) arch base with true hinge.
C1.1.2 Arch Peak. The connection at the peak typically employs use of a shear plate or plates with thrubolt(s) and is
typically prefabricated in a manufacturing facility to establish proper fit and alignment. For arches with slopes of 3:12 or
more, typical connections employ shear plates and bolts or a combination of shear plates and bolts and dowels to transfer
both horizontal and vertical forces. For low pitch (low slope) arches, steel side plates on each face are used in combination
with shear plates. Figure C1.1.2 shows one example of a peak connection.
Figure C1.1.2 Typical arch peak connection detail.
The bevel cuts shown at the top of the arch peak connection are used to minimize wood crushing and permit rotation due to
downward deflection of the peak connection of deep members. They are not required for all designs but should be
considered by the designer where significant rotation is expected. Bevel cuts generally are not used on the bottom side of the
connection.
Figure C1.3.3 (a) Mode III and Mode IV yielding for single and double shear connections
Figure C1.3.3 (b) Mode IV yielding from a double shear connection test, and (c) cyclic curve for single shear bolted connection  Mode IIIs (3/8 inch diameter bolt, 4x6 wood member, ¼ inch steel side plate).
4000
3000
2000
1000
0
1000
2000
3000
4000
1.2 0.8 0.4 0 0.4 0.8 1.2
Displacement, in
Load, lbf
271
Figure C1.3.3 (b) Mode IV yielding from a double shear connection test
C1.2 Nominal Connection Capacity. Determination of nominal capacity does not include adjustment factors for group
action and geometry to more conservatively estimate nominal connection capacity. These factors are 1.0 or less in value and
address wood strength limit states that are to be checked explicitly per Appendix E and the shear provisions of the NDS.
C1.3 Member Requirements. Prescriptive limits on d/b match those in the NDS for arches.
C1.3.2 End Grain Bearing. Consistent with typical construction details used for these systems, a metal plate with sufficient
strength and stiffness to distribute the applied load is used at the base (see Figure C1.1.1) regardless of the level of stress in
end grain bearing. This bearing plate also prevents direct contact between the arch and the concrete, thus preventing moisture
from wicking into the arch from the concrete.
C1.3.3 Compression Perpendicular to Grain. Compression stress perpendicular to the grain in the arch member at the
base should be through bearing on a metal plate with sufficient strength and stiffness to distribute the applied load.
C1.4 Member Resistance. The requirements of Section 1.4 are intended provide excess capacity in the member relative to
connections because little or no inelastic deformation is expected from the arch member itself except in bearing modes.
Limited inelastic deformation can occur through wood bearing and fastener yielding in the connection region at the base (see
Figure C1.3.3a and b for examples of Mode III and Mode IV yielding and Figure C1.3.3c for cyclic behavior of a bolted steel
side plate to wood connection).
Double Shear
Single Shear
(a) (b)
(c)
Figure C1.3.3 (a) Mode III and Mode IV yielding
for single and double shear connections, (b)
Mode IV yielding from a double shear connection
test, and (c) cyclic curve for single shear bolted
connection  Mode IIIs (3/8 inch diameter bolt,
4x6 wood member, ¼ inch steel side plate).
LRFD factored
resistance for
seismic loading.
arrow
C1.4.1 Moment, Tension, Compression, and Shear. Arch member design strength must equal or exceed the force based
on the overstrength load combinations of ASCE/SEI 705 but need not exceed nominal forces developed by connections in
accordance with Section 1.4.2a. Design for bending, tension, compression and shear, per Section 1.4.1, is based on applicable
net section or net bearing areas in accordance with the NDS. Member design at connections, including provisions for shear at
connections at member ends and local stresses in fastener groups, is in accordance Section 1.4.2.
C1.4.2 Member Resistance at Connections. This section requires member design at connections for forces that can be
developed in the connections or the ASCE/SEI 705 overstrength load combinations to increase capacity based on wood
strength limit states relative to connection capacity and to provide for limited inelastic behavior at base and peak connections
by either wood bearing or fastener yielding or a combination thereof.
In Section 1.4.2, required design wood strength at connections is taken as the lesser of: (a) the nominal strength of the
connection for LRFD or the nominal strength divided by 1.35 for ASD or (b) the force based on the ASCE/SEI 705
overstrength load combinations. Case b generally will apply when loads other than seismic control the size and number of
fasteners in the arch base. When the connection has design strength in excess of that needed to resist seismic forces (e.g.,
forces from wind exceed calculated seismic forces), it is necessary only to ensure that the wood member has sufficient design
strength to resist loads from special load combinations, not the expected strength of the fasteners.
For ASD, wood strength limit states are checked using the nominal strength of the connection divided by a factor of 1.35.
The 1.35 factor is specified to provide for consistent design whether provisions of ASD or LRFD are used. For member
design (except compression perpendicular to grain) and connection design, the ratio of the LRFD adjusted design value (10
minute basis) to the ASD adjusted design value (10 minute basis) is 2.16/1.6 = 1.35. The factor of 2.16 is the constant in the
format conversion factor, KF, and adjusts the ASD reference design values (10 year basis) to LRFD design values (10 minute
basis) and 1.6 is the load duration factor, CD, which adjusts the ASD reference design values (10 year basis) to the ASD
design values at a 10 minute basis.
C1.5 Transfer of Forces to the Arch Members. Adequate transfer of inplane diaphragm forces and outof plane wall
and roof forces can be addressed by use of the NDS for wood member and connection resistance and the provisions of
ASCE/SEI 7. For anchorage of concrete or masonry structural walls, see ASCE/SEI 7 Sections 12.11 and 12.14.7.5; for
bearing walls and shear walls, see ASCE/SEI 7 Section 12.14.7.6; and for nonstructural components, see ASCE/SEI 7
Section 12.14.7.7.
C1.6 End Fixity. Threehinge arch systems are designed assuming pin behavior when typical construction details of AITC
104 are used; however, it is recognized that limited moment fixity is introduced at the arch base and arch peak connection
regions by the presence of connectors and the bearing of the member cross section. For example, at the arch base, rotation
about the inside face of the arch at the base coupled with the presence of connections in the arch shoe will provide moment
fixity beyond the assumed condition of an ideally pinned joint. The intent of Section 1.6 is to consider the effect of such end
fixity as the arch resists anticipated loading.
It is difficult to generate precise estimates of anticipated deformations that may be detrimental to overall connection and
member performance. Their effect at the base connection is mitigated through: (a) the use of dowel fasteners in yielding
mode, (b) increased strength of dowel fasteners loaded parallel to grain when compared to the same fastener loaded
perpendicular to grain, (c) the presence of localized bearing deformations about the arch base and surrounding the dowel, and
(d) dowel placement. At the arch peak, tapering of the arch member minimizes fixity created by wood bearing as the arch
deforms (see Figure C1.1.2).
Limited cyclic data for single shear, single bolt connections consisting of a steel side plate and a wood main member indicate
an average displacement of 0.8 inch at maximum load (see Anderson). For the particular connection tested, the ratio of
average maximum strength to LRFD factored resistance was approximately 2.6. Displacement at maximum load and ratio of
maximum load to the LRFD factored resistance will vary by connection configuration.
C1.7 Arch Moment Splice. Large arches may employ arch moment splices in locations of reduced moment to facilitate
shipping. Like the connection at the peak, these connections are typically prefabricated in a manufacturing facility to
establish proper fit and alignment. Compression stress in the moment splice region is resisted by end grain bearing on a
metal bearing plate between the connected members. Tension is taken across the splice by steel straps and shear plates, shear
is taken by shear plates in end grain, and side plates are used to hold sides and tops of members in position.
Figure C1.1.3 Showing Typical arch moment splice.
Figure C1.1.3 Typical arch moment splice.
REFERENCES
Anderson, G. T. Experimental Investigation of Group Action Factor for Bolted Wood Connections, Thesis for Master of
Science at Virginia Tech, Blacksburg, Virginia.
American Institute of Timber Construction. 2003. Typical Construction Details, AITC 10403. AITC, Denver, Colorado.
American Forest and Paper Association. 2005. National Design Specification. for Wood Construction (NDS),
ANSI/AF&PA NDS. AF&PA, Washington D.C.
American Society of Civil Engineers. 2005. Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 705.
ASCE, Reston, Virginia.
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Figure 1 Showing Structural elements in series (column, base plate, anchorage, foundation, and soil).
Foundation
Anchorage
Base Plate
Column
Force Force
Resource Paper 8
APPROPRIATE SEISMIC LOAD COMBINATIONS FOR BASE
PLATES, ANCHORAGES, AND FOUNDATIONS
The suitability of existing load combinations has been increasingly questioned as building code provisions have shifted from
an allowable stress design (ASD) basis towards a strength or load and resistance factor design (LRFD) basis. Foundation
design requirements remain grounded in ASD because consensus is lacking on how to convert these requirements to an
ultimate strength basis. Disagreement also exists concerning which requirements for base plates and anchorage are
appropriate in that building designers are inclined to specify use of the special seismic load combination for these elements
whereas designers of nonbuilding structures tend to rely on inelastic behavior and, to some extent, uplift or sliding. This
resource paper presents the findings of a study conducted to determine appropriate load conditions for base plates,
anchorages (via anchor bolts, anchor rods, or other), and foundations (either shallow or deep).
CONTROLLING BEHAVIOR OF STRUCTURAL COMPONENTS IN SERIES
The system created when a structural element is attached to a base plate, anchorage, and foundation is a “series” combination
of structure elements as shown in Figure 1. In the simplest sense, a series combination can be conceptualized as a chain of
components in which the maximum strength and deformation capacity of the combination is controlled by whichever
component is the weakest in the series.
Figure 1 Structural elements in series (column, base plate, anchorage, foundation, and soil).
In actuality, each component has different strength and deformation capacities. Figure 2 illustrates the strength and
deformation capacities of three imaginary components. System 1 is a flexible ductile element; System 2 is a rigid and weaker
but ductile element; and System 3 is a rigid and brittle but strong element.
If these elements are connected into a series, the combined strength and deformation capacity of the system would be
determined by summation of the individual displacements of each element at any given force level (Figure 3). This type of
combination is referred to as a forcedependent structural system.
For the example shown in Figure 2, the combined strength and ductility capacity of the structural system is entirely controlled
by System 2, because both the yield and ultimate strength of System 2 is less than the yield strength of either System 1 or
System 3. For purposes of discussion, the behavior of System 1 might be imagined as that of a building structural element,
System 2 might be the rocking behavior of a shallow foundation, and System 3 might be that of a lowductility base plate and
anchorage. The low ductility of System 3 is not a problem because this element always remains elastic; however, the low
strength of System 2 may be a problem because it prevents the relatively good ductility of System 1 from being utilized.
In order to transition the controlling behavior and mechanism from System 2 to that of System 1, the required strength of
System 2 needs to be increased until the ultimate strength of System 1 is less than that of System 2 as shown in Figure 3.
This demonstrates that appropriate scaling of the seismic component in load combinations is a necessary factor in controlling
structural behavior.
Figure 2 Force versus displacement of seriesconnected elements.
Displacement
Force
Figure 3 Using load factors to increase required strength
of System 2 causes behavior to be controlled by System 1.
Base Plates and Anchorages. Base plates and anchorages are commonly used for: steel structures; lightframe structures;
large nonbuilding structures such as tanks, vessels, and signs; equipment attachments; and nonstructural component
attachments. Design standards and ductility requirements vary considerably for these items. Table 1 summarizes some of the
broad variety of criteria currently used to define the seismic strength requirements and permitted capacity values for various
types of structural elements that typically use some form of anchor rods/bolts and base plates or anchorages.
Current design standards for steel buildings specify use of the special load combination for base plates and anchor rods1 for
steel columns unless the provisions of ASCE/SEI 705 Table 12.21 System (H) are permitted. When anchor rods may be
needed to attach elements other than columns, increased strength requirements are not currently required.
When anchor bolts are required for lightframe construction, current design standards generally do not require any different
strength requirements than for the attached structural component.
1 AISC has introduced the term “anchor rod” to describe a bolt that attaches steel to concrete, but other standards groups continue to use the
term “anchor bolt.” This paper uses the term “anchor rod” when specifically referring to AISC standards and the term “anchor bolt” with
respect to anchorage in general.
Figure 2 Force versus displacement of seriesconnected elements.
0
0
System 3
System 2
Combined
System
Reaches
System 2
Displ. Limit
System 1
Combined System Figure 3 Using load factors to increase required strength of System 2 causes behavior to be controlled by System 1.
0
0 Displacement
Force
System 1
System 2
System 3
Combined System
Ultimate Strength
and Deformation
Controlled by
System 1
Designers of some types of nonbuilding structure have shown a preference for using foundation anchor bolts as a yield
mechanism to provide structural ductility. For example, ASCE/SEI 705 Section 15.7.5 and API standards require that the
vertical vessel structures typically found in oil refineries, which do not have significant ductility, be intentionally designed to
create a plastic mechanism of tensile yielding in the anchor bolts used to attach the vessel to its foundation. The anchor bolts
are specified to use ductile material and to be installed in a manner that facilitates tensile yielding over a significant length of
the bolt. The anchorage used to attach the anchor bolts to the vessel as well as the vessel itself is then designed to mobilize
the full strength of the anchor bolts.
Table 1 Summary of Selected Criteria
System Type
Rmax
Element
Required
Seismic
Load Effect
Design Criteria
Average Anchor or
Attachment Strength
Relative to Supported Item
Steel
Buildings
High seismic;
SDC DF
(AISC definition)
SPSWf
R = 7
Attachments
E
AISC Seismic
Same
Anchorage
Uncertain
ACI D3.3
w/AISC
modifications
Same
Other
system
types,
Rmax = 8
Base plate
Em
AISC Seismic
Same
Anchorage
Em
ACI D3.3
w/AISC
modifications
Same
Low seismic; SDC
AC
(AISC definition)
Systems
with > 3
(Same as highseismic SDC DF requirements)
Systems
with
R = 3.0
Base plate
E
AISC 360
Same or weakerb
Anchorage
E
ACI D3.3
Same or weakerb
LightFrame
Buildings
Shear wall
7.0
Uplift devices
E/1.4
ICCES
Varies
Uplift anchorage
E
ACI D3.3,
SDC CF
Strongera
E
ACI D3.3,
SDC AB
Same
Shear anchorage
E
ACI D3.3, SDC CF
Strongera
E
ACI D3.3, SDC AB
Same
Nonbuilding
Structures
Having buildinglike
structural
systems
8.0
Same as steel buildings including high and low seismic categorization
Other types
3.5
Base plate and
attachments
E
AISC 360e
Same
Anchorage
E
ACI D3.3, SDC CF
other industry
standards may
govern
Strongera
E
ACI D3.3, SDC AB
Same
Nonstructural
Components
Supports and
attachments
for ductwork or
welded piping
Rp = 10.0d
max
Base plate and
attachments
E or E/1.4
Generally from
ICCES ESRs
Same
Supports and
attachments
for other
components
Rp = 6.0
max
Base plate and
attachments
E or E/1.4
Generally from
ICCES ESRs
Same
Anchors
seismicallyqualified
or per
ACI D3.3)
Rp = 6.0
max
Anchorage
per
ASCE 13.4
E
ICCES AC193,
AC308
?
ACI D3.3, SDC CF
Strongera
ACI D3.3, SDC AB
Same
Other nonductile
anchors
Rp = 1.5
Anchorage
per
ASCE 13.4
(1.5/Rp) E
ICCES AC193,
AC308
Stronger
a Presumed stronger because ACI D3.3 applies a 0.75 strength reduction factor to the anchor strength.
b Weaker when supported item strength is determined by drift or other considerations.
c ASD strengths determined using ICCES reports are based on tests.
d Welded piping with Rp =12 is effectively only Rp =10 because of the Fp min requirement.
e API and AWWA requires anchorage to be designed for yield load of anchor.
f SPSW = steel plate shear walls.
Nonstructural components such as fan motors, piping systems, and building facades often have castin or postinstalled
anchors with limited or no ductility for support. In some instances, the anchorage or bracket used to attach the component to
the anchor is the element most capable of providing some degree of ductility in the attachment. In many cases, imposed
displacements are the controlling factor in the anchorage design.
There is too much variety in structure and attachment types to define any single target behavior about which load
combinations might be developed. Considering the wide variety of structures and components that utilize base plates and
anchorages, there exist valid justifications to define ductility requirements for the structural element, the base
plate/anchorage, or the anchor bolt. Recommended future code development should instead target rational rules within the
three basic arenas of yield mechanisms. For each situation, specific design and detailing rules are appropriate to include in
conjunction with the intended yield mechanism.
For the anchor rod/bolt as a yield mechanism:
1. Design the base plate/anchorage to resist the actual (not specified) tensile strength of the anchor bolt.
2. Design the foundation anchorage to resist the actual tensile strength of the anchor bolt.
3. Use ductile steel for the anchor bolt and nuts capable of developing the anchor bolt strength.
4. In the case of castin and postinstalled grouted anchors, consider debonding the anchor bolt from the concrete over a
significant length (inelastic length) to permit development of meaningful displacements.
5. Either use continuously threaded rod to ensure uniform yielding over the inelastic length of the anchor bolt or ensure that
the rod material has sufficient tensile strength relative to its yield strength that the rod is fully yielded before tension
fracture occurs. Upset threads are not considered necessary for anchors resisting seismic loads.
6. Consider use of nuts on both sides of the base plate so that progressive elongation of the anchor bolt is reduced and
cyclic reversals have a chance to cycle rod in compression (however, anchor bolts are not recommended for direct
transfer of shear forces).
7. Provide adequate stretch length in the yielding section of anchor bolts to accommodate maximum expected inelastic
displacements and rotations.
For the anchorage/base plate as a yield mechanism:
1. Design the anchor bolt, particularly if nonductile (e.g., an expansion bolt), to be stronger (elastic strength) than the yield
strength of the anchorage assembly and with adequate displacement capacity to accommodate maximum joint
movements.
2. Qualify postinstalled anchor bolts by appropriate testing to confirm adequate strength and ductility characteristics under
anticipated design conditions.
3. Although using an anchorage or base plate as the intended yield mechanism may be successful at protecting a nonductile
anchor bolt from failure, the total work performed in a small anchorage may not provide adequate hysteresis to reduce
global structural seismic behavior.
For an unyielding anchorage/anchor bolt assembly:
1. Utilize the design requirements for the nonductile structural elements that currently exist.
2. Ensure that the loadamplification provisions for the anchor bolt/rod and base plate which are expected to remain elastic
do not overlap.
FOUNDATIONS
A geotechnical engineer tends to define the ultimate strength of a foundation at a point when either an unstable soil
movement is imminent or a limiting value of displacement is reached. A structural engineer tends to define the ultimate
strength of a foundation at a point when either the occurrence of an unstable mechanism within the structure is imminent
(such as rocking) or a structural capacity is reached. In other words, the geotechnical engineer assumes that the soil will fail
before the structure, and the structural engineer assumes that soil behavior can be simplified to the extent of being a simple
fluid or force; neither assumption is correct.
In conventional design, the geotechnical engineers need to define soil strength values for both seismic and longterm load
conditions early in the design process when the size, shape, and ultimate loading on the foundations are, at best, only rough
estimates. Unless ultimate foundation strengths can be reevaluated by the geotechnical engineer at a later design stage when
the sizes, shapes, and loading of foundations are relatively definite, the geotechnical engineer typically will maintain some
degree of conservatism with respect to potential geotechnical mechanisms.
Figure 4 Showing Progressive settlement during repeated cycling.
1
3 2
The traditional practice of arbitrarily defining a onethird increase in permitted longterm soil pressures for seismic loading
does not adequately reflect what is necessary to transition from ASD to an ultimate strength design. While the onethird
increase might be suitable for checking stresses for a 100year wind event, it is not suitable for determining adequacy for a
limitstate seismic event. It is therefore necessary to separately define design limit values for limitstate and longterm load
conditions.
Table 1804.2 of the 2006 International Building Code (IBC) reproduced below requires substantial revision as part of any
change to strength design procedures.
2006 IBC Table 1804.2 Allowable Foundation and Bearing Pressure
CLASS OF MATERIALS
Allowable
Foundation Pressure
(psf)d
Lateral Bearing
(psf/ft below natural
grade)d
Lateral Sliding
Coefficient of
frictiona
Resistance
(psf)b
1. Crystalline bedrock
12,000
1,200
0.70

2. Sedimentary and foliated rock
4,000
400
0.35

3. Sandy gravel and/or gravel (GW and GP)
3,000
200
0.35

4. Sand, silty sand, clayey sand, silty gravel and
clayey gravel (SW, SP, SM, SC, GM, and GC)
2,000
150
0.25

5. Clay, sandy clay, silty clay, clayey silt, silt and
sandy silt (CL, ML, MH and CH)
1,500c
100

130
aCoefficient to be multiplied by the dead load.
bLateral sliding resistance value to be multiplied by the contact area as limited by Section 1804.3.
cWhere the building official determines that inplace soils with an allowable bearing capacity of less than 1,500 psf are likely to be present at
the site, the allowable bearing capacity shall be determined by a soils investigation.
dAn increase of onethird is permitted when using the alternate load combinations in Section 1605.3.2 that include wind or earthquake loads.
Performance Statement for Soil LimitState Condition. In order to define the soil and foundation strength values
associated with limitstate design, a definitive performance statement for structural and geotechnical conditions at the limit
state needs to be developed.
When structural actions result in repeated cycles of loading at or near the limitstate soil pressure, some degree of progressive
foundation settlement is expected to occur due to compaction and local shear movements of soil materials beneath the
foundation as shown in Figure 4. The total and differential settlements resulting from repeated cycles of loading should be
considered in the light of the performancebased design criteria. Large total settlement may not be detrimental if the
differential settlements between adjacent foundations are within acceptable limits.
Figure 4 Progressive settlement during repeated cycling.
Rotational mechanisms of foundations due to soil shear failures as shown in Figure 5 should not be permitted. Maximum
structure overturning moments should maintain a factor of safety against soil shear failure mechanisms of at least 2;
otherwise foundations should be interconnected by grade beams so that the resulting soil loading will be primarily direct
compression.
Lateral sliding of buildings and other structures may be resisted by both friction and passive soil pressure. Lateral
displacement or sliding of foundations during the design event may be permissible; however, structural stability must be
maintained.
Strength and Overstrength of Shallow Foundations. Past and current code provisions for both shallow and deep
foundations have been based on allowable strength design methodology. FEMA 4501 includes an appendix that has
proposed a new strength design methodology. An evaluation of foundation design provisions must address both
methodologies.
Selected 2006 IBC sections relative to seismic load combination requirements for shallow foundations are:
Figure 5 Showing Foundation rotational mechanism within soil.
1. Section 1605.2.1 – permits use of strength load combinations in conjunction with the maximum 25 percent reduction in
overturning moment permitted in ASCE/SEI 7 Section 12.13.4.
2. Section 1605.3.1 – permits use of ASD load combinations [D + H + F + 0.7E] and [0.6D + 0.7E + H].
3. Section 1605.3.2 – permits use of alternative ASD load combinations [D + L + S + E/1.4] and [0.9D + E/1.4] without
the overturning reduction permitted by ASCE/SEI 705 Section 12.13.4.
4. Table 1804.2, Footnote d, permits a onethird increase in allowable soil pressures when using the alternate load
combinations that include seismic loads.
Figure 5 Foundation rotational mechanism within soil.
Proposed new IBC Table (expected to follow existing Table 1804.2) Limitstate Foundation and Bearing Pressure
(for use with Section xxx, Load Conditions)
Class of Materials
Ultimate
Foundation
Pressure (psf)
Lateral Bearing
(psf/ft below
natural grade)
Lateral Sliding
Coefficient of
friction
Resistance
(psf)
1. Crystalline bedrock
24,000
2,500
0.70

