1 Structural Analysis: Example 1
Twelve-story Moment Resisting Steel Frame
2 Analysis of a 12-Story Steel Building
In Stockton, California
3 Building Description
• 12 Stories above grade, one level below grade
• Significant Configuration Irregularities
• Special Steel Moment Resisting Perimeter Frame
• Intended Use is Office Building
• Situated on Site Class C Soils
4 Analysis Description
• Equivalent Lateral Force Analysis (Section 12.8)
• Modal Response Spectrum Analysis (Section 12.9)
• Linear and Nonlinear Response History Analysis (Chapter 16)
5 Overview of Presentation
• Describe Building
• Describe/Perform steps common to all analysis types
• Overview of Equivalent Lateral Force analysis
• Overview of Modal Response Spectrum Analysis
• Overview of Modal Response History Analysis
• Comparison of Results
• Summary and Conclusions
6 Overview of Presentation
• Describe Building
• Describe/Perform steps common to all analysis types
• Overview of Equivalent Lateral Force analysis
• Overview of Modal Response Spectrum Analysis
• Overview of Modal Response History Analysis
• Comparison of Results
• Summary and Conclusions
7 Plan at First Level Above Grade
8 Plans Through Upper Levels
9 Section A-A
10 Section B-B
11 3-D Wire Frame View from SAP 2000
12 Perspective Views of Structure (SAP 2000)
13 Overview of Presentation
• Describe Building
• Describe/Perform steps common to all analysis types
• Overview of Equivalent Lateral Force analysis
• Overview of Modal Response Spectrum Analysis
• Overview of Modal Response History Analysis
• Comparison of Results
• Summary and Conclusions
14 Seismic Load Analysis: Basic Steps
1. Determine Occupancy Category (Table 1-1)
2. Determine Ground Motion Parameters:
• SS and S1 USGS Utility or Maps from Ch. 22)
• Fa and Fv (Tables 11.4-1 and 11.4-2)
• SDS and SD1 (Eqns. 11.4-3 and 11.4-4)
3. Determine Importance Factor (Table 11.5-1)
4. Determine Seismic Design Category (Section 11.6)
5. Select Structural System (Table 12.2-1)
6. Establish Diaphragm Behavior (Section 11. 3.1)
7. Evaluate Configuration Irregularities (Section 12.3.2)
8. Determine Method of Analysis (Table 12.6-1)
9. Determine Scope of Analysis [2D, 3D] (Section 12.7.2)
10.Establish Modeling Parameters
15 Determine Occupancy Category
16 Ground Motion Parameters for Stockton
17 Determining Site Coefficients
18 Determining Design Spectral Accelerations
• SDS=(2/3)FaSS=(2/3)x1.0x1.25=0.833
•
• SD1=(2/3)FvS1=(2/3)x1.4x0.40=0.373
19 Determine Importance Factor, Seismic Design Category
1 Seismic Design Category = D
2 I = 1.0
20 Select Structural System (Table 12.2-1)
Building height (above grade) = 18+11(12.5)=155.5 ft
Select Special Steel Moment Frame: R=8, Cd=5.5, W0=3
21 Establish Diaphragm Behavior and Modeling Requirements
1 12.3.1 Diaphragm Flexibility.
The structural analysis shall consider the relative stiffness of diaphragms and the vertical elements of the seismic force–resisting system. Unless a diaphragm can be idealized as either flexible or rigid in accordance with Sections 12.3.1.1, 12.3.1.2, or 12.3.1.3, the structural analysis shall explicitly include consideration of the stiffness of the diaphragm (i.e., semi-rigid modeling assumption).
12.3.1.2 Rigid Diaphragm Condition.
Diaphragms of concrete slabs or concrete filled metal deck with span-to-depth ratios of 3 or less in
structures that have no horizontal irregularities are permitted to be idealized as rigid.
2 Due to horizontal irregularities (e.g. reentrant corners) the diaphragms must be modeled as semi- rigid. This will be done by using Shell elements in the SAP 2000 Analysis.
22 Determine Configuration Irregularities
Horizontal Irregularities
Irregularity 2 occurs on lower levels. Irregularity 3 is possible but need not be evaluated because it has same consequences as irregularity 3. Torsional Irregularities will be assessed later.
23 Determine Configuration Irregularities
Vertical Irregularities
Irregularities 2 and 3 occur due to setbacks. Soft story and weak story irregularities are highly unlikely for this system and are not evaluated.
24 Selection of Method of Analysis (ASCE 7-05)
ELF is not permitted:
Must use Modal Response Spectrum or Response History Analysis
25 Selection of Method of Analysis (ASCE 7-10)
ELF is not permitted:
Must use Modal Response Spectrum or Response History Analysis
26 Overview of Presentation
• Describe Building
• Describe/Perform steps common to all analysis types
• Overview of Equivalent Lateral Force analysis
• Overview of Modal Response Spectrum Analysis
• Overview of Modal Response History Analysis
• Comparison of Results
• Summary and Conclusions
27 Comments on use of ELF for This System ELF is NOT allowed as the Design Basis Analysis. However, ELF (or aspects of ELF) must be used for:
• Preliminary analysis and design
• Evaluation of torsion irregularities and amplification
• Evaluation of system redundancy factors
• Computing P-Delta Effects
• Scaling Response Spectrum and Response History results
28 Determine Scope of Analysis
1 12.7.3 Structural Modeling.
A mathematical model of the structure shall be constructed for the purpose of determining member forces and structure displacements resulting from applied loads and any imposed displacements or
P-Delta effects.
The model shall include the stiffness and strength of elements that are significant to the distribution of forces and deformations in the structure and represent the spatial distribution of mass and stiffness throughout the structure.
2 Note: P-Delta effects should not be included directly in the analysis. They are considered indirectly in Section 12.8.7
29 Determine Scope of Analysis
(Continued)
1 Continuation of 12.7.3:
Structures that have horizontal structural irregularity Type 1a, 1b, 4, or 5 of Table 12.3-1 shall be analyzed using a 3-D representation.
Where a 3-D model is used, a minimum of three dynamic degrees of freedom consisting of translation in two orthogonal plan directions and torsional rotation about the vertical axis shall be included at each level of the structure.
Where the diaphragms have not been classified as rigid or flexible in accordance with Section
12.3.1, the model shall include representation of the diaphragm’s stiffness characteristics and such additional dynamic degrees of freedom as are required to account for the participation of the diaphragm in the structure’s dynamic response.
2 Analysis of structure must be in 3D, and diaphragms must be modeled as semi-rigid
30 Establish Modeling Parameters
Continuation of 12.7.3:
•
In addition, the model shall comply with the following:
•
a)Stiffness properties of concrete and masonry elements shall consider the effects of cracked sections.
b)For steel moment frame systems, the contribution of panel zone deformations to overall story drift shall be included.
31 Modeling Parameters used in Analysis
1) The floor diaphragm was modeled with shell elements, providing nearly rigid behavior in-plane.
•
2) Flexural, shear, axial, and torsional deformations were included in all columns and beams.
•
3) Beam-column joints were modeled using centerline dimensions. This approximately accounts for deformations in the panel zone.
•
4) Section properties for the girders were based on bare steel, ignoring composite action. This is a reasonable assumption in light of the fact that most of the girders are on the perimeter of the building and are under reverse curvature.
(continued)
5) Except for those lateral load-resisting columns that terminate at Levels 5 and 9, all columns of the lateral load resisting system were assumed to be fixed at their base.
6) The basement walls and grade level slab were explicitly modeled using 4-node shell elements. This was necessary to allow the interior columns to continue through the basement level. No additional lateral restraint was applied at the grade level, thus the basement level acts as a very stiff first floor of the structure. This basement level was not relevant for the ELF analysis, but did influence the MRS and MRH analysis as described in later sections of this example
•
7) P-Delta effects were not included in the mathematical model. These effects are evaluated separately using the procedures provided in section 12.8.7 of the Standard.
33 Equivalent Lateral Force Analysis
1. Compute Seismic Weight, W (Sec. 12.7.2)
2. Compute Approximate Period of Vibration Ta (Sec. 12.8.2.1)
3. Compute Upper Bound Period of Vibration, T=CuTa (Sec. 12.8.2)
4. Compute “Analytical” Natural periods
5. Compute Seismic Base Shear (Sec. 12.8.1)
6. Compute Equivalent Lateral Forces (Sec. 12.8.3)
7. Compute Torsional Amplification Factors (Sec. 12.8.4.3)
8. Determine Orthogonal Loading Requirements (Sec. 12.8)
9. Compute Redundancy Factor (Sec. 12.3.4)
10.Perform Structural Analysis
11.Check Drift and P-Delta Requirements (Sec. 12.9.4 and 12.9.6)
12.Revise Structure in Necessary and Repeat Steps 1-11 [as appropriate]
13.Determine Design-Level Member Forces (Sec. 12.4)
34 Notes on Computing the Period of Vibration
Ta (Eqn.12.8-7) is an approximate lower bound period, and is based on the measured response of buildings in high seismic regions.
T=CuTa is also approximate, but is somewhat more accurate than Ta alone because it is based on the “best fit” of the
measured response, and is adjusted for local seismicity. Both of these adjustments are contained in the Cu term.
CuTa can only be used if an analytically computed period, called Tcomputed herein, is available from a computer analysis
of the structure.
35 Using Empirical Formulas to Determine Ta
36 Adjusted Empirical Period T=CuTa
37 Use of Rayleigh Analysis to Determine Tcomputed
38 Use of Rayleigh Analysis to Determine Tcomputed
X-Direction Tcomputed = 2.85 sec. Y-Direction Tcomputed = 2.56 sec.
39 Periods Computed Using Eigenvalue Analysis
40 Range of Periods Computed for This Example
Ta=1.59 sec
•
CuTa=2.23 sec
•
Tcomputed = 2.87 sec in X direction
2.60 sec in Y direction
•
41 Periods of Vibration for Computing
Seismic Base Shear
(Eqns 12.8-1, 12.8-3, and 12.8-4)
if Tcomputed is not available use Ta
if Tcomputed is available, then:
• if Tcomputed > CuTa use CuTa
• if Ta <= Tcomputed <= CuTa use Tcomputed
• if Tcomputed < Ta use Ta
42 Area and Line Weight Designations
43 Area and Line Weight Values
44 Weights at Individual Levels
45 Calculation of ELF Base Shear
46 Concept of Reffective
47 Issues Related to Period of Vibration and Drift
12.8.6.1 Minimum Base Shear for Computing Drift
The elastic analysis of the seismic force-resisting system for computing drift shall be made using the prescribed seismic design forces of Section 12.8.