2. Sedimentary and foliated rock
10,000
1,000
0.35

3. Sandy gravel and/or gravel (GW and GP)
8,000
600
0.35

4. Sand, silty sand, clayey sand, silty gravel and
clayey gravel (SW, SP, SM, SC, GM, and GC)
6,000
500
0.25

5. Clay, sandy clay, silty clay, clayey silt, silt and
sandy silt (CL, ML, MH and CH)
4,500
300

400
The load combinations defined in Section 1605.3.2, in combination with the onethird increase permitted in Table 1804.2 are
commonly used in current practice.
An unusual additional load combination provision is found in ACI 318 Section 15.2.2: “Base area of footing or number and
arrangement of piles shall be determined from unfactored forces and moments transmitted by footing to soil or piles and
permissible soil pressure of permissible pile capacity determined through principles of soil mechanics.” Although ACI 318,
Section 21.10 (seismic foundation requirements), does not override this section, it does conflict with IBC Section 1605,
which would govern over the ACI provision.
Traditionally, the structural design of shallow foundations assumes that soil pressure beneath the foundations can be treated
as a linearlyvarying pressure across the length of the foundation, forming a pressure diagram which, depending upon the
degree of eccentricity, e = M/P, can be described as either trapezoidal or triangular in shape. The 2003 NEHRP
Recommended Provisions (FEMA 450) introduced a foundation strength design approach that permits a Whitney stressblock
approach to be used to simulate an ultimate soil pressure condition to be used to design shallow foundations. Appendix 1 of
this paper presents a summary of Equations 1 and 2, which describe the ASD load limits of simple rectangularinplan
foundations. It also includes an Equation 3 that describes the strength limits for the strength design approach introduced in
2003 Provisions and now described in Resource Paper 4 of this volume. Using Equations 1 through 3, simple load vs.
moment interaction curves can be developed for any rectangular foundation shape.
Figure 6 presents an example interaction curve for a 10foot square foundation with an allowable longterm soil pressure of 3
ksf and an assumed ultimate soil strength of 9 ksf. In the figure:
1. The radial line occurs at e = L/6, the transition from trapezoidal to triangular soil pressure distribution.
2. Line 1 represents an interaction curve using ASD design assumptions with an allowable soil pressure of 3 ksf.
3. Line 2 represents the effect of a 33 percent allowable increase in soil pressure for temporary load conditions to 4 ksf.
4. Line 3 represents the effect of using IBC Section 1605.3.2 to design foundations (the reduction of E/1.4 is represented as
an increase in allowable soil pressure by a factor of 1.4).
5. Line 4 represents the interaction curve at the ultimate soil pressure of 9 ksf using traditional triangular/trapezoidal soil
pressure distribution (i.e., the ultimate soil pressure occurs only at the extreme edge of the foundation).
6. Line 5 represents the interaction curve at the ultimate soil pressure of 9 ksf using a equalpressure soil distribution.
The overstrength of the traditional ASD design approach can be expressed as the ratio between the presumed ultimate (Line
5) and the designlevel (Line 3) interaction curves. The amount of overstrength that results using the ASD design approach is
not constant; it varies significantly depending on how much vertical load is on the foundation. Let us define P as the actual
vertical load on a foundation and as the theoretical maximum permitted vertical load capacity of a concentrically loaded
foundation (equal to the maximum permitted soil pressure times the total footing area). For more lightly loaded foundations
(having P/ < 0.5), the amount of overstrength present varies significantly to the extent that when a foundation is at P/ = 0
(such as when a foundation is loaded in direct uplift), the effective factor of safety present is 1.0 (i.e., no overstrength).
Figure 6 Example interaction curve for a shallow foundation.
Although the foundation strength design approach defined in the FEMA 450 Appendix to Chapter 7, introduced in 2003
Provisions and now described in Resource Paper 4 of this volume, defines procedures that can be used to determine an
ultimate strength design such as shown in Line 5 of Figure 6, it is silent regarding which strength load combinations to use
for design. The available alternatives are either the ASCE/SEI 7 seismic load combinations defined in Section 12.4.2.3 or the
special load combinations defined in Section 12.4.3.2.
The basic strength load combinations are not generally appropriate for use in conjunction with ultimate foundation strength
values. Using load combinations incorporating 1.0E together with the ultimate foundation strength means that the design
procedure permits no overstrength to be present at all in the design (i.e., that foundation failure will always be the dominant
controlling mechanism in any structure). It also means that the expected ductility capacity of the resulting foundation
mechanism must equal or exceed the value of R used in the design (whereas for the building structure the expected ductility
demand is Rd = R / RO. If the special load combination is used in conjunction with ultimate foundation strength values,
foundation rocking or sliding mechanisms are unlikely to be a controlling or participating mechanism in the structure
response. While this might be an acceptable or desired characteristic for structures using highR systems or for essential
facilities, it is probably an undesirable characteristic for ordinaryuse structures using moderate or lowR systems. Because
modest levels of foundation nonlinearity generally are considered to be acceptable for ordinary structures using moderate or
lowR systems, the use of the special load combinations would prevent such action and would result in an increase in their
expected construction cost. Figure 6 Example interaction curve for a shallow foundation.
line 2
line 4
line 1
line 5
line 3
Figure 6 Example interaction curve for a shallow foundation.
L = B = 10 ft,
Qa = 3 ksf, Qu
= 9 ksf
Strength of Deep Foundations. Although the ultimate strength of a deep foundation cannot be simplified in the same
manner as a shallow foundation, simplified methods can be used to predict ultimate strength values with a slight resemblance
to reality. Geotechnical engineers can determine allowable ultimate and longterm load capacities of assumed pile groups,
translate that into individualpile ultimate and longterm load values for the structural engineer, and the structural engineer
then can translate those back into predicted ultimate and longterm pier or pilegroup capacities that may or may not resemble
the values originally determined by the geotechnical engineer.
Appendix 2 of this paper presents two examples of how a structural engineer might estimate the ultimate strength of a pile
group based on individualpile capacities. Both of these approaches are vast oversimplifications of the actual interaction and
response that occurs between the structure and soil of a deep foundation, but they are both simple enough for practicing
engineers to adopt as design practice. The first example is a modification of a current common design practice for multipile
foundations that assumes the ultimate strength point is reached when the outermost pile reaches a defined ultimate strength.
The second example is a plasticanalysis approach that assumes all piles in a pile group are eventually able to reach their
defined ultimate strengths. The plastic analysis approach likely overestimates the strength that a multipile group is capable
of developing; however, the 0.7 f factor will provide significant compensation when using either approach. Further, both
approaches require that the pile cap structure have sufficient strength to accommodate the full expected strength of the
foundation capacity that is used, but many engineers probably would prefer the more conventional linearstrain approach in
order to reduce the required strength of pile caps.
More accurate methods to predict the ultimate strength of deep foundations include field testing of individual piles, reducedscale
testing of pile groups, and prediction of strength and deformation states of both foundation and soil through complex
models of the combined foundation and surrounding soil. Analysis of soil seismic behavior in this manner should include the
straindependent strength of the soil materials due to both foundation loading and ongoing seismic deformations.
Overstrength of Deep Foundations. Deep foundations are significantly different from shallow foundations in that deep
foundations can have tensile strength, overturning strength with low gravity loads, and element overstrength properties
similar to superstructure elements. Deep foundations therefore might be capable of internally developing overstrength values
in the range of tabulated O0 values provided that adequate ductility is present in the piles. Thus, for deep foundation, there is
no clear need for specifying a special or increased load combination in order to offset a lack of overstrength in the foundation
system as there is for lightly loaded shallow foundation systems. However, earthquake damage in deep foundations is
difficult to detect and is probably frequently overlooked in postearthquake damage investigations and, even if detected, it is
very costly to repair. This might justify an increase in deep foundation strength for higher Seismic Design Category
structures since foundations for these structures might be expected to experience more than one damaging earthquake during
the foundation’s service life and the potential lossofuse and repair costs are less acceptable.
Recommendations for Foundations. Foundation design including soil pressures for either shallow or deep foundation
systems might utilize ultimate strength design load combinations in which the value of E is as shown in Tables 2 and 3.
Table 2 Buildings and Buildinglike Nonbuilding Structures
R Value from
ASCE/SEI 7 Table 12.2
1,12.141, or 15.41
FixedBase Analysis
Including Foundation Deformations
per
ASCE/SEI41
For R = 5
2.0 E
1.5 E
R 3 to < 5
1.5 E
1.0 E
R = 3
1.0 E
1.0 E
Table 3 Nonbuilding Structures Not Similar to Buildings
R Value from
ASCE/SEI 7
Table 15.42
FixedBase Analysis
Including Foundation
Deformations per
ASCE/SEI 41
R > 3
1.5 E
1.0 E
R = 3
1.0 E
1.0 E
It is likely that this scaling would apply to the full value of E = Eh + Ev used in design with no other reduction permitted;
however, it is recognized that the full effects of design including redundancy factors, importance factors, and the vertical
seismic component have not been studied in depth and that the results of such an indepth study might warrant further
changes. These load factor scaling factors were selected in conjunction with the foundationsoil strength values (including
phifactors) presented in this paper. Inherently, the load factor of 2.0E is intended to result in a structure in which inelastic
response is preferred in the portions of the structure that are above the foundation and base plate while the load factor of 1.0E
was selected with the intent that some inelastic response might be preferred in the foundation of light structures. The load
factor of 1.5E was selected as a value that would provide for inelastic response in the foundation, in the supported structure,
or in both elements.
It is recognized that simple rules often yield imperfect results and that some structural systems might be identified that defy
the logic of this reasoning. For instance, foundations beneath shear panels of lightframe buildings would be required to be
designed using 2.0E suggesting that the foundations beneath these elements should remain relatively elastic while many
engineers might argue that a load factor of 1.5E might be more appropriate. However, until a more rational means of
determining R values prevails, this relatively simple table was judged to be generally effective in providing the preferred
inelastic behavior distribution.
No distinction was made between the load factor recommendations for deep and shallow foundations because the load factors
recommended appear likely to result in at least as much successful behavior for deep as opposed to shallow foundations.
Common ASD methods currently used for seismic design can be approximately matched with the ultimate foundation
strengths discussed herein by dividing calculated ultimate foundation strengths by a factor of safety of 3.0 and using the
earthquake forces recommended above reduced by a factor of 1.4.
REFERENCES
DeVall, Ronald H. April 2003. “Background information for some of the proposed earthquake design provisions for the
2005 edition of the National Building Code of Canada.” NRC Research Press.
Canadian Commission on Building and Fire Codes. 2005. National Building Code of Canada, Vol. 1 and Commentary.
National Research Council of Canada.
International Code Council. 2006. International Building Code.
American Concrete Institute. 2005. Building Code Requirements for Structural Concrete and Commentary, ACI 31805.
American Institute of Steel Construction. 2005. Seismic Provisions for Structural Steel Buildings, AISC 34105.
Appendix 1, DERIVATION OF SHALLOW FOUNDATION EQUATIONS
P
e
Figure showing Traditional ASD Design
Figure showing Traditional ASD Design
Traditional ASD Design – Full Contact
Figure showing Traditional ASD Design
Figure showing Traditional ASD Design
Given: P = vertical load
Figure showing Traditional ASD Design
M = overturning moment
Figure showing Traditional ASD Design
Figure showing Traditional ASD Design
L = length of rectangular footing
Figure showing Traditional ASD Design
QA
B = width of rectangular footing
L
e = M/P = eccentricity of loading
QA = maximum ASD allowable soil pressure
From the standard ending stress equation:
s = P/A ± M/S, the maximum soil pressure, QA will be:
=
Rearranging,
Introduce the term: P.= QABL so that we can substitute BL=P./QA resulting in
(1)
Traditional ASD Design – Partial Contact
For e = L/6, the soil pressure is assumed as a triangular distribution.
Rearranging,
Substituting QAB = P./L,
(2)
At the transition point between Equations 1 and 2, e = L/6 and P/P. = 1/2. The following is a graph of Equations 1 and 2: Equation
2
6
A
Q P M
BL BL
= + Equation
P 1 6e
BL L
. . +..
. . Equation
1
6
A e L Q BL
P
. . = ..
. . Equation
1 1
6
e P
L P
= .  . . '' . . . Equation
( )
2
3 2
A
Q P
B L e
=
 Equation
2
2 3 A
e L P
Q B
=  Equation
1 1 4
2 3
e P
L P
= .  . .. . . . . '. ...
Figure showing Traditional ASD Design
Graph of equation above
0
0.2
0.4
0.6
0.8
1
1.2
0.000 0.100 0.200 0.300 0.400 0.500 0.600
e/L
P/P' Comparison of Equations for Ultimate vs. ASD Soil Pressure Distribution
0
0.2
0.4
0.6
0.8
1
1.2
0.000
0.100
0.200
0.300
0.400
0.500
0.600
P/P'
e/L
Comparison of Equations for
Ultimate vs. ASD Soil Pressure Distribution
Simplified Ultimate Strength Design Method
e/L
e=L/6
Graph
A simplified ultimate strength design approach, based on the Whitney Stress Block Method, follows:
L/2
Define (in addition to terms used above):
Simplified Ultimate Strength Design Method
Simplified Ultimate Strength Design Method
Simplified Ultimate Strength Design Method
QU = Ultimate Soil Pressure
Simplified Ultimate Strength Design Method
Simplified Ultimate Strength Design Method
Simplified Ultimate Strength Design Method
QU
For an assumed rectangular soil pressure distribution;
Simplified Ultimate Strength Design Method
Simplified Ultimate Strength Design Method
Substituting :
(3)
Graphing this equation against the ASD equations: Equation
2 ( 2 )
U
Q P
B L e
=
 Equation
A
B P
LQ
'
= Equation
1 1
2
A
U
e Q P
L Q P
. . .. .. = .. . .. . '. . ....
P
e
Arrow on graph
Triangular/trapezoidal
soil distribution
Arrow on graph
Rectangular soil
distribution
Appendix 2, ASD AND LRFD INTERACTION DIAGRAMS FOR DEEP FOUNDATIONS
Linear Strain Assumption
Diagram
3ft 3ft
3ft
Assumed
ASD Allowable Pile Capacities
P =
100
kips
T =
50
kips
Ultimate/ASD =
1.7
tension
Ultimate/ASD =
2.5
compression
1
2
3
4
line
(does not include f = 0.7)
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Equation
Point 1  Pure compression
#piles x
Line
# piles
Pile force
x
Px
1
3
300
4.5
1350.0
ASD Capacity
Arrows
2
3
300
1.5
450.0
1200
kips
3
3
300
1.5
450.0
0.0
ft kips
4
3
300
4.5
1350.0
Sum =
1200
0.0
USD Capacity
3000
kips
0.0
ft kips
Diagram
arrow
Diagram
arrow
arrow
Point 2  Max. Moment
Diagram
X
ASD:
#piles x
Line
# piles
Pile force
x
Px
1
3
150
4.5
675.0
ASD Capacity
Diagram
2
3
0
1.5
0.0
300
kips
3
3
150
1.5
225.0
2250.0
ft kips
4
3
300
4.5
1350.0
ASD:
Sum =
300
2250.0
X na =
1.50
ft
USD:
#piles x
USD:
Line
# piles
Pile force
x
Px
X na =
2.22
ft
1
3
255
4.5
1147.5
USD Capacity
2
3
80
1.5
120.0
990
kips
3
3
415
1.5
622.5
5025.0
ft kips
4
3
750
4.5
3375.0
Sum =
990
5025.0
arrow
arrow
Diagram
Diagram
arow Diagram
arrow
Point 3  Pure tension
ASD Capacity
USD Capacity
P = 4 * 3 * 50=
600
kips
1020
kips
M =
0.0
ft kips
0.0
ft kkips
Diagram
arrow
arrow
arrow
arrow
Fully Plastic Assumption
3ft
3ft
3ft
ASD Allowable Pile Capacities
P =
100
kips
T =
50
kips
Ultimate/ASD =
1.7
tension
Ultimate/ASD =
2.5
compression
1
2
3
4
line
(does not include phi = 0.7)
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Diagram
Point 1
#piles x
Line
#
piles
Pile
force
X
Px
USD Capacity
1
3
750
4.5
3375.0
3000
kips
2
3
750
1.5
1125.0
0.0
ft kips
3
3
750
1.5
1125.0
4
3
750
4.5
3375.0
Sum =
3000
0.0
Point 2
#piles x
Line
#
piles
Pile
force
X
Px
1
3
255
4.5
1147.5
2
3
750
1.5
1125.0
3
3
750
1.5
1125.0
USD Capacity
4
3
750
4.5
3375.0
1995
kips
Sum =
1995
4522.5
4522.5
ft kips
Point 3
#piles x
Line
#
piles
Pile
force
X
Px
1
3
255
4.5
1147.5
2
3
255
1.5
382.5
USD Capacity
3
3
750
1.5
1125.0
990
kips
4
3
750
4.5
3375.0
6030.0
ft kips
Sum =
990
6030.0
Point 4
#piles x
Line
#
piles
Pile
force
X
Px
1
3
255
4.5
1147.5
2
3
255
1.5
382.5
USD Capacity
3
3
255
1.5
382.5
15
kips
4
3
750
4.5
3375.0
4522.5
ft kips
Sum =
15
4522.5
Point 5
#piles x
Line
# piles
Pile
force
x
Px
1
3
255
4.5
1147.5
2
3
255
1.5
382.5
USD Capacity
3
3
255
1.5
382.5
1020
kips
4
3
255
4.5
1147.5
0.0
ft kips
Sum =
1020
0.0
Linear Strain Assumption Linear Strain Assumption
1
3
2
USD
arrow
1.33 ASD
arrow
arrow
ASD
Fully Plastic Assumption,
Superimposed on Linear Strain Assumption Fully Plastic Assumption, Superimposed on Linear Strain Assumption
arrow
1
2
3
4
5
USDPlastic
arrow
USDLinear
Resource Paper 9
SEISMIC DESIGN USING TARGET DRIFT, DUCTILITY, AND
PLASTIC MECHANISMS AS PERFORMANCE CRITERIA
Traditional seismic design methods operate in the elastic domain and use a response modification coefficient in conjunction
with a period of vibration to establish required member strengths. This resource paper presents a design approach that
establishes the base shear required to limit ductility and drift demands based on an estimate of the yield displacement and
uses a plastic mechanism analysis to establish required member strengths. It is suggested as an alternative to the equivalent
lateral force procedure and is presented in Part 3 of the 2009 NEHRP Recommended Seismic Provisions in order to expose
the approach to the design community and to elicit feedback from members of that community.
BACKGROUND
Traditional seismic design methods operate in the elastic domain and use a response modification coefficient in conjunction
with a period of vibration to establish required member strengths. The design approach presented here is an alternative to the
equivalent lateral force (ELF) procedure. Several recent developments are combined to achieve simplicity and transparency
in the design process. Unique features of this design approach are:
1. An estimate of the yield displacement in a firstmode pushover analysis is used as an initial basis for proportioning the
seismicforceresisting system in a manner analogous to the way that an estimated period is used in current code
approaches. This approach reduces the need for iterations in proportioning the structural system.
2. Equivalentsingledegreeoffreedom (ESDOF) systems are used explicitly for determining the required base shear
strength; estimates of modal parameters are used in preliminary design.
3. The required base shear strength is determined using a representation of inelastic spectra known as yield point spectra
(YPS). The elastic portion of the YPS is given by smoothed elastic design spectra defined in the 2009 NEHRP
Recommended Seismic Provisions; inelastic portions are derived on the basis of coefficient relationships that were
recommended in a 2005 report published by the Federal Emergency Management Agency, Improvement of Nonlinear
Static Seismic Analysis Procedures (FEMA 440).
4. An improved lateral force distribution is used which results in a more uniform distribution of peak interstory drifts over
the height of the structure as well as a reduction in column design moments relative to those obtained with the current
ELF procedure.
5. A plastic mechanism analysis is used to determine required member strengths given the required base shear strength.
The analysis assists the engineer in visualizing the intended mechanism, makes preliminary sizing of designated yielding
members very simple, and helps ensure that an intended mechanism actually develops.
System ductility demands are a measure of damage to structural components. Values of system ductility corresponding to
currently recognized seismicforceresisting systems are suggested for use with this approach. Interstory drift is a measure of
damage to nonstructural components. Relationships between interstory drift and roof drift are suggested as a basis for
complying with currently recognized allowable story drift limits. System ductility and roof drift limits are explicitly
considered when establishing the required base shear strength, in order to limit damage to structural and nonstructural
components.
In many cases, the estimate of the yield displacement will be sufficiently accurate that no iteration of the preliminary design
will be needed.
Figure 1 illustrates how system ductility and roof drift limits define regions where the yield points of singledegreeoffreedom
(SDOF) and equivalent SDOF (or ESDOF) systems either satisfy the ductility and drift limits or fail to satisfy one or
both of these limits. For a given yield displacement, satisfaction of both limits requires that the larger of the associated yield
strengths be provided. Because a change in strength is usually achieved by changing the amount of structural material, the
stiffness changes as well. Thus, the period of vibration is a consequence of the strength provided to satisfy drift and ductility
limits, and an estimate of the yield displacement is used as a starting point rather than an estimate of the period. The
admissible design region shown in Figure 1 was derived for a particular performance objective; when multiple performance
objectives must be considered, each may further constrain the admissible design region. Details of the construction and
interpretation of YPS are provided in the appendix to this paper.
Figure 1 Showing Limits on ductility and drift demands are used to establish admissible and inadmissible design regions. SDOF and ESDOF oscillators that have yield points located within the admissible design region satisfy the ductility and drift limits shown.
Text Reading Yield Displacement
Because the lateral force distribution results in more uniform peak interstory drifts over the height of the structure, those
structures for which interstory drift is the controlling design parameter can be allowed to achieve larger peak roof drifts
relative to those obtained with current code approaches. As a result, structures that are slightly more flexible (longer period)
than obtained with current code approaches may be found to be acceptable.
Figure 1 Limits on ductility and drift demands are used to establish admissible and
inadmissible design regions. SDOF and ESDOF oscillators that have yield points
located within the admissible design region satisfy the ductility and drift limits
shown.
Because the design is based on estimates of relatively stable parameters (yield displacement, firstmode participation factor,
and firstmode mass coefficient) as well as the use of a plastic mechanism, little or no iteration in member sizes is required in
typical cases. In some cases, by ensuring compatibility of the modal parameters obtained for the elastic model with the
values assumed in the design, one can avoid nonlinear static (pushover) analysis. Schematic design, system selection, and
even preliminary optimization can be done using only pencil and paper, avoiding the effort of developing detailed computer
models.
The design approach presented here focuses on steel and reinforced concrete structural systems that do not have flexible
diaphragms. Reinforced concrete design examples are provided herein; examples of the design of steel moment resistant
frames using YPS are provided by Black and Aschheim (2000). Estimated values provided for initial proportioning presume
fairly typical spatial distributions of lateral stiffness, strength, and mass; departures from typical distributions will increase
the likelihood that design iterations will be needed. Systems with torsional irregularities and other important considerations
(e.g., Pdelta effects) addressed in Chapter 12 of the 2003 NEHRP Recommended Provisions are not addressed here nor are
structural systems composed of materials other than steel and reinforced concrete and those using baseisolation or
supplemental damping.
OVERVIEW OF DESIGN APPROACH
The design process is illustrated in Figure 2 and is described in detail in the sections that follow. An overview of the process
and logic follows.
A structural system having a defined and desirable plastic mechanism is selected by the engineer. The required base shear
strength, Vy, of this mechanism is determined to limit the peak roof displacement to an acceptable value considering
interstory drift and system ductility limits. Vy is determined based on the corresponding ESDOF system using YPS.
Estimates of the yield displacement, Dy, firstmode participation factor, G1, and firstmode mass coefficient, a1
, are based on
the type of structural system and number of stories. The base shear, Vy, is distributed over the height of the structure using an
improved lateral force distribution. A simple plastic mechanism analysis is used to proportion the designated yielding
members of the seismicforceresisting system. A mathematical model of the structure is prepared and the calculated modal
properties are used to assess the validity of the estimates Dy, G1, and a1
and whether changes to the design base shear might
be needed. The preceding steps establish the strength of the intended mechanism. Forceprotected members then can be
proportioned to ensure that the intended mechanism can develop, considering amplification due to higher modes and material
overstrength.
DESIRABLE INELASTIC MECHANISMS
Current seismic design philosophies presume the development of desirable inelastic mechanisms with the concentration of
inelastic deformation demands occurring at locations detailed for ductile response. Figure 3 illustrates desired mechanisms
applicable to several common structural types. Once selected, the desired mechanism is used to determine the required
strengths of the yielding portions of the seismic forceresisting system using a virtual work analysis.
Figure 2 Steps in the design process.
Figure 2 Steps in the design process. Figure 2 Showing steps in the design process
Yes
No
Estimate Dy, G1, a1
Revise Dy
Distribute base shear vertically
Proportion designated yielding members (plastic
mechanism analysis)
Distribute lateral forces horizontally
Design forceprotected members
Establish Vy and Te
Select structural system and plastic mechanism
Establish Du (system ductility, interstory drift)
Verify assumptions (Determine Te, G1, a1)
Does Dy require revision?
ESTIMATES OF YIELD DISPLACEMENT
Nonlinear static or “pushover” analyses subject a model of a structure that includes nonlinear member forcedeformation
relationships to progressively increasing lateral forces. Of particular interest is the plot of base shear as a function of roof
displacement obtained when lateral forces are proportional to the first mode (i.e., lateral force Fi,1 at the ith floor level is
proportional to the mode shape amplitude fi,1 and weight, wi). Such a plot is shown in Figure 4 for a fourstory steel moment
frame. The figure also shows a bilinear curve that has been fitted to approximately represent the initial stiffness and postyield
stiffness of the capacity curve. The breakpoint of the bilinear curve is known as the yield point, which defines the yield
strength, Vy, and yield displacement, Dy.
Experience generally confirms the kinematic expectation that for any given structural system (distribution of mass, stiffness,
and member depths), the yield displacement, Dy, determined in a pushover analysis varies with the yield strength of the steel
members or reinforcement but is nearly independent of the strength of the system – that is, changes in strength achieved by
increasing steel section weights or reinforcement percentages while maintaining member depths generally have a negligible
influence on Dy (Priestley and Kowalsky, 1998; Priestley, 2000). Furthermore, the yield drift ratio (Dy normalized by the
height of the structure) is nearly invariant with changes in the number of stories for a given structural system (e.g., Aschheim,
2000; Paulay, 2002). Thus, it is feasible to provide estimates of yield drift ratio to be used in design. The yield drift ratio
Figure 3 Showing Desirable inelastic mechanisms.
Figure 3 Showing Desirable inelastic mechanisms.
Figure 3 Showing Desirable inelastic mechanisms.
estimates can be used in much the same way that conventional seismic design approaches make use of period estimates.
Periods of vibration, however, may vary significantly during design iterations whereas the yield displacement is fairly stable.
Estimates of the drift ratio at yield, Dy /h, for steel buildings using Grade 50 steel and for reinforced concrete buildings using
Grade 60 reinforcement are given in Table 1.
Du
Du
Du
Du
Du
Figure 3 Desirable inelastic mechanisms.
Figure 4 Showing Capacity curve obtained from a nonlinear static (pushover) analysis.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 5 10 15 20 25 30
Roof Drift, in.
Base Shear / Weight
Figure 4 Capacity curve obtained from a nonlinear static (pushover) analysis.
Table 1 Yield Drift Ratio Estimates
SeismicForceResisting System
Estimated Yield Drift
Ratio, %
Reinforced Concrete Buildings
Moment Frames
0.5 – 0.6
Cantilever Shear Wallsa
0.10 h / lw
Steel Buildings
Moment Frames
1 – 1.2
Special Truss Moment Frames
0.75
Concentrically Braced Frames
0.3
Eccentrically Braced Frames
0.5
Buckling Restrained Braced Frames
0.3 – 0.5
(1)
These drift ratios are considered suitable for preliminary design purposes; however, more refined estimates may be available
in specific cases. The influence of foundation flexibility on the yield displacement and required strength determination also
may be addressed as described in the appendix to this paper.
a Expression is based on Tjhin et al. (2002).
Thus, the yield displacement for a building whose roof is at height h above the base is given as:
Equation
y
y
D
D h
h
. .
=. .
. .
DETERMINATION OF PEAK DISPLACEMENT FOR DESIGN
Peak displacement response is limited to prevent excessive interstory drift and system ductility demands as a means of
protecting nonstructural elements and the seismicforceresisting system from excessive damage.
While the influence of higher modes (or MDOF effects in the case of inelastic response) on peak roof displacement generally
is small, higher modes may play a more prominent role in peak interstory drift demands, particularly for systems that deform
in a “shear” mode (e.g., momentresistant frames). In the equivalent lateral force procedure, limits on allowable story drift
are compared with story drifts determined from an elastic analysis using statically applied lateral forces. Larger interstory
drifts can be expected during dynamic response. Thus, a Provisionscompatible design approach would compare interstory
drifts under a static quasifirstmode pattern of lateral forces with tabulated allowable story drifts.
Values of a coefficient, a3
,stat, are given in Table 2 for different structural systems as a function of the number of stories. This
coefficient is an estimate of the ratio of the maximum interstory drift ratio over the height of the building to the average roof
drift ratio under firstmode lateral forces. Thus, for design purposes, compliance with allowable story drifts is approximately
(and constructively) achieved by limiting the peak roof drift to:
(2)
where .a is the allowable story drift from Table 12.121 of the 2003 NEHRP Recommended Seismic Provisions, h is the
height of the roof level above the base, and hsx is the parameter appearing in this table.
Table 2 Parameter Estimates Equation
,
3,
a
u
sx stat
D h
. h a
.
=
·
Number
of Stories
MomentResistant Frames
Dual Shear WallMoment Frame
Systems
Slender Cantilevered Shear
Walls and Braced Frames
G1
a1
heff,1/h
a3,stat
G1
a1
heff,1/h
a3
,stat
G1
a1
heff,1/h
a3
,stat
1
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
2
1.21
0.94
0.79
1.19
1.24
0.89
0.81
1.00
1.24
0.76
0.86
1.38
3
1.27
0.90
0.73
1.23
1.33
0.85
0.75
1.00
1.35
0.70
0.81
1.49
5
1.32
0.86
0.70
1.26
1.40
0.82
0.71
1.00
1.46
0.66
0.78
1.58
10
1.35
0.82
0.67
1.28
1.45
0.79
0.69
1.00
1.54
0.63
0.75
1.64
= 20
1.37
0.80
0.66
1.29
1.48
0.77
0.68
1.00
1.59
0.62
0.74
1.67
Figure 5 conceptually illustrates the capacity curve and peak roof displacement for a structure responding in the first mode.
The coefficient O represents the true overstrength in contrast to the O0 parameter specified in the 2003 Provisions.
Coefficients C1, C2, a1
, and G1 are defined below. Relative to the effective yield point shown in Figure 5, the system
displacement ductility, µ, is:
(3)
Thus, an inference about the true overstrength coefficient, O, makes it possible to establish system ductility limits that are
consistent with the R and O0 values given in the Provisions.
System ductility limits ( µc
) were derived assuming O = O0 for structures of ordinary importance (I = 1.0) assuming C1 = C2 =
1.0 and taking a1
= 0.90 for momentresistant frames, 0.80 for eccentrically braced frames, and 0.65 for cantilever shear
walls and concentrically braced frames. These values correspond approximately to the point at which ductility limits would
be expected to control rather than drift. For structures with shorter periods, the consideration of shortperiod displacement
amplification visàvis the C1 and C2 coefficients in this design approach will result in better control of system ductility
response than is achieved with the equivalent lateral force procedure because the latter uses periodindependent R factors.
System ductility limits derived with this approach are given in Table 3 and reflect ductility demands relative to the effective
yield displacement, considering overstrength for designlevel ground motions.
Modification of the system ductilities given in Table 3 for building importance is appropriate. Consequently, the design
ductility limit, µd
, is given as µd = µc /I and
(4)
Since either the drift limit or the ductility limit may be more restrictive, the target roof displacement used for design is given
as:
(5)
Consequently, the target ductility demand (considering interstory drift and system ductility limits) is given as: Equation
, 1 2 1
1 2 1
1
1
u d
y
d
D C C S R CC
D I I S
R
µ µ a
a
G
= = =
. O . O G . .
. . Equation
u, d y D D µ = µ · Equation
, , min( , ) u u u D D Dµ
. =
Figure 5 Showing Response of elastic and yielding MDOF systems in the first mode. The “yield point” identifies the change in slope of a bilinear curve that is fitted to the capacity curve over the applicable range of displacement response. O represents the actual overstrength factor, not the value O0 provided in the 2003 NEHRP Recommended Seismic Provisions.
(6) Equation
u
t
y
D
D
µ =
Figure 5 Response of elastic and yielding MDOF systems in the first mode. The “yield point” identifies the
change in slope of a bilinear curve that is fitted to the capacity curve over the applicable range of displacement
response. O represents the actual overstrength factor, not the value O0 provided in the 2003 NEHRP
Recommended Seismic Provisions.
Table 3 System Ductility, µ1
, for Buildings of Ordinary Importance
at Design Basis Level (2/3 of MCE Level per the 2003 Provisions)
Seismic ForceResisting System
Special
Intermediate
Ordinary
Concrete Frame Buildings
Moment Frames
2.4
1.5
0.9
Reinforced Cantilever Shear Walls
1.6
–
1.3
Steel Frame Buildings
Moment Frames
2.4
1.4
1.1
Truss Moment Frames
2.1
–
–
Concentrically Braced Frames
2.0
–
1.1
BucklingRestrained Braced Frames
Momentresisting connections at columns away from links
Nonmomentresisting connections at columns away from links
3.2
2.8
Eccentrically Braced Frames
Nonmomentresisting beamcolumn connections
With momentresisting beamcolumn connections
2.8
2.6
EQUIVALENT SDOF RELATIONSHIPS FOR MDOF SYSTEMS
Because the contribution of higher modes to roof displacement tends to be small, the required base shear strength to limit
drift response is based on an equivalent SDOF model that reflects firstmode contributions. Thus, this section presents
established relationships that allow MDOF properties to be mapped to ESDOF properties and vice versa.
An ESDOF system can be determined having seismic weight W
(7)
* and force and displacement quantities equal to those of the
MDOF system divided by the firstmode participation factor, G1. Since the roof drift at yield, Dy, can be estimated as
indicated above, the yield drift of the ESDOF oscillator can be estimated as:
Equation
*
1
y
y
D
D =
G
where the asterisk (*) signifies a property of the ESDOF system. Estimates of G1 are provided in Table 2.
Once a detailed mathematical model of the structure has been created, a precise value of G1 can be computed. To do so, a
modal analysis is performed and values of the firstmode shape fi
,1 at each level, i, are stored in a vector f1, normalized such
that the amplitude of the roof displacement equals 1. Weights wi at each level, i, are stored in a diagonal matrix W. Then, G1
may be determined as:
(8)
where 1 = a vector of length n in which all entries are ones. Given the estimate of Dy
, (9)
the required base shear strength for the MDOF system may be determined as:
(10)
However, knowing that W
(11)
since W = 1
(12)
Equation 11 can be used to derive an expression that is quite simple to use in practice. Since the yield strength coefficient,
Cy
(13)
Thus, the design base shear is given as:
(14)
An initial estimate of a1 may be obtained from Table 2, while a more precise value can be computed using Equation 12 after
a detailed model of the structure has been developed and evaluated to determine the firstmode shape.
The period of vibration depends on the amount of strength provided to ensure the ESDOF oscillator has a ductility demand
not exceeding µt
. Having established the yield displacement, Dy
(15)
This period can be used in determining the lateral force distribution to be used in design and can be compared to the
fundamental period of vibration determined for a detailed model of the structure, which may be affected by inaccuracy in the
estimates of Dy, a1, and G1.
* from Equation 7, the strength of the
ESDOF oscillator to limit its ductility demand to µt
may be determined using YPS as Vy
* = Cy
*W*. Since
* = f1
TW1,
TW1 and the firstmode mass coefficient, a1, can be defined in terms of weights as:
*, can be determined directly from the design YPS, the base shear coefficient of the MDOF system can be determined
simply as:
*, and the yield strength coefficient, Cy
* , of the ESDOF
oscillator, the corresponding period of vibration, T*, is given by:
Equation
1
1
1 1
T
T G = f W1
f Wf Equation
*
1
y
y
V
V =
G Equation
*
y y 1 V =V ·G Equation
* * * *
1 1 1
T
y y y y y T
V = C W =V ·G = C ·W ·G = C . W .G = . .
. .
f W1
1 W1 Equation
* *
1 1
T
y T y C W C a W
. .
G . . =
. .
f W1
1 W1 Equation
1 1 1
1 1
1 1
T T T
T T T a = f W1 · f W1 = G · f W1
f Wf 1 W1 1 W1 Equation
*
y 1 y C =a C Equation
y y V = C W Equation
*
*
* 2 y
y
D
T
C g
= p
BASE SHEAR STRENGTH DETERMINATION
The response of inelastic oscillators has been the subject of academic inquiry since perhaps 1960. Peak displacement and
peak ductility responses have been related to the peak response of companion elastic oscillators having the same initial
stiffness. In recent work by the Applied Technology Council, the peak displacement of the SDOF oscillator is estimated as
the product of the peak displacement of the companion elastic oscillator, Sd, and coefficients C1 and C2 that account
separately for the effects of strength and degradation of strength and stiffness (FEMA 440, 2005). Since Sd = Sa(Te/2p)
(16)
The effect of yield strength less than that required for elastic response on peak displacement response is represented by the
coefficient, C1, which is evaluated as:
(17)
where R
(18)
For periods greater than 0.7 sec, C2 may be taken equal to one. According to FEMA 440, the value of Te used in Equations 17
and 18 need not be taken less than 0.2 sec.
YPS developed for a particular site by applying the above relationships to a design spectrum determined according to 11.4.5
are presented in Figure 6. The appendix of this paper presents background on the YPS representation of seismic demands.
Having determined Dy
Having estimated a1 and G1, the peak roof displacement and required base shear strength at yield for the multidegreeoffreedom
system can be estimated as Du= µt
Dy = µt
(G1Dy
2g, the
peak displacement of the yielding oscillator, Du
*, may be expressed as:
* = the ratio of the strength required for elastic response and the yield strength of the inelastic oscillator, Te = period
of vibration in seconds, and a is a parameter that varies with Site Class where a can be taken equal to 130 for Site Classes A
and B, 90 for Site Class C, and 60 for Site Classes D, E, and F.
The effect of cyclic degradation of stiffness and strength on peak displacement response is represented by the coefficient C2.
For Te less than 0.7 sec, this coefficient is estimated by
* and µt
, the required Cy
* can be determined by interpolation between the curves of constant µ shown in
the YPS. For example, for Dy
* = 12 in. and µt
= 1.7 chosen somewhat arbitrarily, Figure 6 illustrates that the required
ESDOF base shear coefficient, Cy
*, is approximately 0.37. The expected peak displacement of the ESDOF system is Du
*=
µDy
* = 1.7(12 in.) = 20.4 in. Using Equation 15, the period of vibration of the ESDOF oscillator is:
*) and Vy = Cy
*(a1W), respectively.
Note that it is not necessary to construct admissible design regions when working with a specific value of Dy
*; whether drift
or ductility limits control will be apparent in the determination of µt
. Equation
2
*
1 2 2
e
a
D C C S T g µ p
= . . . .
. . Equation
*
1 2
1 1
e
C R
aT