EXCEPTION: Eq. 12.8-5 need not be considered for computing drift
12.8.6.2 Period for Computing Drift
For determining compliance with the story drift limits of Section 12.12.1, it is permitted to determine the elastic drifts, (?xe), using seismic design forces based on the computed fundamental period of the structure without the upper limit (CuTa) specified in Section 12.8.2.
48 Using Eqns. 12.8-3 or 12.8-5 for Computing ELF Displacements
49 What if Equation 12.8-6 had
Controlled Base Shear?
This equation represents the “true” response spectrum shape for near-field ground motions. Thus, the lateral forces developed on the basis of this equation must be used for determining component design forces and displacements used for computing drift.
50 When Equation 12.8-5 May Control
Seismic Base Shear (S1 < 0.6g)
51 When Equation 12.8-6 May Control
Seismic Base Shear (S1 >= 0.6g)
52 Calculation of ELF Forces
53 Calculation of ELF Forces (continued)
54 Inherent and Accidental Torsion
1 12.8.4.1 Inherent Torsion. For diaphragms that are not flexible, the distribution of lateral forces at each level shall consider the effect of the inherent torsional moment, Mt , resulting from eccentricity between the locations of the center of mass and the center of rigidity. For flexible diaphragms, the distribution of forces to the vertical elements shall account for the position and distribution of the masses supported.
2 Inherent torsion effects are automatically included in 3D structural analysis, and member forces associated with such effects need not be separated out from the analysis.
55 Inherent and Accidental Torsion
(continued)
12.8.4.2 Accidental Torsion. Where diaphragms are not flexible, the design shall include the
inherent torsional moment (Mt ) (kip or kN) resulting from the location of the structure masses plus the accidental torsional moments (Mta ) (kip or kN) caused by assumed displacement of the center of mass each way from its actual location by a distance equal to 5 percent of the dimension of the structure perpendicular to the direction of the applied forces.
•
Where earthquake forces are applied concurrently in two orthogonal directions, the required 5 percent displacement of the center of mass need not be applied in both of the orthogonal directions at the same time, but shall be applied in the direction that produces the greater effect.
56 Inherent and Accidental Torsion
(continued)
57 Determine Configuration Irregularities
Horizontal Irregularities
58 Application of Equivalent Lateral Forces
(X Direction)
59 Application of Torsional Forces
(Using X-Direction Lateral Forces)
60 Stations for Monitoring Drift for
Torsion Irregularity Calculations
with ELF Forces Applied in X Direction
61 Results of Torsional Irregularity Calculations
For ELF Forces Applied in X Direction
Result: There is not a Torsional Irregularity for Loading in the X Direction
62 Results of Torsional Irregularity Calculations
For ELF Forces Applied in Y Direction
Result: There is a minor Torsional Irregularity for Loading in the Y Direction
63 Results of Torsional Amplification Calculations
For ELF Forces Applied in Y Direction
(X Direction Results are Similar)
Result: Amplification of Accidental Torsion Need not be Considered
64 Drift and Deformation
65 Drift and Deformation (Continued)
66 Drift and Deformation (Continued)
67 Computed Drifts in X Direction
68 Computed Drifts in Y Direction
69 P-Delta Effects
P-Delta Effects for modal response spectrum analysis and modal response history analysis are checked using the ELF procedure indicated on this slide.
70 P-Delta Effects
71 Orthogonal Loading Requirements
1 12.5.4 Seismic Design Categories D through F. Structures assigned to Seismic Design Category D, E, or F shall, as a minimum, conform to the requirements of Section 12.5.3.
12.5.3 Seismic Design Category C. Loading applied to structures assigned to Seismic Design Category C shall, as a minimum, conform to the requirements of Section 12.5.2 for Seismic Design Category B and the requirements of this section. Structures that have horizontal structural irregularity Type 5 in Table 12.3-1 shall the following procedure [for ELF Analysis]:
2 Continued on Next Slide
72 Orthogonal Loading Requirements
(continued)
Orthogonal Combination Procedure. The structure shall be analyzed using the equivalent lateral force analysis procedure of Section 12.8 with the loading applied independently in any two orthogonal directions and the most critical load effect due to direction of application of seismic forces on the structure is permitted to be assumed to be satisfied if components and their foundations are designed for the following combination of prescribed loads: 100 percent of the forces for one direction plus 30 percent of the forces for the perpendicular direction; the combination requiring the maximum component strength shall be used.
73 ASCE 7-05 Horizontal Irregularity Type 5
1 Nonparallel Systems-Irregularity is defined to exist where the vertical lateral force-resisting elements are not parallel to or symmetric about the major orthogonal axes of the seismic force– resisting system.
The system in question clearly has nonsymmetrical lateral force resisting elements so a Type 5
Irregularity exists, and orthogonal combinations are required. Thus, 100%-30% procedure given on the previous slide is used.
2 Note: The words “or symmetric about” have been removed from the definition of a Type 5
Horizontal Irregularity in ASCE 7-10. Thus, the system under consideration does not have a Type 5 irregularity in ASCE 7-10.
•
74 16 Basic Load Combinations used in ELF Analysis (Including Torsion)
75 Combination of Load Effects
76 Redundancy Factor
12.3.4.2 Redundancy Factor, ?, for Seismic Design Categories D through F. For structures assigned to Seismic Design Category D, E, or F, ? shall equal 1.3 unless one of the following two conditions
is met, whereby ? is permitted to be taken as 1.0:
a)Each story resisting more than 35 percent of the base shear in the direction of interest shall comply with Table 12.3-3.
b)Structures that are regular in plan at all levels provided that the seismic force–resisting systems consist of at least two bays of seismic force–resisting perimeter framing on each
side of the structure in each orthogonal direction at each story resisting more than 35 percent of the base shear. The number of bays for a shear wall shall be calculated as the length of shear wall divided by the story height or two times the length of shear wall divided by the story height for
light framed construction.
77 Redundancy, Continued
1 TABLE 12.3-3 REQUIREMENTS FOR EACH STORY RESISTING MORE THAN 35% OF THE BASE SHEAR
•
Moment Frames Loss of moment resistance at the beam-to-column connections at both ends of a single beam would not result in more than a 33% reduction in story strength, nor does the resulting system have an extreme torsional irregularity (horizontal structural irregularity Type 1b).
2 It can be seen by inspection that removal of one beam in this structure will not result in a result in a significant loss of strength or lead to an extreme torsional irregularity. Hence ? = 1 for this system. (This is applicable to ELF, MRS, and MRH analyses).
78 Seismic Shears in Beams of Frame 1 from ELF Analysis
Seismic Shears in Girders, kips, Excluding Accidental Torsion
79 Seismic Shears in Beams of Frame 1 from ELF Analysis
Seismic Shears in Girders, kips, Accidental Torsion Only
80 Overview of Presentation
• Describe Building
• Describe/Perform steps common to all analysis types
• Overview of Equivalent Lateral Force analysis
• Overview of Modal Response Spectrum Analysis
• Overview of Modal Response History Analysis
• Comparison of Results
• Summary and Conclusions
81 Modal Response Spectrum Analysis
Part 1: Analysis
1. Develop Elastic response spectrum (Sec. 11.4.5)
2. Develop adequate finite element model (Sec. 12.7.3)
3. Compute modal frequencies, effective mass, and mode shapes
4. Determine number of modes to use in analysis (Sec. 12.9.1)
5. Perform modal analysis in each direction, combining each direction’s results by use of CQC method (Sec. 12.9.3)
6. Compute Equivalent Lateral Forces (ELF) in each direction (Sec. 12.8.1
through 12.8.3)
7. Determine accidental torsions (Sec 12.8.4.2), amplified if necessary
(Sec. 12.8.4.3)
8. Perform static Torsion analysis
82 Modal Response Spectrum Analysis
Part 2: Drift and P-Delta for Systems Without Torsion Irregularity
1 1. Multiply all dynamic displacements by Cd/R (Sec. 12.9.2).
2. Compute SRSS of interstory drifts based on displacements at center of
mass at each level.
3. Check drift Limits in accordance with Sec. 12.12 and Table 12.2-1.
Note: drift Limits for Special Moment Frames in SDC D and above must be divided by the Redundancy Factor (Sec. 12.12.1.1)
4. Perform P-Delta analysis using Equivalent Lateral Force procedure
5. Revise structure if necessary
6.
2 Note: when centers of mass of adjacent levels are not vertically aligned the drifts should be based on the difference between the displacement at the upper level and the displacement of the point on the level below which is the vertical projection of the center of mass of the upper level. (This procedure is included in ASCE 7-10.)
83 Modal Response Spectrum Analysis
Part 2: Drift and P-Delta for Systems With Torsion Irregularity
1. Multiply all dynamic displacements by Cd/R (Sec. 12.9.2).
2. Compute SRSS of story drifts based on displacements at the
edge of the building
3. Using results from the static torsion analysis, determine the drifts at the same location used in Step 2 above. Torsional drifts
may be based on the computed period of vibration (without the
CuTa limit). Torsional drifts should be based on computed displacements multiplied by Cd and divided by I.
4. Add drifts from Steps 2 and 3 and check drift limits in Table 12.12-1.
Note: Drift limits for special moment frames in SDC D and above must be divided by the Redundancy Factor (Sec. 12.12.1.1)
5. Perform P-Delta analysis using Equivalent Lateral Force procedure
6. Revise structure if necessary
84 Modal Response Spectrum Analysis
Part 3: Obtaining Member Design Forces
1. Multiply all dynamic force quantities by I/R (Sec. 12.9.2)
2. Determine dynamic base shears in each direction
3. Compute scale factors for each direction (Sec. 12.9.4) and apply to respective member force results in each direction
4. Combine results from two orthogonal directions, if necessary (Sec. 12.5)
5. Add member forces from static torsion analysis (Sec. 12.9.5). Note that static torsion forces may be scaled by factors obtained in Step 3
6. Determine redundancy factor (Sec. 12.3.4)
7. Combine seismic and gravity forces (Sec. 12.4)
8. Design and detail structural components
85 Mode Shapes for First Four Modes
86 Mode Shapes for Modes 5-8
87 Number of Modes to Include
in Response Spectrum Analysis
12.9.1 Number of Modes
An analysis shall be conducted to determine the natural modes of vibration for the structure. The analysis shall include a sufficient number of modes to obtain a combined modal mass participation of at least 90 percent of the actual mass in each of the orthogonal horizontal directions of response considered by the model.