= + Equation
* 2
2
1 1 1
800 e
C R
T
.  .
= + . .
. . Equation
*
*
* 2
2 2 12 in 1.82 sec
0.37 386.1 in/sec
y
y
D
T
C g
= p = p =
·
DISTRIBUTION OF LATERAL FORCES FOR DESIGN
Because dynamic response indicates story shears in multistory buildings differ significantly from those associated with the
equivalent lateral force procedure of the Provisions. a new lateral force distribution has been recommended (Chao et al.,
2007). This lateral force distribution more closely corresponds to the peak shears observed in nonlinear dynamic response.
This distribution is characterized by the parameter ßi
. In this paper, ßi
is used to represent the ratio of the story shear, Vi, just
below Level i, and the base shear, Vy, corresponding to the effective yield strength, as follows:
(19)
where story weights, wj, and story heights, hj, are defined as wi and hi, respectively, in the Provisions, Vy = effective yield
strength, and a = 0.75. Thus, the equivalent lateral force applied at Level i, Fi,ß , is given by:
(20)
where ßn+1 = 0.
The intended mechanism may yield in response to the overturning moments or the story shears developed by the lateral
forces and deformations. Many systems (e.g., moment frames and shear walls) yield in response to the overturning moments
(associated with the lateral forces acting above the base of the structure) developed during response. Other systems (e.g.,
braced frames) yield in response to the story shears developed by the lateral forces.
The Fi,ß distribution of forces generally increases the story shears in the upper stories relative to the firstmode distribution of
forces and many code force distributions.
The design base shear at yield determined in Equation 14 on the basis of the firstmode is adequate to limit roof displacement
response of the MDOF system. Higher mode (or MDOF) effects have a relatively minor contribution to displacement
response but can have a significant contribution to interstory drifts and story shears and lead to design forces represented by
the Fi,ß distribution.
For those systems that yield in response to overturning moments, distribution of the base shear determined on the basis of
firstmode response over the height of the structure according to the Fi,ß distribution generally will increase the overturning
resistance of the structure above that required to limit displacement response. For this reason, the base shear used in
conjunction with Equations 19 and 20 must be modified for those systems that yield in response to the overturning moments
(e.g., moment frames and shear walls). The modified base shear is given by Vy · (heff,1/heff,ß) where Vy is determined using
Equation 14, heff,1 is the height of the resultant of the firstmode forces, and heff,ß is the height of the resultant of the ßi
lateral
forces. Table 2 provides estimates of heff,1/h. Equation
0.2
1
e
n T
j j
i j i
i n
y
j j
j
w h
V
V w h
a
ß =
=
. .
. .
= = . .
. .
. .
. .
S
S Equation
, 1 ( ) i i i y F V ß ß ß + =  ·
MECHANISMBASED DETERMINATION OF MEMBER STRENGTHS
A plastic mechanism analysis may be used to determine member strengths as described by Goel and Chao (2007). As shown
in Figure 3, the vertical distribution of story strengths (or plastic hinge strengths) may be made proportional to ßi
. Doing so
appears to promote a number of desirable effects, including limiting the column moments obtained in a static (design)
analysis during the development of a mechanism (by providing inflection points within each story) and making the
distribution of peak interstory drifts observed in nonlinear dynamic analyses more uniform over the height of the structure
than is obtained with conventional designs (e.g., Goel et al., 2007).
Thus, with reference to Figure 3, a virtual work analysis may be used to determine member strengths required to provide the
seismicforceresisting system with the required base shear strength. For example, considering a moment frame, the
reference plastic moment strength, Mpbr, may be determined by Equation 21 if beam plastic hinge strengths at the i
(21)
which may be solved for Mpbr once the column plastic hinge strengths at the base of the frame have been established. The
column plastic hinge strengths should be established to provide a sufficient margin against the development of a weakstory
mechanism. For example, using a factor of 1.1, the column plastic hinge strengths for a onebay frame would be determined
as:
(22)
th level are
assigned the value ßi
· Mpbr. Equating external work and internal work leads to:
Equation
, ,
1 1
2
n n
i i p y eff p pc p i pbr p
i i
F h V h M M ß ß . . . ß .
= =
S = = +S Equation
1.1 1
4
b
pc
M V h ·
=
based on the intention that a weakstory mechanism at this location be avoided. Equation 21 may then be solved for the Mpbr;
beam plastic moments at each level are determined as ßi
· Mpbr.
DESIGN VALIDATION/REFINEMENT
After members have been sized, a mathematical model of the structure can be developed and evaluated. A nonlinear static
(pushover) analysis in the first mode may be performed to evaluate the yield point of the MDOF system and establish a more
accurate ESDOF system for use in estimating the expected peak displacement and corresponding system ductility demands.
However, nonlinear static analysis can be avoided entirely for structural systems that do not soften or crack prior to the onset
of yield—in such cases, elastic analysis results may be used to validate the performance of a preliminary design and to
identify refinements when necessary.
As illustrated in Figure 5, the yield point may be estimated based on the actual stiffness and strength provided to the
structure. The strength of the system is the design base shear at yield (Equation 14) or the plastic strength obtained in a
mechanism analysis under the Fi,ß force distribution modified by (heff,1/heff,ß). The firstmode period, Te, reflects the actual
initial stiffness, and this period can be obtained from an eigenvalue analysis of the elastic model (provided that softening or
cracking of the structure does not occur prior to the onset of yield). An improved estimate of the yield displacement of the
MDOF model can be determined for such systems. Because the initial stiffness of the capacity curve is given by
(W
(23)
where W
*/g)(2p/Te)2, the improved estimate of the yield displacement is given by:
*= f1
TW1 should be computed using the firstmode shape obtained for the mathematical model of the structure (with
entries normalized such that the roof displacement amplitude equals one). Since the modal parameter G1 can be determined
for the mathematical model, the yield point of the ESDOF oscillator (Dy
’/G1, Vy/ G1) can be plotted on the YPS in order to
make a more precise estimate of the ductility demand and peak roof displacement. If these values are within the design
limits, the design is considered acceptable. If it should be necessary to reduce the ductility demand, revision of the required
strength may be determined based on the improved estimate of yield displacement (Dy
’/G1) and using modal parameters
determined for the firstmode properties of the mathematical model.
With some experience, however, comparison of Te with the period of the ESDOF system, T*, can provide a sufficient basis
for evaluating the adequacy of the preliminary design. As indicated by Equation 15, a longer period indicates the yield point
has shifted to the right leading to lower ductility demands but higher drifts for a given strength (consider Figures 1 and 6). In
contrast, a shorter period indicates the yield point has shifted to the left leading to higher ductility demands but lower drifts
for a given strength. Provided that the estimates of a1
and G1 are reasonably accurate, comparison of periods may be
sufficient to assess whether refinement of the preliminary design is needed.
Softening and/or cracking prior to yielding would be anticipated for reinforced concrete systems. If these effects are
represented in the mathematical model of the structure (for example, due to gravity loads precompressing reinforced
concrete members that may have been modeled with zero tensile strength), then the initial period of the model cannot
characterize the effective stiffness or period at yield. In such cases, the fundamental period of vibration determined at small
displacements, T1, should be modified to obtain an effective period of vibration (Te) associated with the effective yield point
observed in a nonlinear static (pushover) analysis using firstmode lateral forces.
Estimation of the effective period, Te, is illustrated in the reinforced concrete wall example below. Equation
2
*/ 2
y e
y
V D T
W g p
' = . . . .
. .
DESIGN OF CAPACITYPROTECTED MEMBERS
This paper focuses on the design of the designated yielding members of the seismicforceresisting system. Forceprotected
members or actions include axial forces in collectors and the shears in slender structural walls. Amplification due to higher
modes (or MDOF effects) and member overstrength should be considered for the design of members (or actions) that must
remain elastic to ensure development of the intended mechanism.
Figure 6 Showing Yield point spectra and Figure 7 showing Reinforced concrete wall building plan.
Figure 6 Yield point spectra.
REINFORCED CONCRETE WALL BUILDING EXAMPLE 1
A special reinforced concrete structural wall system was designed to provide lateral force resistance to a sixstory reinforced
concrete building. Four 20foot long walls (labeled W1 in the plan of Figure 7) were designed. Story heights of 12 feet and
dead loads of 175 psf were assumed; design live loads were 50 psf. Lumped masses at the floors and roofs were assumed
uniform over the height of the building. Full dead load plus 20 percent of the live load was assumed present during seismic
loading. For purposes of defining site seismicity, the example building was assumed to be located in Sacramento, California
(in the 95837 Zip Code) on Site Class D soils according to the 2003 NEHRP Recommended Seismic Provisions.
Figure 7 Reinforced concrete wall building plan.
The preliminary design was developed as follows:
Figure 7 Reinforced concrete wall building plan.
4 @ 27 ft
=108 ft
3 @
27 ft
= 81 ft
W1
20 ft
1 ft
N
W1
W1
W1
1. Based on Table 1, the yield drift ratio was estimated as 0.10(h/lw) = 0.10(72 ft)/(20 ft) = 0.36 percent. Therefore, the
yield drift (at the roof level, corresponding to effective yield in a firstmode pushover analysis) is estimated as Dy =
(0.36%)(h) = (0.0036)(72 ft)(12 in./ft) = 3.11 in.
2. From Table 2, the firstmode participation factor, G1, is estimated to be 1.47. Therefore, the yield drift of the
“equivalent” SDOF oscillator is estimated as Dy
* = Dy/G1 = 3.11/1.47 = 2.12 in.
3. A limit on displacement ductility is established by considering drift and system ductility limits.
From Table 3, the allowable system ductility for a special reinforced concrete cantilever shear wall system is 1.6.
Therefore, the peak displacement limit based on the allowable ductility is Du,µ = 1.6(3.11 in.) = 4.98 in.
Figure 8 YPS used in the wall building example.
The allowable story drift, obtained from Table 4.51 of the 2003 NEHRP Recommended Provisions, is 0.020hsx =
0.020(12 ft)(12 in./ft) = 2.88 in. Table 2 provides an estimate of a3,stat = 1.59. Therefore, the roof drift limit associated
with the allowable story drift is approximately (0.020/1.59)(72 ft)(12 in./ft) = 10.87 in.
The more restrictive of the two roof displacement limits governs the design. In this case, Du,µ = 4.98 in., and µt
= Du,µ
/Dy = (4.98 in.)/(3.11 in.) = 1.6.
4. To determine the required yield strength coefficient, YPS are prepared for the design basis ground motion (Figure 8).
For Dy
* =2.12 in. and µt
= 1.6, the minimum base shear coefficient (at yield) is given by Cy
* = 0.19. Using a1 = 0.65 from
Table 2, the required base shear strength coefficient (at yield) for the MDOF system is given by Cy = a1
Cy
* = 0.65(0.19)
= 0.124.
The expected fundamental period of vibration of the building, based on the assumed yield displacement and modal
parameters a1
and G1, is Te = 2p(Dy
*/(Cy
*g))0.5 = 2p [2.12 in./(0.19 · 386.1 in./sec2)]0.5 = 1.07 sec.
5. Since there are four walls, the base shear strength (at yield) required for each wall for response in the first mode is given
by Vy = Cy · W/4 = 0.124(2296 kips) = 285 kips.
6. Because the Fi,ß distribution of lateral forces has a resultant that generally acts at a location that differs from that of the
firstmode distribution, the base shear is adjusted so that the flexural strength of the wall is equal to the product of Vy (=
285 kips) and the height of the resultant of the firstmode lateral forces. The Fi,ß distribution is determined using T =
1.07 sec as given in Table 4. The effective height of the resultant lateral force is given by heff,ß = SFihi/SFi = 15,909 kft/
285 kips = 56.41 ft. Then, heff,ß/h = 56.41 ft / 72 ft = 0.784. Since the first mode is estimated to have heff,1/h = 0.77,
the adjusted base shear is Vy = (285 kips)(0.77/0.784) = 280 kips.
7. The wall is designed using the ßi
distribution (Table 4) of lateral forces for a base shear of 280 kips. The required
strength at the base of the wall is Mn = (280 kips)(0.784)(72 ft)(12 in/ft) = 190,000 kipin. The wall shown in Figure 9
has a nominal strength of 197,000 kipin when subjected to a compressive force associated with its tributary gravity load,
using Grade 60 reinforcement and c = 5 ksi.
Figure 8 YPS used in the wall building example.
Figure 9 Showing Section at the base of the reinforced concrete wall.
120"
3" 3 @ 6"
12"
9"
Horizontal Reinforcement
2 layers of #5 @12" o.c.
Distributed Reinforcement
2 layers of #5 @18" o.c.
End Reinforcement
2 layers of 4 #9
with Single Hoops and
Crossties #5 @8" o.c.
CL Figure 10 Showing Capacity curve obtained in the pushover analysis of a wall.
Table 4 Lateral Force Distribution for Reinforced Concrete Wall Example
Level
hi (ft)
wi (kips)
wihi
(kft)
Swihi
(kft)
ßi
= Vi/Vy
Fi,ß/Vy
Fi,ß (kips)
Fi,ß·hi (kft)
6
72
383
27,554
27,554
0.396
0.396
112.0
8,064
5
60
383
22,962
50,516
0.620
0.224
63.4
3,803
4
48
383
18,370
68,886
0.780
0.160
45.2
2,172
3
36
383
13,777
82,663
0.892
0.113
31.9
1,147
2
24
383
9,185
91,848
0.965
0.072
20.5
491
1
12
383
4,592
96,440
1.000
0.035
10.0
120
S
4.652
1.000
285.0
15,909
Figure 9 Section at the base of the reinforced concrete wall.
To further substantiate the design approach, a firstmode pushover analysis of the wall was conducted. The wall was
modeled in Drain2DX (Prakash et al., 1993) using a fiber element. Materials were modeled using their nominal strengths;
strain hardening of reinforcement was included in the model. Modal properties used to establish the lateral force distribution
for the pushover analysis are based on initial (uncracked) properties. The resulting capacity curve is shown in Figure 10. A
bilinear curve was fitted to the capacity curve. The yield point (Dy, Vy) is given by (3.08 in, 288 kips), which is very close to
the estimate of (3.11, 280 kips) that was used as a basis for the design.
Figure 10 Capacity curve obtained in the pushover analysis of a wall.
The firstmode mass participation factor, based on uncracked sections, is 0.667, and the actual heff,1/h is 0.806. The initial
period based on uncracked sections, T1, is 0.524 sec. The effective period may be determined as Te = Ti(ki/ke)0.5 =
0.524(385/93.5)0.5 = 1.06 sec where ke = Vy/Dy = 288 kips/3.08 in = 93.5 k/in. Because 1.06 sec is approximately equal to the
ESDOF period (1.07 sec), the initial design is deemed adequate.
REINFORCED CONCRETE FRAME BUILDING EXAMPLE 2
A sixstory special reinforced concrete moment frame was designed for a building having the same nominal floor plan and
loading as the reinforced concrete wall example. Figure 11 shows a plan view. Story heights of 12 feet and dead and live
loads of 175 and 50 psf, respectively, were assumed. This example building was also located in Sacramento, California, on
Site Class D soils.
Figure 11 Plan view of reinforced concrete frame building.
The preliminary design was developed as follows:
Figure 11 Plan view of reinforced concrete frame building.
4 @ 27 ft
=108 ft
3 @
27 ft
= 81 ft
N
1. Assuming from Table 1 that the yield drift ratio of the reinforced concrete moment frame is approximately 0.55 percent,
the yield drift (at the roof level, corresponding to effective yield in a firstmode pushover analysis) was estimated as Dy=
(0.55%)(h) = (0.0055)(72 ft)(12 in./ft) = 4.75 in.
2. From Table 2 the firstmode participation factor, G1, was estimated to be 1.33. Therefore, the yield drift of the
“equivalent” SDOF oscillator was estimated as Dy
* = Dy/G1 = 4.75/1.33 = 3.57 in.
3. A limit on displacement ductility was established by considering drift and system ductility limits. From Table 3, the
allowable system ductility for a special reinforced concrete moment frame is 2.4. Therefore, the peak displacement limit
based on the allowable ductility is Du,µ = 2.4(4.75 in.) = 11.4 in. The allowable story drift, obtained from Table 4.51 of
the 2003 NEHRP Recommended Provisions, is 0.020hsx = 0.020(12 ft)(12 in/ft) = 2.88 in. Table 2 provides an estimate
of a3,stat = 1.26. Therefore, the roof drift limit associated with the allowable story drift is approximately (0.020/1.26)(72
ft)(12 in./ft) = 13.71 in. The more restrictive of the two roof displacement limits governs the design. In this case, Du,µ =
11.4 in., and µt
= Du /Dy
= (11.4 in.)/(4.75 in.) = 2.4.
4. To determine the required yield strength coefficient, YPS were prepared for the design basis ground motion (Figure 12).
For Dy
* = 3.57 in. and µt
= 2.4, the minimum base shear coefficient (at yield) is given by Cy
* = 0.048. Using a1
= 0.85
from Table 2, the required base shear strength coefficient (at yield) for the MDOF system was determined to be Cy =
a1Cy
* = 0.85(0.048) = 0.0408. The expected period of vibration is Te = 2p [Dy
*/(Cy
*g)]0.5 = 2p [3.57 in./(0.048 · 386.1
in./sec2)]0.5 = 2.76 sec.
5. If four separate moment frames provide resistance to lateral forces, the base shear strength (at yield) required for each
frame for response in the first mode is given by Vy = Cy · W/4 = 0.0408(2296 kips) = 93.7 kips.
6. Because the Fi,ß distribution of lateral forces has a resultant that generally acts at a location that differs from that of the
firstmode distribution, the base shear was adjusted so that the strength of the mechanism under the lateral forces
corresponds to the overturning moment generated by the firstmode lateral forces over the height of the structure. The
Fi,ß distribution was determined using Te = 2.76 sec as given in Table 5. The effective height of the resultant lateral force
is given by heff,ß = SFihi/SFi = 5433 kft/93.7 kips = 57.98 ft for a period of 2.76 sec. Then, heff,ß /h = 57.98 ft / 72 ft =
0.805. Since the first mode is estimated to have heff,1/h = 0.69, the adjusted base shear is Vy = (93.7 kips)(0.69/0.805) =
80.3 kips.
Figure 12 YPS used in the reinforced concrete frame example.
Figure 12 YPS used in the reinforced concrete frame example.
Table 5 Lateral Force Distribution for Reinforced Concrete Frame Example
Level
hi (ft)
wi (kips)
wihi
(kft)
Swihi
(kft)
ßi
= Vi/Vy
Fi,ß/Vy
Fi,ß (kips)
Fi,ß·hi (kft)
6
72
383
27,554
27,554
0.464
0.464
43.52
3133
5
60
383
22,962
50,516
0.673
0.209
19.55
1173
4
48
383
18,370
68,886
0.814
0.141
13.19
633
3
36
383
13,777
82,663
0.910
0.096
9.00
324
2
24
383
9,185
91,848
0.971
0.061
5.68
136
1
12
383
4,592
96,440
1.000
0.029
2.76
33
S
4.832
1.000
93.70
5433
7. The frame was designed using the Fi,ß distribution (Table 5) of lateral forces for a base shear of 80.3 kips. The first story
column strengths were determined to prevent a story mechanism using Equation 22. Nominal column strengths at the
base had to exceed 1.1(80.3 kips)(12 ft)/4 = 265 kft. Beam plastic hinge strengths (taken equal to the ACI nominal
moment value using specified material properties) were distributed vertically in proportion to the ßi
values given in
Table 5. Thus, a virtual work calculation considering the mechanism of Figure 3a provides that external work, WE, is
given by WE = (80.3 kips)(57.98 ft).p and internal work, WI, is given by WI = 2Mpc.p + S(Vi/Vy)Mpbr.p = 2(265 kft)
.p + 4.832(Mpbr)(2).p where Mpbr is a reference plastic strength. Setting WE = WI results in Mpbr = 428 kft.
8. Conventional reinforced concrete frame details provide a positive moment capacity at the face of a joint that is equal to
at least onehalf the negative moment capacity. To provide sufficient strength to the mechanism, the strengths at
opposite ends of the beam (Mp
+ + Mp
) must equal or exceed 2ßi Mpbr at the ith floor level. In the present example, 20
percent of the live load is considered to be present together with 100 percent of the dead load. Load factors used in a
routine design would lead to unused gravity moment capacity that would contribute to strength and stiffness during
seismic loading and, hence, would increase the lateral strength and reduce the modal periods of the frame.
To avoid incurring these beneficial effects in the example, which both illustrates the design approach and demonstrates its
robustness, only dead loads and 20 percent of the live load were considered in combination with the seismic demands to
determine Mp
. Then, Mp
+ was set equal to 0.5(Mp
). Reinforcement steel was proportioned assuming Mn = Mp
.
The resulting cross sections are shown in Figure 13. Grade 60 reinforcement and concrete having c = 5 ksi were used in the
design and the mathematical models.
Figure 13 Beam and column section designed in the reinforced concrete frame example.
Figure 13 Beam and column section designed in the reinforced concrete frame example.
(4) No. 11
(2) No. 11
16 in.
26 in.
1st Floor
Beams
(2) No. 11
(2) No 10
(2) No. 11
16 in.
26 in.
2nd Floor
Beams
(3) No. 10
(2) No. 8
(2) No. 11
16 in.
26 in.
3rd Floor
Beams
Figure 13 Beam and column section designed in the reinforced concrete frame example.
Figure 13 Beam and column section designed in the reinforced concrete frame example
(2) No. 10
(3) No 8
(2) No. 10
16 in.
26 in.
4th
Floor
Beams
(2) No. 10
(2) No 9
(2) No. 10
16 in.
24 in.
5th
Floor
Beams
(4) No. 9
(2) No. 9
16 in.
20 in.
6th
Floor
Beams
Figure 13 Beam and column section designed in the reinforced concrete frame example.
To validate the assumptions used in the design, a firstmode pushover analysis of a frame was conducted. The frame was
modeled in Drain2DX (Prakash et al., 1993) using fiber elements. Rigid end offsets were used at the joints. Materials were
modeled using their nominal strengths; strain hardening of reinforcement was included in the model. Modal properties used
to establish the lateral force distribution for the pushover analysis are based on initial (uncracked) properties. The resulting
capacity curve is shown in Figure 14. A bilinear curve was fitted to the capacity curve. The yield point (Dy, Vy) is given by
(4.85 in., 104 kips), which is in the vicinity of the estimate of (4.75 in, 93.7 kips) that was used as a basis for the design. The
higher lateral strength obtained in the pushover analysis is attributed to: (1) reinforcement provided to the beams resulted in
beam plastic moment strengths that were slightly greater than the strengths determined in the mechanism analysis; (2)
flexural strength provided to resist tributary gravity loads was mobilized in the pushover analysis; and (3) the mechanism
analysis was based on centerline dimensions, but the use of rigid end offsets caused the plastic hinges to form at or near the
faces of the beamcolumn joints, thereby increasing the shears associated with flexural hinging.
The firstmode participation factor determined for the mathematical model is 1.37 and the mass participation factor is 0.742,
based on uncracked sections. The actual heff,1/h is 0.751. These values are all close to those assumed for the preliminary
design (1.33, 0.85, and 0.69, respectively). The fundamental period of vibration is 2.43 sec, which is significantly less than
the 2.76 sec assumed in the design. Thus, an evaluation of the preliminary design is warranted.
Figure 13 Beam and column section designed in the reinforced concrete frame example
(12) No 9
22 in
22 in
Columns
Grade 60 reinforcement
f’c = 5000 psi
Cover = 11/2 in.
The yield strength coefficient is computed as Cy = Vy/W = (104 kips)/(2296 kips) = 0.0453, and Cy
* = Cy/ a1
= 0.0453/0.742 =
0.061. Noting that Dy
* = 4.85/1.37 = 3.54 in., one may determine from Figure 12 an expected ductility demand µ = 2.2.
Figure 14 Capacity curve determined in a nonlinear static analysis of the reinforced concrete frame.
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
Roof Displacement, in.
Base Shear Force, kips
Thus, system ductility demands are acceptable and the expected peak displacement = µDy = 2.2(4.85 in.) = 10.7 in. is less
than the 13.71 in. limit that was established based on allowable story drifts. The design is considered satisfactory.
Figure 14 Capacity curve determined in a nonlinear static analysis of the reinforced concrete frame.
CONCLUSION
A simple approach was presented for the design of seismicforceresisting systems. Estimated yield drifts given in Table 1
and design parameters given in Table 2 were sufficiently accurate that no iteration was required in the example designs. The
base shear strength, determined to limit ductility and drift demands, was distributed over the height of the structure according
to a new distribution. Required member strengths were determined in conjunction with the development of a desired
mechanism using the equations of virtual work. System ductility limits used in the design were derived for currently
recognized seismicforceresisting systems. Roof drift limits are indexed to current allowable story drifts. Thus, the designs
obtained with this method are nominally consistent with code performance expectations. Detailing requirements and other
limits for such systems as well as other requirements in the 2003 NEHRP Recommended Provisions remain applicable.
NOTATION
a A coefficient that represents the effect of site characteristics on peak displacement response.
C1 A modification factor to account for the influence of inelastic behavior on the response of the system, as determined
by Equation 17.
C2 A modification factor to account for the influence of cyclic degradation of strength and stiffness on the response of
the system, as determined by Equation 18.
Cy Base shear coefficient at yield, equal to Vy/W.
Cy
* Yield strength coefficient for equivalent singledegreeoffreedom oscillator (dimensionless).
Du Roof drift limit, determined as the smaller of Du,µ and Du,..
Du,µ Roof drift limit based on design ductility limit in the direction of interest for the design earthquake.
Du,. Roof drift limit based on allowable story drift in the direction of interest for the design earthquake.
Dy, D`y Effective yield displacement, at the roof.
Dy
* Yield displacement of the equivalent SDOF oscillator.
Du
* Peak displacement of the equivalent SDOF oscillator.
Fi,1 Lateral force at Level i of the structure, distributed in proportion to the product of the mode shape amplitude fi
1 and
seismic weight, wi, at Level i.
Fi,ß Lateral force at Level i of the structure, determined according to Equations 19 and 20.
g Acceleration of gravity.
h Average roof height of structure with respect to the base.
hi, hj Height of ith or jth floor above the base.
heff,1 Height of resultant of lateral forces Fi,1 above the base.
heff,ß Height of resultant of lateral forces Fi,ß above the base.
hsx Story height below Level x.
I Importance factor in Section 11.5.1 of the 2003 NEHRP Recommended Seismic Provisions.
ke Effective stiffness associated with secant stiffness to effective yield point.
ki Initial stiffness, typically associated with elastic properties at small displacement amplitudes.
lw Length of prismatic wall in plan in direction under consideration.
Mn
Nominal flexural strength.
Mp
+ Plastic moment having positive sense.
Mp
 Plastic moment having negative sense.
Mpbr
Reference plastic moment strength.
Mpc
Plastic hinge strength of column.
R* Ratio of strength required for elastic response and yield strength of companion inelastic oscillator.
Sa Design, 5% damped, spectral response acceleration, adjusted for site effects, normalized by g.
Sd Peak displacement of elastic oscillator, equal to Sa g(Te /2p)2.
Te Effective period, associated with secant stiffness to effective yield point, in seconds.
Ti Initial period, associated with initial stiffness properties, in seconds.
Vi Story shear at the ith story above the base.
Vy Effective yield strength, at the base.
Vy
* Yield strength of the equivalent SDOF oscillator.
wi Portion of W that is located at or assigned to Level i.
W Effective seismic weight of the building, as defined in Section 12.7.2.
W* Effective weight of the equivalent SDOF oscillator.
W Diagonal matrix containing the entries wi.
WE External work determined in a virtual work analysis.
WI Internal work determined in a virtual work analysis.
a Coefficient in Equation 19, taken equal to 0.75.
a1
Fundamental mode mass coefficient.
a3
,stat Estimate of maximum ratio of interstory drift ratio and average roof drift ratio for the first mode.
ßi
Ratio of story shear just below Level i and base shear at yield, Vy.
.a Allowable story drift.
fi
,1 Displacement amplitude at Level i of the fundamental mode of vibration of the structure in the direction of interest,
normalized to unity at the roof level.
f1 Vector containing the values of fi
,1.
G1 Participation factor of fundamental mode of vibration of the structure in the direction of interest.
µ System ductility.
µc
Effective ductility capacity in the direction of interest for the design earthquake.
µd
Design ductility limit in the direction of interest for the design earthquake considering the importance factor, I.
µt
Target allowable effective ductility demand in the seismic force resisting system in the direction of interest
considering drift and ductility limits, for the design earthquake.
.p Angle used in virtual work analysis, rad.
APPENDIX: YIELD POINT SPECTRA
This appendix provides details on the interpretation, use, and construction of yield point spectra (YPS). YPS (Aschheim and
Black, 2000) represent the peak displacement response of an oscillator that has a bilinear loaddeformation response. Figure
Figure 15 Yield point spectra.
15 shows such an oscillator and identifies its yield point and peak displacement response schematically. The ductility
demand for such an oscillator can be determined for any specific earthquake record using software to compute inelastic
response. Alternatively, established ductility (RµT) or displacement coefficient (C1, C2) relationships can be applied to
smoothed design spectra to estimate the peak displacement for any combination of period and yield strength.
Figure 15 Yield point spectra.
YPS plot displacement ductility demands as a function of the yield point of an SDOF or ESDOF oscillator. In order to be
general, the yield strength Vy
* = Cy
*W is normalized by the weight of the oscillator’s mass so that yield strength coefficient,
Cy
*, is plotted on the ordinate of the YPS. Thus, YPS can be used to determine the expected ductility demand, which depends
on where the oscillator’s yield point (Dy
*, Cy
*) plots on the spectra. The expected ductility demand allows peak displacement
response to be assessed on the YPS. For example, Figure 15 illustrates how changes in strength influence the peak
displacement response for a given yield displacement. Thus, in the usual design context, the estimated yield displacement is
known and the objective is to determine the strength that limits the drift and ductility demands to acceptable levels.
Increasing the strength (Cy
*) causes a reduction in both ductility and drift responses. This is easily generalized to consider
multiple performance objectives, with each performance objective resulting in a minimum required strength; the largest of the
required strengths provides satisfactory performance for all performance objectives.
Just as in the capacity spectrum method, lines of constant period radiate from the origin. Period is related directly (but not
linearly) to the slope Cy
*/Dy
* by Equation 15. Thus, a minimum strength for a given yield displacement (resulting from drift
and ductility limits) can also be interpreted as a minimum stiffness or maximum period.
YPS differ from the capacity spectrum method in some fundamental ways. Peak displacements are plotted on the abscissa in
the capacity spectrum method, while yield displacements are plotted on the abscissa of YPS. The capacity spectrum method
relies on equivalent linearization to account for the influence of nonlinearity in the loaddeformation response while ductility
or displacement coefficient relationships typically are used with YPS. The terms “yield strength coefficient” and “yield
displacement” are used in YPS as alternatives to the terms “spectral acceleration” and “spectral displacement” used in the
capacity spectrum method because the latter are clearly defined only for elastic response.
Admissible design regions can be constructed by reversing the process for estimating displacement response. The yield
points that correspond to a desired peak displacement can be determined and plotted. For example, points corresponding to a
peak displacement of 24 in. are shown in Figure 16. These points are determined as described below.
An elastic oscillator having a yield displacement of 24 in. would also have a peak displacement of 24 in.; thus, the required
yield strength coefficient, Cy
*, is located on the µ = 1 curve at this yield displacement. Similarly, an oscillator having a yield
displacement of 24/1.3 = 18.5 in. and Cy
* located on the µ = 1.3 curve would have a peak displacement of 24 in. Repeating
this process for each ductility curve results in the family of points shown in Figure 16. A line passing through these points
represents a boundary of the admissible design region; points below this curve have larger ductility demands and, thus, are
Figure 16 Establishment of the drift limit and illustration of the influence of foundation flexibility on response and required strength.
excluded because they would have peak displacements greater than 24 in. For long period systems, results are compatible
with the “equal displacement rule” and result in a limit on the period of vibration of the system. For short period systems,
this procedure accounts for displacement amplification in establishing the boundary of an admissible design region.
Figure 16 Establishment of the drift limit and illustration of the influence of foundation flexibility on
response and required strength.
It is obvious that to ensure ductility demands do not exceed a certain value (e.g., 4) requires excluding yield points below the
curve corresponding to this value. The boundaries established by considering drift and ductility limits can be used to
establish admissible design regions (ADRs). ADRs can be especially useful in schematic design when comparing alternative
seismicforceresisting systems or for tuning the proportions of a given seismicforceresisting system in order to modify its
yield displacement so that the required lateral strength (or cost) can be minimized while satisfying the performance
objective(s).
When appropriate, the influence of elastic foundation flexibility can be addressed using the YPS methodology. Elastic
foundation flexibility will cause the yield displacement to increase in proportion to the lateral force. Thus, the system with
foundation flexibility can be represented by a line that is inclined (to the right) of the line representing fixedbase conditions
(also illustrated in Figure 16). While interstory drift and system ductility limits typically would be unaffected by foundation
flexibility, the increase in yield displacement will require that the ductility demand be reduced in order to satisfy a drift limit.
As illustrated, this causes the required base shear strength to increase for systems that are controlled by drift. Note that for
the shorter period systems controlled by ductility demands, the increase in yield displacement due to foundation flexibility
causes a reduction in the required strength.
The construction of YPS is fairly straightforward. Because design spectra and established ductility and displacement
coefficient relationships are expressed as functions of period, the usual approach is to determine the strength reduction factor
associated with a desired ductility demand for each period of interest. This is usually more straightforward when RµT
relationships are used. A simple approach when using displacement coefficients (Equations 16 through 18) in a spreadsheet
format is to create functions that return C1, C2, and the value of R
(A1)
Then, for any value of µ and T, the yield strength coefficient Cy
* for a given period, target ductility, and site coefficient.
The function for R*(µ, Te, a) may use an iterative approach to the determination of R*, initially assuming R* = µ. In setting up
this function it is useful to note that:
* is determined as: Equation
*
1 2 *
* 1 2
u d
y y
D CC S CC R
D D
µ = = =
(A2)
and Dy
(A3)
The spreadsheet can be organized as shown in Table 6. A smoothed elastic design response spectrum is represented in the
first two columns. The spectral displacement, Sd, is given by:
(A4)
because values of Sa have been normalized by the acceleration of gravity.
Table 6 Illustration of Spreadsheet Organization for Determining YPS
* is determined as:
Equation
*
*
a
y
C S
R
= Equation
2
* *
2
e
y y
D C g T
p
= . . . .
. . Equation
2
2
e
d a
S S g T
p
= . . . .
. .
Elastic Design Spectrum
Inelastic Spectra
µ = 1.30
µ = 1.30
Te
Sa/g
Sd (inch)
R*
Cy ˆ
Dy ˆ(inch)
R*
Cy ˆ
Dy ˆ(inch)
0.00001
0.22
0.0000
1.20
0.18
0.0000
1.43
0.15
0.0000
0.01
0.24
0.0002
1.20
0.20
0.0002
1.43
0.17
0.0002
0.02
0.27
0.0011
1.20
0.23
0.0009
1.43
0.19
0.0007
0.03
0.30
0.0026
1.20
0.25
0.0022
1.43
0.21
0.0018
0.04
0.32
0.0051
1.20
0.27
0.0042
1.43
0.23
0.0036
REFERENCES
Aschheim, M. 2000. “The Primacy of the Yield Displacement in Seismic Design,” Second USJapan Workshop on
PerformanceBased Seismic Design for Concrete Buildings, Sapporo, Japan, September 1012.
Aschheim, M., and E. Black. 2000. “Yield Point Spectra for Seismic Design and Rehabilitation.” Earthquake Spectra,
16(2):317336.
Black, E. F., and M. Aschheim. 2000. Seismic Design and Evaluation of Multistory Buildings Using Yield Point Spectra,
CD Release 0004, MidAmerica Earthquake Center.
Chao, S.H., S. C. Goel, and S.S. Lee. 2007. “A Seismic Design Lateral Force Distribution Based on Inelastic State of
Structures,” Earthquake Spectra, 23(3):547569, Aug.
Federal Emergency Management Agency. 2005. Improvement of Nonlinear Static Seismic Analysis Procedures, FEMA 440.
Federal Emergency Management Agency, Washington, D.C.
Goel, S. C., and S.H. Chao. 2007. “A Performancebased Plastic Design Method (PBPD) for SeismicResistant Structures,”
in review.
Goel, S. C., S. Leelataviwat, S.S. Lee, and S.H. Chao. 2007. “Underlying Theory behind Performancebased Plastic Design
(PBPD) Method for EarthquakeResistant Structures,” in review.
Paulay, T. 2002. “An Estimation of Displacement Limits for Ductile Systems,” Earthquake Engineering and Structural
Dynamics, (31):583599.
Prakash, V., G. H. Powell, and S. Campbell. 1993. Drain2DX Base Program Description and User Guide, Version 1.10,
Report UCB/SEMM93/17. Structural Engineering, Mechanics, and Materials, University of California, Berkeley.
Priestley, M. J. N. and M. J. Kowalsky. 1998. “Aspects of Drift and Ductility Capacity of Rectangular Cantilever Structural
Walls,” Bulletin of the New Zealand National Society for Earthquake Engineering, 31(2):7385.
Priestley, M. J. N. 2000. “Performance Based Seismic Design,” 12th World Conference on Earthquake Engineering,
Auckland, New Zealand, Jan. 30 – Feb. 4.
Tjhin, T., M. Aschheim, and J. Wallace. 2002. “Displacementbased Seismic Design of Reinforced Concrete Structural
Walls,” 7th US National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Boston, July
2125.
Resource Paper 10
SEISMIC DESIGN METHODOLOGY FOR
PRECAST CONCRETE FLOOR DIAPHRAGMS
This resource paper describes a design approach for untopped and topped composite precast concrete diaphragms
applicable for all seismic design categories (SDC). The methodology was developed as an integral part of a large industryendorsed
and supported analytical and experimental research project on precast concrete floor diaphragm. The impetus for
the research was the seismic vulnerability of precast concrete floor systems as demonstrated by their performance in recent
earthquakes, particularly the 1994 Northridge earthquake (EERI, 1994; Iverson and Hawkins, 1994). While several
shortcomings in design practices at that time have been identified (Wood et al., 1995; Fleischman et al., 1996), and positive
incremental changes made to code provisions for precast concrete diaphragm design (Wood et al., 2000; Hawkins and
Ghosh, 2000), it is clear from the recommendations of Appendix A of Chapter 9 of the 2000 NEHRP Recommended
Provisions that a better comprehensive design methodology is needed.
The methodology proposed here specifies:
a. The performance for which the precast concrete diaphragm should be designed in terms of forces, displacements, and
deformations;
b. The precast concrete diaphragm connection details that must be used to provide this performance; and
c. The required stiffness of the precast concrete diaphragm relative to the stiffness of the lateralforceresisting system
(LFRS).
The objective of the design methodology is to provide a reliable design that does not compromise the safety, reliability,
practicality, or economics of precast concrete construction.
The principal researchers for the study described in this paper were: Dr. Robert Fleischman, University of Arizona; Dr.
Clay Naito and Dr. Richard Sause, Lehigh University; and Dr. Jose Restrepo, University of California, San Diego. DSDM
Industry Task Group Members guiding the research were: Tom D’Arcy, DSDM Task Group Chair, PCI R&D Committee;
founder, The Consulting Engineers Group, San Antonio, Texas; Roger Becker, Vice President, Spancrete Industries, Inc.,
Waukesha, Wisconsin; Dr. Ned Cleland, President, Blue Ridge Design, Inc., Winchester, Virginia; David Dieter,
President/General Manager, Mid State Precast, Inc., Cocoran, California; Dr. S. K. Ghosh, DSDM Project CoPrincipal
Investigator, President, S.K. Ghosh Associates, Inc., Skokie, Illinois; Harry Gleich, Vice PresidentEngineering, Metromont
Prestress, Greenville, North Carolina; Dr. Neil Hawkins, Professor Emeritus, University of Illinois, UrbanaChampaign,
Illinois; Paul Johal, PCI Research Director, Precast/Prestressed Concrete Institute, Chicago, Illinois; Dr. Joseph Maffei,
Structural engineer, Rutherford & Chekene Engineers, Oakland, California; Susie Nakaki, President, The Nakaki Bashaw
Group, Inc., Irvine, California; Dr. Douglas Sutton, Chair, PCI Research & Development Committee, and Professor, Purdue
University, West Lafayette, Indiana. The principal researchers were: Dr. Robert Fleischman, University of Arizona; Dr.
Clay Naito and Dr. Richard Sause, Lehigh University; Dr. Jose Restrepo, University of California, San Diego.
PRECAST CONCRETE DIAPHRAGM BEHAVIOR
The following aspects of diaphragm behavior must be addressed in an effective seismic design methodology for precast
concrete diaphragms (Fleischman et al, 2005a):
1. Diaphragm force levels assumed to occur during an earthquake are likely to significantly exceed those prescribed by
current building code provisions;
2. Complex internal force paths can create force combinations/local deformation demands not anticipated by simple
“horizontal beam” representations of a floor diaphragm;
3. Significant diaphragm global deformations can amplify demands on gravityforceresisting system in regions of the
structure distant from the primary (verticalplane) LFRS elements.
These concerns are not unique to precast concrete diaphragms. They are equally applicable to the diaphragms of many large
boxtype and tiltup structures. However, the jointed nature of precast concrete diaphragms creates a condition in which
these factors can lead to poor structural performance if they are not directly considered in the design. (See Section A2 for a
more detailed description of these concerns.)
Because of cracking along the joints between precast units, toppings do not ensure monolithic diaphragm action (Wood et al.,
2000). For untopped or topped precast concrete diaphragms, the critical diaphragm crosssections occur at the joints between
the precast floor units. Thus, the combination of diaphragm forces greater than those specified by codes and internal force
combinations not currently recognized by simple beam idealizations of diaphragms can lead to yielding of the discrete
reinforcement or connectors crossing the joints. In the event of this yielding, inelastic deformation will concentrate locally at
the joints, and the diaphragm stiffness is significantly reduced by cracking and deformation of the elements crossing the
joints.
DESIGN RAMIFICATIONS
Precast concrete diaphragm design has traditionally assumed elastic behavior and focused on providing sufficient strength. It
has not considered that there may be a need for inelastic deformation capability. The potential for localized concentrations of
inelastic deformation demand implies that a prescriptive elastic design for the diaphragm (i.e., one without any ductility
requirements for the diaphragm reinforcement) would need to ensure elastic behavior.
The diaphragm forces expected during strong ground shaking can be much larger than current code specified diaphragm
design force levels (Lee and Kuchma, 2007; Rodriguez et al., 2001). In some cases, the large diaphragm forces are driven by
changes in the structure’s dynamic properties after yielding of the primary elements of the LFRS (Fleischman et al., 2002;
Eberhard and Sozen, 1993). As a result, even a capacity design approach in which the diaphragm is designed considerably
stronger than the primary LFRS (wall or frame) elements and first yielding is successfully produced in those LFRS elements
while the diaphragms are still elastic, is no guarantee of sustained elastic diaphragm behavior throughout the seismic event.
A prescriptive elastic diaphragm design, therefore, may be difficult to achieve economically for all situations.
Given the complex internal force paths inherent in floor systems, including the effect of openings for stairwells, elevators and
parking garage ramps, and the potential for alternate load paths in secondary elements within the floor system, it is unclear
whether designs based on simple horizontal beam representations can avoid localized inelastic deformation demands for all
situations, even if proper account is taken of the actual diaphragm forces likely in large ground shaking events. A
prescriptive elastic diaphragm design, therefore, may be difficult to achieve reliably for all situations.
Deformation capacity needs to be built into the precast floor system (Lee et al., 2007). Accordingly, the approach adopted
for the design methodology is to target elastic diaphragm response but anticipate the need for inelastic deformation capacity.
In this way, impractical (connectors spaced too closely) or uneconomical (cost of significantly more connectors) designs can
be avoided; yet, the penalty for unanticipated load paths or localized concentrated inelastic deformation is no longer a
nonductile failure (loss of load carrying capacity) of the floor system but is instead repairable damage to the floor system.
The use of performance targets allows parallel design requirements related to diaphragm flexibility to be considered at the
same time as diaphragm strength and deformation capacity. The primary requirement in this regard pertains to limiting the
flexiblediaphragm amplified drifts of gravity system columns and walls (outofplane displacement of walls) in regions of
the structure distant from primary LFRS elements.
PROPOSED DESIGN APPROACH
The design approach for the proposed seismic design methodology is based on performance targets for the diaphragm seismic
response. The selected performance targets are enforced through a combination of design factors and detailing requirements.
The design methodology provides the designer with the flexibility of selecting from a number of options.
The basic design option (BDO) targets elastic diaphragm behavior for the design basis earthquake (DBE). As such, a certain
amount of inelastic diaphragm deformation is anticipated in a maximum considered earthquake (MCE). This target is
selected based on the research findings discussed above, showing that attempting to enforce elastic behavior in precast
diaphragms for all seismic response situations can be impractical. Instead, the BDO involves the use of more realistic
diaphragm design forces, higher for most cases than those currently used in practice, in combination with detailing provisions
that build a measure of inelastic deformation capacity into the diaphragm.
In some cases, the basic design objective is neither practical nor necessary. In such cases, two alternatives are offered: an
elastic design option (EDO) that may provide the best design option for less demanding cases (e.g., squat diaphragm
geometry or a low SDC) and a “relaxed” design option (RDO) in which a limited amount of inelastic diaphragm deformation
is accepted in the DBE in order to lower diaphragm design forces. The second option may be necessary for practical designs
in demanding cases (e.g., long span untopped diaphragms for use in high SDCs).
Figure 1 shows a schematic of diaphragm response in terms of monotonic pushover curves (diaphragm force vs. diaphragm
midspan deformation). The lower curve is the expected performance of current diaphragm designs for high SDCs  the
diaphragm force in a significant seismic event is expected to exceed current design forces and, in the absence of any detailing
requirements, the diaphragm will likely undergo a nonductile failure (shown by the lowest X). The upper curve is the
performance intended by the proposed BDO design approach. Shown on this upper curve are key points related to the design
approach.
The design approach employs the following features to achieve its objectives:
1. An amplified diaphragm design force,
2. A higher relative strength for the diaphragm shear reinforcement and the connections to the LFRS than the diaphragm
chord reinforcement,
3. A classification system for diaphragm reinforcement, and
4. Limits on the diaphragm contribution to interstory drift.
As indicated in Figure 1, the following terminology and notation track these measures during the calibration stage: a
diaphragm design force amplification factor, .D; a diaphragm shear overstrength factor, Ov, and an anchorage overstrength
factor, Oa; diaphragm reinforcement and connection classification categories LDE (low deformability elements), MDE
(moderate deformability elements) and HDE (high deformability elements); and a diaphragm drift limit, dx.
The .D factor is applied to the current code specified diaphragm design force to increase the diaphragm
strength to the DBE force target. This approach requires some deformation capacity in the diaphragm reinforcement for the
MCE event, which may be MDE or HDE depending on the parameters of the design. The Ov factor is applied to the
diaphragm shear reinforcement to prevent a nonductile shear failure from occurring while the diaphragm deforms in the
MCE demand. This displacement demand needs to be within allowable drift limits (right side of Figure 1).
Figure 2 shows pushover curve schematics for two situations in which the elastic design option (EDO) may be desirable. The
left side of Figure 2 shows the low seismic hazard case. The BDO also can be used for this case as shown by the lighter
(gray) curve. However, the forces .eFpx required for the EDO (dark black curve) may not be significant in terms of absolute
values and, thus, it may be more desirable to relax the stricter requirements of an HDE design.
The right side of Figure 2 shows the squat geometry case. Again, the BDO can be used for this case. The MCE ductility
demand is not large (due to diaphragm geometry) and so MDE reinforcement can be used. However, since the mass and
length of the squat diaphragm are less than for a longer diaphragm, the internal shear and moment are lower for a given
acceleration. Thus, designing the diaphragm strength .eFpx to the upper diamond in Figure 2 (right) (i.e., an EDO) also is
feasible. The EDO is a reasonable option for a squat diaphragm geometry or a low SDC diaphragm.
Figure 1 Diaphragm response curve (left) and diaphragm force and deformation (right).
.
Load
L
d
.
.
Load
L
d
.
Proposed
design force
.dFpx
Diaphragm force
Diaphragm lateral displacement
Chord
Failure
MCE
ductility
demand
Current
design force
Fpx
DBE force
demand
Ov.dFpx
Shear
Failure
Mn
chord
+shear
Drift limit, dx
LDE, MDE or HDE
Proposed
design force
.dFpx
Diaphragm force
Diaphragm lateral displacement
Chord
Failure
MCE
ductility
demand
Current
design force
Fpx
DBE force
demand
Ov.dFpx
Shear
Failure
Mn
chord
+shear
Drift limit, dx
LDE, MDE or HDE