88 Effective Masses for First 12 Modes
12 Modes Appears to be Insufficient
89 Effective Masses for Modes 108-119
118 Modes Required to Capture Dynamic Response of Stiff Basement Level and Grade Level Slab
90 Effective Masses for First 12 Modes
12 Modes are Actually Sufficient to Represent the Dynamic Response of the Above Grade Structure
91 Inelastic Design Response Spectrum Coordinates
92 Scaling of Response Spectrum Results (ASCE 7-05)
1 12.9.4 Scaling Design Values of Combined Response.
A base shear (V) shall be calculated in each of the two orthogonal horizontal directions using the calculated fundamental period of the structure T in each direction and the procedures of Section
12.8, except where the calculated fundamental period exceeds (Cu )(Ta), then (Cu )(Ta) shall be used in lieu of T in that direction. Where the combined response for the modal base shear (Vt) is less than 85 percent of the calculated base shear (V) using the equivalent lateral force procedure, the forces, but not the drifts, shall be multiplied by
•
•
•
where
• V = the equivalent lateral force procedure base shear, calculated in accordance with this section and Section 12.8
• Vt = the base shear from the required modal combination
2 Note: If the ELF base shear is governed by Eqn. 12.5-5 or 12.8-6 the force V shall be based on the value of Cs calculated by Eqn. 12.5-5 or 12.8-6, as applicable.
93 Scaling of Response Spectrum Results (ASCE 7-10)
12.9.4.2 Scaling of Drifts
Where the combined response for the modal base shear (Vt) is less than 0.85 CsW, and where Cs
is determined in accordance with Eq. 12.8-6, drifts shall be multiplied by:
94 Scaled Static Torsions
Apply Torsion as a Static Load. Torsions can be Scaled to 0.85 times Amplified* EFL Torsions if the
Response Spectrum Results are Scaled.
* See Sec. 12.9.5. Torsions must be amplified because they are applied statically, not dynamically.
95 Method 1: Weighted Addition of
Scaled CQC’d Results
96 Method 2: SRSS of Scaled CQC’d Results
97 Computed Story Shears and Scale Factors from Modal Response Spectrum Analysis
98
99
100
101
102
103
X-Direction Scale Factor = 0.85(1124)/438.1=2.18
Y-Direction Scale Factor = 0.85(1124)/492.8=1.94
Response Spectrum Drifts in X Direction
(No Scaling Required)
Response Spectrum Drifts in Y Direction
(No Scaling Required)
Scaled Beam Shears from
Modal Response Spectrum Analysis
Overview of Presentation
• Describe Building
• Describe/Perform steps common to all analysis types
• Overview of Equivalent Lateral Force analysis
• Overview of Modal Response Spectrum Analysis
• Overview of Modal Response History Analysis
• Comparison of Results
• Summary and Conclusions
Modal Response History Analysis
Part 1: Analysis
1 1. Select suite of ground motions (Sec. 16.1.3.2)
2. Develop adequate finite element model (Sec. 12.7.3)
3. Compute modal frequencies, effective mass, and mode Shapes
4. Determine number of modes to use in analysis (Sec. 12.9.1)
5. Assign modal damping values (typically 5% critical per mode)
6. Scale ground motions* (Sec. 16.1.3.2)
7. Perform dynamic analysis for each ground motion in each direction
8. Compute Equivalent Lateral Forces (ELF) in each direction (Sec. 12.8.1 through 12.8.3)
9. Determine accidental torsions (Sec 12.8.4.2), amplified if necessary
(Sec. 12.8.4.3)
10.Perform static torsion analysis
2 *Note: Step 6 is referred to herein as Ground Motion Scaling (GM Scaling). This is to avoid confusion with Results Scaling, described later.
Modal Response History Analysis Part 2: Drift and P-Delta for Systems Without Torsion
Irregularity
1 1. Multiply all dynamic displacements by Cd/R (omitted in ASCE 7-05).
2. Compute story drifts based on displacements at center of mass
at each level
3. If 3 to 6 ground motions are used, compute envelope of story drift at each level in each direction (Sec. 16.1.4)
4. If 7 or more ground motions are used, compute average story drift at each level in each direction (Sec. 16.1.4)
5. Check drift limits in accordance with Sec. 12.12 and Table 12.2-1.
Note: drift limits for Special Moment Frames in SDC D and above must be divided by the Redundancy Factor (Sec. 12.12.1.1)
6. Perform P-Delta analysis using Equivalent Lateral Force procedure
7. Revise structure if necessary
2 Note: when centers of mass of adjacent levels are not vertically aligned the drifts should be based on the difference between the displacement at the upper level and the displacement of the point on
104
105
106
107
procedure is included in ASCE 7-10.)
Modal Response History Analysis Part 2: Drift and P-Delta for Systems With Torsion
Irregularity
1. Multiply all dynamic displacements by Cd/R (omitted in ASCE 7-05).
2. Compute story drifts based on displacements at edge of building
at each level
3. If 3 to 6 ground motions are used, compute envelope of story drift at each level in each direction (Sec. 16.1.4)
4. If 7 or more ground motions are used, compute average story drift at each level in each direction (Sec. 16.1.4)
5. Using results from the static torsion analysis, determine the drifts at the same location used in Steps 2-4 above. Torsional drifts may be based on the computed period of vibration (without the
CuTa limit). Torsional drifts should be based on computed displacements multiplied by Cd and divided by I.
6. Add drifts from Steps (3 or 4) and 5 and check drift limits in Table 12.12-1.
Note: Drift limits for special moment frames in SDC D and above must be divided by the Redundancy Factor (Sec. 12.12.1.1)
7. Perform P-Delta analysis using Equivalent Lateral Force procedure
8. Revise structure if necessary
Modal Response History Analysis
Part 3: Obtaining Member Design Forces
1 1. Multiply all dynamic member forces by I/R
2. Determine dynamic base shear histories for each earthquake in each direction
3. Determine Result Scale Factors* for each ground motion in each direction, and apply to response history results as appropriate
4. Determine design member forces by use of envelope values if 3 to 6 earthquakes are used, or as averages if 7 or more ground motions are used.
5. Combine results from two orthogonal directions, if necessary (Sec. 12.5)
6. Add member forces from static torsion analysis (Sec. 12.9.5). Note that static torsion forces may be scaled by factors obtained in Step 3
7. Determine redundancy factor (Sec. 12.3.4)
8. Combine seismic and gravity forces (Sec. 12.4)
9. Design and detail structural components
2 *Note: Step 3 is referred to herein as Results Scaling (GM Scaling). This is to avoid confusion with Ground Motion Scaling, described earlier.
Selection of Ground Motions for MRH Analysis
3D Scaling Requirements, ASCE 7-10
1 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 5 percent-damped response
spectra for the scaled components (where an identical scale factor is applied to both components of a pair). Each pair of motions shall be scaled such that in the period range from 0.2T to 1.5T, the average of the SRSS spectra from all horizontal component pairs does not fall below the corresponding ordinate of the response spectrum used in the design, determined in accordance
with Section 11.4.5.
2 ASCE 7-05 Version:
108
109
110
111
112
113
does not fall below 1.3 times the corresponding ordinate of the design response spectrum, determined in accordance with Section 11.4.5 by more than 10 percent.
3D ASCE 7 Ground Motion Scaling
Issues With Scaling Approach
• No guidance is provided on how to deal with different fundamental periods in the two orthogonal directions
• There are an infinite number of sets of scale factors that will satisfy the criteria. Different engineers are likely to obtain different sets of scale factors for the same ground motions.
• In linear analysis, there is little logic in scaling at periods greater than the structure’s fundamental period.
• Higher modes, which participate marginally in the dynamic response, may dominate the scaling process
Resolving Issues With Scaling Approach
No guidance is provided on how to deal with different fundamental periods in the two orthogonal directions:
1. Use different periods in each direction (not recommended)
2.
2. Scale to range 0.2 Tmin to 1.5 Tmax where Tmin is the lesser
of the two periods and Tmax is the greater of the fundamental
periods in each principal direction
3. Scale over the range 0.2TAvg to 1.5 TAvg where TAvg is the average of Tmin and Tmax
Resolving Issues With Scaling Approach
1 There are an infinite number of sets of scale factors that will satisfy the criteria. Different engineers are likely to obtain different sets of scale factors for the same ground motions.
2 Use Two-Step Scaling:
1] Scale each SRSS’d Pair to the Average Period
Resolving Issues With Scaling Approach
1 There are an infinite number of sets of scale factors that will satisfy the criteria. Different engineers are likely to obtain different sets of scale factors for the same ground motions.
2 Use Two-Step Scaling:
1] Scale each SRSS’d Pair to the Average Period
2] Obtain Suite Scale Factor S2
Resolving Issues With Scaling Approach
1 There are an infinite number of sets of scale factors that will satisfy the criteria. Different engineers are likely to obtain different sets of scale factors for the same ground motions.
2 Use Two-Step Scaling:
1] Scale each SRSS’d Pair to the Average Period
2] Obtain Suite Scale Factor S2
114
115
116
117
118
119
120
121
122
123
124
125
126
3] Obtain Final Scale Factors: Suite A: SSA=SA1 x S2
Suite B: SSB=SB1 x S2
Suite C: SSC=SC1 x S2
Ground Motions Used in Analysis
Unscaled Spectra
Average S1 Scaled Spectra
Ratio of Target Spectrum to Scaled SRSS Average Target Spectrum and SS Scaled Average Individual Scaled Components (00)
Individual Scaled Components (90) Computed Scale Factors
Number of Modes for
Modal Response History Analysis
1 ASCE 7-05 and 7-10 are silent on the number of modes to use in Modal
Response History Analysis. It is recommended that the same procedures
set forth in Section 12.9.1 for MODAL Response Spectrum Analysis be used for Response History
Analysis:
2 12.9.1 Number of Modes
An analysis shall be conducted to determine the natural modes of vibration for the structure. The analysis shall include a sufficient number of modes to obtain a combined modal mass participation of at least 90 percent of the actual mass in each of the orthogonal horizontal directions of response considered by the model.
Damping for
Modal Response History Analysis
ASCE 7-05 and 7-10 are silent on the amount of damping to use in Modal Response History
Analysis.
•
Five percent critical damping should be used in all modes considered in the analysis because the
Target Spectrum and the Ground Motion Scaling Procedures are based on 5% critical damping.
Scaling of Results for
Modal Response History Analysis (Part 1)
The structural analysis is executed using the GM scaled earthquake records in each direction. Thus, the results represent the expected elastic response of the structure. The results must be scaled to represent the expected inelastic behavior and to provide improved performance for important structures. ASCE 7-05 scaling is as follows:
1) Scale all component design forces by the factor (I/R). This is stipulated in Sec. 16.1.4 of ASCE
7-05 and ASCE 7-10.