Figure 1 Diaphragm response curve (left) and diaphragm force and deformation (right).
Figure 3 shows the relaxed design option (RDO). This option is desirable when the diaphragm force is sufficiently large to
make the spacing of diaphragm connections impractical as is the case for pretopped long span diaphragms for high SDCs.
By relaxing the elastic diaphragm requirement for the DBE target, all the design forces for the diaphragm are reduced
including the “stacked” factors .DOv applied to the shear reinforcement. Naturally, a larger inelastic deformation capacity is
required for the MCE and, thus, HDE reinforcement will be required. The different features of the design approach are
described below.
Diaphragm Design Force. The diaphragm global performance targets are achieved through specifying appropriate
diaphragm design force levels. The proposed design approach will accomplish this objective through the use of amplified
diaphragm design forces. The required magnitude of the diaphragm design force amplification .D is based on the design
intent (BDO, EDO, RDO) as well as a number of structural parameters including: diaphragm span, LFRS type, building
configuration, and number of stories.
Figure 2 Elastic design option (EDO): low seismic hazard (left) and squat diaphragm geometry (right).
Diaphragm force
Diaphragm lateral displacement
. Elastic design force eFpx
Fpx Current design force
Drift
limit
MCE
ductility
demand
DBE force
demand
Mn
MCE force demand
HDE not required
BDO
EDO
Diaphragm force
Diaphragm lateral displacement
. Elastic design force eFpx
Fpx Current design force
Drift
limit
MCE
ductility
demand
DBE force
demand
Mn
MCE force demand
HDE not required
BDO
EDO
Diaphragm force
Diaphragm lateral displacement
MCE ductility
demand
Fpx Current design force
DBE force demand
Drift limit
Shear Failure
.dFpx
HDE not required
Higher accel.
on less mass .eFpx BDO
EDO
Mn
Diaphragm force
Diaphragm lateral displacement
MCE ductility
demand
Fpx Current design force
DBE force demand
Drift limit
Shear Failure
.dFpx
HDE not required
Higher accel.
on less mass .eFpx BDO
EDO
Mn
Figure 2 Elastic design option (EDO): low seismic hazard (left) and squat diaphragm geometry (right).
The manner in which diaphragm force amplification will be introduced into the design methodology is currently under
consideration (see Section A2). During the research phase, a generic term, the diaphragm design force amplification factor,
.D, has been used for calibration purposes. The .D factor is expressed relative to the code prescribed diaphragm design force
values in place at the onset of the research project in 2003. A constant diaphragm force pattern, regardless of the floor level
in the building, is envisioned for the design methodology. This contrasts with the increasing force values for increasing floor
levels in current codes. The .D factor is calibrated with respect to the maximum diaphragm force relative to current code
force values, (typically the force for the uppermost level diaphragm). The research studies completed to date indicate that
appropriate .D values are 1.4 to 2.0 (BDO), 1.0 to 1.5 (RDO) and 1.75 to 2.5 (EDO).
Diaphragm Reinforcement Relative Strength. The design approach uses capacity design concepts to produce a hierarchy
of design strengths among the reinforcement groups in the diaphragm. This approach recognizes the need to form a ductile
deformation mechanism in an overload situation. The primary diaphragm reinforcement groups are chord reinforcement,
shear reinforcement, and collector/anchorage reinforcement. A hierarchy of design strengths is used that is intended to
protect the shear and anchorage reinforcement against failure and ensure ductile flexural limit states.
The relative strength increases for the diaphragm shear and anchorage reinforcement are a function of the design intent
(BDO, EDO, RDO) as well as structural parameters including diaphragm span, Seismic Design Category, and diaphragm
detail classification.
Figure 3 Relaxed design option (RDO).
.dFpx
Diaphragm force
Diaphragm lateral displacement
Current
design force
Fpx
Ov.dFpx
Ov.dFpx
Lower diaphragm design
strength than BDO
Slight yielding
in DBE
More inelastic
demand in MCE .dFpx
MCE
M DBE n
Lower required
shear overstrength BDO
RDO
.dFpx
Diaphragm force
Diaphragm lateral displacement
Current
design force
Fpx
Ov.dFpx
Ov.dFpx
Lower diaphragm design
strength than BDO
Slight yielding
in DBE
More inelastic
demand in MCE .dFpx
MCE
M DBE n
Lower required
shear overstrength BDO
RDO
Figure 3 Relaxed design option (RDO).
The manner in which the hierarchy of diaphragm reinforcement relative strengths is introduced into the design methodology
is still evolving (see Section A3). During the research phase, generic terms, the diaphragm shear overstrength factor, Ov, and
the anchorage overstrength factor, Oa, have been used for calibration purposes. The overstrength factors for the shear
reinforcement and anchorages are applied to internal force values based on the already amplified diaphragm design force
value (i.e., they are additional to the .D factor). Initial studies indicate that ranges for Ov and Oa are likely to be 1.1 to 1.4 and
2.0 to 2.5, respectively.
Diaphragm Detailing. A classification system ensures that the diaphragm details specified have the necessary
characteristics to produce the desired performance. A classification system is necessary given the many different types of
reinforcing details for precast concrete diaphragms, including proprietary and nonproprietary details.
The diaphragm detail classification system is based on deformation capacity with the following categories: low deformability
elements (LDE), moderate deformability elements (MDE), and high deformability elements (HDE). The use of different
categories recognizes that expected seismic demands, as controlled by the design factors, will not always require the strictest
level of detailing.
The option selected for the diaphragm design will dictate the diaphragm detail categories or vice versa. In general, the EDO
needs only LDE elements while the RDO requires HDE elements. The BDO can use MDE or HDE elements depending on
the parameters of the design.
The detailing requirements for MDE and HDE elements ensures that a hierarchy of strengths exists among the elements
(bars, plates, welds, anchors, etc.) within the reinforcing details so as to promote ductile behavior with the HDE being
required to demonstrate a certain level of deformation capacity.
An examination of current detailing practice for representative details (Naito et al., 2005) indicates that such hierarchies are
not present in many current details. However, certain existing diaphragm connectors that are LDE can be enhanced to MDE
through improved detailing.
The category assigned to a given detail is based on a qualification procedure that includes specifications for detailing
requirements and protocols to demonstrate the detail’s characteristics through physical testing (see Section A4). The
procedure can be used to prequalify existing details or serve as a mechanism for qualifying new detailing concepts.
Diaphragm Stiffness and Strength. The design approach uses an elastic stiffness calculation to ensure that the diaphragm
flexibility is within acceptable limits with respect to interstory drift of gravity system columns and walls in regions of the
structure distant from the primary LFRS elements and to adjust the diaphragm amplification and overstrength factors for the
effect of diaphragm flexibility on the structure’s modal properties.
The design approach requires a flexural strength calculation to select the flexural reinforcement. In accordance with research
findings and consistent with recent code modifications (ACI, 2008), the flexural strength includes the tension contribution of
the diaphragm shear reinforcement to diaphragm flexural strength.
A spreadsheet method has been developed to determine the effective moduli (Geff, Eeff) for the calculations of stiffness and
diaphragm flexural strength (Mn). The method is based on estimating the neutral axis depth (different formulations are used
for strength and stiffness) and spreading the lower joint stiffness over the precast panel (see Section A5). The method has
been initially calibrated with respect to analytical results and is currently being calibrated to experimental results.
Diaphragm Load Path. The design approach implicitly accounts for force combinations on individual reinforcing elements
within the diaphragm and/or entire diaphragm joints since the design factors are calibrated from analytical models that
capture these combined actions. Further, the effects of concentrated inelastic deformations on the local deformation demands
for the diaphragm reinforcement are likewise included in the models used for calibration.
However, a design approach that builds a measure of deformation capacity into the diaphragm must ensure that the
deformation demands are occurring in the intended regions and not in an alternate unanticipated load path. This is
particularly important for precast concrete diaphragms because the precast floor system is an assemblage of several types of
precast elements including socalled “secondary” elements (spandrels, inverted tee beams, lite walls) that are not formally
included in the diaphragm design but nevertheless may participate in the diaphragm action. The connections for these
secondary elements are often industry standard hardware rather than elements designed for a seismic force. These elements
do not usually possess sufficient strength or deformation capacity for plastic redistribution. Thus, if a section along the force
path cannot accommodate the forces or displacements, a nonductile failure may occur.
Finally, if the diaphragm is irregular, an explicit accounting for the load path may be required. The simple “horizontal” beam
procedure currently used in practice can be used if the diaphragm configuration meets certain limiting requirements. If not,
the designer will have two choices: apply internal force amplification factors based on the diaphragm configuration or
perform a static FE analysis of the floor system under inertial force to calculate the factors directly. A similar procedure is to
be used for the collectors and anchorages. Issues pertaining to the load path are discussed in Section A6.
LIST OF ACRONYMS
AR = aspect ratio
BDO = basic design option
DBE = design basis earthquake
DOF = degree of freedom
DSDM = diaphragm seismic design methodology
EDO = elastic design option
ELF = equivalent lateral force
FE = finite element
HDE = high deformability element
LDE = low deformability element
LFRS = lateralforceresisting system
MCE = maximum considered earthquake
MDE = moderate deformability element
NLDTA = nonlinear dynamic transient analysis
RDO = relaxed design option
RDOF = reduced degree of freedom
SDC = Seismic Design Category
SP = spandrel
APPENDIX
A1 Key Aspects of Precast Concrete Diaphragm Behavior
A1.1 Diaphragm Force Levels. Research has shown that the maximum diaphragm force event occurring at a given floor
during a design basis earthquake (DBE) may be substantially larger than current design force levels (Fpx) and even larger
(two or more times larger) in the maximum considered earthquake (MCE) (DSDM, 2006). Furthermore, the maximum
inertial forces may occur in the lower floors of the structure in direct contradiction to current ELF code specified patterns.
Such observations have also been deduced from accelerations measured during earthquakes (Hall, 1995) and in shake table
tests (Kao, 1998). The relative magnitude of the expected maximum diaphragm force to the current design force has been
shown to be dependent on several factors pertaining to building dimensions and configurations, the LFRS type, strength and
layout, and the ground motion intensity.
Necessary Feature of Design Methodology. Specification of appropriate diaphragm design force levels and associated
diaphragm design force patterns.
Design Methodology Approach. Appropriate diaphragm force levels are assigned through the use of a diaphragm force
amplification factor .D (see Section A2).
A1.2 Diaphragm Internal Force Paths. Current U.S. practice uses a horizontal beam model to determine the internal
forces (moment and shear) due to Fpx. Chord reinforcement is provided to carry the inplane bending moment; shear
reinforcement across panel joints parallel to the seismic force is designed to carry the inplane shear; and collectors bring
these forces to the LFRS. The following observations are made with respect to the current design model:
1. Regions of the diaphragm may be subject to complex force combinations (shear, moment, and thrust coinciding at a
section) that are more demanding than the internal forces determined from the simple horizontal beam model. The
additional forces can be due to restraint resulting from, or differential movements of, the vertical elements of the LFRS,
the direction of application of the seismic excitation, and openings or other irregularities in the floor system.
2. Shear strength design equations based on inclined cracking are not consistent with the observed behavior for topped
precast concrete diaphragms (Wood et al., 2000). Further, the 90degree paths associated with collectors do not provide
a fully rational load path to the primary (vertical plane) LFRS elements.
3. In precast concrete diaphragms alternate load paths may occur in the floor system through secondary elements such as
spandrels or inverted tee beams. These paths are unanticipated by the horizontal beam model.
4. In ACI 31808, the assumption that the chord reinforcement alone resisted the assumed design moments is replaced by
an approach permitting all the longitudinal reinforcement in the diaphragm to be assumed to contribute to its flexural
strength.
The horizontal beam assumption relies implicitly on plastic redistribution because it is assumed that the diaphragm forces are
resisted by their intended reinforcement group. However, no formal requirements currently exist for that reinforcement to
have the needed deformation capacity. Sufficient deformation capacity must be provided for precast diaphragm
reinforcement details so that they can develop and maintain the desired joint strength. This requirement is considered in
Section A1.3.
Necessary Features of Design Methodology. An accurate yet simple method is needed for determining diaphragm internal
forces including the likely force combinations on individual reinforcement or reinforcement groups and anticipating alternate
load paths. Using this method requires that:
1. Precast diaphragm reinforcement details should be designed for force combinations when appropriate.
2. More rational load paths should be used to distribute forces to the primary LFRS elements.
3. The alternate load paths in secondary elements should be accounted for or mitigated, including preclusion of nonductile
failure modes in secondary elements.
Design Methodology Approach. The current “horizontal” beam procedure can be used if the diaphragm configuration meets
certain limiting requirements. If not, the designer will have two choices: (1) apply internal force amplification factors based
on diaphragm configuration or (2) perform a static FE analysis of the floor system under inertial force to calculate the factors
directly. A similar procedure is to be used for collectors and their anchorage to the LFRS.
A1.3 Diaphragm Detailing. Existing precast concrete diaphragm connector details have been developed without full
consideration of expected local deformation demands due to joint opening. As described in the previous section, a certain
amount of deformation capacity is needed simply to develop the anticipated joint strength. As an example, consider shear
reinforcement in high flexure regions. This reinforcement is actually under high tension due to inplane bending of the
diaphragm. The tension deformation demand on the shear reinforcement due to joint opening will be similar to that of the
nearby chord reinforcement. Likewise, chord reinforcement in high shear regions must undergo a similar shear deformation
demand due to joint sliding as the shear reinforcement. Thus, for an elastic design based on the horizontal beam model, a
certain level of reliable deformation capacity is required. However, the design philosophy adopted here will in some cases
require the diaphragm to possess a measure of inelastic deformation capacity to provide structural integrity for the diaphragm
during strong ground shaking. The intent of this approach is to assume inelastic deformation in certain diaphragm
reinforcing elements while protecting other elements through capacity design concepts.
Necessary Features of Design Methodology. Necessary to the design methodology are:
1. Specification of appropriate capacity design factors to protect certain diaphragm reinforcing elements;
2. Specification of the expected inelastic deformation demands for other diaphragm details for a given set of design
parameters; and
3. Demonstration of reliable deformation capacity for the diaphragm details in question.
Design Methodology Approach. The relative strength of different diaphragm reinforcement groups is specified by diaphragm
overstrength factors applied to the shear reinforcement (Ov) and the collectors and their anchorages (Oa). The appropriate
factor is selected based on a number of design parameters. A classification system (LDE, MDE or HDE) is used to ensure
that appropriate precast diaphragm primary reinforcement details are used in conjunction with these design factors to meet
the design intent. Precast diaphragm reinforcing elements can be prequalified for a classification or can undergo qualification
testing following an established protocol. Appropriate secondary details are required to mitigate unanticipated load paths
through secondary elements.
A1.4 Diaphragm Flexibility. Precast concrete construction is commonly and effectively used for building systems with
long floor spans. In these structures, distances between the primary LFRS elements can produce a diaphragm that is
relatively flexible. The diaphragm flexibility is further increased by the inherent flexibility of a jointed system in comparison
to a monolithic system. For these flexible diaphragms, the floor system and connected gravity forceresisting columns in
regions removed from the primary LFRS elements can undergo amplified drift demands (Ju and Lin, 1999; TenaColunga
and Abrams, 1992). These drift demands can be significant for long span precast concrete structures in a MCE (Lee and
Kuchma, 2007; Fleischman et al., 2002).
Necessary Feature of Design Methodology. Specification of a diaphragm elastic stiffness calculation procedure that can be
used to properly estimate seismic design forces and check drift limits.
Design Methodology Approach. The interstory drift, typically calculated as the difference in LFRS drift for adjacent floor
levels, must include a diaphragm deformation component.
A2 Determining Appropr iate Diaphragm Force Amplification Factor s
A2.1 Previously Proposed Approaches. Table A21 shows some of the diaphragm force amplification factors proposed in
the past:
1. Nakaki (2000) identified important inconsistencies in the then current code including designing the diaphragm to the
primary LFRS “first yield”. She proposed using a system overstrength factor Oo to amplify the diaphragm design force.
2. Rodriguez, Restrepo and Carr (2001), pointed to the importance of higher mode contributions to diaphragm force and
proposed calculating a diaphragm force Fdia = .Oi (PGA) Wdia where . is the importance factor, PGA is the peak ground
acceleration and Oi is a magnification factor based on the vertical location of the floor and the influence of higher modes
and for which only the first mode acceleration was reduced by the R factor:
3. Fleischman et al, 1998, investigated precast parking structures and proposed that a constant diaphragm design force
pattern be used. Fleischman and Farrow (2003), investigated frame and wall structures with flexible diaphragms, and
proposed calculating the diaphragm force using a diaphragm overstrength factor O* where: O*. targets the elastic
diaphragm response in the DBE and O.*
e targets the response for the MCE; there is a diaphragm flexibility factor ß that
ranges from 0 (rigid) to 0.4 (highly flexible);O* is a function of ß and the number of stories for wall structures (see Table
A22); and O.* is 1.0 for frame structures.
4. The 2000 and 2003 NEHRP Recommended Provisions Appendix A to Chapter 9 for Untopped Precast Diaphragms
proposed a factor that combined the system overstrength factor with the redundancy factor.
Table A21 Comparison of Diaphragm Force Amplification Factors
Researcher
Nakaki
Rodriguez/
Restrepo/Carr
Farrow/Fleischman/
Sause
NEHRP Appdx.
To Chap. 9
Design Force
Approach
Design to LFRS
Ultimate
Use R Factor on 1st
mode only
O is function of diaphragm
flexibility
Higher factor for
untopped
Design Force
Oo = 2.8 a
Oi
O* = 1.03.0
.Oo
a For squat shear walls, use R = 1.
Table A22 Overstrength Values for Differing Story Numbers and Diaphragm Flexibility
Equation
O*
O*.
e
Equation
0.2
0.25
0.3
0.35
0.4
0.2
0.25
0.3
0.35
0.4
1
1.0
1.1
1.2
1.4
1.55
1.9
1.85
1.8
1.7
1.6
2
1.2
1.3
1.45
1.7
1.85
2.3
2.25
2.15
2.05
1.95
3
1.4
1.5
1.7
1.95
2.2
2.7
2.6
2.5
2.4
2.3
4
1.6
1.7
1.95
2.2
2.5
3.1
3.0
2.9
2.75
2.6
5
1.8
1.95
2.2
2.5
2.7
3.45
3.35
3.25
3.15
2.9
6
2.0
2.15
2.45
2.8
3.0
3.8
3.65
3.5
3.35
3.2
Diagonal line
A2.2 DSDM Project Research Approach. The ratio of the magnitude of the expected maximum diaphragm force to the
current code specified force depends on several factors related to building dimensions and configurations, LFRS type and
layout, and ground motion intensity (DSDM, 2006). The DSDM project is calibrating the appropriate ratio (Fleischman et
al., 2005b) using two research activities:
1. A comprehensive statistical analytical parameter study using nonlinear dynamic transient analysis (NLDTA) of reduced
degreeoffreedom (RDOF) models being performed at UCSD.
2. A smaller number of NLDTAs using large degree of freedom threedimensional finite element (3DFE) models of
prototype structures being performed at the University of Arizona.
The analytical models were built using characteristics obtained from experiments on individual diaphragm reinforcing details
performed as part of the overall project (Naito et al. 2005). The analytical models are being verified through comparisons
with the results of hybrid testing of joint subassemblages at Lehigh University and a halfscale shake table test at UCSD
(Fleischman et al, 2005b).
RDOF Study. The left side of Figure A21 shows a representation of the RDOF model. The diaphragm is modeled as a beam
with its shear and flexural stiffness determined using the method described in Section A5. The parameters varied in this
study include: diaphragm span, LFRS type, building configuration, number of stories, Seismic Design Category (SDC),
design target, and detailing. Structures are designed for four sites as shown in Table A23 and are subjected to suites of 10
ground motions for each site.
Table A23 Representative Seismic Sites
Location
Soil
SS
Fa
SMS
SDS
S1
Fv
SM1
SD1
SDC
Knoxville
C
0.58
1.17
0.68
0.45
0.147
1.65
0.24
0.16
C
Seattle
C
1.58
1.00
1.58
1.05
0.55
1.30
0.71
0.47
D
Berkeley
C
2.08
1.00
2.08
1.39
0.92
1.30
1.21
0.81
E
Charleston
F
1.39
0.94
1.30
0.87
0.40
2.75
1.10
0.73
E
The right side of Figure A21 shows sample results from a suite of 10 earthquake motions for a single set of design
parameters (Berkeley DBE, threestory, perimeter shear wall layout, aspect ratio of 2). Median floor acceleration is plotted
along the length of the floor for each story. The current code design value is shown as a straight broken line. For this design
case, a .D factor of approximately 1.4 is required to target elastic response for the median response in the DBE for all the
diaphragms in the structure.
3DFE Analysis. On the left, Figure A23 shows an example of a 3DFE model for a threebay twostory parking structure.
Spring elements with cyclic characteristics represent the shear and chord reinforcement, described further in Appendix 3, and
the plastic hinging in the walls. The effect of secondary elements such as spandrels and their connections are included.
On the right, Figure A23 shows sample results of chord reinforcement axial, (opening), deformation demand for designs
using different .D (OD) factors. A .D =1.0 leads to a maximum (inelastic) chord deformation demand of 0.9 inch in the
DBE. This value drops to 0.35 inch for .D = 1.5, and the response is fully elastic for .D = 2.0. The MCE demands for the
latter two cases are 0.5 and 0.12 inch, respectively.
Figure A21 Schematic of RDOF model (left) and sample results for the floor (right).
Figure A21 Schematic of RDOF model (left) and sample results for the floor (right).
Figure A23 Schematic of 3DFE model (left) and sample results for chord force vs. opening.ght).
Chor d For ce Vs. Openi ng
 300
 200
 100
0
100
200
300
 0. 1 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9
Openi ng ( i n)
F( k)
OD=2 DBE
OD=2 MCE
OD=1 DBE
OD=1. 5 DBE
OD=1. 5 MCE
Figure A23 Schematic of 3DFE model (left) and sample results for chord force vs. opening.ght).
Such results allow calibration of .D with respect to diaphragm detail classification (LDE, MDE and HDE).
Testing has shown that HDE chord details can reliably achieve cyclic tension deformation amplitudes of 0.6 inch
and that MDE details reliably achieve 0.25 inch deformation (see Section A4). For this design, the use of .D = 1.5
and HDE details is a viable RDO solution. For a BDO solution, .D = 2.0 would be required although MDE reinforcement
could be used.
Possible Expression for Diaphragm Force Amplification. The proposed form for the amplification factor is:
where Fx = the story force; .dia = the dynamic amplification of diaphragm (depends on story); .vert = the overstrength of
vertical LFRS; and µdia = the ductility capacity of the diaphragm as a whole – depends on connections used (for elastic
diaphragm design (e.g., short spans, low SDC), µdia = 1.0). Equation
dia vert
px x
dia
F w F
µ
.
=
A3 Determining Appropriate Diaphragm Reinforcement Relative Strength. The methodology uses a capacity design
approach to protect specific diaphragm reinforcement groups (Standards New Zealand, 1997). The required relative strength
of the panel to panel shear reinforcement, and the diaphragm to LFRS anchorage reinforcement, to the chord reinforcement
has been found to depend on several factors including diaphragm dimensions and configurations, and diaphragm detailing
(Fleischman and Wan, 2007). The DSDM project is calibrating the shear and anchorage relative strength factors using two
research activities:
1. A comprehensive parameter study of precast floor diaphragms using nonlinear static “pushover” analyses of simplified
representations of individual diaphragms (Fleischman and Wan, 2007).
2. A smaller number of 3DFE nonlinear dynamic transient analyses (NLDTA) of prototype structures to calibrate or verify
the findings from the first research activity.
2DFE Study. The graphic on the left side of Figure A31 shows a schematic of the 2D diaphragm model used for nonlinear
pushover analyses. The parameters that were varied for this model were diaphragm span and aspect ratio (AR), Seismic
Design Category (SDC), and diaphragm detailing classification.
On the right, Figure A31 shows the diaphragm pushover curves for a single set of diaphragm design parameters (AR = 3, L
=180’, Charleston) with increasing diaphragm shear reinforcement relative strength Ov. The greater the Ov value, the greater
the deformation capacity achieved by the diaphragm. A Ov of 2.15 is needed to develop the full diaphragm flexural strength.
However, using less shear reinforcement (Ov of 1.76 and 1.37), while not preventing shear failure, delays the failure
sufficiently to allow some increased inelastic deformation in the diaphragm. Note that, as indicated in the inserts in Figure
A31, a chord failure occurs at midspan while a shear failure occurs at the first paneltopanel joint (assuming that Oa > Ov).
The performance is also characterized by the overall ductility of the diaphragm, µ.
Design charts have been constructed using the results of the studies. On the left, Figure A32 shows, for a given diaphragm
geometry, the Ov values required to achieve specific design targets (diaphragm yield strength, My: diaphragm ultimate
strength, Mu; diaphragm ductility ratio, µ; and interstory drift, f). Likewise, by examining the internal state of the diaphragm,
the right side of Figure A32, the required deformation capacity of the diaphragm chord reinforcement, dt,max, needed to
achieve a given design target was determined.
The appropriate design target for a given design is being determined from the second research step: NLDTAs of 3DFE
models of the prototype structures.
3DFE Analysis. The 3D FE analyses determine the expected local demands on diaphragm reinforcement crossing
diaphragm joints by realistically modeling the connector behavior in finite element models of prototype precast structures.
These structures are designed for differing SDCs per current code with requirements adjusted using the diaphragm design
factors described in this document. The structures are subject to a suite of 10 ground motions scaled to the expected seismic
hazard (DBE and MCE) for the design in question.
The finite element models employ discrete coupled springs that represent the sheartension response of the diaphragm
reinforcement crossing the joint. Contact elements are placed in parallel to model the compression zone and friction
contributions. The characteristics for the spring elements are obtained from experiments on panels with differing individual
diaphragm reinforcement details.
On the left, Figure A33 shows a photograph of one of the Lehigh Phase 1 tests used to determine FE connector model
characteristics (Naito et al., 2005). On the right, Figure A33 shows a sample test result for a shear connector under cyclic
loads and the response of the calibrated spring element adjusted to match the test result.
Figure A31 Schematic of 2D FE model (left) and sample results for diaphragm shear overstrength factor OV.
L. L L .
L'
s/2
ssssss
s/2
0.91m
0.91m
b
d
Joint #: 1 2 … n 2 1
Fpx
Shear reinforcement
Chord reinforcement
…
Basic
Model
To
confine
joints
For
M/V
rat io
s Figure A31 Schematic of 2D FE model (left) and sample results for diaphragm shear overstrength factor OV.
Figure A32 Design charts: OV vs. aspect ratio (left) and deformation capacity c vs. aspect ratio (right).
Figure A32 Design charts: OV vs. aspect ratio (left) and deformation capacity c vs. aspect ratio (right) and Figure A33 Lehigh Phase 1 test specimen and sample results for cyclic shear response (test & FE model) (right).
Figure A32 Design charts: OV vs. aspect ratio (left) and deformation capacity c vs. aspect ratio (right).
Figure A33 Lehigh Phase 1 test specimen and sample results for cyclic shear response (test & FE model) (right).
C onnector
25
20
15
10
5
0
5
10
15
20
25
0.6 0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
D(in)
F( ki ps)
Ansyscyclic loading
Test
Figure A33 Lehigh Phase 1 test specimen and sample results for cyclic shear response (test & FE model) (right).
Figure A31 Schematic of 2D FE model (left) and sample results for diaphragm shear overstrength factor OV.
Figure A34 shows the pushover curve global results (diaphragm force vs. diaphragm deformation) for an AR = 3, L = 180’,
and the Charleston site for the critical floor from the 3DFE model (threestory structure, .D=1.5) under the Charleston MCE.
As can be seen, this technique allows a target displacement to be determined for the diaphragm for a given set of design
parameters. For instance, use of Ov = 2.15 (shown previously to develop the full flexure strength of the diaphragm) is
unnecessary. Instead, an Ov somewhat greater than 1.4 is sufficient to accommodate the MCE diaphragm demands for this
structure.
Figure A34 Superposition of 3DFE global EQ demand results on 2D pushover.
Figure A34 Superposition of 3DFE global EQ demand results on 2D pushover.
Figure A35 shows how the 3DFE earthquake simulations are used to calibrate Ov. Shown are the response demands for the
critical shear connector at the critical shear joint in the diaphragm (lower insert in Figure A34) for a given MCE earthquake.
A shear overstrength factor Ov of 1.1 was used on the left side of Figure A35. This value was insufficient to prevent the
connector from undergoing shear degradation for this single deterministic evaluation of one structure, one design and one
ground motion. Raising the Ov value to 1.3 on the right side of Figure A35 was sufficient to keep this critical detail elastic
throughout the MCE event.
Figure A35 Sample results for critical shear connector,..D = 1.5 Berkeley MCE: (a) Ov = 1.1, (b) Ov =
1.3. deformation demand.
Figure A35 Sample results for critical shear connector, .D = 1.5 Berkeley MCE: (a) Ov = 1.1, (b) Ov = 1.3. deformation demand.
Connect or shear Vs. Sl i di ng
 25
 20
 15
 10
 5
0
5
10
15
20
25
 0. 2  0. 15  0. 1  0. 05 0 0. 05 0. 1 0. 15 0. 2
Openi ng ( i n)
F( k)
OV =1.1
Connect or shear Vs. Sl i di ng
 25
 20
 15
 10
 5
0
5
10
15
20
25
 0. 2  0. 15  0. 1  0. 05 0 0. 05 0. 1 0. 15 0. 2
Openi ng ( i n)
F( k)
OV =1.1
Connect or shear Vs. Sl i di ng
 20
 15
 10
 5
0
5
10
15
 0. 1  0. 05 0 0. 05 0. 1
Openi ng ( i n)
F( k)
OV =1.3
Connect or shear Vs. Sl i di ng
 20
 15
 10
 5
0
5
10
15
 0. 1  0. 05 0 0. 05 0. 1
Openi ng ( i n)
F( k)
OV =1.3
A4 Diaphragm Detail Classification and Qualification Procedures. Proper performance of connection details is critical
for the effective design and safety of precast concrete building systems. As part of the design methodology a qualification
procedure is proposed that provides a systematic approach for assessing the strength and deformation capacity of embedded
connections as used in conventional double tee panel systems (Ren and Naito, 2007). In addition, a recommendation is
provided for categorizing connectors based on measured performance. The recommendation is limited to testing of the in
plane and outofplane response of connections. A catalog of connections that have undergone this qualification and
classification procedure is being compiled.
The ACI 318 code used for prestressed and nonprestressed concrete construction in the United States provides limited
guidance on the design of precast connections. As noted in its Chapter 16, the various components in a connection have
different properties, and those properties affect the overall behavior of the connection. Therefore, when a connection is
designed using materials with different structural properties, their relative stiffness, strength, and ductility must be considered
in evaluating performance.
A ductile flexural mechanism cannot form unless the connection components are designed to ensure that performance. A
typical diaphragm connection consists of anchorage bars, welded plate, slug, and slug weld components. The desired
connection performance is achieved by the development of a predictable yield mechanism in the anchorage bars and the
protection of all other components against premature failure. For example, the weld strength must be not less than the
anchorage bar strength.
Scope. The qualification document provides both a testing procedure and a classification framework that establish specific
acceptance criteria for inplane and outofplane performance of precast concrete diaphragm connections. For consistency
with the emerging design methodology, acceptance criteria are based on prequalification of the deformation capacity. The
terminology of low deformability element (LDE), medium deformability element (MDE) and high deformability element
(HDE) is used to categorize the response of connections. A procedure for determining the capacity of connectors based on
experimental results is described.
Testing Agency. Testing is to be performed by a recognized independent testing agency. That testing and reporting must be
supervised by a professional engineer familiar with the proposed design procedure and experienced in testing and seismic
structural design.
Test Modules. A minimum of two modules should be tested for each characteristic connection configuration in the prototype
diaphragm. Connections are to be tested full scale unless both connections and modules have a scale large enough to
represent fully the complexities and behavior of the real materials and of the load transfer mechanisms in the prototype
diaphragm. For modules that are to be subjected to loadings that include inplane loadings there must be at least two
connections per module.
Reference Deformation. For each connection type, a monotonic test to failure must first be conducted to obtain a reference
deformation used in subsequent cyclic tests. This reference deformation characterizes the effective yield deformation of the
connection. That deformation is the deformation corresponding to the maximum load on a secant stiffness line drawn
through the load and deformation for 75 percent of the maximum load.
Inplane Displacement Based Protocols. The modules are to be loaded under inplane pure shear, pure tension, shear
combined with tension, and outofplane shear. Tests are to be conducted under displacement control at quasistatic rates (<
0.05 in./sec) and force control. The specified testing sequence for cyclic loading is shown in Figure A43 where, at a
ductility ratio of 1.0, the applied displacement is equal to the reference deformation.
Data Acquisition. Data must be recorded from the test such that a quantitative, as opposed to qualitative, interpretation can
be made of the performance of the test module. A continuous record must be made of the force versus deformation. For inplane
tests, the axial and shear forces and the deformations transverse and parallel to the joint are to be recorded. For outofplane
tests the vertical force and deformation are to be recorded. For static testing, data are to be recorded at a rate of 1.0
cycle/second.
Test Observations. Photographs must be taken that show the condition of the test module at the completion of testing as well
as significant points throughout the testing history. Ideally, photos should be taken at the end of each group of cycles.
Photos taken at points of interest, such as first cracking, yield, ultimate load and posttest, are adequate for most evaluations.
Test Report. The test report must be sufficiently complete and selfcontained for a qualified expert to be satisfied that the
tests have been designed and conducted in accordance with the required criteria and that the results satisfy the intent of the
qualification document.
The test report must contain sufficient evidence for an independent evaluation of the performance of each test module. As a
minimum, all of the following information is needed:
1. A description of the theory used to predict test module strength and deformation.
2. Details of test module design and construction, including engineering drawings.
3. Specified materials properties used for design and actual material properties obtained by testing.
4. Description of test setup, including panel details and photographs.
Figure A41 Connection classification per ASCE/SEI 41 procedures.
5. Description of instrumentation, location, and purpose.
6. Description and graphical presentation of applied loading protocol.
7. Description of observed performance, including photographic documentation, of test module condition at key loading
cycles.
8. Graphical presentation of force versus deformation response.
9. Test data, report data, name of testing agency, report author(s), supervising professional engineer, and test sponsor.
Acceptance Criteria. Based on the requirements in FEMA 356 and ASCE/SEI 4106 (ASCE/SEI41), each component is
classified as a primary or secondary element or component prior to the development of component acceptance criteria and the
intended response of each connection is classified as deformationcontrolled (ductile) or forcecontrolled (nonductile). It is
assumed that the connection represents a primary component of the structural system and that all actions applied to the
connection can be classified as deformationcontrolled or forcecontrolled.
As depicted in Figure A41 taken from ASCE/SEI 41, Type 1 and Type 2 responses are representative of ductile behavior.
There is an elastic range (point 0 to point 1) followed by a plastic range (point 1 to point 3). Type 3 response is representative
of a brittle or nonductile behavior. There is an elastic range (point 0 to point 1) followed by a loss of strength.
If connections display the Type 1 or Type 2 response and have .e > 2.g, they are classified as deformationcontrolled;
otherwise, they are classified as forcecontrolled. If connections display the Type 3 response, they are classified as forcecontrolled.
Figure A41 Connection classification per ASCE/SEI 41 procedures.
Deformability Category. Based on the experimental data collected to date and finite element analyses of diaphragms with
differing sizes and differing configurations subject to differing earthquake records, the typical required tension opening, dt,
and shear displacement, dv, values for deformability categorization are as shown in Table A41. The typical required
ductility demands,µ, and joint rotation demands, f, obtained from finite element analysis for diaphragms of differing sizes
subject to differing earthquake records are shown in Figure A42. That figure illustrates how the information gained through
the activities described in Section A3 are combined with the classification system described in this section. The results of
Figure A42 are based on the data shown in Figure A32, crossreferenced to the requirements of the deformability
categories.
Table A41 Typical Values for Deformability Categorization
Deformability Category
Tension deformation dt [in.]
Shear deformation dv [in.]
Low deformability
0.00 < d = 0.15
0.00 < d = 0.30
Medium deformability
0.15 < d = 0.50
0.30 < d = 0.70
High deformability
D > 0.50
D > 0.70
Figure A43 Example of specified test sequence.
Figure 42 Component response classification.
Figure 42 Component response classification.
Figure 42 Component response classification.
Figure A43 Example of specified test sequence.
A5 Diaphragm Strength and Stiffness Calculations. Several methods have been proposed for calculating the stiffness of a
precast concrete diaphragm (Zheng and Oliva, 2005; Farrow and Fleischman, 2003; Nakaki,2000). The methodology uses
the spreadsheetcompatible method, developed by Wan and Fleischman (2009), that has similarities to the prior approaches.
The spreadsheet method is used to calculate the elastic stiffness of the precast diaphragm in terms of equivalent elastic
modulus and shear modulus and the flexural yield strength of the precast diaphragm including any contributions from the
shear reinforcement to that strength. The calculation is based on a rational method and is used in the proposed design
methodology to either manually determine the diaphragm deflection or conveniently model the floors in design software. It
also is used to determine the nominal strength of the diaphragm for comparison to the design moment Mu caused by .DFpx.
The method is calibrated by comparisons to finite element analyses of diaphragms with differing geometries and reinforcing
details. The method assumes that plane sections remain plane at joints between precast units and that theconcrete in the
precast unit is linear elastic and uncracked and the slab thickness is constant (i.e., contributions of washes and curbs in
parking garage floors are ignored). Reinforcement in the diaphragm compression zone is ignored in determining
compression stiffness (i.e., deformation is based on precast concrete unit only). The same number and type of shear
connectors are used at all joints in the diaphragm and are evenly distributed along the length of the joint. Shear
reinforcement is assumed to respond elastically at diaphragm yield, in accordance with the proposed design methodology
(Fleischman et al., 2005a).
The method also assumes initial positions for the neutral axis and center of compression and calculates an effective flexural
stiffness of the joint based on those positions and the elastic stiffness of the discrete diaphragm reinforcing elements. This
value is combined with the elastic stiffness of the panel to create an overall flexural rigidity and, finally, Eeff. Shear stiffness
of the joint and the panels are calculated and combined in a similar manner to find an effective diaphragm shear modulus Geff.
A similar approach is used to find the diaphragm moment strength except that discrete strengths are used instead of discrete
stiffnesses and a different formulation is used to determine the position of the neutral axis at yield than in the elastic state.
Figure A62 Joint deformation profiles including spandrel effects.
0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8 9
Joint #
Joint Opening (in)
SDC: C
Without SP
With SP
SDC: D
SDC: E
C
D
E Figure A61 Schematics of interaction between spandrels and precast floor units and Figure A62 Joint deformation profiles including spandrel effects.
0
0.05
0.1
0.15
0.2
0.25
1 2 3 4 5 6 7 8 9
Joint #
Shear deformation (in)
Without SP
With SP
SDC: C
SDC: D
SDC: E
The left part of Figure A41 compares the stiffness calculated by this method with that determined from FEM analyses (Wan
and Fleischman, 2009). The right side of Figure A41 shows the same comparison for strength. The method shows
reasonable agreement with FEM results. In addition, the methods are being calibrated using experimental results from the
hybrid panel tests and will be further validated in the in the halfscale shake table.
A6 Diaphragm Load Path. Several methods exist for determining diaphragm internal load paths that are alternates to the
horizontal beam approach. For example, strut and tie methods are used outside the United States ( Fédération Internationale
du Béton, 2003). The design methodology maintains the horizontal beam approach but recognizes alternate methods may be
useful and provides for use of those methods.
The design methodology imposes structural integrity requirements. Required are:
1. Adequate anchorage of diaphragms to the primary LFRS elements, including the carrying of superimposed gravity loads
and accommodating imposed rotations from walls (Menegotto, 2000);
2. Maintenance of seating for the precast units (MejiaMcMaster and Park,1994); and
3. Provision of minimum ductility requirements for joint reinforcing details.
An important component of the structural integrity measures is also the treatment of secondary members such as spandrels
(see Figure A61 where the spandrel is SP). The effect of the spandrel (e.g., as shown in Figure A62) has been quantified
through analytical studies (Wan and Fleischman, 2008).
(a) High shear region (b) High flexure region
Figure A61 Schematics of interaction between spandrels and precast floor units.
Figure A61 Schematics of interaction between spandrels and precast floor units.
Leading
Free Body Diagram
(Forces in SP longitudinal
direction removed for
Forces in DTSP
connectors
Precast
units
Trailing SP
Shear
wall
0
1
Uncovered joint
not at max
0
1
3
3:
Inertia
l force
Ls
Confining
effect within
SP span due to
Leading SP
Trailing SP
Precas
t units
Concentrated
Limited
Free Body Diagram
(Forces in SP transverse
direction removed for
(a) Joint sliding (b) Joint opening
Figure A62 Joint deformation profiles including spandrel effects.
A7 Draft Precast Diaphragm Seismic Design Procedure. This section provides a draft design procedure showing the use
of the concepts from the design methodology. The generic design terminology used previously in this document is used in
this draft procedure. This outline is intended only to show one possible procedure, and this procedure will not necessarily be
the final procedure recommended.
It is assumed that the following parameters of the design have been established:
1. Design base shear coefficients based on SDC and hazard maps,
2. Structural floor plan, and
3. Vertical element lateral force system (LFRS) layout.
Step 1. Calculate roof force Fi (as per 2006 IBC)
Step 2. Determine the maximum floor span, aspect ratio
. Determine the length between vertical elements of the LFRS, Lcl.
. Calculate effective span, Leff = a.L
cl where the “effective span” factor a (see Figure A71 for examples) takes
value of
i. a = 1.0 perimeter
ii. a = 0.7 interior
iii. a = .2.0 overhang
. Determine the diaphragm effective aspect ratio, AR = Leff/d
. Determine the diaphragm configuration  squat, intermediate, or long
. Use Table A71
. Use the critical AR from all floors, all spans
Step 3. Select diaphragm design option and diaphragm reinforcement
Case 1  No predetermined diaphragm reinforcement
A. Select diaphragm design option (EDO, BDO, RDO).
. Base on effective floor span and SDC,
. See Table A72.
• Determine restrictions on design options (shaded areas are restricted in Table A7
2).
B. Determine classifications for primary diaphragm reinforcement
. For each primary diaphragm reinforcement group
. Chord reinforcement
. Shear reinforcement
. Collectors/anchorages
• Determine allowable categories
• See Table A73
• Select category (LDE, MDE, HDE)
C. Select primary diaphragm reinforcement
. Select prequalified connectors
• Match the selected classification for each primary reinforcement group
Case 2  Predetermined diaphragm reinforcement
A. Determine classifications for primary diaphragm reinforcement
. For prequalified connectors  look up
. For nonprequalified connectors
• Qualify connectors following qualification protocol of Section A4
B. Determine allowable design option
. Use Table A73
. Check design option with Table A72
Step 4. Determine diaphragm force amplification factor, .d
. .d factor based on
i.Design option
ii.Leff and AR
iii.LFRS type
iv.Number of stories
v.Building configuration
. Take factor from Table A74
. Or determine using a series of design coefficients:
i. Determine design force modification factors
. Cn = f(n) where n = number of stories
. CLRFS = 1.0 for frame and 1.5 for wall
. Cconfig = 1.0
Step 5. Estimate diaphragm properties
. Calculate Kdia
i. Eeff
ii. Geff
. Calculate My
i. Based on chord and shear reinforcement
ii. Use spreadsheet method of Section A5
iii. Modify values for secondary elements
Step 6. Estimate diaphragm target deformation
. Estimate based on
i. SDC
ii. Leff and/or AR
iii. LFRS type
iv. .d factor
v. Diaphragm properties
Step 7. Calculate shear overstrength factor, Ov
. Estimate based on
i. Leff and/or AR
ii. Design intent
iii. Diaphragm properties
iv. Target deformation
v. Shear reinforcement classification
. Use set of tables or charts to determine Ov
Step 8. Check diaphragminduced drifts
. Calculate story drift in normal fashion
. Determine drift amplifier
i. Based on
. Kdia
. AR, Leff
. Number of stories
. LFRS type
. For drift, use worst case of Leff or AR.
. For diaphragm force calculations use average among all spans
Draft Design Tables
Table A71 Diaphragm Configuration Designation
AR
Designation
AR < 1.5
Squat (SQT)
1.5 < AR < 3.0
Intermediate (INT)
AR > 3.0
Long (LNG)
Table A72 Applicability of Diaphragm Design Options
Seismic Design Category
A, B
C, D
E, F
Configuration
SQT
INT
LNG
SQT
INT
LNG
SQT
INT
LNG
Elastic (EDO)
Basic (BDO)
Relaxed (RDO)
Dark circle on table
Dark circle on table
Shaded circle
Dark circle on table
Light circle meaning allowable
Shaded circle meaning alternative
light circle meaning allowable
Dark circle on table
light circle meaning allowable
Dark circle on table
Dark circle on table
Dark circle on table
Shaded circle meaning alternative
Dark circle on table
Stripes meaning not allowed
Key: Recommended Alternative Allowable Not allowed
Table A73 Applicability of Diaphragm Detail Classification
Light circle meaning allowable
Shaded circle meaning alternative
Dark circle on table means recommended
Seismic Design Category
Chord in Tension
Shear in Tension
Shear in Shear
Classification
LDE
MDE
ID
HDE
LDE
MDE
HDE
LDE
MDE
HDE
Elastic (EDO)
Classification
Basic (BDO)
Relaxed (RDO)
Dark circle on table meaning recommended
Shaded circle meaning alternative
light circle meaning allowable
Dark circle on table meaning recommended
Shaded circle meaning alternative
light circle meaning allowable
light circle meaning allowable
Dark circle on table meaning recommended
Shaded circle meaning alternative
Dark circle on table meaning recommended
light circle meaning allowable
Dark circle on table meaning recommended
Dark circle on table meaning recommended
Dark circle on table meaning recommended
light circle meaning allowable
Dark circle on table meaning recommended
Dark circle on table meaning recommended
Dark circle on table meaning recommended
Shaded circle meaning alternative
Stripes meaning not allowed
Key: Recommended Alternative Allowable Not allowed
Table A74 Diaphragm Force Amplification Factor
light circle meaning allowable
Shaded circle meaning alternative
Dark circle on table meaning recommended
A. Specify strength reduction and detailing requirements for each classification
OD
SD
Reinforcement
Equation
f
detailing
Equation
f
detailing
Equation
f
detailing
Collector
0.75