2) Scale all displacement quantities by the factor (Cd/R). This requirement
was inadvertently omitted in ASCE 7-05, but is included in Section 16.1.4 of ASCE 7-10.
Response Scaling Requirements when
MRH Shear is Less Than Minimum Base Shear
Response Scaling Requirements when
MRH Shear is Greater Than Minimum Base Shear
127
128
129
130
131
132
133
134
135
136
137
138
Response Scaling Requirements when
MRH Shear is Greater Than Minimum Base Shear
12 Individual Response History Analyses Required
1.A00-X: SS Scaled Component A00 applied in X Direction
2.A00-Y: SS Scaled Component A00 applied in Y Direction
3.A90-X: SS Scaled Component A90 applied in X Direction
4.A90-Y: SS Scaled Component A90 applied in Y Direction
5.
5.B00-X: SS Scaled Component B00 applied in X Direction
6.B00-Y: SS Scaled Component B00 applied in Y Direction
7.B90-X: SS Scaled Component B90 applied in X Direction
8.B90-Y: SS Scaled Component B90 applied in Y Direction
9.
9.C00-X: SS Scaled Component C00 applied in X Direction
10.C00-Y: SS Scaled Component C00 applied in Y Direction
11.C90-X: SS Scaled Component C90 applied in X Direction
12.C90-Y: SS Scaled Component C90 applied in Y Direction
Result Maxima from Response History Analysis
Using SS Scaled Ground Motions
I/R Scaled Shears and Required 85% Rule
Scale Factors
Response History Drifts for all X-Direction Responses
Load Combinations for Response History Analysis
Envelope of Scaled Frame 1 Beam Shears from Response History Analysis
Overview of Presentation
• Describe Building
• Describe/Perform steps common to all analysis types
• Overview of Equivalent Lateral Force analysis
• Overview of Modal Response Spectrum Analysis
• Overview of Modal Response History Analysis
• Comparison of Results
• Summary and Conclusions
Comparison of Maximum X-Direction
Design Story Shears from All Analysis
Comparison of Maximum X-Direction
Design Story Drift from All Analysis
Comparison of Maximum Beam Shears from All Analysis
Overview of Presentation
• Describe Building
• Describe/Perform steps common to all analysis types
• Overview of Equivalent Lateral Force analysis
139
• Overview of Modal Response Spectrum Analysis
• Overview of Modal Response History Analysis
• Comparison of Results
• Summary and Conclusions
Required Effort
• The Equivalent Lateral Force method and the Modal Response Spectrum methods require similar levels of effort.
•
• The Modal Response History Method requires considerably more effort than ELF or MRS. This is primarily due to the need to select and scale the ground motions, and to run so many response history analyses.
140
141
142
Accuracy
It is difficult to say whether one method of analysis is “more accurate” than the others. This is because each of the methods assume linear elastic behavior, and make simple adjustments (using R and Cd) to account for inelastic behavior.
•
Differences inherent in the results produced by the different methods are reduced when the results are scaled. However, it is likely that the Modal Response Spectrum and Modal Response History methods are generally more accurate than ELF because they more properly account for higher mode response.
Recommendations for Future Considerations
1.Three dimensional analysis should be required for all Response Spectrum and
Response History analysis.
2.Linear Response History Analysis should be moved from Chapter 16 into Chapter
12 and be made as consistent as possible with the Modal Response Spectrum Method. For example, requirements for the number of modes and for scaling of results should be the same for the two methods.
3.A rational procedure needs to be developed for directly including Accidental Torsion in
Response Spectrum and Response History Analysis.
4.A rational method needs to be developed for directly including P-Delta effects in
Response Spectrum and Response History Analysis.
5.The current methods of selecting and scaling ground motions for linear response history analysis can be and should be much simpler than required for nonlinear response history analysis. The use of “standardized” motion sets or the use of spectrum matched ground motions should be considered.
6.Drift should always be computed and checked at the corners of the building.
Questions
Title
slide
Structural
Analysis:
Part
1 -1
This
example
demonstrates
three
linear
elastic
analysis
procedures
provided
by
ASCE
7-05:
Equivalent
Lateral
Force
analysis
(ELF),
Modal
Response
Spectrum
Analysis
(MRS),
and
Modal
Response
History
Analysis.
The
building
is
a
structural
steel
1 Example 2:
Six-story Moment Resisting Steel Frame
2 Description of Structure
• 6-story office building in Seattle, Washington
• Occupancy (Risk) Category II
• Importance factor (I) = 1.0
• Site Class = C
• Seismic Design Category D
• Special Moment Frame (SMF), R = 8, Cd = 5.5
3 Floor Plan and Gravity Loads
4 Elevation view and P-Delta Column
5 Member Sizes Used in N-S Moment Frames
? Sections meet the width-to-thickness requirements for special moment frames
? Strong column-weak beam
6 Equivalent Lateral Force Procedure
7 Equivalent Lateral Force Procedure
8 Computer Programs NONLIN-Pro and DRAIN 2Dx
Shortcomings of DRAIN
• It is not possible to model strength loss when using the ASCE 41-06 (2006) model for girder plastic hinges.
• The DRAIN model for axial-flexural interaction in columns is not particularly accurate.
• Only Two-Dimensional analysis may be performed.
•
Elements used in Analysis
• Type 1, inelastic bar (truss) element
• Type 2, beam-column element
• Type 4, connection element
•
•
9 Description of Preliminary Model
• Only a single frame (Frame A or G) is modeled.
• Columns are fixed at their base.
• Each beam or column element is modeled using a Type 2 element. For the columns, axial, flexural, and shear deformations are included. For the girders, flexural and shear deformations are included but, because of diaphragm slaving, axial deformation is not included. Composite action in the floor slab is ignored for all analysis.
• All members are modeled using centerline dimensions without rigid end offsets.
• This model does not provide any increase in beam-column joint stiffness due to the presence of doubler plates.
• The stiffness of the girders was decreased by 7% in the preliminary analyses, which should be a reasonable approximate representation of the 35% reduction in the flange sections. Moment rotation properties of the reduced flange sections are used in the detailed analyses.
10 Results of Preliminary Analysis : Drift
11 Results of Preliminary Analysis :
Demand Capacity Ratios (Columns-Girders)
12 Results of Preliminary Analysis : Demand Capacity Ratios (Panel Zones)
13 Results of Preliminary Analysis : Demand Capacity Ratios
• The structure has considerable overstrength, particularly at the upper levels.
• The sequence of yielding will progress from the lower level girders to the upper level girders.
• With the possible exception of the first level, the girders should yield before the columns. While not shown in the Figure, it should be noted that the demand-to-capacity ratios for the lower story columns were controlled by the moment at the base of the column. The column on the leeward (right) side of the building will yield first because of the additional axial compressive force arising from the seismic effects.
• The maximum DCR of girders is 3.475, while maximum DCR for panel zones without doubler plates is 4.339. Thus, if doubler plates are not used, the first yield in the structure will be in the panel zones. However, with doubler plates added, the first yield is at the girders as the maximum DCR of the panel zones reduces to 2.405.
•
14 Results of Preliminary Analysis: Overall System Strength
15 Results of Preliminary Analysis: Overall System Strength
• As expected, the strength under uniform load is significantly greater than under triangular or Standards load.
• The closeness of the Standards and triangular load strengths is due to the fact that the vertical-load-distributing parameter (k) was 1.385, which is close to 1.0.
• Slightly more than 15 percent of the system strength comes from plastic hinges that form in the columns. If the strength of the column is taken simply as Mp (without the influence of axial force), the “error” in total strength is less than 2 percent.
• The rigid-plastic analysis did not include strain hardening, which is an additional source of overstrength.
16 Description of Model Used for Detailed Structural Analysis
17 Description of Model Used for Detailed Structural Analysis
• Nonlinear static and nonlinear dynamic analyses require a much more detailed model than was used in the linear analysis.
• The primary reason for the difference is the need to explicitly represent yielding in the girders, columns, and panel zone region of the beam-column joints.
18 Plastic Hinge Modeling and Compound Nodes
• Compound nodes are used to model plastic hinges in girders and deformations in the panel zone region of beam-column joints
• Typically consist of a pair of single nodes with each node sharing the same point in space. The X and Y degrees of freedom of the first node of the pair (the slave node) are constrained to be equal to the X and Y degrees of freedom of the second node of the pair (the master node), respectively. Hence, the compound node has four degrees of freedom: an X displacement, a Y displacement, and two independent rotations.
19 Modeling of Beam-Column Joint Regions
20 Modeling of Beam-Column Joint Regions
Krawinkler model assumes that the panel zone has two resistance mechanisms acting in parallel:
1. Shear resistance of the web of the column, including doubler plates and
2. Flexural resistance of the flanges of the column.
3.
3.
3.
3.
3.
• Fy = yield strength of the column and the doubler plate,
• dc = total depth of column,
• tp = thickness of panel zone region = column web + doubler plate thickness,
• bcf = width of column flange,
• tcf = thickness of column flange, and
• db = total depth of girder.
21 Modeling of Beam-Column Joint Regions
22 Modeling Girders
• The AISC Seismic Design Manual (AISC, 2006) recommends design practices to force the plastic hinge forming in the beam away from the column.
•
1.Reduce the cross sectional properties of the beam at a specific location away from the column
2.Special detailing of the beam-column connection to provide adequate strength and toughness in the connection so that inelasticity will be forced into the beam adjacent to the column face.
23 Modeling Girders
24 Modeling Girders
25 Modeling Girders
26 Modeling Columns
27 Results of Detailed Analysis: Period of Vibration
• P-delta effects increases the period.
• Doubler plates decreases the period as the model becomes stiffer with doubler plates.
• Different period values were obtained from preliminary and detailed analyses.
• Detailed model results in a stiffer structure than the preliminary model especially when doubler plates are added.
28 Static Pushover Analysis
• Pushover analysis procedure performed in this example follows the recommendations of
ASCE/SEI 41-06.
• Pushover analysis should always be used as a precursor to nonlinear response history analysis.
• The structure is subjected to the full dead load plus 50 percent of the fully reduced live load, followed by the lateral loads.
• For the entire pushover analyses reported for this example, the structure is pushed to 37.5 in. at the roof level. This value is about two times the total drift limit for the structure where the total drift limit is taken as 2 percent of the total height.
• The effect of lateral load distribution, strong and weak panel zones (doubler plates) and P- delta are investigated separately in this example.