0.75
Regulara
0.6
Speciala
Chord
0.9

0.9
Regular
0.9
Special
Web
Type B
Shear
0.75

0.75

0.6

Tension
b
Type A

Type B

Type C
B. Select approach for force resistance mechanisms.
Web Reinforcement
Tensile Characteristics
Type A
Type C
AF
dt
AF
dt (in) c
AF
dt (in) c
Tension Compliantd



1.2
0.3
1.4
0.6
Tension
Resistantd
Ductile
Equation
f = 0.9
1.2
0.2
1.4
0.5
Elastic
Equation
f = 0.6


1.25

1.5
0.3
Strut and Tie
C. Define diaphragm stiffness requirement
Diaphragm Stiffness Required for
Serviceability
Deflection
Diaphragm
Force Levels
Lateral System Force
Distribution
Gravity System
Seismic Drifts
Design procedure can use
Diaphragm clear
span between
lateral system
elements
(Absolute)
Diaphragm
Stiffness
Value
Stiffness relative to the
lateral system
or diaphragm flexibility
index
Diaphragm
Deflection
Calculation
Diaphragm stiffness based on
Diaphragm span
Boundary
conditions
Construction type
(topped/untopped)
Reinforcement
size, type,
spacing
Diaphragm
Stiffness
Components
Contributor
Chord steel,
pour strips,
bond beams
Welded wire
fabric
Flangetoflange
connectors
Shear keys
Components
Flexure, dowel
Shearfriction,
flexure
Shear, flexure (nontension
compliant)
Shear
a Regular and special detailing differ in requirements for spacing, cover, transverse reinforcement etc to obtain two levels of ductility
for collector and chords.
b See Table A74B, Web Reinforcement Tensile Characteristics.
c du > dt where dt is the target tension displacement and du is the failure displacement demand as defined in the qualification testing
protocol (see Table A75). These values are being determined by UCSD and UA research on global/local ductility demands.
d See stiffness requirements (Table A74C).
Figure A71 Example.
Le Lm Le
aL1= 0.7Lm
aL2= 2.0Le
aL= 2.0 (½Lb)
aL= 1.0La
aL= 1.0Lb
La
Lb
½ Lb
½ Lb
Le Lm Le
aL1= 0.7Lm
aL2= 2.0Le
aL= 2.0 (½Lb)
aL= 1.0La
aL= 1.0Lb
La
Lb
½ Lb
½ Lb
Table A75 Qualification Testing
(Testing Protocol  .Connector tension capacity to be determined through cycling component testing)
Shear Loading
Tension Loading
Shear/Tension Loading
Capacity
Monotonic
1 test a
1 test a

du d
Cyclic
1 test b
1 test b
2 test c
du d
a To determine monotonic envelope
b Displacement control loading, cycled twice at ductility ratios of 0.75, 1.0, 1.5, 2.0, 3.0, etc.
cProportional components of equal tension/compression and reversing shear.
d du is defined as either the displacement of first fracture of weld or component; displacement of anchor pullout; or displacement
corresponding to strength degradation at which response drops below 80 percent of the nominal strength.
Table A76 Prequalified Details
Construction
Type
Welded wire fabrica
Slab bar
reinforcementb
Flange Connector
Shear Key
A
B
C
A
B
C
A
B
C
A
B
C
Topped
Composite