•
•
29 Static Pushover Analysis
Effect of Different Lateral Load Distribution
In this example, three different load patterns were initially considered:
UL = Uniform load (equal force at each level)
ML = Modal load (lateral loads proportional to first mode shape)
BL = Provisions load distribution (Equivalent lateral forces used for preliminary analysis)
•
30 Static Pushover Analysis
Effect of Different Lateral Load Distribution
31 Static Pushover Analysis
32 Static Pushover Analysis
Effect of Different Lateral Load Distribution
33 Static Pushover Analysis
Effect of P-Delta on Pushover Curve
34 Static Pushover Analysis
Effect of P-Delta on Pushover Curve
35 Static Pushover Analysis
Effect of Panel zones (Doubler Plates) on Pushover Curve
36 Static Pushover Analysis: Sequence and Pattern of Plastic Hinging with NonlinPro
37 Static Pushover Analysis
Sequence and Pattern of Plastic Hinging for Strong Panel Model
38 Static Pushover Analysis
DCR – Plastic Hinge Sequence Comparison for Girders and Columns
39 Static Pushover Analysis
DCR – Plastic Hinge Sequence Comparison for Panel Zones
40 Static Pushover Analysis
Sequence and Pattern of Plastic Hinging for Strong Panel Model
41 Static Pushover Analysis
Sequence and Pattern of Plastic Hinging for Weak Panel Model
42 Static Pushover Analysis
DCR – Plastic Hinge Sequence Comparison for Panel Zones
43 Static Pushover Analysis
Target Displacement
•
44 Static Pushover Analysis
This spectrum is for BSE-2 (Basic Safety Earthquake 2) hazard level which has a 2%
probability of exceedence in 50 years.
45 Static Pushover Analysis
• Nonlinear force-displacement relationship between base shear and displacement of control node shall be replaced with an idealized force-displacement curve. The effective lateral stiffness and the effective period depend on the idealized force-displacement curve.
• The idealized force-displacement curve is developed by using an iterative graphical procedure where the areas below the actual and idealized curves are approximately balanced up to a displacement value of . is the displacement at the end of second line segment of the idealized curve and is the base shear at the same displacement.
• should be a point on the actual force displacement curve at either the calculated target displacement, or at the displacement corresponding to the maximum base shear, whichever is the least.
• The first line segment of the idealized force-displacement curve should begin at the origin and finish at , where is the effective yield strength and is the yield displacement of idealized curve.
• The slope of the 1st line segment is equal to the effective lateral stiffness , which should be taken as the secant stiffness calculated at a base shear force equal to 60% of the effective yield strength of the structure.
46 Static Pushover Analysis
47 Static Pushover Analysis
• Story drifts are also shown at the load level of target displacement.
• Negative stiffness starts after target displacements for both models.
48 Response History Analysis
• Response response history analysis method is used to estimate the inelastic deformation demands for the detailed structure.
• Three ground motions were used. (Seven or more ground motions is generally preferable.)
• The analysis considered a number of parameters, as follows:
? Scaling of ground motions to the DBE and MCE level
? With and without P-delta effects
? Two percent and five percent inherent damping
? Added linear viscous damping
• Identical structural model used in Nonlinear Pushover Analyses and 2nd order effects were included through the use of leaning column.
• All of the model analyzed had “Strong Panels” (wherein doubler plated were included in the interior beam-column joints).
49 Response History Analysis
Rayleigh Damping
• Rayleigh proportional damping was used to represent viscous energy dissipation in the structure.
• The mass and stiffness proportional damping factors were initially set to produce 2.0 percent damping in the first and third modes.
• It is generally recognized that this level of damping (in lieu of the 5 percent damping that
is traditionally used in elastic analysis) is appropriate for nonlinear response history analysis.
50 Response History Analysis
• Because only a two-dimensional analysis of the structure is performed using DRAIN, only a single component of ground motion is applied at one time.
• For the analyses reported herein, the component that produced the larger spectral acceleration at the structure’s fundamental period was used.
• A complete analysis would require consideration of both components of ground motions, and possibly of a rotated set of components.
51 Response History Analysis
52 Response History Analysis
1.Each spectrum is initially scaled to match the target spectrum at the structure’s fundamental period.
2.
2.
2.
2.
2.
2.The average of the scaled spectra are re-scaled such that no ordinate of the scaled average spectrum falls below the target spectrum in the range of periods between 0.2 and 1.5T.
3.
3.
3.
3.
3.
3.
3.
3.The final scale factor for each motion consists of the product of the initial scale factor (different for each ground motion), and the second scale factor (which is the same for each ground motion).
53 Results of Response History Analysis
DBE Results for 2% Damped Strong Panel Model with P-D Excluded / P-D Included
MCE Results for 2% Damped Strong Panel Model with P-D Excluded / P-D Included
55 Results of Response History Analysis
56 Results of Response History Analysis
Energy Response History, Ground Motion A00 (DBE), including P-delta effects
57 Results of Response History Analysis
58 Response History Analysis
A00 Motion Ground Acceleration, Velocity and Displacement
59 Response History Analysis
A00 Motion tripartite Spectrum
60 Results of Response History Analysis
Yielding locations for structure with strong panels subjected to MCE scaled B90 motion, including P-delta effects
61 Results of Response History Analysis
Comparison with Results from Other Analyses
62 Results of Response History Analysis
Reasons of the differences between Pushover and Response History Analyses
• Scale factor of 1.367 was used for the 2nd part of the scaling procedure.
• The use of the first-mode lateral loading pattern in the nonlinear static pushover response.
• The higher mode effects shown in the Figure are the likely cause of the different hinging patterns and are certainly the reason for the very high base shear developed in the response history analysis.
63 Results of Response History Analysis
Effect of Increased Damping on Response
• Excessive drifts occur in the bottom three stories.
• Additional strength and/or stiffness should be provided at these stories.
• Considered next, Added damping is also a viable approach.
• Four different damper configurations were used.
• Dampers were added to the Strong Panel frame with 2% inherent damping.
• The structure was subjected to the DBE scaled A00 and B90 ground motions.
• P-delta effects were included in the analyses.
64 Modeling Added Dampers
• Added damping is easily accomplished in DRAIN by use of the stiffness proportional component of Rayleigh damping.
• Linear viscous fluid damping device can be modeled through use of a Type-1 (truss bar)
element.
•
•
•
•
•
• Set damper elastic stiffness to negligible value. = 0.001 kips/in.
Effect of Increased Damping on Response
Effect of different added damper configurations when SP model is subjected to DBE scaled
A00 motion, including P-delta effects
66 Results of Response History Analysis
Effect of Increased Damping on Response
Effect of different added damper configurations when SP model is subjected to DBE scaled
B90 motion, including P-delta effects
67 Results of Response History Analysis : Roof Displacements
68 Results of Response History Analysis: Energy Plots
69 Results of Response History Analysis: Energy Plots
70 Results of Response History Analysis: Base Shear
71 Results of Response History Analysis:
Deflected Shape of by NonlinPro for Added Damper Frame (4th combination) During B90 Motion
72 Summary and Conclusions
73 Questions?
In
this
example,
the
behavior
of
a
simple,
six-story
structural
steel
moment-resisting
frame
is
investigated
using
a
variety
of
analytical
techniques.
The
structure
was
initially
proportioned
using
a
preliminary
analysis,
and
it
is
this
preliminary
design
that
is
investigated.
The
analysis
will
show
that
the
structure
falls
short
of
several
performance
expectations.
In
an
attempt
to
improve
performance,
viscous
fluid
dampers
are
considered
for
use
in
the
structural
system.
Complete
details
for
the
analysis
are
provided
in
the
written
example,
and
the
example
should
be
used
as
the
“Instructors
Guide”
when
presenting
this
slide
set.
Many,
but
not
all
of
the
slides
in
this
set
have
“Speakers
Notes”,
and
these
are
intentionally
kept
very
brief.
Strustural
Analysis:
Part
2 -1
According
to
the
descriptions
in
ASCE
7-05
Table
1-1,
the
building
is
assigned
to
Occupancy
Category
II.
This
is
similar
to
Risk
Category
II
in
ASCE
7-10
Table
1.5-1.
From
ASCE
7-05
Table
11.5-1,
the
importance
factor
(I)
is
1.0.
Importance
factor
is
provided
in
Table
1.5-2
in
ASCE
7-10.
Ie
(seismic
importance
factor)
is
1.0
for
Risk
Category
II.
Site
classification
is
provided
in
Standard
Table
20.3-1.
Seismic
design
category
is
provided
in
Tables
11.6-1
and
11.6-2
in
Standard.
Response
modification
coefficient
(R),
overstrength
factor
(Oo),
and
deflection
amplification
factor
(Cd)
for
seismic
force-resisting
systems
are
provided
in
Table
12.2-1
in
Standard.
Strustural
Analysis:
Part
2 -2
The
lateral-load-resisting
system
consists
of
steel
moment-resisting
frames
on
the
perimeter
of
the
building.
There
are
five
bays
at
28
ft
on
center
in
the
N-S
direction
and
six
bays
at
30
ft
on
center
in
the
EW
direction.
The
lateral
load-resisting
system
consists
of
steel
moment-resisting
frames
on
the
perimeter
of
the
building.
For
the
moment-resisting
frames
in
the
N-S
direction
(Frames
A
and
G),
all
of
the
columns
bend
about
their
strong
axes,
and
the
girders
are
attached
with
fully
welded
moment-resisting
connections.
The
expected
plastic
hinge
regions
of
the
girders
have
reduced
flange
sections,
detailed
in
accordance
with
the
AISC
341-05
Seismic
Provisions
for
Structural
Steel
Buildings
(AISC,
2005a).
For
the
frames
in
the
E-W
direction
(Frames
1
and
6),
moment-resisting
connections
are
used
only
at
the
interior
columns.
At
the
exterior
bays,
the
E-W
girders
are
connected
to
the
weak
axis
of
the
exterior
(corner)
columns
using
non-momentresisting
connections.
All
interior
columns
are
gravity
columns
and
are
not
intended
to
resist
lateral
loads.
A
few
of
these
columns,
however,
would
be
engaged
as
part
of
the
added
damping
system
described
in
the
last
part
of
this
example.
With
minor
exceptions,
all
of
the
analyses
in
this
example
will
be
for
lateral
loads
acting
in
the
N-S
direction.
Analysis
for
lateral
loads
acting
in
the
E-W
direction
would
be
performed
in
a
similar
manner.
Strustural
Analysis:
Part
2 -3
The
typical
story
height
is
12
ft-6
in.
with
the
exception
of
the
first
story,
which
has
a
height
of
15
ft.
There
is
a
5-ft-tall
perimeter
parapet
at
the
roof
and
one
basement
level
that
extends
15
ft
below
grade.
For
this
example,
it
is
assumed
that
the
columns
of
the
moment
resisting
frames
are
embedded
into
pilasters
formed
into
the
basement
wall.