6x6
10x10

reg.
special

DTPQBc
DTPQCc

HCPQB
c
HCPQC
c
Topped
Noncomposite

6x6
10x10

reg.
special
Untopped

DTPQB
DTPQC

HCPQB
HCPQC
a Mesh matrix geometry, wire size deformed and plain that meets the B and C detail requirements in Table A76 as determined by the
Lehigh research tests.
b Embedded slab reinforcement to follow detailing requirements as described in Table A74.
c These represent details that can be prequalified by meeting the criteria determined in the research. The data can originate from previous
tests, tests in the Lehigh pilot program or other parallel testing programs (Pincheira et al., 2005). For instance, DTPQB may contain
standard hairpin flangetoflange connections; DTPQC may contain proprietary connectors such as the JVI connector (Oliva, 2000,
Shaikh and Feile, 2002). The HCPQC could for instance include serrated hollowcore units studied by Menegotto, 2000.
Figure A71 Example.
REFERENCES
ACI Committee 318. 2008. Building Code Requirements for Structural Concrete, ACI 31808, and Commentary, ACI
R31808. American Concrete Institute, Farmington Hills, Michigan
American Society of Civil Engineers. 2007. Seismic Rehabilitation of Existing Buildings, ASCE/SEI 4106. ASCE, Reston,
Virginia.
Building Seismic Safety Council. 2000. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and
Other Structures, FEMA 369 (Commentary). Federal Emergency Management Agency, Washington, DC, 2000.
DSDM. 2006. Year 2 Report to National Science Foundation: GOALI Project “Development of a Precast Floor
Diaphragm Seismic Design Methodology (DSDM), August 17.
Eberhard, M. O., and M. A. Sozen. 1993. “BehaviorBased Method to Determine Design Shear in EarthquakeResistant
Walls,” American Society of Civil Engineers, Journal of Structural Engineering, 119(2): 619640.
Earthquake Engineering Research Institute (EERI). 1994. Northridge Earthquake, January 17, 1994, Preliminary
Reconnaissance Report. EERI, Oakland, California.
Farrow, K. T., and R. B. Fleischman. 2003. “Effect of Dimension and Construction Detail on the Capacity of Diaphragms in
Precast Parking Structures,” PCI Journal, 48(5): 4661.
Federal Emergency Management Agency. 2000. NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of
Buildings.”
Fédération Internationale du Béton, Commission 7 Task Group. 2003. StateoftheArt Report on the Seismic Design of
Precast Concrete Building Structures, edited by Robert Park.. SprintDigitalDruck, Stuttgart, Germany.
Fleischman, R. B., and G. Wan. 2007. “Appropriate Overstrength of Shear Reinforcement in Precast Concrete
Diaphragms”, American Society of Civil Engineers, Journal of Structural Engineering, Special Issue: Precast/Prestressed
Concrete Structures under Natural and HumanMade Hazards, edited by Y. Kurama 133(11); 161626
Fleischman, R. B., C. J. Naito, J. Restrepo, R. Sause, and S. K. Ghosh. 2005a. “Seismic Design Methodology for Precast
Concrete Diaphragms, Part 1: Design Framework,” PCI Journal, 50(5): 6883.
Fleischman R. B., C. J. Naito, J. Restrepo, R. Sause, S. K. Ghosh, G. Wan, M. Schoettler, and L. Cao. 2005b. "Seismic
Design Methodology for Precast Concrete Diaphragms, Part 2: Research Program," PCI Journal, 51(6): 219.
Fleischman, R. B., and K. T. Farrow. 2003. “Seismic Design Recommendations for Precast Concrete Diaphragms in Long
Floor Span Construction,” PCI Journal, 48(6): 4662.
Fleischman, R. B., K. T. Farrow, and K. Eastman. 2002. “Seismic Performance of Perimeter LateralSystem Structures with
Highly Flexural Diaphragms,” Earthquake Spectra, 18(2).
Fleischman, R. B., and K. T. Farrow. 2001. “Dynamic Response of Perimeter LateralSystem Structures with Flexible
Diaphragms,” Earthquake Engineering and Structural Dynamics, 30(5): 745763.
Fleischman, R. B., R. Sause, S. Pessiki, and A. B. Rhodes. 1998. “Seismic Behavior of Precast Parking Structure
Diaphragms,” PCI Journal, 43(1):3853.
Fleischman, R. B., R. Sause, A. B. Rhodes, and S. Pessiki. 1996. “Seismic Behavior of Precast Parking Structure
Diaphragms,” in Proceedings, XIV ASCE/SEI Structures Congress, Building an International Community of Structural
Engineers, Vol. 2, edited by S. K. Ghosh, Chicago, Illinois, April 1518, pp. 11391146.
Hall, J. F. (Editor). 1995. “Northridge Earthquake Reconnaissance Report,” Earthquake Spectra, 11, Supplement C(1): 523.
Hawkins, Neil M., and S. K. Ghosh. 2000. "Proposed Revisions to 1997 NEHRP Recommended Provisions for Seismic
Regulations for Precast Concrete Structures: Part 3 – Diaphragms," PCI Journal, 45(6).
International Code Council. 2006. International Building Code, 2006 Edition, International Code Council, Inc., Falls
Church, Virginia.
Iverson, J. K., and N. M. Hawkins. 1994. “Performance of Precast/Prestressed Concrete Building Structures During
Northridge Earthquake,” PCI Journal, 39(2): 3855.
Ju, S.H., and M. C. Lin. 1999. “Comparison of Building Analyses Assuming Rigid or Flexible Floors,” ASCE/SEI Journal
of Structural Engineering, 125(25).
Kao, G. 1998. “Design and ShakeTable Tests of a FourStorey Miniature Structure Built with Replaceable Plastic Hinges,”
M.E. Thesis, Department. of Civil Engineering, University of Canterbury, Christchurch, New Zealand.
Lee, H. J., and D. A. Kuchma. 2007. “Seismic Overstrength of Shear Walls in Parking Structures with Flexible
Diaphragms,” Journal of Earthquake Engineering, 11(1): 86109.
Lee, H. J., D. A. Kuchma, and M. A. Aschheim. 2007. “Strength–Based Design of Flexible Diaphragms in LowRise
Structures Subjected to Earthquake Loading,” Engineering Structures, 29(7):12771295.
Lee, H. J., M. A. Aschheim, and D. Kuchma. 2007. “Interstory Drift Estimates for LowRise Flexible Diaphragm
Structures,” Engineering Structures, 29(7):13751397.
MejiaMcMaster, J. C., and R. Park. 1994. “Tests on Special Reinforcement for End Support of HollowCore Slabs,” PCI
Journal, 39(5): 90105.
Menegotto, M. 2000. “Precast Floors Under Seismic Action,” in Proceedings, The Second International Symposium on
Prefabrication, Helsinki, Finland, May 2000.
Naito, C., and L. Cao. 2004. “Precast Diaphragm Panel Joint Connector Performance,” Paper 2722 in Proceedings, 13th
World Conference on Earthquake Engineering, Vancouver, Canada
Naito, C., W. Peter, and L. Cao. 2006. “ Development of a Seismic Design Methodology for Precast Diaphragms, Phase 1
Summary Report,” ATLSS Report 0603, Lehigh University, Bethlehem, Pennsylvania.
Nakaki, S. D. 2000. “Design Guidelines for Precast and CastinPlace Concrete Diaphragms,” 1998 NEHRP Professional
Fellowship Report, Earthquake Engineering Research Institute.
Oliva, M. G. 2000. Testing of the JVI Flange Connector for Precast Concrete DoubleTee Systems. Structures and
Materials Test Laboratory, College of Engineering, University of Wisconsin.
Pincheira, J. A., M. G. Oliva, and W. Zheng. 2005. “Behavior of DoubleTee Flange Connectors Subjected to InPlane
Monotonic and Reversed Cyclic Loads,” PCI Journal, 50(6): 3254.
Ren, R., and C. J. Naito. 2007. "Acceptance Criteria for Precast Concrete Diaphragm Connectors Based on Structural
Testing,", ATLSS Report 07XX, Lehigh University, Bethlehem, Pennsylvania.
Rodriguez, M., J. I. Restrepo, and A. J. Carr. 2001. “Earthquake Induced Floor Horizontal Accelerations in Buildings,”
Earthquake Engineering and Structural Dynamics, 31.
Shaikh, A. F., and E. P. Feile. 2004. “Load Testing of a Precast Concrete Double Tee Flange Connector,” PCI Journal,
49(3): 8494.
Standards New Zealand. 1997. “Concrete Structures Standard—The Design of Concrete Structures” and “Commentary on
the Design of Concrete Structures,” NZS 3101, Parts 1 and 2, 1995, and “Amendment 1 to NZS 3101, 1997.” Wellington,
New Zealand.
TenaColunga, A., and D. P. Abrams. 1992. Response of an Unreinforced Masonry Building During the Loma Prieta
Earthquake, Structural Research Series 576, Department of Civil Engineering, University of Illinois at UrbanaChampaign.
Wan, G., and R. B. Fleischman. 2009. “A Rational Method for Calculating the Service Stiffness and Yield Strength of
Precast Floor Diaphragms,” in preparation for submission to PCI Journal.
Wan, G., and R. B. Fleischman. 2008. “Effect of Spandrel Beam to Double Tee Connection Characteristic on Precast
Diaphragm Response,” submitted to the ASCE/SEI Structures Journal.
Wood, S. L., J. F. Stanton, and N. M. Hawkins. 2000. “New Seismic Design Provisions for Diaphragms in Precast Concrete
Parking Structures,” PCI Journal, 45(1): 5065.
Wood, S. L., J. F. Stanton, and N. M. Hawkins. 1995. “Performance of Precast Parking Garages During the 1994
Northridge Earthquake,” in Proceedings, XIII ASCE/SEI Structures Congress, Restructuring: America and Beyond, Vol. 1,
New York, New York, pp. 563566.
Zheng, W., and M. G. Oliva. 2005. “A Practical Method to Estimate Elastic Deformation of Precast Pretopped Double Tee
Diaphragms,” PCI Journal, 50(2): 4455.
Resource Paper 11
SHEAR WALL LOADDEFLECTION PARAMETERS AND
PERFORMANCE EXPECTATIONS
Lightframe shear wall buildings of wood and cold formed steel (CFS) exhibit both similarities and differences in design,
construction, and anticipated seismic performance. This resource paper is intended to identify anticipated loaddeflection
parameters and define performance expectations towards which both wood and CFS standard committees can steer future
standard updates and future detailing recommendations. It was developed by a joint task group of TS6, Steel Design, and
TS7, Wood Design, for consideration by the design community.
Discussed are wood and cold formed steel (CFS) lightframe buildings with seismicforceresisting systems designed in
accordance with the 2006 International Building Code and ASCE/SEI 705 (ASCE/SEI 7). The main objective of the
ASCE/SEI 7 seismic design provisions is to protect the health, safety, and welfare of the general public by minimizing the
earthquakerelated risk to life. Structural and nonstructural damage can be expected as a result of the “design ground
motions” since ASCE/SEI 7 allows inelastic response in the structural system. For ground motions in excess of the design
levels, the intent of these design provisions is for the structure to have a low likelihood of collapse.
RECOMMENDATIONS
1.1 Systems with R = 6.5 and 7.0. This section addresses wood and CFS lightframe shear wall systems with wood
structural panel sheathing. Bearing wall systems are assigned a seismic response modification coefficient, R, of 6.5 and
building frame systems, an R of 7.0. Details of design and construction are to be in accordance with the Special Design
Provisions for Wind and Seismic (SDPWS) (AF&PA, 2005) for wood construction, and AISI S21307, Standard for Cold
Formed Steel Framing – Lateral Design (AISI, 2007), for CFS construction.
1.1.1 Analysis Model. ASCE/SEI 705 equivalent lateral force or simplified seismic design procedures for determination of
seismic demand are intended to be used with an analysis model that includes designated portions of the seismicforceresisting
systems sheathed with wood structural panels.
1.1.2 Vertical Shear Wall Element Parameters. Table 11 documents observed load deflection behavior and related
parameters in sitebuilt wood structural panel shear walls. Behavior that varies from these parameters is outside the scope of
this paper. See Figure 11 for an illustration of these parameters.
Table 11 Vertical Shear Wall Element Parametersa
Vertical Shear Wall Element Parameter
Value
1. Ratio of peak capacity (VU) to ASD design capacity (VASD)
2.5 to 5.0b
2. Minimum ratio of drift at 0.80VU post peak capacity (.0.8VU) to drift at ASD design
capacity (.ASD)
11
3. Minimum drift at 0.80 VU post peak capacity (.0.8VU)
0.028hc
4. Drift at peak element strength (VU)
0.01h to 0.04h
5. Minimum equivalent viscous damping in a single loading cycle reaching peak
strength (VU)
15 percent of critical
a h = story clear height.
b Where the ratio exceeds 5, vertical and lateral element detailing must consider the effect of additional overstrength.
c This value is the minimum drift at 0.80VU post peak capacity for elements with a drift at peak element strength less than 0.028h. This
minimum drift at residual strength should always be greater than the drift at peak strength (see Figure 11).
The parameters given in Table 11 are derived from wood structural panel sheathed shear walls with wood framing tested
using the CUREE protocol (CUREE, 2001a). In particular, Parameters 1 through 3 are taken from a database of 48 woodframe
shear walls assembled by the AC322 Seismic Equivalency Task Group (2007). Data from the following test reports
are included: Martin, Skaggs and Keith (2005), Martin (2004), Martin and Skaggs (2003), Martin (2002), Rosowsky, Elkins
and Carroll (2004), and Pardoen et al. (2003). Variation in the parameters is known to occur within the broad range of wood
structural panel shear walls based on differences in framing type, framing design, detailing, fasteners, and with testing
Equation
Applied Load
Overall Lateral Displacement
0.8*Vu
Vu
VASD
.ASD
.U
.0.8VU
protocols that vary from the CUREE protocol such as the sequential phased displacement protocol (SPD) (SEAOSC, 1997).
See Section C1.1.2 for further discussion.
Figure 11 Vertical shear wall element parameters.
1.1.3 Vertical Shear Wall Element Performance Expectations. The following recommendations for vertical shear wall
elements are intended to allow development of a yield mechanism in the sheathing to framing connection to enable
performance as specified in Section 1.1.2:
1. Shear wall shear capacity is intended to act as the weak link in the shear wall assembly.
2. Vertical boundary member tension strength should not act as a weak link in the shear wall assembly. Boundary member
design for tension should address reduced net sections and accumulated tension from multiple stories.
3. Vertical boundary member compression strength should not act as a weak link in the shear wall assembly. Boundary
member design for compression should include consideration of member buckling, and transfer of compression loads in
and out of compression members.
4. Boundary member tension connections between elements (i.e., floortofloor) and to the foundation should not act as a
weak link in the shear wall assembly.
5. Shear transfer connections between elements and to the foundation should not act as a weak link in the shear wall
assembly.
6. Collector members, splices in collectors, and connection of collectors to vertical shear wall elements should not act as a
weak link in the shear wall assembly.
7. Boundary member and connection deformation should be accounted for in shear wall design and detailing, including
connections floortofloor and to the foundation.
1.1.4 Estimated Peak Unit Shear Capacity, vu. For CFS elements, the shear wall peak unit shear capacity, vU, is intended
to be determined from monotonic or cyclic (CUREE, 2004) testing. If the SPD protocol is used to determine the nominal
unit shear strength for wood structural panel shear walls with CFS framing, the unit shear strength should be increased by 20
percent (Boudreault, 2005). In addition, if the stabilized backbone curve is used, the unit shear strength should be increased
another 10 percent. If the CUREE protocol is used, no adjustment is required. As an alternative, the shear wall peak unit
shear capacity, vu, may be estimated as the AISI tabulated nominal seismic unit shear strength times 1.3.
For wood elements, the shear wall peak unit shear capacity, vU, is intended to be determined from monotonic or cyclic
(CUREE, 2004) testing but also may be taken from nominal unit shear values set forth in Table 4.3A, Column B, of AF&PA
Special Design Provisions for Wind and Seismic (SDPWS).
1.2 Systems with R = 2.0 and 2.5. In ASCE/SEI 7, wood and CFS lightframe shear walls are assigned seismic response
modification coefficients, R, equal to 2.0 or 2.5 if they are sheathed with other than wood structural panels or steel sheets.
Sheathing materials may include gypsum wallboard, interior plaster, exterior threecoat Portland cement plaster (stucco),
fiberboard, particleboard, and diagonal lumber sheathing when permitted by the applicable AF&PA or AISI standard. This
section applies only if the R = 2.0 or 2.5 system is used in the building direction under consideration in each story from the
level under consideration to the roof; mixed seismicforceresisting systems are beyond the scope of this paper.
1.2.1 Analysis Model. ASCE/SEI 7 equivalent lateral force or simplified seismic design procedures for determination of
seismic demand are intended to be used with an analysis that includes designated portions of the seismicforceresisting
system. All vertical elements considered in the analysis model are intended to meet the aspect ratio, design, and detailing
requirements of the applicable AF&PA or AISI standard.
1.2.2 Vertical Shear Wall Element Parameters. Table 12 documents observed load deflection behavior and related
parameters in sitebuilt lightframe shear walls sheathed with other than wood structural panels (and other than sheet steel).
Parameters are given in Table 12 for both the CUREE protocol and the SPD protocol. Behavior that varies from these
parameters is outside the scope of this paper.
Table 12 Vertical Shear Wall Element Parametersa
Vertical Shear Wall Element Parameter
Value
1. Minimum drift (.U) at peak element strength (VU)
0.0025 h
2. Minimum ratio of peak capacity (VU) to ASD design capacity (VASD)
2.0
a h = story clear height.
1.2.3 Vertical Shear Wall Element Performance Expectations. Adequate seismic performance of buildings designed
using shear walls sheathed with other than wood structural panel shear walls (or steel sheets, also an R = 6.5 system) is
almost entirely dependent on shear wall element strength rather than on ductility. Building drift demands are anticipated to
be significantly less than those for R = 6.5 or 7 buildings. To accommodate this behavior, it is recommended that the
nominal strength of the following be adequate to match or exceed the peak capacity, VU, of the shear wall sheathing:
1. Boundary member tension connections between elements and to the foundation.
2. Shear transfer between elements and to the foundation.
3. Collector member splices and connections to vertical elements.
4. Members and connections supporting discontinued shear walls or frames (revises ASCE/SEI 7 Section 12.3.3.3)
1.3 Details of Construction
Seismic performance of lightframe shear walls requires attention to details of construction and quality assurance. Provisions
for construction and quality assurance are incorporated in the AFPA, AISI, and ASCE/SEI 7 standards and the model
building codes.
COMMENTARY
This resource paper was developed by a joint task group of TS6 and TS7 members in recognition of both the similarities and
the differences between wood and cold formed steel (CFS) lightframed shear wall systems with wood structural panel
sheathing. Because of differences in material behavior and cyclic load response, a simple transcription of design
requirements for wood to steel and steel to wood is not practical. The approach taken is to identify performance expectations
for lightframe shear wall seismicforceresisting systems; material specific differences in design method can then be
accommodated in future development of approaches to achieving the desired performance. This paper includes performance
expectations for those systems currently included in ASCE/SEI 7 – that is, systems with R = 6.5 and 7 as well as systems
with R = 2 and 2.5. Questions regarding appropriateness of the assigned R factors are beyond the scope of this paper. Steel
sheet shear walls also are beyond the scope of this paper.
C1.1 Systems with R = 6.5 and 7.0
Section 1.1 addresses wood structural panel sheathed shear wall systems. It is intended that, except as specifically addressed
in this paper, these systems be designed in accordance with ASCE/SEI 7, AF&PA Special Design Provisions for Wind and
Seismic for wood construction, and AISI S21307, North American Standard for ColdFormed Steel Framing – Lateral
Design, for CFS construction. Because the R factors assigned to these systems are relatively high, significant inelastic
behavior is anticipated in design level seismic events, including potential for loading in the range of postpeakcapacity
deflections.
The typical wood lightframe building responds to a seismic event by racking the wall elements while the floor and roof
diaphragms remain close to elastic. Consequently, the walls largely determine the seismic response characteristics of lightframe
construction. In R = 6.5 and 7.0 wood structural panel shear wall systems, sheathing is most commonly installed in 4
foot by 8 to 10 foot sheets and fastened to wall framing with nails (for wood frame) and screws (for CFS). The primary
source of seismic drift and energy dissipation of wood shear walls is the bending and yielding of the shear wall sheathing to
framing fasteners around the perimeter of each sheathing panel accompanied by slip between the sheathing and framing. In
CFS frame shear walls, drift and energy dissipation are generally related to the tilting (rotation) of the sheathing fasteners as
well as the bearing deformations in the wood structural panel or steel adjacent to the connections; again, the deformations at
the sheathing fasteners are accompanied by slip between the sheathing and framing.
This paper addresses only the combinations of sheathing and fastening currently included in the AF&PA and AISI standards.
This is because the cycled load behaviors of these combinations are known to provide for required inelastic behavior. Other
combinations of sheathing and fastening and other methods of attachment should be tested in reversecyclic loading.
C1.1.1 Analysis Model. Virtually all wood or CFS shear wall buildings are designed for seismic loads using the ASCE/SEI
7 equivalent lateral force method or simplified method. Analysis for these systems includes vertical wall elements that are
designated to be part of the seismicforceresisting system. For R = 6.5 and 7 systems, all designated shear walls will be
sheathed with wood structural panel sheathing. Recent studies have confirmed that, for these buildings, the strength and
stiffness contribution of finish materials and partition walls plays a significant role in the seismic performance of these
buildings. Despite this understanding, analysis models used to evaluate and distribute seismic demand are intended to
include only designated wood structural panel shear walls. This does not preclude consideration of the effect of walls
sheathed with other than wood structural panels when evaluating a building for presence of structural irregularities.
C1.1.2 Vertical Shear Wall Element Parameters The parameters addressed in this section are intended to allow
discussion of hysteretic behavior for sitebuilt wood structural panel shear walls from which performance expectations and
detailing recommendations can follow. The parameters in Table 11 were accepted by the authors of this paper for wood
structural panel shear walls with wood framing; they were accepted as interim values for wood structural panel shear walls
with CFS framing. A database of testing with CFS members was not accepted by the AC322 Seismic Equivalency Task
Group in time for consideration in this paper.
The parameters are not intended to be used to assign R factors to vertical shear wall systems nor are they intended to address
prefabricated shear wall elements. Vertical elements whose parameters do not conform to those described in Table 11 are
outside the scope of this paper.
Parameters 1 through 3 in Table 11 mirror parameters recommended by the AC322 task group (AC322, 2007). The values
are derived from a group of 48 wood lightframe shear walls sheathed with wood structural panel sheathing nailed to wood
framing and tested using the CUREE protocol. The tabulated numbers for parameters two and three are the average values
minus one standard deviation. Further commentary on the Table 11 parameters follows:
1. Parameter 1  Provision of overstrength beyond ASD design capacity is understood to be fundamental to earthquake
performance of buildings braced with wood structural panel shear walls.
2. Parameter 2  Deformation capacity at peak strength well beyond deformation capacity at design level is understood to
be fundamental to earthquake performance of buildings braced with wood structural panel shear walls. In this parameter,
80 percent postpeak capacity is specified.
3. Parameter 3  Testing and analysis suggests that wood structural panel sheathed shear walls are capable of supporting
postpeak loading. At a postpeak capacity of 80 percent of peak, the shear wall element drift of not less than 0.028h is
expected.
4. Parameter 4  The range of vertical element drift recognizes both the allowable story drift permitted by ASCE/SEI 7 and
some variation of vertical shear wall elements above and below this drift.
5. Parameter 5  The criterion looks at one cycle in which the shear wall element reaches peak strength. If the CUREE
protocol is used, this would be anticipated to be in the range of the 6th to 8th loading cycle. The areas within the curve for
both positive and negative excursions are intended to be summed and an equivalent viscous damping ratio calculated.
See Filiatrault et al. (2003) for details of equivalent viscous damping calculation.
See Line, Waltz, and Skaggs (2008) for further discussion of the AC322 parameters. The parameters currently included do
not consider degrading reloading stiffness. This parameter might be considered for inclusion at a future time.
C1.1.3 Vertical Shear Wall Element Performance Expectations. Performance expectations described in this section
support the sheathingtoframing fastening as the primary source of inelastic behavior and energy dissipation in the vertical
shear wall elements. Failure of the boundary members or connections addressed in Section 1.1.3, Items b, c, d, e, and f could
cause a more critical and possibly sudden and brittle failure of the vertical shear wall element. In general, further study is
needed to determine whether or not the desired behavior requires detailing provisions beyond those currently required by
ASCE/SEI 7, SDPWS, and AISI S213.
Item 2, vertical boundary member tension design  Tension boundary members should be sized such that they are not the
weak link in the shear wall assembly. For wood boundary members, it is recognized that most members will be stronger than
the calculated nominal capacity due to the 5 percent basis of reference wood member strength properties in underlying design
and product standards. It is also recognized that tension post capacity in use will be sensitive to placement of knots and other
characteristics because the strength controlling characteristic of the wood member is not always located in the area of
maximum tension force.
This section also includes a reminder that net tension at reduced net sections and accumulated tension from multiple stories
need to be considered. In addition, tension member design should include consideration of flexure due to the eccentricity of
the tiedown load.
Item 3, vertical boundary member compression design  Compression boundary members should be sized such that they are
not the weak link in the shear wall assembly. See also comments on tension design above.
Item 4, boundary member tension connections between elements and to the foundation  Tension connections for boundary
members are required as part of a complete load path through the building. This includes both tension connections from
boundary members above to boundary members below and anchorage to the foundation. Tension connections use tiedown
brackets, steel straps, or continuous rod or cable systems. Again, the tension connection should not be the weak link in the
shear wall element.
Item 5, shear transfer connections  The lateral forces at the foundation are resisted by a distributed connection along the
shear walls oriented parallel to and in the plane of the load. These connections are most commonly anchor bolts at
foundation sill plates and nailing or sheet metal angles at framed floors. This connection is typically designed to be
independent of the connections used to resist the overturning forces (i.e., resists only horizontal shear and not tension due to
overturning). This connection should be designed such that it is not the weak link in the shear wall system.
Item 6, collectors  There has been a lack of observed failures in lightframe collector elements. To ensure that the failure is
not in the collector, however, the connection of the collector to the shear wall or the splice of the collector should be designed
such that they are not the weak link in the shear wall system.
Item 7, boundary member and connection deformation  Excessive deformation of boundary members and their connections
can lead to the premature failure of sheathing to framing fastening due to large imposed deformations. See the discussion in
Commentary Sections 12.2.3.11 and 12.2.3.12 of the 2003 NEHRP Recommended Provisions (BSSC, 2003). Deformation in
top plates, collectors, and shear transfer connections is not currently specifically discussed. Consideration might be given the
these sources of deformation in the future.
C1.1.4 Estimated Peak Unit Shear Capacity, vU. It is intended that estimated values of the peak unit shear capacity, vU, be
used in evaluating the performance expectations of Section 1.1.3. Because the referenced testing of woodframe shear walls
uses the CUREE protocol, it is not anticipated that conversion of peak unit shear capacity from other protocols will be
needed. Under no circumstances is it intended that tests conducted using the SPD protocol be converted to compare to the
five parameters of Table 11 since accurate adjustments of all five parameters are not available.
C1.2 Systems with R = 2.0 and 2.5
In ASCE/SEI 7, wood and CFS lightframe walls are assigned seismic response modification coefficients, R, equal to 2.0 or
2.5 if they are sheathed with other than wood structural panels or steel sheets. Specifically, R, Cd,, and O0, are 2.0, 2.5, and
2.0 for bearing wall systems and 2.5, 2.5, and 2.5 for building frame systems. This commonly includes sheathing with
gypsum wallboard, interior plaster, exterior threecoat Portland cement plaster (stucco), particle board, fiberboard and
diagonal lumber sheathing. This may also include wood structural panel sheathing used alone or in combination with other
sheathing materials.
Adequate seismic performance of buildings designed using shear walls sheathed with other than wood structural panels (or
sheet steel) is almost entirely dependent on shear wall element strength rather than ductility. As ductility is replaced with
strength, reliability of the bracing system becomes highly dependent on adequate capacity, adequate detailing, and adequate
understanding of seismic demand. For the materials currently included in the AISI and AF&PA standards, there is a level of
comfort with design for R = 2 or 2.5 systems. This comes both from a history of design of these systems using R = 4.5 under
the Uniform Building Code (ICBO, various) and recent analytical studies suggesting generally adequate performance with R
= 2 design (ATC, 2007).
C1.2.1 Analysis Model. Since a low R value is being utilized, the level of inelastic response is assumed to be lower than if
an R = 6.0 were to be used. Therefore, the combination of the relatively brittle finish materials with the more ductile wood
structural panel walls is allowed, provided the R of 2 or 2.5 is used for all vertical elements. This level of design is often used
when the building design has a relatively large number of interior walls that will be used as resistance since interior walls are
usually sheathed with brittle materials such as gypsum wallboard.
C1.2.2 Vertical Shear Wall Element Parameters. The vertical shear wall elements included in this group have widely
varying loaddeformation characteristics. In general, however, it is anticipated that they have much less ductility and
deformation capacity and more rapid postpeak drop in capacity than wood structural panel sheathing.
For Table 12, Parameter 1, the minimum drift criterion of 0.0025h recognizes that a building braced with these shear wall
types will have measurable drift during design level earthquake loading.
For Table 12, Parameter 2, it is anticipated that shear walls using sheathing materials currently assigned R = 2 or 2.5 have
ratios of ASD to peak capacity of 2 or higher.
CUREE (CUREE, 2001a) and SPD (SEAOSC, 1997) protocols are combined in Table 12 because available test data are not
sufficient to identify separate parameters for each.
C1.2.3 Vertical Shear Wall Element Performance Expectations. For this group of shear wall sheathing materials, the
failure would ideally be the sheathing fastening to framing (or the sheathing material) rather than the boundary members or
their connections. This preferred failure would allow development of the sheathing fastening capacity and avoid what might
be a more critical failure mode such as sliding or overturning of the wall framing. As a step towards achieving this, the intent
of Section 1.4.3 is to have the sheathing peak shear capacity and the capacity of the boundary members and their connections
balanced or close to balanced.
For sheathing materials having an ASD to peak strength ratio of approximately 2 from ASD capacity to peak capacity,
standard ASD or LRFD detailing practice is thought to provide boundary member connection factors of safety adequate to
support failure in the sheathing. Factors of safety of 2.1 to 5 might be anticipated for individual fasteners. Factors of safety
of 2.5 to 3 are commonly anticipated for prefabricated connectors. It is anticipated, however, that some connections such as
steel straps that are controlled by steel net section might have lower factors of safety.
For sheathing materials having an ASD to peak strength ratio greater than 2, it is recognized that failure could occur in
connections of boundary members. At this time, recommendations to design connections to support the higher ratios are
viewed as too stringent.
Boundary members (shear wall chords and collector members) are specifically excluded from the detailing list because these
members are not viewed as possible weak links given the current range of tabulated unit shears for the sheathing materials. If
sheathing members with higher unit shears are to be used, boundary member design should be reconsidered.
REFERENCES
AC322 Seismic Equivalency Task Group. 2007. “Methodology for Seismic Coefficient Equivalency,” presented to ICC ES,
July 31, 2007, by Ronald Nelson, Chair, Hermosa Beach, California.
American Forest & Paper Association. 2005. Special Design Provisions for Wind and Seismic with Commentary (SDPWS).
AF&PA, Washington, DC.
American Iron and Steel Institute. 2007. North American Standard for ColdFormed Steel Framing – Lateral Design, S213
07. AISI, Washington, DC.
American Society of Civil Engineers. 2005. Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 705.
ASCE, Reston, Virginia.
Applied Technology Council. 2007. Recommended Methodology for Quantification of Building System Performance and
Response Parameters, ATC 63 90 percent draft. ATC, Redwood City, California.
Boudreault. 2005. “Seismic Analysis of Steel Frame / Wood Panel Shear Walls,” M.Eng. Thesis, Department of Civil
Engineering and Applied Mechanics, McGill University, Montreal, Quebec, Canada.
Building Seismic Safety Council. 2003. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and
Other Structures, FEMA 450. Federal Emergency Management Agency, Washington, DC.
Consortium of Universities for Research in Earthquake Engineering. 2001a. Development of a Testing Protocol for
Woodframe Structures, CUREE W02. CUREE, Richmond, California.
Consortium of Universities for Research in Earthquake Engineering. 2001b. Shake Table Tests of a TwoStory Woodframe
House, CUREE W06. CUREE, Richmond, California.
Consortium of Universities for Research in Earthquake Engineering. 2004. Recommendations for Earthquake Resistance in
the Design and Construction of Woodframe Buildings, CUREE W30. CUREE, Richmond, California.
Filiatrault, A., H. Isoda, and B. Folz. 2003. “Hysteretic Damping of Wood Framed Buildings,” Engineering Structures,
25(4): 461471.
International Code Council. 2006. International Building Code (IBC), 2006 edition. ICC, Falls Church, Virginia.
Line, P., N.Waltz, and T. Skaggs. 2008. “Seismic Equivalence Parameters for Engineered Woodframe Wood Structural
Panel Shear Walls,” Wood Design Focus, Summer (Madison, Wisconsin).
Martin, Z. 2002. Effect of Green Lumber on Wood Structural Panel Shear Wall Performance, APA Technical Report
T200253. APA The Engineered Wood Association, Tacoma, Washington.
Martin, Z., and T. Skaggs. 2003. Shear Wall Lumber Framing: Double 2x’s vs. Singe 3x’s at Adjoining Panel Edges, APA
Technical Report T200322. APA The Engineered Wood Association, Tacoma, Washington.
Martin, Z. 2004. Wood Structural Panel Lateral and Shear Wall Connections with Common, Galvanized Box and Box Nails,
APA Technical Report T200414. APA The Engineered Wood Association, Tacoma, Washington.
Martin, Z., T. Skaggs, and E. Keith. 2005. Using Narrow Pieces of Wood Structural Panel Sheathing in Wood Shear Walls,
APA Technical Report T200508. APA The Engineered Wood Association, Tacoma, Washington.
Pardoen, G., A. Waltman, R. Kazangy, E. Freund, and C. Hamilton. 2003. Testing and Analysis of OneStory and TwoStory
Shear Walls Under Cyclic Loading, CUREE Report W25. Consortium of Universities for Research in Earthquake
Engineering, Richmond, California.
Rosowsky, D., L. Elkins, and C. Carroll. 2004. Cyclic Tests of Engineered Shear Walls Considering Different Plate
Washers, Report for the American Forest and Paper Association. Oregon State University, Corvallis.
Structural Engineers Association of Southern California. 1997. Standard Method of Cyclic (Reversed) Load Test for Shear
resistance of Framed Walls for Buildings, SEAoSC Ad Hoc Committee on Testing Standards for Structural Systems and
Components in conjunction with the City of Los Angeles.
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Resource Paper 12
EVALUATION OF GEOLOGIC HAZARDS AND
DETERMINATION OF SEISMIC LATERAL EARTH PRESSURES
Summarized in this resource paper are the procedures commonly used for evaluating potential site geologic hazards and
seismic lateral earth pressures due to earthquakes. The geologic hazards include slope instability, liquefaction, ground
displacement, and surface fault rupture. Geologic hazards evaluations should be carried out by qualified geotechnical
professionals and documented in a report. Reporting requirements are given in Part 1 of the 2009 NEHRP Recommended
Seismic Provisions Exception to ASCE/SEI 705 (ASCE/SEI 7) Section 11.8. Seismic lateral earth pressure discussions
consider both yielding and nonyielding walls.
GEOLOGIC HAZARDS
Screening Evaluation. Evaluation of an earthquakeinduced geologic hazard may initially consist of a screening evaluation.
Although a screening evaluation typically does not require use of detailed analytical procedures, it should be based on
detailed site information including topography, geology, groundwater conditions, subsurface soil and rock stratigraphy and
engineering properties, and level of ground shaking. The potential for changes in site conditions over time or as part of site
development should be considered. If the findings of a screening evaluation clearly demonstrate the absence of a geologic
hazard, then more detailed evaluations, using procedures such as those described in the following sections, need not be
conducted. If a screening evaluation does not demonstrate the absence of a hazard, the more comprehensive quantitative
evaluations described below should be conducted to assess the potential for slope instability, liquefaction, ground
displacement, and surface fault rupture.
The following reference publications provide guidelines on screening evaluations:
1. Slope instability  Blake et al. (2002), Stewart et al. (2003), U.S. Army Corps of Engineers (2005), and California
Geological Survey (2008).
2. Liquefaction  Martin and Lew (1999) and California Geological Survey (2008). As noted later in this section under
“Recent Updates to the SPT Procedure,” the “Chinese Criteria” for identifying clayey soils susceptible to liquefaction
should be abandoned in favor of more recent research.
3. Total and differential settlement  Martin and Lew (1999) and California Geological Survey (2008). Total and
differential settlement can be important design considerations at sites underlain by poorly compacted fills or loose young
alluvium.
4. Surface fault rupture  California Geological Survey (2002) and U.S. Army Corps of Engineers (2005).
Slope Instability Hazard. When subjected to earthquakeinduced ground shaking, sloping ground can pose a hazard to
structures located on or in proximity to a slope. The potential severity of the hazard depends on the steepness of the slope,
soil and groundwater conditions within the slope, the strength and duration of ground shaking, and the potential
consequences of slope movement. In some situations, acceptable slope movement can be on the order of feet whereas in
other situations – particularly where buildings are involved – movements of more than a few inches may be unacceptable. A
critical first step in the assessment of the slope instability hazard is, therefore, to establish the performance criteria for the
slope. Normally this requires detailed discussions between the geotechnical engineer and the structural designer and with the
project owner.
Pseudostatic Method of Analysis. The stability of slopes composed of dense (nonliquefiable) or nonsaturated sandy soils or
nonsensitive clayey soils can be determined using either pseudostatic or deformationbased procedures. For initial
evaluations, the pseudostatic analysis may be used although the deformational analysis described in the next section is now
preferred.
In the pseudostatic analysis, inertial forces generated by earthquake shaking are represented by an equivalent static horizontal
force acting on the slope. The seismic coefficient for this analysis is generally taken as proportional to the site peak ground
acceleration, amax (see details in Stewart et al., 2003). The vertical component of ground acceleration is normally assumed to
be zero during this representation. The factor of safety for a given seismic coefficient can be estimated by using traditional
slope stability calculation methods. A factor of safety of less than 1.0 indicates that the slope will yield and slope
deformation can be expected, and a deformational analysis should be made using the techniques discussed below.
A common practice when using the pseudostatic method is to define the seismic coefficient used in the stability analysis as a
fraction of the peak ground acceleration. The reduction is introduced to account for the transitory nature of the ground
motions. Implicit within this approach is that deformation of the slope is acceptable. To limit permanent displacements to
less than 2 inches (5 cm), the recommended approach is to use the peak ground acceleration multiplied by feq, as discussed in
Blake et al. (2002) and Stewart et al. (2003), in the pseudostatic analysis and then, if the resulting factor of safety is less than
1.0, to conduct a deformational analysis.
When conducting a pseudostatic stability analysis, two key assessments must be made by the designer during the setup of
the stability model:
1. An accurate characterization of the site must be developed. This characterization needs to consider the final slope
geometry, the soil types and layering within the slope, and groundwater conditions likely to exist during the seismic
event. The existence of thin soil layers that could serve as slip planes is particularly important in the characterization
process.
2. The appropriate soil strength to use for the seismic analyses must be selected. This determination will depend on various
factors including whether the soil is fine or coarsegrained, the effective stress conditions, the degree of saturation of the
material, and the stress history for the soil. For saturated materials, in most situations the undrained strength of the soil
is appropriate because of the short duration of seismic loading. Blake et al. (2002) provides important guidance on the
use of drained or undrained soil properties, the appropriate type of testing, the use of peak versus residual strengths, and
whether reductions in strength are appropriate to account for the effects of loading rate and repeated cycles of load.
For sites where soils could liquefy or where sensitive soils are known to occur, special studies will be required. If
liquefaction is predicted under the seismic event, the strength of the soil in a liquefied state should be used in the pseudostatic
stability analyses. Additional discussions of the strength of liquefied soils are presented below in the liquefaction hazard
section of this resource paper. If sensitive clayey soils exist, special laboratory tests may be required to establish the amount
of degradation in soil strength that will occur with cyclic loading.
Deformational Methods of Analysis. Deformational analyses resulting in estimates of slope displacement are now accepted
practice. The most common analysis, termed a Newmark analysis (Newmark, 1965), uses the concept of a frictional block
sliding on a sloping plane or arc. In this analysis, seismic inertial forces are calculated using a history of horizontal
acceleration as the input motion. Slope movement occurs when the driving forces (gravitational plus inertial) exceed the
resisting forces. This approach estimates the cumulative displacement of the sliding mass by doubleintegrating increments
of relative acceleration that occur during periods of time when the driving forces exceed the resisting forces. Expressed
differently, displacement or yield occurs when the earthquake ground accelerations exceed the acceleration required to
initiate slope movement or yield acceleration.
The yield acceleration depends primarily on the strength of the soil and the gradient and height and other geometric attributes
of the slope. The same comments on the characterization of the slope and soil strength given above for the pseudostatic
analysis apply for the deformational analysis; however, consideration can be given to the modification of strength with cycles
of earthquake loading. See Figure 1 for forces and equations used in analysis and Figure 2 for a schematic illustration for a
calculation of the displacement of a soil block toward a bluff.
Two methods are commonly used to estimate slope displacements by the Newmark method. The more rigorous approach
involves use of earthquake records that will be representative of expected ground shaking at the site during a seismic event.
These records need to be scaled to be consistent with the response spectra adjusted for site response effects. If more than one
characteristic source mechanism contributes to the earthquake hazard, it may be necessary to select sets of records that are
characteristic of each source mechanism. In this case, multiple potential sources are considered because of the dependency of
slope displacement on earthquake magnitude or duration  i.e., a large distant earthquake may result in lower peak ground
acceleration but longer duration of shaking, which potentially could result in more cumulative deformation than a nearby
earthquake of higher peak ground acceleration but short duration. Computer programs (e.g., Jibson and Jibson, 2003) are
typically used to determine the cumulative displacement from the earthquake records.
An acceptable alternative method for the determination of displacements on many projects involves the use of charts or
simplified equations that show or estimate displacements for different acceleration ratios, where the acceleration ratio is
defined as the ratio of yield acceleration to the maximum horizontal equivalent acceleration (MHEA) in the slide mass.
These charts and equations have been developed by calculating the cumulative displacement following the Newmark method
for large sets of earthquake records. The charts include those by Franklin and Chang (1977), Makdisi and Seed (1978),
Wong and Whitman (1982), Hynes and Franklin (1984), Martin and Qiu (1994), Bray and Rathje (1998), Bray et al. (1998),
and Jibson (2007). Simple equations include those by Bray and Travasarou (2007), Jibson (2007), Saygili and Rathje (2008),
and Rathje and Saygili. (2008). Figure 3 shows the simplified chart from Bray et al. (1998) that was recommended for use by
Blake et al. (2002). The D595 term in this figure is the significant duration of shaking – with its relationship differing
Figure 1 Forces and equations used in analysis of translatory landslides for calculating permanent lateral displacements from earthquake ground motions (National Research Council, 1985; from Idriss, 1985).
Figure 2 Schematic illustration for calculating displacements of soil block toward the bluff (National Research Council, 1985; from Idriss, 1985, adapted from Goodman and Seed, 1966).
depending on whether or not the site is within 10 km of the earthquake source. Choosing which charts to use should be made
on the basis of the type of slope and the degree of conservatism necessary for the project. It is important to recognize that
when using one of the charts, or the Newmark method in general, a number of simplifying assumptions are made regarding
the relationship between the MHEA and the peak acceleration at the site as well as other factors. These assumptions may
limit the degree of accuracy to which the deformations can be estimated.
Figure 2 Schematic illustration for
calculating displacements of soil block
toward the bluff (National Research
Council, 1985; from Idriss, 1985, adapted
from Goodman and Seed, 1966).
Slope deformations also can be estimated using more rigorous twodimensional computer modeling methods. FLAC (Itasca,
1997) and PLAXIS (Plaxis, 2008) are programs commonly used by practitioners for evaluating the response of slopes to
seismic loads. These computer programs allow various soil geometries, soil layering, and groundwater conditions to be
modeled. Earthquake records representative of the seismic event are used to conduct the timehistory analysis. Results
provide an understanding of the development of deformations with time, the location of critical surfaces of deformation, and
the effects of pore water pressure buildup on slope movement. As with any rigorous model, the accuracy of the deformation
estimate is critically dependent on the properties and geometry of the model and earthquake record selection.
Figure 1 Forces and equations used in analysis
of translatory landslides for calculating
permanent lateral displacements from
earthquake ground motions (National Research
Council, 1985; from Idriss, 1985).
Figure 3 Normalized sliding displacement (Bray et al., 1998) as recommended by Blake et al. (2002).
Figure 3 Normalized sliding displacement (Bray et al., 1998) as recommended by Blake et al. (2002).
Mitigation of Slope Instability Hazard. Three general mitigative measures might be considered for locations where slope
instability is determined to represent a hazard: (a) design the structure to resist the hazard, (b) stabilize the site to reduce the
hazard, or (c) choose an alternative site. Ground displacements generated by slope instability are similar in destructive
character to fault displacements generating similar senses of movement: compression, shear, extension or vertical. Thus, the
general comments on structural design to prevent damage described in the fault displacement section of this paper apply
equally to slope displacement.
Techniques to stabilize a site include increasing the resistance of the soil to displacement by subsurface drainage, buttresses,
retaining walls, ground anchors, reaction piles or shafts; ground improvement using densification or soil mixing methods; and
chemical treatment. Additional details for these mitigation methods can be found in various reports including Blake et al.
(2002).
Liquefaction Hazard. Liquefaction is the second and, perhaps, the most widely known geologic hazard that must be
considered at a building site. This hazard occurs when earthquakeinduced ground shaking results in loss of strength within
watersaturated, loose granular soils. The consequence of this strength loss relative to a building can be reduction in bearing
capacity, total and differential settlement, and horizontal ground displacement from lateral spreading or flow failures within
the ground. In this section, the hazard of differential settlement, whether due to liquefaction of watersaturated soils or
compaction of nonsaturated soils, is addressed.
Design to prevent damage due to liquefaction consists of: (a) evaluation of the liquefaction hazard, (b) evaluation of
potential ground displacement, and (c) when necessary, mitigation of the hazard by designing to resist either ground
displacement or strength loss, by reducing the potential for liquefaction, or by choosing an alternative site with less hazard.
Before providing guidance in these areas, the following subsections summarize the methods used to evaluate the liquefaction
hazard and recent updates to the most commonly used method of assessing a liquefaction hazard – the empirical standard
penetration test procedure.
Methods of Liquefaction Hazard Evaluation. The liquefaction hazard at a site is commonly expressed in terms of a factor of
safety. This factor is defined as the ratio between the available liquefaction resistance, expressed in terms of the cyclic
stresses required to cause liquefaction, and the cyclic stresses generated by the earthquake. Both of these stress parameters
are commonly normalized with respect to the effective overburden stress at the depth in question to define a cyclic resistance
ratio (CRR) and a cyclic stress ratio induced by the earthquake (CSR).
Three different methods have been proposed and are used to various extents for evaluating liquefaction potential:
1. Empirical methods are the most widely used methods in practice. These procedures rely on correlations between
observed cases of liquefaction/nonliquefaction and measurements made in the field with conventional exploration
methods. Seed and Idriss (1971) first published the widely used “simplified procedure” utilizing the standard penetration
test (SPT). Since then, field test methods in addition to the SPT have been utilized in similar simplified procedures.
These methods include cone penetrometer tests (CPTs), Becker hammer tests (BHTs), and shear wave velocity tests
(SVTs). These empirical procedures are summarized in the proceedings from a workshop (referred to as the
Liquefaction Workshop) held in 1996 (NCEER, 1997; Youd et al., 2001). Martin and Lew (1999) provides additional
details on the use of these procedures relative to engineering practice; Idriss and Boulanger (2008) summarize recent
developments in use of empirical methods for assessing liquefaction potential in a recently published EERI Monograph
Soil Liquefaction during Earthquakes. The Idriss and Boulanger (2008) EERI Monograph updates an earlier EERI
Monograph by Seed and Idriss (1982).
2. Analytical methods are used less frequently to evaluate liquefaction potential; however, they may be required for special
projects or where soil conditions are not amenable to the empirical method. Analytical methods also are likely to
continue to gain prominence with time as numerical methods and soil models improve and are increasingly validated.
The analytical method originally (circa 1970s) involved determination of the induced shearing stresses with a program
such as SHAKE and comparison of these stresses to results of cyclic triaxial or cyclic simple shear tests. Today, the
analytical method usually refers to a computer program that incorporates a soil model that calculates the buildup in pore
water pressure. These more rigorous numerical methods include onedimensional nonlinear effective stress codes such
as DESRA, DMOD, SUMDES, and TESS and twodimensional nonlinear effective stress codes such as FLAC, TARA,
and DYNAFLOW. This new generation of analytical methods features soil models that are fitted to or derived from
laboratory data or from liquefaction curves developed from SPTs or other field information. These methods are limited
by the ability to represent the soil model from either the laboratory or field measurements and by the complexity of the
wave propagation mechanisms, including the ability to select appropriate earthquake records to use in the analyses.
3. Physical modeling originally involved the use of centrifuges or relatively smallscale shaking tables to simulate seismic
loading under welldefined boundary conditions. Physical model testing also now includes large laminar boxes mounted
on very large shake tables (e.g., Kagawa et al., 2004) and fullscale field blast loading tests (e.g., Ashford et al., 2004 and
Ashford et al., 2006). This type of modeling is one of the main focus areas of the 20042014 Network for Earthquake
Engineering Simulation (NEES) supported by the National Science Foundation. Soil used in the smallscale and laminar
box models is reconstituted to represent different density and geometrical conditions. Because of difficulties in precisely
modeling in situ conditions at liquefiable sites, smallscale and laminar box models have seldom been used in design
studies for specific sites. However, physical models are valuable for analyzing and understanding generalized soil
behavior and for evaluating the validity of constitutive models under welldefined boundary conditions. Blast loading
tests have been conducted to capture the in situ characteristics of the soil for research and design purposes (e.g., at
Treasure Island, California; for the Cooper River Bridge in South Carolina, and in Japan). However, the cost and safety
issues of blasting methods limit their use to only special design or research projects.
Most liquefaction hazards assessments for buildings involve use of the SPT empirical method  partly because of the wide
acceptance of this method and also because it can be easily integrated into the geotechnical investigations normally
performed during building design. The SPT method is based on recommendations developed at the Liquefaction Workshop
as described in NCEER (1997) and Youd et al. (2001) or on one of the updates to this methodology as discussed below.
Although the SPT empirical method is the most commonly used of the empirical approaches, it is important to recognize that
for certain site conditions alternate empirical methods, such as the CPT, BHT, and SVT methods, are acceptable and even
preferred. This is particularly the case with the CPT method. Advantages of the CPT method compared to the SPT method
are the ability of this method to detect thin liquefiable layers that could serve as sliding surfaces and the greater
standardization of the method; however, the CPT approach has the disadvantage that soil samples are not obtained. When
possible, a combination of procedures is recommended to take advantage of the best features of each.
Recent Updates to the SPT and CPT Procedures. The methods presented in the Liquefaction Workshop and summarized in
the following section represent a consensusbased approach for determining the onset or triggering of liquefaction; however,
the consensus workshop occurred over 10 years ago. A number of significant modifications to the methods presented in the
Liquefaction Workshop have been recommended over the past 10 years. These modifications include:
1. Changes to the stress reduction coefficient (rd),
2. Modifications to the magnitude scaling factor (MSF) which also is referred to as the duration weighting factor (DWF),
3. Revisions to the overburden correction term for CRR (Ks) and the fines correction term (FC),
4. Refinements to the overburden correction for penetration resistance (CN), and
5. Changes to the relationship between cyclic stress ratio causing liquefaction and the normalized penetration resistance
(i.e., the fundamental liquefaction strength curve such as shown in Figure 4).
These modifications are discussed in detail in papers by Cetin et al. (2004), Idriss and Boulanger (2004, 2006, 2008), and
Moss et al. (2006); each set of recommended revisions resulted after detailed study and supplementation of the databases of
case histories upon which the original relationships were developed.
Another important observation during the past 10 years involves the fines criteria used to judge whether or not a soil is
liquefiable. Originally, the “Chinese Criteria” was accepted as the method to determine whether or not a cohesionless soil
was liquefiable. However, recent work summarized in Boulanger and Idriss (2006), Bray and Sancio (2006), and Idriss and
Boulanger (2008) indicates that the Chinese Criteria will be unconservative in some situations, and alternate methods of
assessing whether a soil with cohesive fines will be susceptible to liquefaction or cyclic strength reduction need to be
considered. The methods recommended by Boulanger and Idriss (2006) and Bray and Sancio (2006) also establish whether
the simplified empirical field methods described previously should be used to estimate liquefaction potential or whether other
methods, such as laboratory testing, would be more suitable for evaluating the effects of cyclic loading on soil strength.
Methods are also now available for treating the probability of liquefaction, given a certain ground motion and SPT
blowcount. Cetin et al. (2004) and Moss et al. (2006) present a comprehensive treatment of liquefaction probability. These
researchers suggest that following the deterministic approach for estimating liquefaction potential discussed above results in
approximately 15 percent probability of liquefaction. The approach presented by Cetin et al. (2004) allows limiting SPT
blowcounts to be determined for alternate probabilities and the probability associated with a given set of blowcounts and
ground motions (in terms of CSR) to be defined. Kramer and Mayfield (2007) show how the probability of ground shaking
can be combined with the probability of liquefaction in a performancebased approach to evaluating liquefaction potential.
This probabilistic framework forms an important basis for the performancebased design methods currently being developed.
Despite these many important modifications to the general approach for assessing liquefaction hazards over the past 10 years,
the profession has not developed a consensus on which of the modifications should be used as a baseline for evaluating
liquefaction hazard – similar to the recommendations in NCEER (1997) and Youd et al. (2001) based on the Liquefaction
Workshop. Procedures suggested by Idriss and Boulanger (2004, 2006, 2008) and those developed by Cetin et al. (2004) and
Moss et al. (2006) present important changes to the liquefaction hazard analysis. However, until a consensus is reached or an
adequate period of vetting occurs, it is difficult to recommend which of these procedures should be used.
It is important that the newer methods be used consistently. In other words, the Idriss and Boulanger method should be used
with the various improvements recommended by Idriss and Boulanger including the revised liquefaction strength plot.
Likewise, if the Cetin et al. method is going to be used, it should be used in its entirety. It also is important to use these new
methods with some caution, particularly at the limits of the procedure (e.g., at higher blowcounts, deeper depths, and higher
CSR values). If the more recent methods are used, the prudent approach will be to check the liquefaction hazard with an
alternate method, such as the SPT procedure discussed below. Differences between the hazard estimates resulting from
different methods could reflect a real uncertainty in the prediction, and this uncertainty would need to be considered when
judging the hazard at a site.
Empirical SPT Method for Evaluating Liquefaction Hazard. Procedures for evaluating the liquefaction hazard using the
Liquefaction Workshop methodology are summarized below. As discussed above, the recent changes in the methodology
proposed by Idriss and Boulanger (2004, 2006, 2008), Cetin et al. (2004), and Moss et al. (2006) offer alternatives to this
approach.
1. The first step in the liquefaction hazard evaluation using the empirical SPT approach is to define the normalized cyclic
shear stress ratio (CSR) from the peak horizontal ground acceleration expected at the site. This evaluation is made using
the following equation:
(1) Equation
CSR = 0.65(a max g)(s 0 s 0' )rd
Figure 4 SPT clean sand base curve for magnitude 7.5 earthquakes with data from liquefaction case histories (modified from Seed et al., 1985, to reflect NCEER, 1997, and Youd et al., 2001).
where (amax/g) is the peak horizontal acceleration at ground surface expressed as a decimal fraction of gravity, s0 is the
vertical total stress in the soil at the depth in question, s0' is the vertical effective stress at the same depth, and rd is the
deformationrelated stress reduction factor. The peak ground acceleration, amax, commonly used in liquefaction analysis
is that which would occur at the site in the absence of liquefaction. Thus, the amax used in Eq. 1 is the estimated rock
acceleration corrected for soil site response but with neglect of excess porewater pressures that might develop.
The stress reduction factor, rd, used in Eq. 1 was originally determined using a plot developed by Seed and Idriss (1971)
showing the reduction factor versus depth. The consensus from the Liquefaction Workshop was to represent rd by the
following equations:
For z = 9.15 m, rd = 1.0 – 0.00765z (2a)
For 9.15 m < z = 23 m, rd = 1.174 – 0.267z (2b)
2. The second step in the liquefaction hazard evaluation using the empirical approach involves determination of the
normalized cyclic resistance ratio (CRR). The most commonly used empirical relationship compares CRR with
corrected SPT resistance, (N1)60, from sites where liquefaction did or did not develop during past earthquakes. Figure 4
shows this relationship for magnitude 7.5 earthquakes with an adjustment at low values of CRR recommended by the
Liquefaction Workshop. Similar relationships have been developed for determining CRR from CPT soundings, from
BHT blowcounts, and from shear wave velocity data as discussed by Youd et al. (2001) and as presented in detail in
NCEER (1997).
Figure 4 SPT clean sand base curve for magnitude 7.5 earthquakes with data from liquefaction case
histories (modified from Seed et al., 1985, to reflect NCEER, 1997, and Youd et al., 2001).
It should be noted that nearly all the field data used to develop the simplified procedure are for depths less than 50 feet;
therefore, there is greater uncertainty in the use of empirical approaches at greater depths. Common practice is to use the
Figure 5 Magnitude scaling factors derived by various investigators (NCEER, 1997; Youd et al., 2001).
SPT or CPT method to depths of 75 feet. In some locations, deep deposits of low blowcount or low CPT end resistance
values occur (e.g., in the Puget Sound area and along the Columbia River). It is still prudent to consider these low
blowcount materials as susceptible to liquefaction even if they are located at depths greater than 75 feet. For these sites,
it is important to correct the CRR with an overburden correction factor (Ks). Alternatively, it may be appropriate to use
strainbased procedures (Dobry et al., 1982) or onedimensional effective stress modeling methods.
In Figure 4, CRRs calculated for various sites are plotted against (N1)60, where (N1)60 is the SPT blowcount normalized
for an overburden stress of 100 kPa and for an energy ratio of 60 percent. Solid symbols represent sites where
liquefaction occurred and open symbols represent sites where surface evidence of liquefaction was not found. Curves
were drawn through the data to separate regions where liquefaction did and did not develop. As shown, curves are given
for soils with fines contents (FC) ranging from less than 5 to 35 percent.
The (N1)60 in Figure 4 is adjusted for various factors before its use as recommended by the Liquefaction Workshop and
discussed by Youd et al. (2001). These include an adjustment for fines, such that only the clean sand curve in Figure 4 is
used, as well as adjustments for a number of other testing related parameters, including whether or not liners are used in
the SPT sampler and the energy calibration factor. These adjustments are all in conventional use by the profession and
can readily be found in references by Martin and Lew (1999) and by Youd et al. (2001).
It is very important that the engineer consider these correction factors when conducting the liquefaction analyses.
Failure to consider these corrections can result in inaccurate liquefaction estimates  leading to either excessive cost to
mitigate the liquefaction concern or excessive risk of poor performance during a seismic event – potentially resulting in
unacceptable damage.
Special mention needs to be made of the energy calibration term, CE. This correction has a very significant effect on the
(N1)60 used to compute CRR. The value of this correction factor can vary greatly depending on the SPT hammer system
used in the field and on site conditions. The automatic hammer now used to conduct SPTs avoids much of the
uncertainty in energy; however, even it should be periodically calibrated. These calibration measurements are relatively
inexpensive and represent a small increase in overall field exploration costs. Many drilling contractors in areas that are
seismically active provide calibrated equipment as part of their routine service.
Before computing the factor of safety from liquefaction, the CRR result obtained from Figure 4, using the corrected SPT
blow count identified in the equation for (N1)60, must be corrected for earthquake magnitude M if the magnitude differs
from 7.5. The magnitude correction factor is shown in Figure 5. This plot was developed during the Liquefaction
Workshop on the basis of input from experts attending the workshop. The range shown in Figure 5 is used because of
uncertainties. Research conducted since the Liquefaction Workshop has shown that magnitude scaling factors near the
lower limit of the recommended range are appropriate for M < 7.5 (Liu et al., 2001; Cetin et al., 2004; Boulanger and
Idriss, 2006).
Figure 5 Magnitude scaling factors derived by various investigators (NCEER, 1997; Youd et al., 2001).
The magnitude, M, needed to determine a magnitude scaling factor from Figure 5 should be consistent with the hazard
level used in the ground motion determination. When the general procedure for ground motion estimation is used
(ASCE/SEI 7 Sections 11.4.1 to 11.46) and the MCE (per ASCE/SEI 7) is determined probabilistically, the magnitude
used in these evaluations can be obtained as the dominant magnitude(s) determined from deaggregation information
available by latitude and longitude from a U.S. Geological Survey (USGS) website:
http://earthquake.usgs.gov/research/hazmaps/. When the general procedure is used and the MCE is bounded
deterministically near known active fault sources, the magnitude of the MCE should be the characteristic maximum
magnitude assigned to the fault in the construction of the MCE ground motion maps. Where the sitespecific procedure
for ground motion estimation is used (ASCE/SEI 7 Sections 11.4.7 and Chapter 21), the magnitude of the MCE should
be similarly determined from the sitespecific analysis. In all cases, it should be remembered that the likelihood of
liquefaction at the site (as defined later by the factor of safety FL in Eq. 3) is determined jointly by amax and M and not by
amax alone. Because of the longer duration of strong groundshaking, large distant earthquakes may in some cases
generate liquefaction at a site while smaller nearby earthquakes may not generate liquefaction even though amax of the
nearer events is larger than that from the more distant events.
A more recent procedure developed by Kramer and Mayfield (2007) estimates the return period for liquefaction directly
without the use of the magnitude scaling factors. This approach considers both the peak acceleration hazard curve and
the distribution of earthquakes contributing to the ground motion hazard.
3. The final step in the liquefaction hazard evaluation using the empirical approach involves the computation of the factor
of safety (FL) against liquefaction using the equation:
FL = CRR/CSR (3)
If FL is greater than 1.0, then liquefaction should not develop. If at any depth in the sediment profile, FL is equal to or
less than 1.0, then there is a liquefaction hazard. Although the curves shown in Figure 4 envelop the plotted data, it is
possible that liquefaction may have occurred beyond the enveloped data and was not detected at the ground surface. For
this reason, a factor of safety of 1.1 to 1.3 is usually appropriate for building sites  with the actual factor selected on the
basis of the importance of the structure and the potential for ground displacement at the site.
Additional guidance on the selection of the appropriate factor of safety is provided by Martin and Lew (1999). They suggest
that the following factors be considered when selecting the factor of safety:
1. The type of structure and its vulnerability to damage.
2. Levels of risk accepted by the owner or governmental regulations with questions related to design for life safety, limited
structural damage, or essentially no damage.
3. Damage potential associated with the particular liquefaction hazard. Flow failures or major lateral spreads pose more
damage potential than differential settlement. Hence factors of safety could be adjusted accordingly.
4. Damage potential associated with the earthquake magnitude. A magnitude 7.5 event is potentially more damaging than a
6.5 event.
5. Damage potential associated with SPT values; low blowcounts have a greater cyclic strain potential than higher
blowcounts.
6. Uncertainty in SPT or CPTderived liquefaction strengths used for evaluations. Note that a change in silt content from 5
to 15 percent could change a factor of safety from, say, 1.0 to 1.25.
7. For high levels of ground motion, factors of safety may be indeterminate. For example, if (N1)60cs = 20, M = 7.5 and
fines content = 35 percent, liquefaction strengths cannot be accurately defined due to the vertical asymptote on the
empirical strength curve.
Martin and Lew (1999) indicate that the final choice of an appropriate factor of safety must reflect the particular conditions
associated with the specific site and the vulnerability of siterelated structures. Table 1 summarizes factors of safety
suggested by Martin and Lew.
As a final comment on the assessment of liquefaction hazards, it is important to note that soils composed of sands, silts, and
gravels are most susceptible to liquefaction while clay soils generally are not susceptible to this phenomenon. The curves in
Figure 4 are valid for soils composed primarily of sand. The curves should be used with caution for soils with substantial
amounts of gravel. Verified corrections for gravel content have not been developed; a geotechnical engineer, experienced in
liquefaction hazard evaluation, should be consulted when gravelly soils are encountered.
Evaluation of Potential for Loss of Ground Support, Increased Loads, and Ground Displacements. Liquefaction by itself
may or may not be of engineering significance. Only when liquefaction is accompanied by loss of ground support, increased
soil loads, and/or ground deformation does this phenomenon become important to structural design. Surface manifestations,
loss of bearing capacity, increased lateral earth pressures, ground settlement, flow failure, and lateral spread are ground
failure mechanisms that have caused structural damage during past earthquakes. These types of ground failure are described
in National Research Council (1985), Martin and Lew (1999), and U.S. Army Corps of Engineers (2005) and are discussed
below. The type of failure and amount of ground displacement are a function of several parameters including the looseness
of the liquefied soil layer, the thickness and extent of the liquefied layer, the thickness and permeability of unliquefied
material overlying the liquefied layer, the ground slope, and the nearness of a free face.
Table 1 Factors of Safety for Liquefaction Hazard Assessment (from Martin and Lew, 1999)
Consequences of
Liquefaction
(N1)60cs
Factor of Safety
Settlement
= 15
1.1
= 30
1.0
Surface manifestations
= 15
1.2
= 30
1.0
Lateral spread
= 15
1.3
= 30
1.0
Evaluation of Potential for Loss of Ground Support, Increased Loads, and Ground Displacements. Liquefaction by itself
may or may not be of engineering significance. Only when liquefaction is accompanied by loss of ground support, increased
soil loads, and/or ground deformation does this phenomenon become important to structural design. Surface manifestations,
loss of bearing capacity, increased lateral earth pressures, ground settlement, flow failure, and lateral spread are ground
failure mechanisms that have caused structural damage during past earthquakes. These types of ground failure are described
in National Research Council (1985), Martin and Lew (1999), and U.S. Army Corps of Engineers (2005) and are discussed
below. The type of failure and amount of ground displacement are a function of several parameters including the looseness
of the liquefied soil layer, the thickness and extent of the liquefied layer, the thickness and permeability of unliquefied
material overlying the liquefied layer, the ground slope, and the nearness of a free face.
Surface manifestations refer to sand boils and ground fissures on level ground sites. For structures supported on shallow
foundations, the effects of surface manifestations on the structure could be tilting or cracking. Criteria are given by Ishihara
(1985) and Youd and Garris (1995) for evaluating the influence of thickness of layers on surface manifestation of
liquefaction effects for level sites. These criteria may be used for noncritical or nonessential structures on level sites not
subject to lateral spreads (see later in this section). Differential settlements associated with these surface manifestations may
also require consideration.
Loss of bearing capacity can occur if the foundation is located within or above the liquefiable layer. The consequence of
bearing failure could be settlement or tilting of the structure. Usually, loss of bearing capacity is not likely for light structures
with shallow footings founded on stable, nonliquefiable materials overlying deeply buried liquefiable layers, particularly if
the liquefiable layers are relatively thin. Simple guidance for how deep or how thin the layers must be has not yet been
developed. Martin and Lew (1999) provide some preliminary guidance based on the Ishihara (1985) method. Final
evaluation of the potential for loss of bearing should be made by a geotechnical engineer experienced in liquefaction hazard
assessment.
Another possible consequence of liquefaction is increased lateral pressures against basement and retaining walls. The
liquefied material will have an atrest earth pressure coefficient (K0) between 1.0 and the K0 value for the nonliquefied soil,
depending on the strength of the liquefied soil. A common approach is to conservatively assume that the liquefied soil is a
dense fluid having a unit weight of the liquefied soil. The wall then is designed assuming that hydrostatic pressure for the
dense fluid acts against the wall. If unsaturated soil is present above the liquefied soil, it is treated as a surcharge that
increases the fluid pressure within the underlying liquefied soil by an amount equal to the thickness times the total unit
weight of the surcharge soil. This procedure applies equivalent horizontal earth pressures that are greater than typical atrest
earth pressures but less than passive earth pressures.
To prevent buoyant rise of a structure as a consequence of liquefaction, the total weight of the structure should be greater
than the volume of the basement or other cavity times the unit weight of liquefied soil. Structures with insufficient weight to
counterbalance buoyant effects could differentially rise during an earthquake.
For saturated or dry granular soils in a loose condition, the amount of ground settlement can approach 3 to 4 percent of the
thickness of the loose soil layer in some cases. This amount of settlement could cause tilting or cracking of a building, and
therefore, it is usually important to evaluate the potential for ground settlement during earthquakes.
Tokimatsu and Seed (1987) published an empirical procedure for estimating ground settlement. It is beyond the scope of this
discussion to outline that procedure which, although explicit, has several rather complex steps. The Tokimatsu and Seed
Figure 6 Measured versus predicted displacements for displacements up to 2 meters (Youd et al., 2002).
procedure can be applied whether liquefaction does or does not occur. For dry cohesionless soils, the settlement estimate
from Tokimatsu and Seed should be multiplied by a factor of 2 to account for multidirectional shaking effects as discussed
by Martin and Lew (1999). Duku et al. (2008) present updated relationships for the calculation of settlement of unsaturated
clean sands. An alternate approach for settlement of liquefiable soils is that proposed by Ishihara and Yoshimine (1992).
Earthquakeinduced ground settlement usually will not occur uniformly at a site. Differences in soil layering and soil
consistency will lead to differential settlement. The amount of differential settlement can be estimated if sufficient
geotechnical information is available for a site. If such information is not available, a common approach is often to assume
that differential settlement will range from 0.5 to 0.75 times the total settlement obtained from one of the above predictive
methods.
Flow failures or flow slides are the most catastrophic form of ground failure that may be triggered when liquefaction occurs.
They may displace large masses of soils tens of feet. Flow slides occur when the average static shearing stresses on potential
failure surfaces are less than the average shear strengths of liquefied soil on these surfaces. Standard limit equilibrium static
slope stability analyses may be used to assess flow failure potential with the residual strength of liquefied soil used as the
strength parameter in the analyses.
The determination of residual strengths is very inexact, and consensus as to the most appropriate approach has not been
reached to date. Relationships for residual strength of liquefied soil that are often used in practice are those of Seed and
Harder (1990), Olson and Stark (2002), and Idriss and Boulanger (2007). These strengths have been empirically determined
from forensic analyses of flow failures.
Lateral spreads are groundfailure phenomena that can occur on gently sloping ground underlain by liquefied soil. They may
result in lateral movements in the range of a few inches to several feet. Earthquake groundshaking affects the stability of
gently sloping ground containing liquefiable materials by seismic inertial forces combined with static gravity forces within
the slope and by shakinginduced strength reductions in the liquefiable materials. Temporary instability due to seismic
inertial forces is manifested by lateral “downslope” movement. For the duration of ground shaking associated with
moderate to largemagnitude earthquakes, there could be many such occurrences of temporary instability during earthquake
shaking producing an accumulation of “downslope” movement.
Various analytical and empirical techniques have been developed to estimate lateral spread ground displacement; however,
no single technique has been widely accepted for engineering design. Three approaches are used depending on the
requirements of the project: Empirical procedures, simplified analytical methods, and more rigorous computer modeling use
correlations between past ground displacement and site conditions under which those displacements occurred. Youd et al.
(2002) presents an empirical method that provides an estimate of lateral spread displacements as a function of earthquake
magnitude, distance, topographic conditions, and soil deposit characteristics. As shown in Figure 6, the displacements
estimated by the Youd et al. (2002) method are generally within a factor of two of the observed displacements.
Figure 6 Measured versus predicted displacements for displacements up to 2 meters (Youd et al., 2002).
Bardet et al. (2002) presents an empirical method having a formulation similar to that of Youd et al. (2002) but using fewer
parameters to describe the soil deposit. The Bardet et al. (2002) model was developed to assess lateral spread displacements
at a regional scale rather than for sitespecific applications. Various other empirical methods are also available, including an
alternate SPT method by Rausch and Martin (2000) and both SPT and CPTbased methods by Zhang et al. (2004). These
methods can result in large differences in predicted displacement; therefore, it is usually best to use several methods when
estimating displacement. Because of the uncertainty in results, these methods normally are used for preliminary screening or
comparative evaluations.
Simplified analytical techniques generally apply some form of Newmark’s analysis of a rigid body sliding on an infinite or
circular failure surface with ultimate shear resistance estimated from the strength of the liquefied soil. Additional discussion
of the simplified Newmark method is provided in the discussion of slope instability hazard. A key question for this approach
is the method of defining the strength of the liquefied soil. The same residual strength as used for flow failure assessments
often has been used for the spreading analyses. However, many researchers will argue that lateral spreads do not involve the
same boundary conditions as occur for lateral flows and, specifically, that the ratcheting mechanism of loading with dilation
at larger strains is not properly considered. No consensus currently exists on the most suitable method for obtaining the
liquefied strength for lateral spreading analyses; however, the use of the residual strength from flow failures is thought to be
conservative for most lateral spreading analyses. Work by Olson and Johnson (2008) appear to support the acceptability of
use of the residual strength. In view of the current uncertainties, a cautious approach must be taken when estimating
deformations for cases involving liquefaction.
More rigorous computer modeling typically involves use of nonlinear finite element or finite difference methods to predict
deformations (e.g., using the FLAC and PLAXIS software). As noted previously, the accuracy of this approach is critically
dependent on the properties and geometry of the model as well as the earthquake record selection. Of particular importance
for the liquefaction problem is the completeness of the pore pressure model and its ability to handle various soil conditions.
For example, the soil model within the nonlinear computer analysis programs often is calibrated for only specific conditions.
If the site is not characterized by these conditions, errors in estimating the displacement by a factor of two or more can easily
occur.
Mitigation of Liquefaction Hazard. Three general measures might be considered for mitigation of liquefaction hazards: (a)
design the structure to resist the hazard, (b) stabilize the site to reduce the hazard, or (c) choose an alternative site.
Structural measures that are used to reduce the hazard include deep foundations, mat foundations, or footings interconnected
with ties:
1. Deep foundations have performed well at level sites where liquefaction effects were limited to ground settlement and
ground oscillation with no more than a few inches of lateral displacement. Deep foundations, such as piles, must
consider the potential for reduced soil support through the liquefied layer and may be subjected to lateral displacements
across the layer. Loss in lateral support may require ground improvement around the deep foundations or strengthening
of the pile. Downdrag forces resulting from postseismic soil settlement must also be considered. Downdrag forces can
result in pile settlement after the earthquake as liquefied soils settle relative to the pile. These downdrag forces result in
added structure load and potentially pile settlement, depending on the strength of the soil below the deepest depth of
liquefaction. Mitigation procedures for downdrag can include use of bitumen coatings or sleeves that isolate the pile
from downdrag forces.
2. Well reinforced mat foundations also have performed well at localities where ground displacements were less than 1
foot, although releveling of the structure was required in some instances (Youd, 1989). Strong ties between footings also
should provide increased resistance to damage where differential ground displacements are less than 1 foot.
Evaluations of structural performance following two Japanese earthquakes, 1993 Hokkaido NanseiOki and 1995 (Kobe)
HyogoKen Nanbu, indicate that small structures on shallow foundations performed well in liquefaction areas where ground
displacements were small. Sand boil eruptions and open ground fissures in these areas indicate minor effects of liquefaction
including ground oscillation and up to 1 foot of lateral spread displacement. Many small structures (mostly houses, shops,
schools, etc.) were structurally undamaged although a few tilted slightly. Foundations for these structures consist of
reinforced concrete perimeter wall footings with reinforced concrete interior wall footings tied into the perimeter walls at
intersections. These foundations acted as diaphragms causing the soil to yield beneath the foundation which prevented
fracture of foundations and propagation of differential displacements into the superstructure.
At sites where expected ground displacements are unacceptably large or where excessive strength loss beneath a foundation
needs to be mitigated, ground modification to lessen the liquefaction or ground failure hazard may be required. Techniques
for ground stabilization to prevent liquefaction of potentially unstable soils include removal and replacement of soil;
compaction of soil in place using vibrations, heavy tamping, compaction piles, or compaction grouting; buttressing; chemical
stabilization with grout; and installation of drains. Further discussion of mitigation methods is given by the National
Research Council (1985) and Martin and Lew (1999).
In some situations the structure cannot be strengthened and ground improvement is not practical or possible. For these
locations selection of an alternative site may be required.
Surface Fault Rupture Hazard. Fault ruptures during past earthquakes have led to large surface displacements that are
potentially destructive to engineered construction. Displacements, which range from a fraction of an inch to tens of feet, may
occur along traces of active faults. The sense of displacement ranges from horizontal strikeslip to vertical dipslip to many
combinations of these components. The following paragraphs summarize procedures to consider when assessing the hazard
of surface fault rupture. Sources of detailed information for evaluating the hazard of surface fault rupture include Slemmons
and dePolo (1986), the Utah Section of the Association of Engineering Geologists (1987), Swan et al. (1991), Hart and
Bryant (1997), Hanson et al. (1999), and California Geological Survey (2002). Other beneficial references are given in the
bibliographies of these publications.
Assessment of Surface Faulting Hazard. The evaluation of surface fault rupture hazard at a given site is based extensively on
the concepts of recency and recurrence of faulting along existing faults. The magnitude, sense, and frequency of fault rupture
vary for different faults or even along different segments of the same fault. Even so, future faulting generally is expected to
recur along preexisting active faults. The development of a new fault or reactivation of a long inactive fault is relatively
uncommon and generally need not be a concern. For most engineering applications related to foundation design, a sufficient
definition of an active fault is given in CDMG Special Publication 42 (Hart and Bryant, 1997): “An active fault has had
displacement in Holocene time (about the last 11,000 years).”
As a practical matter, fault investigations should be conducted by qualified geologists and directed at the problem of locating
faults and evaluating recency of activity, fault length, the amount and character of past displacements, and the expected
amount and potential of future displacement. Identification and characterization studies should incorporate evaluation of
regional fault patterns as well as detailed study of fault features at and in the near vicinity (within a few hundred yards to a
mile) of the site. Detailed studies can include trenching to accurately locate, document, and date fault features.
The following approach should be considered in fault hazard assessment, and some of the investigative methods outlined
should be carried out beyond the site being investigated:
1. A review should be made of the published and unpublished geologic literature about the region along with records
concerning geologic units, faults, groundwater barriers, etc.
2. A stereoscopic study of aerial photographs and other remotely sensed images should be made to detect faultrelated
topography/geomorphic features, vegetation and soil contrasts, and other lineaments of possible fault origin. The study
of predevelopment aerial photographs often is essential to the detection of fault features. Recently, the use of LiDAR
(LIght Detection And Ranging) has been found to provide excellent identification of fault traces in areas where tree
growth and vegetation normally would obscure evidence of faulting from the air.
3. A field reconnaissance study generally is required and should include observation and mapping of features such as
bedrock and soil units and structures, geomorphic surfaces, faultrelated geomorphic features, springs, and deformation
of manmade structures due to fault creep. Field study should be detailed within the site with less detailed
reconnaissance of an area within a mile or so of the site. Evidence from prehistoric liquefaction (paleoliquefaction) also
can provide important information regarding the magnitude and timing of fault displacement in the site area or region.
4. Subsurface investigations may be necessary to evaluate location and activity of fault traces when uncertainty exists about
the location or activity of a fault. These investigations may include trenches, test pits, and/or boreholes to permit
detailed and direct observation of geologic units and faults.
5. The geometry of faults may be further defined by geophysical investigations including seismic refraction, seismic
reflection, gravity, magnetic intensity, resistivity, ground penetrating radar, etc. These indirect methods require
knowledge of specific geologic conditions for reliable interpretation.
6. Geophysical methods alone never prove the absence of a fault, and they typically do not identify the recency of activity.
7. More sophisticated and more costly studies may provide valuable data when special geological conditions exist or when
requirements for critical structures demand a more intensive investigation. These methods might involve repeated
geodetic surveys, strain measurements, or monitoring of microseismicity and radiometric analysis (C14, KAr),
stratigraphic correlation (fossils, mineralology) soil profile development, paleomagnetism (magnetostratigraphy), or
other dating techniques (thermoluminescense, cosmogenic isotopes) to evaluate the age of faulted or unfaulted units or
surfaces.
The following information should be developed to provide documented support for conclusions relative to location and
magnitude of faulting hazards:
1. Maps should be prepared showing the existence (or absence) and location of active faults on or near the site. The
distribution of faulting (fault zone width) and faultrelated surface deformation should be shown.
2. The type, amount, and sense of displacement of past surface faulting episodes should be documented, if possible.
3. From this documentation, estimates of location, magnitude, and likelihood or relative potential for future fault
displacement can be made, preferably from measurements of past surface faulting events at the site, using the premise
that the general pattern of past activity will repeat in the future. Estimates also may be made from published empirical
correlations between fault displacement and fault length or earthquake magnitude (e.g., Wells and Coppersmith, 1994).
Where fault segment length and sense of displacement are defined, these correlations may provide an estimate of future
fault displacement (either the maximum or the average to be expected). Probabilistic studies may be considered to
evaluate the probability of fault displacement (e.g., Youngs et al., 2003).
4. The degree of confidence and limitations of the data should be addressed.
Both deterministic and probabilistic methods are available for estimating the amount or probability of future fault
displacement (e.g., Youngs et al., 2003). Because techniques for making these estimates are not standardized, peer review of
reports is useful to verify the adequacy of the methods used and the estimated amount or frequency of movement, to aid the
evaluation by the permitting agency, and to facilitate discussion between specialists that could lead to the development of
standards.
The following guidelines are given for the safe siting of engineered construction in areas crossed by active faults:
1. Where ordinances have been developed that specify safe setback distances from traces of active faults or active fault
zones, those distances must be complied with and accepted as the minimum for safe siting of buildings. ASCE/SEI 7
Section 11.8 precludes structures in Seismic Design Category E or F from being sited where there is a known potential
for an active fault to cause rupture of the ground surface at the structure. States also may adopt more definitive
requirements. For example, the general setback requirement in California is 50 feet from the traces of an active fault.
That setback distance is mandated for structures near faults unless a sitespecific special geologic investigation shows
that a lesser distance could be safely applied (California Code of Regulations, Title 14, Division 2, Section 3603(a)).
2. In general, safe setback distances may be determined from geologic studies and analyses as noted above. Setback
requirements for a site should be developed by the site engineers and geologists in consultation with professionals from
the building and planning departments of the jurisdiction involved.
Where sufficient geologic data have been developed to accurately locate the zone containing active fault traces and the zone
is not complex, a smaller setback distance may be specified. For complex fault zones, greater setback distances may be
required. Dipslip faults, with either normal or reverse motion, typically produce multiple fractures within rather wide and
irregular fault zones. These zones generally are confined to the hangingwall side of the fault leaving the footwall side little
disturbed. Setback requirements for such faults may be rather narrow on the footwall side, depending on the quality of the
data available, and larger on the hanging wall side of the zone. Some fault zones may contain broad deformational features
such as pressure ridges and sags rather than clearly defined fault scarps or shear zones. Nonessential structures may be sited
in these zones provided structural mitigative measures are applied as noted below. Studies by qualified geologists and
engineers are required for such zones to assure that either (a) the structure is not sited across the trace of an active fault or (b)
building foundations can withstand probable ground deformations in such zones.
Mitigation of Surface Faulting Hazards. There is no mitigative technology that can be used to prevent fault rupture from
occurring. Thus, where a surface faulting hazard exists, the site must be avoided or the structure must be designed to
withstand ground deformation or surface fault rupture.
In general practice, it is economically impractical to design a structure to withstand more than a few inches of fault
displacement. Some buildings with strong foundations, however, have successfully withstood or diverted a few inches or
even feet of surface fault rupture without damage to the structure (Youd, 1989; Kelson et al., 2001). Well reinforced mat
foundations and strongly intertied footings have been most effective. Deep foundations such as driven piles or drilled shafts
are not preferred. In general, less damage has been inflicted by compressional or shear displacement than by vertical or
extensional displacements.
SEISMIC LATERAL EARTH PRESSURES
Determination of Lateral Pressures on Basement and Retaining Walls Due to Earthquake Motions. Paragraph 1 of
Section 11.8.3 as modified by the 2009 Provisions Part 1 exception requires that seismic lateral pressures on basement walls
and retaining walls be determined for Seismic Design Category D, E, and F structures but does not specify the methods for
calculating these pressures. Discussion and guidance regarding different approaches for determining seismic lateral pressures
are given below.
Observations after past earthquakes have found that retaining walls for waterfront structures often have performed poorly in
major earthquake due to excess pore water pressure and liquefaction conditions developing in relatively loose, saturated
granular soils. However, damage reports for basement walls and retaining structures away from waterfronts are generally
limited with only a few cases of stability failures or large permanent movements (Whitman, 1991). Due to the apparent
conservatism or overstrength in static design of most walls, the complexity of nonlinear dynamic soilstructure interaction
and the poor understanding of the behavior of retaining structures with cohesive or dense granular soils, Whitman (1991)
recommends that “engineers must rely primarily on a sound understanding of fundamental principles and of general patterns
of behavior.”
Seismic earth pressures on retaining walls are discussed below for two categories of walls: “yielding” walls that can move
sufficiently to develop minimum active earth pressures and “nonyielding” walls that do not satisfy this movement condition.
Note that in this context, yielding refers to permanent displacement of the wall as a result of the seismic event and does not
mean that stresses within the structural system were exceeded. The amount of movement to develop minimum active
pressure is very small. A displacement at the top of the wall of 0.002 times the wall height is typically sufficient to develop
the minimum active pressure state. Generally, freestanding gravity or cantilever walls are considered to be yielding walls
(except massive gravity walls founded on rock) whereas building basement walls restrained at the top and bottom often are
considered to be nonyielding.
Yielding Walls. Limit Equilibrium Force Approach. At the 1970 Specialty Conference on Lateral Stresses in the Ground
and Design of Earth Retaining Structures, Seed and Whitman (1970) made a significant contribution by reintroducing and
reformulating the MononobeOkabe (MO) seismic coefficient analysis (Mononobe and Matsuo, 1929; Okabe, 1926), the
earliest method for assessing the dynamic lateral pressures on a retaining wall. The MO method is a limitequilibrium
approach based on a Coulomb failure wedge with the assumption that the wall displaces or rotates outward sufficiently to
produce the minimum active earth pressure state.
The MO formulation is expressed as:
PAE = (1/2).H2 (1 – kv)KAE (4)
where PAE is the total (static + dynamic) lateral thrust, . is unit weight of backfill soil, H is the height of backfill behind the
wall, kV is vertical ground acceleration divided by gravitational acceleration, and KAE is the static plus dynamic lateral earth
pressure coefficient which is dependent on (in its most general form) angle of friction of backfill, angle of wall friction, slope
of backfill surface, and slope of back face of wall as well as horizontal and vertical ground acceleration. The formulation for
KAE is given in textbooks on soil dynamics (Prakash, 1981; Das, 1983; Kramer, 1996) and discussed in detail by Ebeling and
Morrison (1992).
The value of amax used in the KAE determination is the instantaneous peak acceleration, not an average of the ground motion
over the duration of strong shaking. In the past, it was common practice for geotechnical engineers to reduce the
instantaneous peak by a factor from 0.5 to 0.7 to represent an average seismic coefficient for determining the seismic earth
pressure on a wall. The reduction factor was introduced in a manner similar to the method used in a simplified liquefaction
analyses to convert a random acceleration record to an equivalent average series of cyclic loads. This approach can result in
confusion on the magnitude of the seismic active earth pressure and, therefore, is not recommended. Any further reduction to
represent average rather than instantaneous peak loads is a structural decision and must be an informed decision made by the
structural designer. As discussed in this paper in the section on the displacementbased approach, a reduction in amax is,
however, permitted if the wall can undergo permanent displacements. There is no consensus on the appropriate amax value to
use in the earth pressure determination. Recent centrifuge modeling work by Al Atik and Sitar (2007) suggests that
estimating seismic lateral earth pressures utilizing the full peak ground acceleration overestimates the seismic earth pressure
forces for some structures.
The MO equation makes several other very important assumptions, including that the soil behind the retaining wall is a
uniform, cohesionless soil and that the groundwater elevation is below the base of the retaining wall. The implications of
these assumptions are discussed later in this section.
Seed and Whitman (1970), as a convenience in design analysis, proposed to evaluate the total lateral thrust, PAE, in terms of
its static component (PA) and dynamic incremental component (.PAE):
PAE = PA + .PAE (5a)
or
KAE = KA + .KAE (5b)
or
.PAE = (1/2).H2 .KAE (5c)
Seed and Whitman (1970), based on a parametric sensitivity analysis, further proposed that for practical purposes:
.KAE = (3/4)Kh (6)
.PAE = (1/2).H2 (3/4)kh = (3/8)kh.H2 (7)
where kh is horizontal ground acceleration divided by gravitational acceleration. Unless permanent displacement of the wall
is acceptable, kh should be taken equal to the site peak ground acceleration, amax. For the distribution of the dynamic thrust,
.PAE, Seed and Whitman (1970) recommended that the resultant dynamic thrust act at 0.6H above the base of the wall (i.e.,
inverted trapezoidal pressure distribution). Note that this approach assumes dry, cohesionless backfill material. If soil
conditions behind the wall have a cohesive soil component (i.e., a cf soil), this simplified approach is no longer appropriate.
Equation 7 generally is referred to as the simplified MO formulation and is not applicable for sloping ground above the wall.
For walls that are in excess of 15 feet in height, special studies also can be conducted to evaluate the coherency of ground
motions behind the wall from which an average seismic coefficient can be developed. Anderson et al. (2008) provide
simplified guidance on the selection of factors that adjust for coherency. These special studies require consideration of the
frequency characteristics of ground motion, as well as the stiffness of the soil and the wall height, and usually require use of a
finite element or difference computer model.
Since its introduction, there has been a consensus in geotechnical engineering practice that the simplified MO formulation
reasonably represents the dynamic (seismic) lateral earth pressure increment for yielding retaining walls. However, there are
limitations associated with the MO approach, and these limitations can have a significant effect on the magnitude of
estimated seismic active earth pressure.
Although the MO approach is simple to use, certain designs become very difficult to solve with the standard MO equations.
These designs involve high ground accelerations, combinations of moderatetohigh ground accelerations and steep
backslopes, and mixed backfill conditions (i.e., either cf soils occur or only a thin zone of granular backfill is placed
between the wall and the native soil behind the fill zone, particularly where the native soils is cohesive or rock). For these
cases, the MO approach does not provide realistic answers.
An acceptable alternative approach for these cases is to use a generalized limit equilibrium (slope stability) computer
program. With this alternate approach, appropriate soil properties and geometry can be modeled, and the seismic coefficient
can be defined on the basis of the peak ground acceleration or a reduced seismic coefficient if displacement is acceptable.
For most seismic loading cases, the total stress (undrained) cf parameters will be appropriate for design because of the rate
of seismic loading. With this generalized limit equilibrium method, the external force required for stability is computed.
This force represents the dynamic earth pressure on the wall. The total force can be distributed as a uniform seismic pressure
or the seismic increment can be determined and applied as an inverted triangle. Note that when subtracting the static force
from the total seismic earth pressure, it is necessary to determine the static earth pressure under the conditions used during
the pseudostatic seismic analysis. This could mean determining the static earth pressure for the same cf combination as
used for the seismic analysis.
Displacementbased Approach. The alternate approach for the design of yielding walls is to evaluate the movement of the
wall during seismic loading. Various methods are available for conducting displacementbased analyses ranging from
extensions of the MO formulations to two and threedimensional computer modeling. One of the key requirements for the
displacementbased approach is the determination of the level of acceptable displacements. This determination will depend
both on the wall type and on the nature of facilities next to the wall. These nearby facilities can range from buildings to
buried utilities.
Careful attention needs to be given to the characterization of soil conditions behind the wall when using a displacementbased
approach. Both the geometry of fill and native deposits, as well as the strength of the soil under cyclic loading, must be
considered. Initially, the peak strength of the soil can be used for the analysis; however, if significant deformations are
predicted, it may be necessary to repeat the analysis using the residual strength of the soil. See discussions of site
characterization in the seismic slope stability section for additional guidance on the selection of soil strengths.
Richards and Elms (1979) introduced a method for seismic design analysis of yielding walls considering translational sliding
as a failure mode and based on tolerable permanent displacements for the wall. Elms and Martin (1979) showed that kh =
amax/2 is adequate for design if the wall is allowed to slide up to 10amax where amax is the seismic ground motion and
displacement is in inches. For seismically active areas, the displacement associated with 10 amax can be 4 to 6 inches.
In practice, kh = amax/2 often is used without regard for the displacement that is associated with this assumption. Clearly,
several inches of movement can be tolerable for some types of yielding walls, but not all. For example, a semigravity
cantilever wall could be designed to slide several inches; however, the anchors for a tieback wall would likely restrict this
level of movement from occurring for a well designed anchored wall. Use of kh = amax/2 requires that the designer check to
confirm that deformations will develop without damaging the wall or other nearby facilities. Various factors can limit
displacements, such as physical obstructions or underestimating the amount of soil strength that will be mobilized. If
movement cannot be tolerated or if the wall may not move enough to mobilize the yield condition, then either the full amax
should be used for determination of seismic earth pressure or more rigorous procedures such as described below should be
used.
There are a number of other empirical formulations for estimating permanent displacements under a translation mode of
failure; these have been reviewed by Whitman and Liao (1985). Nadim (1980) and Nadim and Whitman (1984) incorporated
the failure mode of wall tilting as well as sliding by employing coupled equations of motion that were further formulated by
Siddharthan et al. (1992) as a design method to predict the seismic performance of retaining walls taking into account both
sliding and tilting. Alternatively, Prakash et al. (1995) described design procedures and presented design charts for
estimating both sliding and rocking displacements of rigid retaining walls. These design charts are the results of analyses for
which the backfill and foundation soils were modeled as nonlinear viscoelastic materials. A simplified method that considers
rocking of a wall on a rigid foundation about the toe was described by Steedman and Zeng (1996) and allows the
determination of the threshold acceleration beyond which the wall will rotate. A simplified procedure for evaluating the
critical threshold accelerations for sliding and tilting was described by Richards et al. (1996).
Validation of methods for evaluating tilting of yielding walls has been limited to a few case studies and backcalculation of
laboratory test results. Evaluation of wall tilting requires considerable engineering judgment. Because the tilting mode of
failure can lead to instability of a yielding retaining wall, it is suggested that this mode of failure be avoided in the design of
new walls by proportioning the walls to prevent rotation in order to displace only in the sliding mode.
An alternative displacementbased approach is the use of twodimensional computer codes such as FLAC and PLAXIS.
These methods allow a more detailed evaluation of soilstructure interaction for different wall geometries and external loads,
different soil and structural properties, and different earthquake loading conditions. Results from these analyses can be
particularly helpful in understanding the deformations that occur within and near the retaining wall including the soil in front
of and behind the wall. As noted above, these methods require considerable expertise in terms of soil and structural modeling
and selection of earthquake records and should be used with particular care. Although results may appear very reasonable,
small changes in model setup or input parameters selection can significantly affect the quality of results, potentially leading
to unconservative design decisions.
Nonyielding Walls. By definition, nonyielding walls do not deform when subjected to seismic earth pressures. This type of
response requires a very stiff wall in combination with a rigid base condition. Most nonyielding walls will be located on rock
or very stiff soil. Even in this condition, wall flexibility can be sufficient to develop active seismic earth pressures
significantly reducing the loading on basement walls. Where a basement wall is located on rock or very stiff soil and where
structural analyses determine that the wall flexibility is such that deformations will not develop seismic active earth pressures
(i.e., deformations < 0.002H where H is the wall height), the wall should be designed as a nonyielding wall. The following
discussion provides guidance on two methods for dealing with cases where rigid wall conditions occur. Also included is a
discussion of soilstructure interaction methods for evaluating earth pressures on basement walls where uncertainties on the
flexibility of the wall occur.
Simplified Wood Approach. Wood (1973) analyzed the response of a rigid nonyielding wall retaining a homogeneous linear
elastic soil and connected to a rigid base. For such conditions, Wood established that the dynamic amplification was
insignificant for relatively lowfrequency ground motions (i.e., motions at less than half of the natural frequency of the
unconstrained backfill), which would include many earthquake problems. For uniform, constant kh applied throughout the
elastic backfill, Wood (1973) developed the dynamic thrust, .PE, acting on smooth rigid nonyielding walls as:
.PE = Fkh.H2 (8)
The value of F is approximately equal to unity (Whitman, 1991) leading to the following approximate formulation for a rigid
nonyielding wall on a rigid base:
.PE = kh.H2 (9)
As for yielding walls, the point of application of the dynamic thrust is taken typically at a height of 0.6H above the base of
the wall.
It should be noted that the model used by Wood (1973) does not incorporate any effect on the pressures of the inertial
response of a superstructure connected to the top of the wall. This effect may modify the interaction between the soil and the
wall and thus modify the pressures from those calculated assuming a rigid wall on a rigid base.
Although the study performed by Wood included dynamic analysis of a rigid wall with fixed base condition, the solution
commonly used and presented in Equations 8 and 9 is based on static “1g” loading of the soil and wall and does not include
the effects of the wave propagation in the soil. The subject of soilwall interaction is addressed in the following sections.
Ostadan Rigid Wall Approach. Ostadan (2005) observed that for partially embedded structures subjected to ground shaking,
the characteristics of the dynamic earth pressure amplitudes versus frequency of the ground motion were those of a singledegree
offreedom (SDOF) system and proposed a simplified method to estimate the magnitude and distribution of dynamic
thrust. Results provided by Ostadan (2005) utilizing this simplified method, which also were confirmed by dynamic finite
element analyses, indicate that, depending on the dynamic properties of the backfill as well as the frequency characteristics of
the input ground motion, a range of dynamic earth pressure solutions would be obtained for which the MO solution and the
Wood (1973) solution represent a “lower” and an “upper” bound, respectively.
The solution by Ostadan considers the kinematic soilstructure interaction effects and is based on the dynamic soil properties
and the ground motion characteristics. This solution assumes a rigid wall on rigid foundation and does not include the effect
of the superstructure and its inertia on seismic soil pressure.
The fivestep method to compute the seismic soil pressure following Ostadan’s method is:
1. Perform freefield soil column analysis and obtain the ground response motion at the depth corresponding to the base of
the wall in the freefield. The response motion in terms of acceleration response spectrum at 30 percent damping should
be obtained. The freefield soil column analysis may be performed using the computer program SHAKE with input
motion specified either at the ground surface or at the depth of the foundation basemat. The choice for location of
control motion should be consistent with the development of the ground motion.
2. Use Equation 10 to compute the total soil mass (m) using the Poisson’s ratio (.) and mass density of the soil.
m = 0.50(.)H2 (..) (10)
where . is the mass density of the soil (total weight density divided by acceleration of gravity), H is the height of the
wall, and .. is a factor to account for the Poisson’s ratio as defined by the following equation.
.. = 2 / [(1.)(2 .)]0.5 (11)
3. Obtain the total lateral seismic force from the product of the total mass obtained in Step 2 and the acceleration spectral
value of the freefield response at the soil column frequency obtained at the depth of the bottom of the wall (Step 1). The
soil column frequency (fs) is an output provided by SHAKE:
fs = vs/(4H) (12)
where vs is the average straincompatible shear wave velocity of the soil column over the height of the wall.