P-Delta
effects
are
modeled
using
the
leaner
“ghost”
column
shown
in
Figure
at
the
right
of
the
main
frame.
This
column
is
modeled
with
an
axially
rigid
truss
element.
P-Delta
effects
are
activated
for
this
column
only
(P-Delta
effects
are
turned
off
for
the
columns
of
the
main
frame).
The
lateral
degree
of
freedom
at
each
level
of
the
P-Delta
column
is
slaved
to
the
floor
diaphragm
at
the
matching
elevation.
Where
P-Delta
effects
are
included
in
the
analysis,
a
special
initial
load
case
was
created
and
executed.
This
special
load
case
consists
of
a
vertical
force
equal
to
one-half
of
the
total
story
weight
(dead
load
plus
50
percent
of
the
fully
reduced
live
load)
applied
to
the
appropriate
node
of
the
P-Delta
column.
Strustural
Analysis:
Part
2 -4
Prior
to
analyzing
the
structure,
a
preliminary
design
was
performed
in
accordance
with
the
AISC
Seismic
Provisions.
All
members,
including
miscellaneous
plates,
were
designed
using
steel
with
a
nominal
yield
stress
of
50
ksi
and
expected
yield
strength
of
55
ksi.
Detailed
calculations
for
the
design
are
beyond
the
scope
of
this
example.
The
sections
shown
in
Table
meet
the
width-to-thickness
requirements
for
special
moment
frames,
and
the
size
of
the
column
relative
to
the
girders
should
ensure
that
plastic
hinges
will
form
in
the
girders.
Due
to
strain
hardening,
plastic
hinges
will
eventually
form
in
the
columns.
However,
these
form
under
lateral
displacements
that
are
in
excess
of
those
allowed
under
the
Design
Basis
Earthquake
(DBE).
Doubler
plates
of
0.875
in.
thick
are
used
at
each
of
the
interior
columns
at
Levels
2
and
3,
and
1.00
in.
thick
plates
are
used
at
the
interior
columns
at
Levels
4,
5,
6,
and
R.
Doubler
plates
were
not
used
in
the
exterior
columns.
Strustural
Analysis:
Part
2 -5
Although
the
main
analysis
in
this
example
is
nonlinear,
equivalent
static
forces
are
computed
in
accordance
with
the
Section
12.8
of
the
Standard.
These
forces
are
used
in
a
preliminary
static
analysis
to
determine
whether
the
structure,
as
designed,
conforms
to
the
drift
requirement
limitations
imposed
by
Section
12.12
of
the
Standard.
For
the
purpose
of
analysis,
it
is
assumed
that
the
structure
complies
with
the
requirements
for
a
special
moment
frame,
which,
according
to
Standard
Table
12.21,
has
the
following
design
values:
R
=
8
Cd
=
5.5
Oo
=
3.0
Note
that
the
overstrength
factor
O0
is
not
needed
for
the
analysis
presented
herein.
In
Standard
section
12.8.6.2,
it
is
permitted
to
determine
the
elastic
drifts
using
seismic
design
forces
based
on
the
computed
fundamental
period
of
the
structure
without
the
upper
limit
on
calculated
approximate
period
(CuTa).
Thus,
a
new
set
of
lateral
forces
(
Vdrift
in
Figure)
were
calculated
and
elastic
drifts
were
found
using
these
forces.
Drift
limitations
of
Standard
Section
12.12
were
satisfied
with
the
amplified
drifts
(.drift
in
Figure)
found
with
these
new
set
of
lateral
forces.
Strustural
Analysis:
Part
2 -6
Vertical
distribution
of
lateral
forces
were
calculated
in
accordance
with
Standard
Section
12.8.3.
The
lateral
forces
acting
at
each
level
(Fx)
and
the
story
shears
(Vx)
at
the
bottom
of
the
story
below
the
indicated
level
are
summarized
in
the
table.
Note
that
these
are
the
forces
acting
on
the
whole
building.
Thus,
for
analysis
of
a
single
frame,
one-half
of
the
tabulated
values
are
used.
Strustural
Analysis:
Part
2 -7
Loss
of
strength
generally
occurs
at
plastic
hinge
rotations
well
beyond
the
rotational
demands
produced
under
the
DBE
ground
motions.
Maximum
plastic
rotation
angles
of
plastic
hinges
were
checked
with
the
values
in
Table
5-6
of
ASCE
41-06.
The
rules
employed
by
DRAIN
to
model
column
yielding
are
adequate
for
event-to-event
nonlinear
static
pushover
analysis,
but
leave
much
to
be
desired
where
dynamic
analysis
is
performed.
The
greatest
difficulty
in
the
dynamic
analysis
is
adequate
treatment
of
the
column
when
unloading
and
reloading.
Two
dimensional
analysis
is
reasonable
for
the
structure
considered
in
this
example
because
of
its
regular
shape
and
because
full
moment
connections
are
provided
only
in
the
N-S
direction
for
the
corner
columns.
Strustural
Analysis:
Part
2 -8
P-delta
effects
are
modeled
using
the
leaner
“ghost”
column
shown
which
is
laterally
constrained
to
the
main
frame,
as
explained
before.
Strustural
Analysis:
Part
2 -9
The
results
of
the
preliminary
analysis
for
drift
are
shown
in
Tables
for
the
computations
excluding
and
including
P-delta
effects,
respectively.
In
each
table,
the
deflection
amplification
factor
(Cd)
equals
5.5,
and
the
acceptable
story
drift
(story
drift
limit)
is
taken
as
2%
of
the
story
height
which
is
the
limit
provided
by
Standard
Table
12.12-1.
As
explained
before,
a
new
set
of
lateral
loads
based
on
the
computed
period
of
the
actual
structure
were
found
and
applied
to
the
structure
to
calculate
the
elastic
drifts.
When
P-delta
effects
are
included,
the
drifts
can
also
be
estimated
as
the
drifts
without
P-delta
times
the
quantity
1/(1-.),
where
.
is
the
stability
coefficient
for
the
story.
As
can
be
seen
in
bottom
Table,
back
calculated
drift
values
from .
are
fairly
consistent
with
the
real
results
obtained
by
running
the
analyses
with
P-delta
effects.
The
difference
is
always
less
than
2%.
Strustural
Analysis:
Part
2 -10
For
DCR
analysis,
the
structure
is
subjected
to
full
dead
load
plus
0.5
times
the
fully
reduced
live
load,
followed
by
equivalent
lateral
forces
found
without
R
factor.
Equivalent
lateral
forces
are
applied
towards
right
in
the
analyses.
P-delta
effects
are
included.
Since
the
DCRs
in
the
Figure
are
found
from
preliminary
analyses,
in
which
the
centerline
model
is
used,
doubler
plates
are
not
added
into
the
model.
For
girders,
the
DCR
is
simply
the
maximum
moment
in
the
member
divided
by
the
member’s
plastic
moment
capacity
where
the
plastic
capacity
is
ZeFye.
Ze
is
the
plastic
section
modulus
at
center
of
reduced
beam
section
and
Fye
is
the
expected
yield
strength.
For
columns,
the
ratio
is
similar
except
that
the
plastic
flexural
capacity
is
estimated
to
be
Zcol(Fye
-Pu/Acol)
where
Pu
is
the
total
axial
force
in
the
column.
The
ratios
are
computed
at
the
center
of
the
reduced
section
for
beams
and
at
the
face
of
the
girder
for
columns.
Strustural
Analysis:
Part
2 -11
The
values
in
parentheses
(in
blue)
represent
the
DCRs
without
doubler
plates.
The
maximum
DCR
values
with
and
doubler
plates
added
are
highlighted
in
the
Figure.
Since
the
DCRs
in
Figure
are
found
from
preliminary
analyses,
in
which
the
centerline
model
is
used,
doubler
plates
aren’t
added
into
the
model.
Thus,
the
demand
values
shown
in
the
Figure
are
the
same
with
and
without
doubler
plates.
However,
since
the
capacity
of
the
panel
zone
increases
with
added
doubler
plates,
the
DCRs
decrease
at
the
interior
beam
column
joints
as
the
doubler
plates
are
used
only
at
the
interior
joints.
As
may
be
seen
in
Figure,
the
DCR
at
the
exterior
joints
are
the
same
with
and
without
doubler
plates
added.
To
find
the
shear
demand
at
the
panel
zones,
the
total
moment
in
the
girders
(at
the
left
and
right
sides
of
the
joint)
is
divided
by
the
effective
beam
depth
to
produce
the
panel
shear
due
to
beam
flange
forces.
Then
the
column
shear
at
above
or
below
the
panel
zone
joint
was
subtracted
from
the
beam
flange
shears,
and
the
panel
zone
shear
force
is
obtained.
This
force
is
divided
by
the
shear
strength
capacity
to
determine
the
DCR
of
the
panel
zones.
Strustural
Analysis:
Part
2 -12
Note
that
although
the
maximum
DCR
for
the
columns
(4.043)
is
greater
than
the
maximum
DCR
for
the
beams
(
3.475),
it
is
likely
that
the
beam
will
yield
earlier
than
the
column.
Column
DCR
gets
bigger
here
because
of
the
huge
additional
axial
compressive
force
arising
from
the
seismic
load
which
was
applied
without
R
factor.
Strustural
Analysis:
Part
2 -13
The
total
lateral
strength
of
the
frame
is
calculated
using
virtual
work.
In
the
analysis,
it
is
assumed
that
plastic
hinges
are
perfectly
plastic.
Girders
hinge
at
a
value
ZeFye,
and
the
hinges
form
at
the
center
of
the
reduced
section
(approximately
15
inches
from
the
face
of
the
column).
Columns
hinge
only
at
the
base,
and
the
plastic
moment
capacity
is
assumed
to
be
Zcol(Fye
-Pu/Acol).
Strustural
Analysis:
Part
2 -14
Three
lateral
force
patterns
are
used:
uniform,
upper
triangular,
and
Standard
(where
the
Standard
pattern
is
consistent
with
the
vertical
force
distribution
provided
in
Slide
7).
The
rigid-plastic
analysis
does
not
consider
the
true
behavior
of
the
panel
zone
region
of
the
beam-column
joint.
Yielding
in
this
area
can
have
a
significant
effect
on
system
strength.
Strustural
Analysis:
Part
2 -15
The
DRAIN
model
used
for
the
nonlinear
analysis
is
shown
in
the
Figure.
In
detailed
model,
Krawinkler
type
panel
zones
are
added
to
the
model.
Plastic
hinges
are
assigned
at
the
reduced
flange
sections.
P-Delta
effects
are
included
by
use
of
a
linear
column
similar
to
preliminary
model.
Strustural
Analysis:
Part
2 -16
The
detail
illustrates
the
two
main
features
of
the
model:
an
explicit
representation
of
the
panel
zone
region
and
the
use
of
concentrated
plastic
hinges
in
the
girders.
Connection
elements
(Type
4)
are
used
for
both
girder
plastic
hinges
and
panel
zone
panel
and
flange
springs.
Strustural
Analysis:
Part
2 -17
In
most
cases,
one
or
more
rotational
spring
connection
elements
(DRAIN
element
Type
4)
are
placed
between
the
two
single
nodes
of
the
compound
node,
and
these
springs
develop
bending
moment
in
resistance
to
the
relative
rotation
between
the
two
single
nodes.
If
no
spring
elements
are
placed
between
the
two
single
nodes,
the
compound
node
acts
as
a
moment-free
hinge.
Strustural
Analysis:
Part
2 -18
Krawinkler
model
represents
the
panel
zone
stiffness
and
strength
by
an
assemblage
of
four
rigid
links
and
two
rotational
springs.
The
links
form
the
boundary
of
the
panel,
and
the
springs
are
used
to
provide
the
desired
inelastic
behavior.
Strustural
Analysis:
Part
2 -19
The
Krawinkler
model
assumes
that
the
panel
zone
has
two
resistance
mechanisms
acting
in
parallel:
1.
Shear
resistance
of
the
web
of
the
column,
including
doubler
plates
2.
Flexural
resistance
of
the
flanges
of
the
column
Strustural
Analysis:
Part
2 -20
The
complete
resistance
mechanism,
in
terms
of
rotational
spring
properties,
is
shown
in
Figure.
This
trilinear
behavior
is
represented
by
two
elastic-perfectly
plastic
springs
at
the
opposing
corners
of
the
joint
assemblage.
Strustural
Analysis:
Part
2 -21
A
side
view
of
the
reduced
beam
sections
is
shown
in
Figure.
The
distance
between
the
column
face
and
the
edge
of
the
reduced
beam
section
was
chosen
as
a
=
0.625bbf
and
the
reduced
section
length
was
assumed
as
b
=
0.75db.
Both
of
these
values
are
just
at
the
middle
of
the
limits
stated
in
AISC
358.
Plastic
hinges
of
the
beams
are
modeled
at
the
center
of
the
reduced
section
length.
Strustural
Analysis:
Part
2 -22
To
determine
the
plastic
hinge
capacities,
a
moment-curvature
analysis
of
the
cross
section,
which
is
dependent
on
the
stress-strain
curve
of
the
steel
used
in
girders,
was
implemented.
Figure
demonstrates
the
moment-curvature
graph
for
the
W27x94
girder.
As
may
be
seen
in
the
figure,
the
moment-curvature
relationship
is
different
at
each
section
of
the
reduced
length.
The
locations
of
the
different
reduced
beam
sections
used
in
Figure
1,
named
as
“bf1”,
“bf2”,
and
“bf3”,
can
be
seen
in
Figure
2.
Note
that
because
of
closely
adjacent
locations
chosen
for
“0.65bf”
and
“bf3”
(See
Figure
1),
their
moment-curvature
plots
are
nearly
indistinguishable
from
other
in
Figure
2.
Strustural
Analysis:
Part
2 -23
Figure
1
shows
the
curvature
diagram
when
the
curvature
ductility
reaches
20.
The
curvature
difference
(bump
at
the
center
of
RBS
in
Figure)
section
is
less
prominent
when
the
ductility
is
smaller.
Given
the
curvature
distribution
along
cantilever
beam
length,
the
deflections
at
the
point
of
load
(tip
deflections)
can
be
found
by
using
the
moment
area
method.
Figure
2
illustrates
the
force-displacement
relationship
at
the
end
of
the
½
span
cantilever
for
the
W27x94
with
the
reduced
flange
section.
Strustural
Analysis:
Part
2 -24
To
convert
the
force-tip
displacement
diagram
into
moment-rotation
of
the
plastic
hinge,
the
following
procedure
is
followed.
1.
Using
the
trilinear
force
displacement
relationship
shown
in
previous
slide
(Figure
2)
,
find
the
moment
at
the
plastic
hinge
for
P1,
P2
and
P3
load
levels
and
call
them
as
M1,
M2
and
M3.
To
find
the
moments,
the
tip
forces
(P1,
P2
and
P3)
were
multiplied
with
the
difference
of
the
½
span
cantilever
length
and
the
plastic
hinge
distance
from
the
column
face.
2.
Calculate
the
change
in
moment
for
each
added
load
(For
ex:
dM1=
M2-M1).
3.
Find
the
flexural
rigidity
(EI)
of
the
beam
given
tip
displacement
of
1
in.
under
the
1st
load
(P1
in
Figure
2
of
previous
slide).
4.
Calculate
the
required
rotational
stiffnesses
of
the
hinge
between
M1
and
M2,
and
then
M2
and
M3.
5.
Calculate
the
change
in
rotation
from
M1
to
M2,
and
from
M2
to
M3
by
dividing
the
change
in
moment
found
at
Step
2
by
the
required
rotational
stiffness
values
calculated
at
Step
4.
6.
Find
the
specific
rotations
at
M1,
M2
and
M3
using
the
change
in
rotation
values
found
in
step
5.
Note
that
the
rotation
is
zero
at
M1.
7.
Plot
moment-rotation
diagram
of
the
plastic
hinge
using
the
values
calculated
at
Step1
and
Step6.
Strustural
Analysis:
Part
2 -25
All
columns
in
the
analysis
were
modeled
in
DRAIN
with
Type-2
elements.
Preliminary
analysis
indicated
that
columns
should
not
yield,
except
at
the
base
of
the
first
story.
Subsequent
analysis
showed
that
the
columns
will
yield
in
the
upper
portion
of
the
structure
as
well.
For
this
reason,
column
yielding
had
to
be
activated
in
all
of
the
Type-2
column
elements.
The
columns
were
modeled
using
the
built-in
yielding
functionality
of
the
DRAIN
program,
wherein
the
yield
moment
is
a
function
of
the
axial
force
in
the
column.
The
yield
surfaces
used
by
DRAIN
for
all
the
columns
in
the
model
are
shown
in
Figure.
Strustural
Analysis:
Part
2 -26
Slide
shows
vibration
of
periods
of
vibration
using
different
analysis
assumptions.
Strustural
Analysis:
Part
2 -27
Slide
is
self-explanatory.
Describes
procedure
for
nonlinear
static
pushover
analysis.
Strustural
Analysis:
Part
2 -28
Relative
values
of
these
load
patterns
are
summarized
in
Table.
The
loads
have
been
normalized
to
a
value
of
15
kips
at
Level
2.
Strustural
Analysis:
Part
2 -29
Figure
shows
the
pushover
response
of
the
SP
structure
to
all
three
lateral
load
patterns
where
P-delta
effects
are
excluded.
In
each
case,
gravity
loads
are
applied
first
and
then
the
lateral
loads
are
applied
using
the
displacement
control
algorithm.
Strustural
Analysis:
Part
2 -30
Figure
plots
two
base
shear
components
of
the
pushover
response
for
the
SP
structure
subjected
to
the
ML
loading.
The
kink
in
the
line
representing
P-delta
forces
occurs
because
these
forces
are
based
on
first-story
displacement,
which,
for
an
inelastic
system,
generally
will
not
be
proportional
to
the
roof
displacement.
Strustural
Analysis:
Part
2 -31
Figure
shows
the
pushover
response
of
the
SP
structure
to
all
three
lateral
load
patterns
where
P-delta
effects
are
included.
Strustural
Analysis:
Part
2 -32
The
response
of
the
structure
under
ML
loading
with
and
without
P-delta
effects
is
illustrated
in
Figure.
Clearly,
P-delta
effects
are
an
extremely
important
aspect
of
the
response
of
this
structure,
and
the
influence
grows
in
significance
after
yielding.
This
is
particularly
interesting
in
the
light
of
the
Standard,
which
ignores
P-delta
effects
in
elastic
analysis
if
the
maximum
stability
ratio
is
less
than
0.10
(see
Sec.
12.8-7).
For
this
structure,
the
maximum
computed
stability
ratio
is
0.0862
(see
Slide
10),
which
is
less
than
0.10
and
is
also
less
than
the
upper
limit
of
0.0909.
The
upper
limit
is
computed
according
to
Standard
Equation
12.8-17
and
is
based
on
the
very
conservative
assumption
that
.
=
1.0.
While
the
Standard
allows
the
analyst
to
exclude
P-delta
effects
in
an
elastic
analysis,
this
clearly
should
not
be
done
in
the
pushover
analysis
(or
in
response
history
analysis).
In
the
Provisions
the
upper
limit
for
the
stability
ratio
is
eliminated.
Where
the
calculated
.
is
greater
than
0.10,
a
pushover
analysis
must
be
performed
in
accordance
with
ASCE
41,
and
it
must
be
shown
that
that
the
slope
of
the
pushover
curve
is
positive
up
to
the
target
displacement.
The
pushover
analysis
must
be
based
on
the
MCE
spectral
acceleration
and
must
include
P-delta
effects
[and
loss
of
strength,
as
appropriate].
If
the
slope
of
the
pushover
curve
is
negative
at
displacements
less
than
the
target
displacement,
the
structure
must
be
redesigned
such
that
.
is
less
than
0.10
or
the
pushover
slope
is
positive
up
to
the
target
displacement.
Strustural
Analysis:
Part
2 -33
The
first
significant
yield
occurs
at
a
roof
displacement
of
approximately
6.5
inches
and
that
most
of
the
structure’s
original
stiffness
is
exhausted
by
the
time
the
roof
displacement
reaches
13
inches.
For
the
case
with
P-delta
effects
excluded,
the
final
stiffness
shown
in
Figure
is
approximately
10.2
kips/in.,
compared
to
an
original
value
of
139
kips/in.
Hence,
the
strain-hardening
stiffness
of
the
structure
is
0.073
times
the
initial
stiffness.
This
is
somewhat
greater
than
the
0.03
(3.0
percent)
strain
hardening
ratio
used
in
the
development
of
the
model
because
the
entire
structure
does
not
yield
simultaneously.
Where
P-delta
effects
are
included,
the
final
stiffness
is -1.6
kips
per
in.
The
structure
attains
this
negative
residual
stiffness
at
a
displacement
of
approximately
23
in.
Strustural
Analysis:
Part
2 -34
Figure
shows
that
the
doubler
plates,
which
represent
approximately
2.0
percent
of
the
volume
of
the
structure,
increase
the
strength
and
initial
stiffness
by
approximately
10
percent.