4. Obtain the maximum lateral seismic soil pressure at the ground surface level by dividing the lateral force obtained in
Step 3 by the area under the normalized seismic soil pressure, 0.744H.
5. Obtain the pressure profile by multiplying the peak pressure from Step 4 by the pressure distribution relationship given
by:
p(y) = 0.0015+5.05y15.84y2+28.25y324.59y4+8.14y5 (13)
where y is the normalized height ratio (Y/H) measured from the bottom of the wall (ranging from 0 at the bottom of the
wall to 1 at the top of the wall) and Y is the distance of the point under consideration from the bottom of the wall.
The area under the seismic soil pressure curve can be obtained from integration of the pressure distribution over the height of
the wall. The total area is 0.744H x pmax for a wall with the height of H and maximum pressure of pmax at the top.
With this method, the sitespecific dynamic soil properties, soil nonlinear effects, and the characteristics of the ground motion
are considered in the computation of the seismic soil pressure. A complete verification of the fivestep method against finite
element solutions and comparison with the Wood solution and the MO method is presented by Ostadan (2005).
Soilstructureinteraction Approach and Modeling for Partially Embedded Structures. Lam and Martin (1986), Soydemir
and Celebi (1992), Veletsos and Younan (1994a and 1994b), and Ostadan (2005), among others, argue that the earth
pressures acting on the walls of partially embedded structures (e.g., basement walls) during earthquakes are primarily
governed by soilstructure interaction (SSI) and, thus, these partially embedded structures should not be treated as a
nonyielding wall. Soilstructure interaction includes both a kinematic component  i.e., the interaction of a massless rigid
wall with the adjacent soil as modeled by Wood (1973) but including the wave propagation in the soil  and an inertial
component  i.e., the interaction of the wall, connected to a responding superstructure, with the adjacent soil. Detailed SSI
analyses incorporating kinematic and inertial interaction may be considered for the estimation of seismic earth pressures on
critical walls.
Whitman (1991) has suggested that SSI effects on basement walls of buildings reduce dynamic earth pressures and that MO
pressures may be used in design except where structures are founded on rock or hard soil (i.e., where no significant rocking
occurs). In the latter case, the pressures given by the Ostadan (2005) method with the Wood (1973) formulation as the upper
bound would appear to be more applicable. The effect of rocking in reducing the dynamic earth pressures on basement walls
also has been suggested by Ostadan and White (1998). This condition may be explained if it is demonstrated that the
dynamic displacements induced by kinematic and inertial components are out of phase. Chang et al. (1990) have found that
dynamic earth pressures recorded on the wall of a largescale model nuclear reactor containment building (e.g., 1/4 the size of
a fullsize power block) were consistent with dynamic pressures predicted by the MO solution. Analyses by Chang et al.
(1990) indicate that the dynamic wall pressures were strongly correlated with the rocking response of the structure.
Effect of Saturated Backfill on Wall Pressures. The previous discussions of yielding and nonyielding walls are limited to
backfills that are not watersaturated. In current (2009) practice, drains typically are incorporated in the design to prevent
groundwater from building up within the backfill. This is not practical or feasible, however, for waterfront structures (e.g.,
quay walls) where most of the earthquakeinduced failures have been reported (Seed and Whitman, 1970; Ebeling and
Morrison, 1992; ASCETCLEE, 1998) or for some types of structures located below groundwater.
During ground shaking, the presence of water in the pores of a backfill can influence the seismic loads that act on the wall in
three ways (Ebeling and Morrison, 1992; Kramer, 1996): (a) by altering the inertial forces within the backfill, (b) by
developing hydrodynamic pressures within the backfill, and (c) by generating excess porewater pressure due to cyclic
straining. Effects of the presence of water in cohesionless soil backfill on seismic wall pressures can be estimated using
formulations presented by Ebeling and Morrison (1992) and Kramer (1996). The effects of soil liquefaction associated with
excess porewater pressure generation on wall pressures are treated in the discussion of increased lateral earth pressure in the
liquefaction hazard section of this resource paper.
REFERENCES
American Society of Civil Engineers, Technical Committee on Lifeline Earthquake Engineering. 1998. Seismic Guidelines
for Ports, edited by S. D. Werner, Monograph 12. ASCE, Reston, Virginia.
Al Atik, L., and N. Sitar. 2007. "Dynamic Centrifuge Study of Seismically Induced Lateral Earth Pressures," in Proceedings,
4th International Conference on Earthquake Geotechnical Engineering . EERI, Oakland, California.
Anderson, D. G., G. R. Martin, I. P. Lam, and J. N. Wang. 2008. Seismic Design and Analysis of Retaining Walls, Buried
Structures, Slopes and Embankments, NCHRP Report 611. Transportation Research Board, National Cooperative Highway
Research Program, Washington, D.C.
Ashford, S. A., T. Juirnarongrit, T. Sugano, and M. Hamada. 2006. “SoilPile Response to BlastInduced Lateral Spreading.
I. Field Test,” ASCE/SEI Journal of Geotechnical and Geoenvironmental Engineering, 132(2).
Ashford, S. A., K. M. Rollins, and J. D. Lane. 2004. “BlastInduced Liquefaction for FullScale Foundation Testing,”
ASCE/SEI Journal of Geotechnical and Geoenvironmental Engineering, 130(8).
Bardet, J. P., T. Tobita, N. Mace, and J. Hu. 2002. ”Regional Modeling of LiquefactionInduced Ground Deformation,”
Earthquake Spectra, 18(1): 1946.
Blake, T. F., R. A. Hollingsworth, and J. P. Stewart, editors. 2002. Recommended Procedures for Implementation of DMG
Special Publication 117, Guidelines for Analyzing and Mitigating Landslide Hazards in California. Southern California
Earthquake Center, University of Southern California, Los Angeles, California.
Boulanger, R. W., and I. M. Idriss. 2006. “Liquefaction Susceptibility Criteria for Silts and Clays,” ASCE/SEI Journal of
Geotechnical and Geoenvironmental Engineering, 132(11).
Bray, J. D., and E. M. Rathje. 1998. “Earthquakeinduced Displacements of Solidwaste Landfills,” ASCE/SEI Journal of
Geotechnical and Geoenvironmental Engineering, 124: 242253.
Bray, J. D., E. M. Rathje, A. J. Augello, and S. M. Merry. 1998. “Simplified Seismic Design Procedure for Geosynthetic
Lined, SolidWaste Landfills,” Geosynthetics International5(12).
Bray, J. D., and R. B. Sancio. 2006. “Assessment of the Liquefaction Susceptibility of FineGrained Soils,” ASCE/SEI
Journal of Geotechnical and Geoenvironmental Engineering, 132(9).
California Geological Survey. 2008. Guidelines for Evaluating and Mitigating Seismic Hazards in California, Special
Publication 117A.
California Geological Survey. 2002. Guidelines for Evaluating the Hazard of Surface Fault Rupture, California Geological
Survey Note 49.
Cetin, K. O., R. B. Seed, A. Der Kiureghian, K. Tokimatsu, L. F. Harder, R. E. Kayen, and R. E. S. Moss. 2004. “Standard
Penetration TestBased Probabilistic and Deterministic Assessment of Seismic Soil Liquefaction Potential,” ASCE/SEI
Journal of Geotechnical and Geoenvironmental Engineering, 130(12).
Chang, C. Y., M. S. Power, C. M. Mok, Y. K. Tang, and H. T. Tang. 1990. “Analysis of Dynamic Lateral Earth Pressures
Recorded on Lotung Reactor Containment Model Structure,” in Proceedings, Fourth U.S. National Conference on
Earthquake Engineering. EERI, Oakland, California.Das, B. M. 1983. Fundamentals of Soil Dynamics. Elsvier, New
York, New York.
Dobry, R, R. S. Ladd, F. Y. Yokel, R. M. Chung, and D. Powell. 1982. “Prediction of Pore Water Pressure Buildup and
Liquefaction of Sands During Earthquakes by the Cyclic Strain Method,” National Bureau of Standards Building Science
Series 138. NIST, Gaithersburg, Maryland.
Duku, P. M., J. P. Stewart, D. H. Whang, and E. Yee. 2008. “Volumetric Strains of Clean Sands Subject to Cyclic Loads,”
ASCE/SEI Journal of Geotechnical and Geoenvironmental Engineering,134(8).
Ebeling, R. M., and E. E. Morrison. 1992. The Seismic Design of Waterfront Retaining Structures, Technical Report ITL
9211. U.S. Army Corps of Engineers Waterways Experiment Station, Vicksburg, Mississippi.
Elms, D. A., and G. R. Martin. 1979. “Factors Involved in the Seismic Design of Bridge Abutments,” in Proceedings of the
Workshop on Seismic Problems Related to Bridges. Applied Technology Council, Redwood City, California.
Franklin, A. G., and F. K. Chang. 1977. "Earthquake Resistance of Earth and RockFill Dams; Permanent Displacements of
Earth Embankments by Newmark Sliding Block Analysis," Miscellaneous Paper S7117, Report 5. U.S. Army Corps of
Engineers Waterways Experiment Station, Vicksburg, Mississippi.
Goodman, R. E., and H. B. Seed. 1966. “Earthquakeinduced Displacements in Sand Embankments,” ASCE/SEI Journal of
Soil Mechanics and Foundation, 92(SM2).
Hart, E. W., and W. A. Bryant. 1997 (revised). Faultrupture Hazard Zones in California, Special Publication 42.
California Department of Conservation, Division of Mines and Geology (now California Geological Survey).
Hanson, K. L., K. I. Kelson, M. A. Angell, and W. R. Lettis. 1999. Techniques for Identifying Faults and Determining Their
Origin, NUREG/CR5503. U.S. Nuclear Regulatory Commission.
Hynes, M. E., and A. G. Franklin. 1984. "Rationalizing the Seismic Coefficient Method," Miscellaneous Paper GL8413.
U.S. Army Corps of Engineers Waterways Experiment Stations, Vicksburg, Mississippi.
Idriss, I. M. 1985. “Evaluating Seismic Risk in Engineering Practice” in Proceedings of the 11th International Conference
on Soil Mechanics and Foundation Engineering, Vol. 1, p. 155.
Idriss, I. M., and R. W. Boulanger. 2004. “Semiempirical Procedures for Evaluating Liquefaction Potential During
Earthquakes,” in Proceedings of the 11th International Conference on Soil Dynamics and Earthquake Engineering, and 3rd
International Conference on Earthquake Geotechnical Engineering, Vol. 1, pp 3256. Stallion Press, Hawthorne, California.
Idriss, I. M., and R. W. Boulanger. 2008. Soil Liquefaction During Earthquakes, Monograph MNO12. Earthquake
Engineering Research Institute, Oakland, California.
Idriss, I. M., and R. W. Boulanger. 2007. “SPT and CPTbased Relationships for the Residual Shear Strength of Liquefied
Soils,” Earthquake Geotechnical Engineering, edited by K. D. Titilakis,
Idriss, I. M., and R. W. Boulanger. 2006. ”Semiempirical Procedures for Evaluating Liquefaction Potential During
Earthquakes,” Soil Dynamic and Earthquake Engineering, 26: 115130.
Ishihara, Kenji. 1985. “Stability of Natural Deposits during Earthquakes” in Proceedings of the 11th International
Conference on Soil Mechanics and Foundation Engineering, Vol. 1, pp. 321376.
Ishihara, K., and M. Yoshimine. 1992. “Evaluation of Settlements in Sand Deposits Following Liquefaction During
Earthquakes,” Soils and Foundations, JSSMFE, 32(1).
Itasca Consulting Group. 1997. User’s Manual for FLAC, V. 3.4. Itasca, Minneapolis, Minnesota.
Jibson, R. W., and M. W. Jibson. 2003. Java Programs for Using Newmark’s Method and Simplified Decoupled Analysis to
Model Slope Performance During Earthquakes, U.S. Geological Survey OpenFile Report 03005, Version 1.0.
Jibson, R. W. 1993. “Predicting EarthquakeInduced Landslide Displacements Using Newmark’s Sliding Block Analysis,”
in EarthquakeInduced Ground Failure Hazards, Transportation Research Record, No. 1411. Transportation Research
Board. National Research Council, Washington, D.C.
Kagawa, T., M. Sata, C. Minowa, A. Abe, and T. Tazoh. 2004. “Centrifuge Simulations of LargeScale Shaking Table
Tests: Case Studies,” ASCE/SEI Journal of Geotechnical and Geoenvironmental Engineering, 130(7).
Kelson, K. I., K.H. Kang, W. D. Page, C.T. Lee, and L. S. Cluff. 2001. “Representative styles of deformation along the
Chelungpu fault from the 1999 ChiChi (Taiwan) Earthquake: Geomorphic characteristics and responses of manmade
structures,” Bulletin of the Seismological Society of America, 91(5): 930952.
Kramer, S. L. 1996. Geotechnical Earthquake Engineering. Prentice Hall, New Jersey.
Kramer, S. L., and R. T. Mayfield. 2007. “Return Period of Soil Liquefaction.” ASCE/SEI Journal of Geotechnical and
Geoenvironmental Engineering, 133(7).
Lam, I., and G. R. Martin. 1986. Seismic Design of Highway Bridge Foundations  Design Procedures and Guidelines,
Report FHWA/RD86/102. Federal Highway Administration, Washington, D.C.
Liu, A. H., J. P. Stewart, N. A. Abrahamson, and Y. Moriwaki. 2001. “Equivalent Number of Uniform Stress Cycles for Soil
Liquefaction Analysis,” ASCE/SEI Journal of Geotechnical and Geoenvironmental Engineering, 127(12).
Makdisi, F. T., and H. B. Seed. 1978. “Simplified Procedure for Estimating Dam and Embankment EarthquakeInduced
Deformations.” ASCE/SEI Journal of Geotechnical Engineering, 104(GT7).
Martin, G. R., and P. Qiu. 1994. "Effects of Liquefaction on Vulnerability Assessment," NCEER Highway Project on
Seismic Vulnerability of New and Existing Highway Construction, One Year Research Tasks – Technical Research Papers.
NCEER, State University of New York, Buffalo.
Martin, G. R., and M. Lew. 1999. Recommended Procedures for Implementation of DMG SpecialTechnical Publication
117, Guidelines for Analyzing and Mitigating Liquefaction in California. Southern California Earthquake Center, University
of Southern California.
Monobe, N., and H. Matsuo. 1929. “On the Determination of Earth Pressures During Earthquakes” in Proceedings, World
Engineering Congress.
Moss, R. E. S., R. B. Seed, R. E. Kayen, J P. Stewart, A. Der Kiureghian, and K. O. Cetin. 2006. “CPTBased Probabilistic
and Deterministic Assessment of In Situ Seismic Soil Liquefaction Potential,” ASCE/SEI Journal of Geotechnical and
Geoenvironmental Engineering, 132(8).
Nadim, F. 1980. “Tilting and Sliding of Gravity Retaining Walls,” MS thesis, Department of Civil Engineering,
Massachusetts Institute of Technology, Cambridge.
Nadim, F., and R. V. Whitman. 1984. “Coupled Sliding and Tilting of Gravity Retaining Walls During Earthquakes” in
Proceedings of the Eighth World Conference on Earthquake Engineering, pp. 477484. National Center for Earthquake
Engineering Research (NCEER). 1997. Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of
Soils, Technical Report NCEER970022. NCEER, State University of New York, Buffalo.
National Research Council, Committee on Earthquake Engineering. 1985. Liquefaction of Soils during Earthquakes.
National Academy Press, Washington, D.C.
Newmark, N. M. 1965. “Effects of Earthquakes on Dams and Embankments,” Geotechnique (London, England), 5(2).
Okabe, S. 1926. “General Theory of Earth Pressure,” Journal of the Japan Society of Civil Engineers, 12(1).
Olson, S. M., and C. I. Johnson. 2008. “Analyzing LiquefactionInduced Lateral Spreads Using Strength Ratios,”
ASCE/SEI Journal of Geotechnical and Geoenvironmental Engineering, 134(8).
Olson, S. M., and T. D. Stark. 2002. “Liquefied Strength Ratio from Liquefaction Flow Failure Case Histories,” Canadian
Geotechnical Journal, 39(June).
Ostadan, F. 2005. “Seismic Soil Pressure for Building Walls – an Updated Approach,” Journal of Soil Dynamics and
Earthquake Engineering, 25: 785793; also published in Proceedings of the 11th International Conference on Soil Dynamics
and Earthquake Engineering and 3rd International Conference on Earthquake Geotechnical Engineering, University of
California, Berkeley, 2004.
Ostadan, F., and W. H. White. 1998. “Lateral Seismic Soil Pressure  An Updated Approach,” in Preproceedings of UJNR
Workshop on SoilStructures Interaction, U.S. Geological Survey, Menlo Park, California.
Plaxis. 2008. Plaxis Dynamics – A 2Dimensional Program for Evaluating Response of SoilStructure Systems to
Earthquake Loading, Plaxis BV, The Netherlands.
Prakash, S. 1981. Soil Dynamics. McGrawHill Book Co., New York, New York.
Prakash, S., Y. Wu, and E. A. Rafnsson. 1995. Displacement Based Aseismic Design Charts for Rigid Walls. Shamsher
Prakash Foundation, Rolla, Missouri.
Rathje, E. M., and G. Saygili. 2008. “Probabilistic Seismic Hazard Analysis for the Sliding Displacement of Slopes: Scalar
and Vector Approaches,” ASCE/SEI Journal of Geotechnical and Geoenvironmental Engineering, 134(6).
Rausch, A. F., and J. M. Martin. 2000. “EPOLLS Model for Predicting Average Displacement on Lateral Spreads,”
ASCE/SEI Journal of Geotechnical and Geoenvironmental Engineering, 126(4).
Richards, R. J., and D. Elms. 1979. “Seismic Behavior of Gravity Retaining Walls,” ASCE/SEI Journal of the Geotechnical
Engineering Division, 105(GT4).
Richards, R., K. L. Fishman, and R. Devito. 1996. “Threshold Accelerations for Rotation or Sliding of Bridge Abutments,”
ASCE/SEI Journal of Geotechnical Engineering, 105(GT4).
Saygili, G., and E. M. Rathje. 2008. “Empirical Predictive Models for EarthquakeInduced Sliding Displacements of
Slopes,” ASCE/SEI Journal of Geotechnical and Geoenvironmental Engineering, 134(6).
Seed, H. B., and I. M. Idriss. 1971. “Simplified Procedure for Evaluating Soil Liquefaction Potential,” Journal of the
ASCE/SEI Soil Mechanics and Foundations Division, 97(SM9).
Seed, H. B., K. Tokimatsu, L. F. Harder, and R. M. Chung. 1985. The Influence of SPT Procedures in Soil Liquefaction
Resistance Evaluations, Report UBC/EERC84/15. Earthquake Engineering Research Center, Berkeley, California.
Seed, H. B., and I. M. Idriss. 1982. Ground Motions and Soil Liquefaction During Earthquakes, Vol. 5 of Engineering
Monographs on Earthquake Criteria, Structural Design, and Strong Motion Records. Earthquake Engineering Research
Institute, El Cerrito, California.
Seed, H. B., and R. V. Whitman. 1970. “Design of Earth Retaining Structures for Dynamic Loads,” in Proceedings,
ASCE/SEI Specialty Conference on Lateral Stresses in the Ground and Design of EarthRetaining Structures, pp. 103147.
Cornell University, Ithaca, New York.
Seed, R. B., and L. F. Harder. 1990. “SPTBased Analysis of Cyclic Pore Pressure Generation and Undrained Residual
Strength,” in Proceedings of the H. Bolton Seed Memorial Symposium, Vol. 2, BiTech Publishers, Ltd, Vancouver, pp. 351
376.
Siddarthan, R., S. Ara, and G. Norris. 1992. “Simple Rigid Plastic Model for Seismic Tilting of Rigid Walls,” ASCE/SEI
Journal of Structural Engineering, Vol. 118, No. 2, pp. 469487.
Slemmons, D. B., and C. M. dePolo. 1986. “Evaluation of Active Faulting and Associated Hazards,” in Studies in
Geophysics  Active Tectonics, pp. 4562. National Academy Press, Washington, D.CSoydemir, C., and M. Celebi. 1992.
“Seismic Design of Buildings with MultiLevel Basements,” in Proceedings, Tenth World Conference on Earthquake
Engineering, Madrid, Spain, Vol. 6, Balkema, Rotterdam, pp. 17311734.
Steedman, R. S., and X. Zeng. 1996. “Rotation of Large Gravity Retaining Walls on Rigid Foundations Under Seismic
Loading,” in Analysis and Design of Retaining Walls Against Earthquakes, ASCE/SEI Geotechnical Special Publication 60,
edited by S. Prakash, pp. 3856. ASCE, Reston, Virginia.
Stewart, J. P., T. M. Blake, and R. A. Hollingsworth. 2003. “A Screen Analysis Procedure for Seismic Slope Stability,”
Earthquake Spectra, 19(3).
Swan, F. H., J. C. Stepp, and R. K. McGuire. 1991. “Assessment of the Potential for Tectonic Fault Rupture for HighLevel
Nuclear Waste Repositories,” Quarterly Journal of Engineering Geology, 24: 337346.
Tokimatsu, K., and H. B. Seed. 1987. “Evaluation of Settlements in Sands Due to Earthquake Shaking,” ASCE/SEI Journal
of Geotechnical Engineering, 113(8).
U.S. Army Corps of Engineers. 2005. Design: Seismic Design for Buildings, Unified Facilities Criteria, UFC 331003A,
formerly TI80904 (1998), Appendix F, Geologic Hazards Evaluations.
Utah Section of the Association of Engineering Geologists. 1987. Guidelines for Evaluating Surface Fault Rupture Hazard
in Utah, Utah Geological and Mineral Survey Miscellaneous Publication N.
Veletsos, A., and A. H. Younan. 1994a. “Dynamic Soil Pressure on Rigid Vertical Walls,” Earthquake Engineering and
Soil Dynamics, 23: 275301.
Veletsos, A. and A. H. Younan. 1994b. “Dynamic Modeling and Response of SoilWall Systems,” ASCE/SEI Journal of
Geotechnical Engineering, 120(12).
Wells, D. L., and K. J. Coppersmith. 1994. "New Empirical Relationships Among Magnitude, Rupture Area, and Surface
Displacement," Bulletin of the Seismological Society of America, 84: 9741002.
Whitman, R. V. 1991. “Seismic Design of Earth Retaining Structures,” in Proceedings, Second International Conference on
Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, Missouri.
Whitman, R. V., and S. Liao. 1985. Seismic Design of Retaining Walls, Miscellaneous Paper GL851. U.S. Army Corps of
Engineers Waterways Experiment Station, Vicksburg, Mississippi.
Wong, C. P., and R. V. Whitman. 1982. "Seismic Analysis and Improved Seismic Design Procedure for Gravity Retaining
Walls," Research Report 8283. Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge.
Wood, J. H. 1973. EarthquakeInduced Soil Pressures on Structures, Report EERL 7305. California Institute of
Technology, Pasadena.
Youd, T. L. 1989. “Ground Failure Damage to Buildings during Earthquakes,” in Foundation Engineering  Current
Principles and Practices, Vol. 1, pp. 758770. American Society of Civil Engineers, Reston, Virginia.
Youd, T. L., and C. T. Garris. 1995. “LiquefactionInduced Ground Surface Disruption,” ASCE/SEI Journal of
Geotechnical Engineering, 121(11).
Youd, T. L., and S. K. Noble. 1997. “Magnitude Scaling Factors,” in Proceedings of the NCEER Workshop on Evaluation
of Liquefaction Resistance of Soils, pp. 149165. National Center for Earthquake Engineering Research, State University of
New York, Buffalo.
Youd, T. L., C. M. Hansen, and S. F. Bartlett. 2002. “Revised Multilinear Repression Equations for Prediction of Lateral
Spread Displacement,” ASCE, Journal of Geotechnical and Geoenvironmental Engineering, 128(12).
Youd, T. L., I. M. Idriss, R. D. Andrus, I. Arango, G. Castro, J. T. Christian, R. Dobry, W. Finn, D. L. Harder, Jr., M. E.
Hynes, K. Ishihara, J. P. Koester, S. S. C. Liao, W. F. Marcuson III, G. R. Martin, J. K. Mitchell, Y Moriwaki, M. S. Power,
P. K. Robertson, R. B. Seed, and K. H. Stokoe II. 2001. “Liquefaction Resistance of Soils: Summary Report from the 1996
NCEER and 1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils,” ASCE/SEI Journal of
Geotechnical Geoenvironmental Engineering, 127(10).
Youngs, R. R., W. J. Arabasz, R. E. Anderson, A. R. Ramelli, J. P. Ake, D. B. Slemmons, J. P. McCalpin, D. I. Doser, C. J.
Fridrich, F. H. Swan III, A. M. Rogers, J. C. Yount, L. W. Anderson, K. D. Smith, R. L. Bruhn, P. L. K. Kneupfer, R. B.
Smith, C. M. dePolo, D. W. O’Leary, K. J. Coppersmith, S. K. Pezzopane, D. P. Schwartz, J. W. Whitney, S. S. Olig, and G.
R. Toro. 2003. “A Methodology for Probabilistic Fault Displacement Hazard Analysis (PFDHA),” Earthquake Spectra,
19(1).
Zhang, G., P. K. Robertson, and R. W. I. Brachman. 2004. “Estimating LiquefactionInduced Lateral Displacements Using
the Standard Penetration Test of Cone Penetration Test,” ASCE Journal of Geotechnical and Geoenvironmental Engineering,
130(8).
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Resource Paper 13
LIGHTFRAME WALL SYSTEMS
WITH WOOD STRUCTURAL PANEL SHEATHING
This resource paper provides commentary on shear wall design, performance, and the state of practice for seismicforceresisting
systems using lightframe walls with wood structural panel sheathing as recognized in ASCE/SEI 705 (ASCE/SEI
7) Table 12.21, Items A13 and B23. This commentary is intended to supplement existing applicationoriented commentary
provided by the applicable American Iron and Steel Institute (AISI) and American Forest and Paper Association (AF&PA)
standards and is being provided with the intent that applicable portions be integrated into relevant standards or other design
guidance documents.
GLOBAL STRENGTH, DRIFT, AND DUCTILITY
Wood and coldformed steel (CFS) lightframe structures using wood structural panel shear walls for seismic resistance rely
on a significant level of ductility and displacement capacity in addition to strength. Vertical elements of the lateralforceresisting
system will often have strengthlevel (LRFD) calculated deflections of between 0.5 and 0.75 percent of the story
height under the designbased earthquake (DBE), implying an expected real interstory drift (du) on the order of 2 to 3 percent
of the story height for the DBE and more for the risktargeted maximum considered earthquake (MCER). Although nonlinear
timehistory analysis, laboratory shake table testing (wood lightframe systems), and observed building performance suggest
this level of drift can occur, all three also indicate that drifts can be substantially less (Cecotti and Karacabeyli, 2002;
Christovasilis et. al., 2007; CUREE, 2001a, 2001b, 2002a, 2002b, and 2002c; Pryor et al., 2000). This wide variation in
response is primarily attributable to the added strength and stiffness of finish materials on both the interior and exterior of the
structure as well as other sources of redundancy. Several shake table studies have underscored this contribution of finish
material (CUREE, 2001b; Christovasilis et al., 2007). Testing and analysis of structures with finishes included have also
shown a tendency for drifts in multistory lightframe buildings to be concentrated in the lowest story which is typically the
softest and weakest.
ELEMENTS IN THE LATERALFORCERESISTING SYSTEM
Laboratory shake table testing and observed building performance to date indicate that the primary seismic response of lightframe
wood structural panel shear wall buildings is the inplane racking displacement of the wall elements while the
deformation demand on floor and roof diaphragms remains small. The few recorded instances of diaphragm failures in lightframe
buildings have involved irregularly shaped diaphragms with reentrant corners (CUREE, 2001a; Christovasilis et al.,
2007). Consequently, the walls are the structural elements that determine the seismic response characteristics of lightframe
shear wall buildings. Note that lightframe diaphragms can have a significant influence on the seismic behavior of concrete
and masonry shear wall buildings, which are beyond the scope of this paper.
Wood structural panel sheathed shear wall systems are intended to be designed in accordance with ASCE/SEI 705, AF&PA
Special Design Provisions for Wind and Seismic for wood construction, and AISI S21307, North American Standard for
ColdFormed Steel Framing – Lateral Design for CFS construction. Structural assemblies in lightframe construction are
formed by a system of closely spaced repetitive wood or coldformed steel (CFS) floor, roof, and wall framing members. In
wood structural panel shear wall systems, sheathing is most commonly installed in 4 foot by 8 to 10 foot sheets and fastened
to wall framing with nails, screws, or similar small diameter doweltype fasteners.
Seismic design in accordance with ASCE/SEI 7 anticipates cyclic loading of vertical shear wall elements in the inelastic
range, often to or beyond peak capacity. The primary source of drift and energy dissipation of woodframe shear walls is the
bending and yielding of the shear wall sheathing to framing fasteners around the perimeter of each sheathing panel
accompanied by slip between the sheathing and framing. In most woodframe shear walls, the racking of the wall causes
yielding of sheathing to framing fasteners, along with local crushing of the framing and sheathing due to fastener bearing. In
most CFS frame shear walls, the racking of the wall causes fastenerrelated bearing deformations along with dimpling of the
framing members. The sheathing in both wood and CFS walls rotates about its center of rigidity and the maximum number
of fasteners is engaged in resisting the lateral loads.
Addressed here are the combinations of sheathing and fastening currently included in the American Forest and Paper
Association (AF&PA) and American Iron and Steel Institute (AISI) standards. New combinations of sheathing and fastening
should be tested in reversecyclic loading; some combinations of sheathing materials and methods of attachment (such as
adhesive) have not shown similar ductility levels in laboratory tests. This paper also reflects the behavior of shear walls with
overturning restraint (tiedowns or similar) provided at each end as is common in an engineered structure; laboratory testing
of shear walls without overturning restraint has shown increases in deflection and reductions in strength (CUREE, 2004;
Dolan and Heine, 1997a and 1997b).
EFFECTS OF WALL FINISH MATERIALS
The effect of wall finish materials (gypsum wallboard, exterior stucco or siding, etc) on seismic performance varies with the
seismic demand level. The shake table testing of a fullscale townhouse building as part of the NEESWood benchmark
(Christovasilis et al., 2007) testing showed a significant influence of finish materials at a ground motion level of roughly 50
percent of the DBE, with resulting average interstory drift of approximately 0.75 percent. It is anticipated that the influence
of finish materials will be somewhat less for the full DBE with anticipated interstory drifts on the order of 3 to 4 percent. For
structures near collapse, estimated at approximately 7 percent interstory drift based on structures tested on Japan’s EDefense
table, it is thought that there is little contribution of finish materials left in the structure. Nonetheless, the inclusion of finish
materials in analytical studies for FEMA P695 (ATC, 2008) did improve the collapse margin to an acceptable level so wall
finish materials can improve performance. More study of the influence of finish materials is needed.
The NEESWood benchmark testing showed that the reduction of drift due to finish materials was greatest for gypsum
wallboard applied to walls detailed as shear walls (i.e., there was positive force transfer between the wall and the diaphragm
and overturning restraint was provided). When gypsum wallboard was applied to nonstructural partition walls not detailed
for force transfer from the diaphragms, the contribution was minimal. Several studies have also shown that stucco can be
very effective in reducing interstory drift demand whereas the NEESWood benchmark testing showed only a modest effect
from the stucco exterior finish.
When considering stucco as part of the seismicforceresisting system, there are several limiting issues. There is concern
over the longterm performance of the stucco since stucco in combination with building paper/barriers is the weather barrier
for the structure. Staples often are used to attach the lath to the studs, but staple legs do not have much thickness to resist
longterm corrosion. Galvanized or stainless steel staples would be more resistant to corrosion.
Finish materials such as gypsum wallboard and stucco have much lower displacement at peak capacity (around 0.5 to 1
percent of the story height) than the more ductile wood structural panel elements (1.5 to 5 percent of the story height). This
prevents a simple summation of capacities and complicates estimated performance. Although not directly considered in the
design, it seems clear that when a building is responding with interstory drifts on the order of 2 to 3 percent, well beyond the
peak capacity of the gypsum or stucco, those elements can provide important hysteretic damping to help attenuate the
movement of the structure. Similarly, CUREE shake table tests of a twostory woodframe house examined the effects of
fully sheathed walls (extra sheathing used in a segmented shear wall design above and below the openings). The shake table
tests of segmented walls without the horizontal segments had increased wall displacements by a factor of more than two,
suggesting that the sheathing above the below the openings has a significant effect on the performance of the structure
(CUREE, 2001b) .
While not directly addressed in the International Building Code (IBC), the effect of finishes can be considered qualitatively.
In contrast to moment frame construction, the mode shape of traditional lightframe multistory buildings tends to degrade to a
singledegreeoffreedom system as a story reaches its ultimate strength and deforms predominately in shear. As a result, the
majority of the displacement demand of the structure is concentrated in the weakest story. The other stories tend to remain in
the elastic range. Finishes, which tend to be more concentrated in upper stories, contribute to this behavior and tend to cause
significant displacement demand in the first story. Detailing of shear wall boundary members and anchorage connections is
vital to adequate seismic performance of the soft or weak story of a structure.
ANALYTICAL MODELING
In order to evaluate the distribution of design forces and drifts, a building analytical model in accordance with ASCE/SEI 7
Section 12.7.3, is needed. Generally, the analysis uses either the simplified alternative structural design criteria (ASCE/SEI
7, Section 12.14) or equivalent lateral force procedure (ASCE/SEI 7, Section 12.8). The primary analysis model includes
only those elements designated as structural shear walls and diaphragms.
Vertical distribution of forces should be in accordance with ASCE/SEI 7, which dictates a triangular (first mode) distribution
for buildings under the equivalent lateral force procedure and a rectangular distribution with a slight increase in base shear
under the simplified alternative structural design criteria.
Analytical modeling of the horizontal distribution of seismic forces at a theoretical level is based on the relative stiffness of
the diaphragms, shear walls, and any other force resisting elements. Horizontal distribution should be in accordance with
three categories identified in ASCE/SEI 7: diaphragms that are clearly very flexible relative to the vertical elements,
diaphragms that are clearly very rigid relative to the vertical elements, and everything else. For “everything else,” it is
required that a semirigid diaphragm model be used for distribution of horizontal seismic forces.
ASCE/SEI 7 includes an exception permitting one and twofamily residential buildings with diaphragms of wood structural
panel or untopped steel decking to be categorized as flexible. The simplified alternative structural design criteria of
ASCE/SEI 7, Section 12.14, also permits assumption of a flexible diaphragm force distribution for wood structural panel
diaphragms, untopped steel decking, or similar panelized construction (Section 12.4.5) with a small increase in base shear for
multistory buildings.
Other buildings braced by wood and CFS lightframe shear walls fall into the “everything else” category. For these other
buildings, one approach to meeting this requirement is evaluating force distribution using both rigid and flexible diaphragm
models and designing each shear wall and diaphragm for the worst case force. For this approach, the flexible diaphragm
model should be solved first, followed by an iterative rigid diaphragm distribution analysis.
Where nonuniform distribution of finish materials might trigger significant torsional behavior in the structure, additional
analytical study including the effects of finish materials should be considered.
ADHESIVE ATTACHMENT OF SHEATHING IN WOOD AND CFS LIGHTFRAME
BUILDINGS
Ductility in woodframe shear walls with wood structural panel sheathing is provided by the fasteners used to attach the
sheathing to the framing members. Testing has shown brittle failure when adhesives are used for this attachment in place of
mechanical fasteners. This is discussed further in Recommended Lateral Force Requirements and Commentary (SEAOC,
1999), Section C804.3. For this reason, the 2006 edition of IBC Section 2305.3.10 states: "Adhesive attachment of shear
wall sheathing is not permitted as a substitute for mechanical fasteners, and shall not be used in shear wall strength
calculations alone, or in combination with mechanical fasteners in Seismic Design Category D, E or F.” The 2005 edition of
AF&PA Special Design Provisions for Wind and Seismic (SDPWS) Section 4.3.6.3.1 states: "Adhesive attachment of shear
wall sheathing shall not be used alone, or in combination with mechanical fasteners." Both of these provisions address
adhesive attachment in woodframe shear walls.
To date, adhesives are not known to have been used for structural attachment of wood structural panel sheathing to CFS stud
walls. There is no discussion of adhesive attachment of CFS frame shear walls as of yet in either the IBC or AISI S213
(2007); however, a commentary note was added to AISI S213. Limited testing to date (Serrette, 2006) suggests some
similarities to the brittle behavior seen in woodframe shear walls with adhesives. For this reason, adhesive attachment to
CFS studs should not be undertaken without adequate study of seismic behavior.
SHEATHING FASTENERS FOR WOOD AND CFS LIGHTFRAME BUILDINGS
Overdriven Fasteners. Fasteners that are driven past the top of the sheathing have reduced bearing area on the sheathing.
Consequently, this can lead to a shear load reduction of sheathed assemblies. APA Technical Note TT012 states that no
reduction is required for woodsheathed shear walls or diaphragms when the fasteners are overdriven up to 1/16 in. under dry
conditions. In addition, no reduction is necessary if no more than 20 percent of the perimeter fasteners are driven between
1/16 and up to 1/8 inch. Also, an article entitled “Capacity of Oriented Strand Board Shear Walls with Overdriven Sheathing
Nails” reports on a testing program of overdriven oriented strand board (OSB) sheathing fasteners (Jones and Fonseca, 2002).
The 2001 Canadian code, CSA O86 Cl. 9.5.3.4 states: “Nails shall be firmly driven into framing members but shall not be
overdriven into sheathing. For structural woodbased sheathing, nails shall not be overdriven more than 15 percent of the
panel thickness.”
Significant reductions in strength have been observed in laboratory tests of CFS frame shear wall assemblies when the screw
sheathing fasteners are overdriven. This may be due to the countersunk screw head removing or damaging more of the wood
sheathing than an overdriven common sheathing nail. Additional testing is required to determine what effect overdriven
screw fasteners may have on shear strength for CFS frame shear wall assemblies.
Fastener Locations. The location of the sheathing fasteners affects the performance of shear wall assemblies. If the
sheathing fasteners are located too close to the panel edge, they may pull through the sheathing panel before the shear wall
assembly reaches its expected capacity. In addition, if the fasteners penetrate into the framing member too close to the
framing member’s edge or if the fasteners are spaced too close together, they may cause the wood framing member to split
before the assembly obtains the expected load.
Wood Framing Considerations. The AF&PA NDS Commentary (American Forest and Paper Association, 2005b) includes
spacing and edge distance recommendations for fasteners less than ¼ in. diameter used for wood framing. In addition, IBC
Section 2305.1.2.1 (ICC 2006) and SDPWS Section 4.3.7 require that fasteners not be placed less than 3/8 in. from the panel
edge. The IBC and AF&PA SDPWS woodframe shear wall table require a minimum of a 3 in. nominal framing member at
abutting panel edges and staggered placement of fasteners when fasteners are spaced at 2½ in. on center or closer or for 3 in.
on center spacing when 10d commons penetrate in the framing members more than 1½ in.
CFS Framing Considerations. AISI S100 (American Iron and Steel Institute, 2007b) includes spacing and edge distance
requirements for fasteners used for steeltosteel connections. AISI S213, Section C2.2, requires that fasteners be 3/8 in.
from the panel edge for all of the sheathing panels shown in the standard. The 2007 edition of AISI S21 incorporates a
Canadian provision requiring minimum of ½ in. edge distance for woodsheathed CFS frame shear wall assemblies based on
edge distance used in the testing.
Salenikovich (2000) tested walls with different edge distances for the sheathing fasteners and found that the strength/capacity
does not increase very much with increased edge distance, but the displacement capacity significantly increased and the
building as a whole is toughened (displacement and load cycling ability). The edge distance of the fasters along the bottom
of the wall (between the sheathing and the bottom plate of the wall framing) is especially important to achieve the toughening
effect.
HOLDDOWN CONNECTOR SLIP FOR WOOD AND CFS LIGHTFRAME BUILDINGS
The aspect ratio of the shear wall affects how much horizontal wall drift is due to vertical deflection of the holddown
connection. Higher aspect ratio shear wall assemblies are more sensitive to holddown connection slip or deformation. This
slip/deformationrelated drift is addressed in one part of the lightframe shear wall deflection equation that determines the
horizontal wall drift due to the vertical deflection of the holddown connection. Holddown deflection may be comprised of
fastener slip, device elongation/movement, and/or anchor bolt elongation.
COMBINATION OF MATERIALS FOR WOOD AND CFS LIGHTFRAME BUILDINGS
Combining shear walls that have different sheathing materials is not permitted by either the IBC or ASCE/SEI 7. It is
permitted to have one side opposite the wood sheathed side to be sheathed with gypsum board, and there are load values for
that combination of sheathing materials on opposite sides of the same shear wall assembly. This prohibition is due to the
difference in stiffness, strength, and performance of shear walls with different sheathing materials that, when combined, may
result in unexpected load distribution and failure. However, if the gypsum is to be used to resist the lateral forces in the
design, the walls included in the design must have the gypsum attached to the top and bottom plates of the wall framing.
This is not the typical attachment used by most drywall installers. The concept of floating corners has been recommended by
most drywall manufacturers to prevent cracking of the taped drywall walltoceiling joint. If floating corners are used, the
gypsum is totally ineffective in resisting any lateral loads unless the wall deformation causes the gypsum panel to bear on an
adjacent structural element (e.g., in a corner).
ASPECT RATIO FOR WOOD AND CFS LIGHTFRAME BUILDINGS
Shear wall aspect ratio also plays a role in the performance of lightframe shear wall assemblies. Although similar strength
may be observed for shear walls of different aspect ratios, with ratios over 2:1 flexural bending of the wall becomes more
dominant than shear/fastener deformation. Testing showed that these high aspect ratio walls are more flexible and will not
satisfy the required seismic drift limit performance objective without a reduction in design capacity and corresponding design
level drift. Therefore, a reduction factor, 2w/h, was implemented in the AF&PA standard for those shear wall assemblies
exceeding 2:1 but not exceeding 3.5:1. The same reduction is applied in the AISI standard for shear wall assemblies with
aspect ratios not exceeding 4:1. Also, it should be noted that as walls get narrower, it is crucial to ensure proper installation
of the shear wall components (e.g., holddown connections) since poor installation will lower the performance significantly
more (i.e., excessive top of wall drift) than would be seen by a lower aspect ratio wall.
WOOD MOISTURE ISSUES
Significant changes in moisture content (> 8 percent) can affect physical wood properties by swelling or shrinking wood
fibers which, in turn, can affect wood connections. Testing by APA shows that woodframe shear walls do not lose capacity
due to moisture changes; however, nail slip is increased and, thus, shear wall deflections increase (APA, 2002). To minimize
any negative effects of increased shear wall deflections, the designer should specify dry lumber or engineered wood products
(which are typically dry) for optimized structures.
WOOD FRAMING FORCES AND CONNECTIVITY
Tension Failures of Wood Posts. It is unusual for tension posts in walls to fail in tension if the only tension force is the
induced force associated with the racking and overturning of the wall segment itself. However, if the load path from upper
stories causes significant additional tension forces in the post, failure can occur through three possible mechanisms: net
section failure, combined bending and tension failure, and connection failure. Tension posts should be designed with checks
for all three failure mechanisms.
Compression Failure of Wood Posts. Compression failures in wood posts are typically associated with high compression
load due to accumulation of load due to load path considerations. The possible failure mechanisms are: traditional buckling
and beamcolumn action.
Buckling of the post is usually restricted to the outofplane direction of the wall because of the continuous support provided
by the sheathing in the plane of the wall. The designer must account for the entire load being supplied to the compression
post including the compression induced by the racking and overturning of the wall element itself plus the compression forces
being transferred to the post by the stories above and any headers attached to the post. Buckling of isolated, standalone
posts must be checked in both directions.
Weak Axis Bending of Wood Studs. Shear failures in studs have been observed in wall tests and field studies where strong
sheathing materials (e.g., stucco) fail at connections along the bottom of the wall. This causes the next row of fasteners from
the bottom of the wall to transfer all of the lateral loads into the studs, thus loading the studs in bending about their weak axis.
Typically, the failure occurs at about 1/3 the height of the stud.
Wood CrossGrain Bending. Crossgrain bending of wood members leads to failure at relatively low loads. Of particular
concern are locations where ledger boards are loaded perpendicular to their length and at shear wall foundation sill plates.
For ledgers, the connection between the diaphragm and the masonry or concrete wall should connect the longitudinal
diaphragm framing member (or a series of blocked joists) directly to the wall rather than to the ledger. In shear walls, wide
steel plate washers and stiff holddown connectors or straps should be used to reduce the crossgrain bending action.
Bearing Failure of Wood Plate. The failure of the bottom plate of the wall due to compression perpendicular to grain
causes damage to the wood member holding sheathing fasteners along the bottom of the wall. Added deformation of walls
with wood framing loaded perpendicular to grain at wood floor levels compared to walls located on slabsongrade has been
observed in testing and should be accounted for in analysis of drift. Guidance on this effect needs to be developed.
Sheathing Connectors to Wood Studs. The primary source of drift and energy dissipation of woodframe shear walls is the
bending and yielding of the shear wall sheathing to framing fasteners around the perimeter of each sheathing panel
accompanied by slip between the sheathing and framing. In most woodframe shear walls, the racking of the wall causes
yielding of sheathing to framing fasteners along with local crushing of the framing and sheathing due to fastener bearing.
Other common sheathing fastener behaviors include nail heads pulled through the sheathing and withdrawal of the nail from
the framing member. A less desirable behavior is the tearout of the fastener through the edge of the sheathing; increasing
the edge distance from the center of the fastener to the edge of the sheathing panel to not less than ½ in. can help to reduce
the occurrence of this behavior.
COLDFORMED STEEL MEMBER CONSIDERATIONS
Local Damage of Framing. The thinwalled nature (i.e., small thickness) of CFS framing members makes them vulnerable
to physical damage that may have an adverse effect on the structural performance (AISI S20007). Full damage assessment
is not within the scope of the AISI standards and, consequently, when damage alters the crosssection geometry of a framing
member beyond the specified tolerances, the designer should be consulted (American Iron and Steel Institute, 2007c).
Web Holes. As with any material, large holes may affect the structural performance of CFS framing members. Therefore,
CFS framing standards (AISI S20007) require that: “Holes in webs of studs, joists and tracks shall be in conformance with
an approved design, AISI S100, or an approved design standard. Webs with holes not conforming to the above shall be
reinforced or patched in accordance with an approved design or approved design standard.”
In CFS framing members, a “punchout” is defined as a hole made during the manufacturing process in the web of a steel
framing member (AISI S20007). Suitable dimensions and locations of standard punchouts are further defined (AISI S201
07; AISI, 2007d).
Nominal shear strengths for shear walls that have been included in industry design standards are based on tests with studs
with 1.5in. (38 mm) x 4in. (100 mm) punch outs at a centertocenter spacing of 24 inches (600 mm) and, as a result, the
use of studs with standard punch outs is permitted when using these values (AISI S21307).
Local Buckling of CFS Framing Members. CFS framing members are susceptible to local buckling when loaded in
compression. Consequently, local buckling is a necessary design consideration for CFS members. To that end, CFS framing
standards (AISI S21307) specify that: “The proportioning, design and detailing of coldformed steel lightframe systems,
members, connections and connectors … be in accordance with AISI S100.”
AISI S10007 considers local buckling of individual elements of CFS members as a major design criterion. As such, AISI
S10007 requires that the design of such members provide sufficient safety against the failure mode with due consideration to
postbuckling strength. Postbuckling strength of plate elements was identified experimentally in 1928. In order to utilize
the postbuckling strength for design purposes, AISI has used the effective design width approach to determine the section
properties since 1946.
The designer should pay particular attention to the buckling performance for collectors and headers that are acting as drag
struts. These members can have relatively high compression forces and must be designed for cyclic loading. The local
transfer of forces into wall or diaphragm elements also becomes an area where localized buckling can occur.
Bending Failure of CFS Framing Members. The difference in local buckling behavior between stiffened and unstiffened
elements results in a significant difference in the weak axis bending strength between stud and track members. Weak axis
bending strength of a track member is typically lower than that of a stud. This makes proper design and detailing of wall
anchorage important in order to minimize bending loads on track members. Connection of the anchorage device directly to
the chord stud is a common detail that effectively eliminates bending loads on track members.
Bending Deformation of CFS Track Web. CFS framing members offer limited strength and stiffness to resist transverse
concentrated loads such as would be applied by an anchor bolt with standard cut washer through the track web if used to
resist wall uplift forces. This is similar to the concern regarding cross grain bending in a wood bottom plate with a similar
anchorage detail.
Consequently, the AISI CFS framing standards (AISI S21307) require that: “Studs or other vertical boundary members at
the ends of wall segments, that resist seismic loads, braced with either sheathing or diagonal braces, … be anchored such that
the bottom track is not required to resist uplift by bending of the track web.”
Connection of the anchorage device directly to the chord stud is the most common detail that effectively eliminates transverse
concentrated loads on track members. Use of a Cshape section (i.e., stud) reinforcement or a plate washer at anchor bolts are
other ways to distribute transverse concentrated loads that may avoid this problem.
CFS Sheathing Connectors. As with woodframe shear walls, in CFS shear walls inelastic behavior is primarily
concentrated at the fasteners connecting the sheathing to the wallframing members. However, the behavior of sheathing
screw fasteners in CFS framing members is different from the behavior of sheathing nails in wood framing.
Nguyen et al. (1996) report: “In general, racking of the wall resulted in the screw fasteners rocking (tilting) about the plane
of the stud flange material immediately around the screw. This behavior resulted in permanent lateral deflection of the wall
and appears to be the main source of energy dissipation in the walls. As the lateral displacement of the wall increased, the
panel pulled over the screw heads and became unzipped.”
Screw size must be sufficient to preclude the screw shear failure mode. Thus, the screw size needs to be properly matched
with framing member thickness to assure the desired behavior. The AISI CFS framing standards (AISI S21307) require
that: “Unless noted as (min.), substitution of a stud or track of a different designation thickness is not permitted.”
For CFS framing, AISI S20007 indicates: “Ends of structural wall studs shall have square end cuts and shall be seated tight
against the tracks. For the purpose of this section, seated tight shall mean that a maximum gap tolerance of 1/8 inch (3.2 mm)
will be acceptable between the end of wall framing member and the track.” The CFS framing end gap does not adversely
affect strength, but it is likely to contribute to system flexibility and shear wall deflection.
Testing has shown that a smaller gap tolerance may be suitable in some situations. For instance, testing of thicker materials
(greater than 0.054 in.) showed that “the relative movement between the stud and track could result in shear failure of the
screws.” In these cases, a smaller gap tolerance of 1/16 in. (1.6 mm) may be more appropriate. AISI S20007 further
indicates: “a smaller gap tolerance may also be desirable in multistory structures where the accumulation of these gap
closures may become significant. Depending on track radius, it may be necessary to oversize the depth of the track to assure
that the stud flanges do not prematurely engage the track radius and result in an excessive gap.”
The designer should take the above into consideration when calculating shear wall deflections by considering the effect of the
end gap in the fourth term of the deflection equation (i.e., lateral contribution from anchorage/holddown deformation)(AISI
S21307).
PullOut Resistance of CFS Screw Fasteners. The pullout resistance of screw fasteners may be reduced when the
fasteners are cyclically loaded (Mahendran and Maharaachchi, 2000). Consequently, CFS framing standards (AISI S21307)
require that: “The pullout resistance of screws … not be used to resist seismic forces.”
REFERENCES
American Forest and Paper Association. 2005a. Special Design Provisions for Wind and Seismic with Commentary
(SDPWS), 2005 edition. AF&PA, Washington, D.C.
American Forest and Paper Association. 2005b. National Design Specification for Wood Construction. AF&PA,
Washington, D.C.
APAThe Engineered Wood Association. 2002. Effect of green Lumber Framing on Wood Structural Panel Shear Wall
Performance, Report T200253. APA, Tacoma, Washington.
American Iron and Steel Institute. 2007a. North American Standard for ColdFormed Steel Framing – Lateral Design,
S21307. AISI, Washington, D.C.
American Iron and Steel Institute. 2007b. North American Specification for the Design of ColdFormed Steel Structural
Members, S10007. AISI, Washington, D.C.
American Iron and Steel Institute. 2007c. North American Standard for ColdFormed Steel Framing – General Provisions,
S20007. AISI, Washington, D.C.
American Iron and Steel Institute. 2007d. North American Standard for ColdFormed Steel Framing – Product Data, S201
07, AISI S20107. AISI, Washington, D.C.
American Society of Civil Engineers. 2005. Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 705.
ASCE, Reston, Virginia.
Applied Technology Council. 2008. Recommended Methodology for Quantification of Building System Performance and
Response Parameters: ATC 63 90 percent draft, FEMA P695. Federal Emergency Management Agency, Washington, D.C.
Building Seismic Safety Council. 2003. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and
Other Structures, FEMA 450. Federal Emergency Management Agency, Washington, DC.
Cecotti, A., and E. Karacabeyli. 2002. “Validation of Seismic Design Parameters for Woodframe Shearwall Systems,”
Canadian Journal of Civil Engineering, 29: 484498. National Research Council, Ottawa, Canada.
Christovasilis, I. P., A. Filiatrault,, and A. Wanitkorkul. 2007. Seismic Testing of a FullScale TwoStory LightFame
Building: NEESWood Benchmark Test, Report NW01. Prepared as part of the NEESWood Project, Development of a
PerformanceBased Seismic Design Philosophy for MidRise Woodframe Construction,
www.engr.colostate.edu/NEESWood.
Canadian Standards Association. 2001. Engineering Design in Wood, CAN/CSAO86. Canadian Standards Association,
Mississauga, Ontario, Canada.
Consortium of Universities for Research in Earthquake Engineering. 2001a. Woodframe Project Case Studies, CUREE W
04. CUREE, Richmond, California.
Consortium of Universities for Research in Earthquake Engineering. 2001b. Shake Table Tests of a TwoStory Woodframe
House, CUREE W06. CUREE, Richmond, California.
Consortium of Universities for Research in Earthquake Engineering. 2002a. Northridge Earthquake Field Investigations:
Statistical Analysis of Woodframe Damage, CUREE W09. CUREE, Richmond, California.
Consortium of Universities for Research in Earthquake Engineering. 2002b. Seismic Modeling of Woodframe Index
Buildings, CUREE W12. CUREE, Richmond, California.
Consortium of Universities for Research in Earthquake Engineering. 2002c. Seismic Evaluation on an Asymmetric Three
Story Woodframe Buildings, CUREE W19. CUREE, Richmond, California.
Consortium of Universities for Research in Earthquake Engineering. 2004. Recommendations for Earthquake Resistance in
the Design and Construction of Woodframe Buildings, CUREE W30. CUREE, Richmond, California.
Dolan, J. D., and C. P. Heine. 1997a. Monotonic Tests of Woodframe Shear Walls with Various Openings and Base
Restraint Configurations, Timber Engineering Center Report TE1997001. Virginia Polytechnic Institute and State
University, Blacksburg
Dolan, J. D., and C. P. Heine. 1997b. Sequential Phased Displacement Cyclic Tests of Woodframe Shear Walls with
Various Openings and Base Restraint Configurations, Timber Engineering Center Report TE1997002. Virginia
Polytechnic Institute and State University, Blacksburg.
International Code Council. 2006. International Building Code (IBC), 2006 edition. ICC, Country Club Hills, Illinois.
Jones, Scott N., and Fernando S. Fonesca. 2002. “Capacity of Oriented Strand Board Shear Walls with Overdriven
Sheathing Nails,” ASCE/SEI Journal of Structural Engineering, 128(7)..
Mahendran, M., and D. Maharaachchi. 2000. “Cyclic Pullout Strength of Steel Roof and Wall Cladding Systems” in
Proceedings of the 15th International Specialty Conference on ColdFormed Steel Structures, Department of Civil
Engineering University of MissouriRolla, Rolla.
Nguyen Hoang, Georg Hall, and Reynaud Serrette. 1996. Shear Wall Values for Lightweight Steel Framing. Santa Clara
University, Santa Clara, California.
Pryor, S., G. Taylor, and C. Ventura. 2000. “Seismic Testing and Analysis Program on High Aspect Ratio Wood Shear
Walls” in International Timber Engineering Conference 2000, Whistler, British Columbia, Canada.
Structural Engineers Association of California. 1999. Recommended Lateral Force Requirements and Commentary.
SEAOC, Sacramento, California.
Serrette, Reynaud. 2006. “ColdFormed Steel Frame Shear Walls Utilizing Structural Adhesives,” ASCE/SEI Journal of
Structural Engineering.
Salenikovich, A. 2000. The Racking Performance of LightFrame Shear Walls, dissertation submitted as partial fulfillment
of the requirements for Ph.D. at Virginia Tech, Blacksburg.