Strustural
Analysis:
Part
2 -35
This
slide
shows
a
movie
which
is
obtained
using
the
snapshot
tool
of
NonlinPro.
Yielded
displaced
shape
showing
sequence
and
pattern
of
plastic
hinging
is
displayed.
Strustural
Analysis:
Part
2 -36
It
appears
that
the
structure
is
somewhat
weak
in
the
middle
two
stories
and
is
relatively
strong
at
the
upper
stories.
The
doubler
plates
added
to
the
interior
columns
prevented
panel
zone
yielding.
Figure
shows
the
first
yielding
locations
of
the
girder,
column
and
panel
zones.
Some
observations:
•
There
is
no
hinging
in
Levels
6
and
R.
•
There
is
panel
zone
hinging
only
at
the
exterior
columns
at
Levels
4
and
5.
Panel
zone
hinges
do
not
form
at
the
interior
joints
where
doubler
plates
are
used.
•
Hinges
form
at
the
base
of
all
the
Level
1
columns.
•
Plastic
hinges
form
in
all
columns
on
Level
3
and
all
the
interior
columns
on
Level
4.
Strustural
Analysis:
Part
2 -37
The
demand
capacity
ratios
match
the
plastic
hinge
formation
sequence,
i.e.
first
plastic
hinges
form
at
the
maximum
DCR’s
for
columns,
girders
and
panel
zones.
The
highest
DCR
was
observed
at
the
girders
of
3rd
level
beginning
from
the
bays
at
the
leeward
(right)
side.
As
may
be
seen,
first
plastic
hinges
form
at
the
same
locations
of
the
building.
As
may
be
seen
in
the
previous
slide
the
first
column
hinge
forms
at
the
base
of
the
fifth
column.
However,
the
DCR
of
the
sixth
column
(leeward
side)
is
the
maximum.
This
is
due
to
huge
axial
compressive
forces
that
reduce
the
capacity
of
the
leeward
side
column
when
DCR
is
calculated.
Note
that
if
R=8
is
used
for
the
lateral
load
of
DCR
analysis,
the
base
of
the
fifth
column
results
in
the
maximum
DCR
which
would
match
better
with
the
hinging
sequence
of
the
pushover
analysis.
In
addition,
as
seen
in
the
Figure
of
Slide
37,
base
column
hinges
form
almost
simultaneously.
Strustural
Analysis:
Part
2 -38
First
panel
zone
hinge
forms
at
the
beam
column
joint
of
the
sixth
column
at
the
fourth
level
(see
Slide
37),
and
this
is
where
the
highest
DCR
values
were
obtained
for
the
panel
zones
in
preliminary
DCR
analyses.
Strustural
Analysis:
Part
2 -39
Diagram
shows
sequencing
of
plastic
hinge
formation
on
a
pushover
curve.
Figure
shows
the
sequence
of
the
hinging
on
the
pushover
curve.
These
events
correspond
to
numbers
shown
in
Figure
of
Slide
37.
The
pushover
curve
only
shows
selected
events
because
an
illustration
showing
all
events
would
be
difficult
to
read.
Strustural
Analysis:
Part
2 -40
As
may
be
seen
in
Figure,
first
yielding
occurs
in
the
panel
zones
when
doubler
plates
are
not
used.
Panel
hinges
of
Level
4
form
first.
Strustural
Analysis:
Part
2 -41
Figure
shows
the
same
plot
displayed
in
Slide
12
(DCR
of
panel
zones
by
preliminary
analysis).
The
values
in
parentheses
(in
blue)
represent
the
DCRs
without
doubler
plates.
As
may
be
seen
in
Figure,
the
hinges
of
the
panels,
where
highest
DCR
are
obtained
from
preliminary
analyses,
form
first
(Compare
Figure
with
the
Figure
in
the
previous
slide).
Strustural
Analysis:
Part
2 -42
The
formula
is
from
section
3.3.3.3.2
of
ASCE
41
which
uses
the
coefficient
method
for
calculating
target
displacement.
Strustural
Analysis:
Part
2 -43
Spectral
acceleration
at
the
fundamental
period
of
the
structure
was
found
from
the
2%
damped
horizontal
response
spectrum
as
described
in
Section
1.6.1.5
of
ASCE
41-06.
Strustural
Analysis:
Part
2 -44
Slide
explains
static
pushover
analysis.
Strustural
Analysis:
Part
2 -45
Target
displacement
is
22.9
in.
for
Strong
Panel
model
and
24.1
in.
for
Weak
Panel
model.
Negative
tangent
stiffness
starts
at
22.9
inches
and
29.3
inches
for
strong
and
weak
panel
models,
respectively.
Thus
negative
tangent
stiffness
starts
after
target
displacements
for
both
models.
Strustural
Analysis:
Part
2 -46
Slide
describes
Target
Displacements.
Strustural
Analysis:
Part
2 -47
The
structure
is
subjected
to
dead
load
and
half
of
the
fully
reduced
live
load,
followed
by
ground
acceleration.
The
incremental
differential
equations
of
motion
are
solved
in
a
stepby-
step
manner
using
the
Newmark
constant
average
acceleration
approach.
Time
steps
and
other
integration
parameters
are
carefully
controlled
to
minimize
errors.
The
minimum
time
step
used
for
analysis
is
as
small
as
0.0005
second
for
the
first
earthquake
and
0.001
second
for
the
second
and
third
earthquakes.
A
smaller
integration
time
step
is
required
for
the
first
earthquake
because
of
its
impulsive
nature.
Strustural
Analysis:
Part
2 -48
Note
that
......and
....
are
directly
proportional
to
..
To
increase
the
target
damping
from
2percent
to
5percent
of
critical,
all
that
is
required
is
a
multiplying
factor
of
2.5
on
.....
and
.....
Strustural
Analysis:
Part
2 -49
Slide
describes
development
of
ground
motion
records
for
Response
History
Analysis.
Strustural
Analysis:
Part
2 -50
Slide
shows
the
acceleration
time
histories
and
response
spectra
of
the
selected
motions.
Strustural
Analysis:
Part
2 -51
When
analyzing
structures
in
two
dimensions,
Section
16.1.3.1
of
the
Standard
(as
well
as
ASCE
7-10)
gives
the
following
instructions
for
scaling:
“The
ground
motions
shall
be
scaled
such
that
the
average
value
of
the
5
percent
damped
response
spectra
for
the
suite
of
motions
is
not
less
than
the
design
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.”
The
scaling
requirements
in
Provisions
Part
3
Resource
Paper
3are
similar,
except
that
the
target
spectrum
for
scaling
is
the
MCER
spectrum.
In
this
example,
the
only
adjustment
is
made
for
scaling
when
the
inherent
damping
is
taken
as
2percent
of
critical.
In
this
case,
the
ground
motion
spectra
are
based
on
2percent
damping,
and
the
DBE
or
MCE
spectrum
is
adjusted
from
5percent
damping
to
2percent
damping
using
the
modification
factors
given
in
ASCE
41.
The
scaling
procedure
described
above
has
a
“degree
of
freedom”
in
that
there
are
an
infinite
number
of
scaling
factors
that
can
fit
the
criterion.
To
avoid
this,
a
two-step
scaling
process
is
used
wherein
each
spectrum
is
initially
scaled
to
match
the
target
spectrum
at
the
structure’s
fundamental
period,
and
then
the
average
of
the
scaled
spectra
are
re-
scaled
such
that
no
ordinate
of
the
scaled
average
spectrum
falls
below
the
target
spectrum
in
the
range
of
periods
between
0.2T
and
1.5T.
The
final
scale
factor
for
each
motion
consists
of
the
product
of
the
initial
scale
factor
and
the
second
scale
factor.
Strustural
Analysis:
Part
2 -52
Part
(a)
of
each
table
provides
the
maximum
base
shears,
computed
either
as
the
sum
of
column
forces
(including
P-delta
effects
as
applicable),
or
as
the
sum
of
the
products
of
the
total
acceleration
and
mass
at
each
level.
In
each
case,
the
shears
computed
using
the
two
methods
are
similar,
which
serves
as
a
check
on
the
accuracy
of
the
analysis.
Had
the
analysis
been
run
without
damping,
the
shears
computed
by
the
two
methods
should
be
identical.
As
expected
base
shears
decrease
when
P-delta
effects
are
included.
The
drift
limits
in
the
table,
equal
to
2percent
of
the
story
height,
are
the
same
as
provided
in
Standard
Table
12.12-1.
Standard
Section
16.2.4.3
provides
for
the
allowable
drift
to
be
increased
by25
percent
where
nonlinear
response
history
analysis
is
used;
these
limits
are
shown
in
the
tables
in
parentheses.
Provisions
Part
2
states
that
the
increase
in
drift
limit
is
attributed
to
“the
more
accurate
analysis,
and
the
fact
that
drifts
are
computed
explicitly.”
Drifts
that
exceed
the
increased
limits
are
shown
in
bold
text
in
the
tables.
It
is
interesting
that
P-Delta
effects
more
or
less
reduces
the
drifts
for
B90
motion.
These
values
are
the
maximum
values
though
i.e.
they
don’t
necessarily
occur
at
the
same
time.
Strustural
Analysis:
Part
2 -53
The
limits
are
1.5
times
those
allowed
by
Standard
Section
12.2.1.
The
50
percent
increase
in
drift
limits
is
consistent
with
the
increase
in
ground
motion
intensity
when
moving
from
DBE
to
MCE
ground
motions.
Earthquake
A00
results
in
62.40-inch
displacement
at
the
roof
level
and
approximately
between
15-to
20-inch
drifts
at
the
first
three
stories
of
the
structure.
These
story
drifts
are
well
above
the
limits.
When
P-delta
effects
are
included
with
the
same
level
of
motion,
roof
displacement
increases
to
101.69
inches
with
approximately
20-to
40-inch
displacement
at
the
first
three
stories.
It
is
clear
from
Part
(b)
of
Tables
that
Ground
Motion
A00
is
much
more
demanding
with
respect
to
drift
than
are
the
other
two
motions.
The
drifts
produced
by
Ground
Motion
A00
are
particularly
large
at
the
lower
levels,
with
the
more
liberal
drift
limits
being
exceeded
in
the
lower
four
stories
of
the
building.
When
P-delta
effects
are
included,
the
drifts
produced
by
Ground
Motion
A00
increase
significantly;
drifts
produced
by
Ground
Motions
B90
and
C90
change
only
slightly.
Strustural
Analysis:
Part
2 -54
Figure
1
shows
response
histories
of
roof
displacement
and
first
story
drift
for
the
2percent
damped
SP
model
subjected
to
the
DBE-scaled
A00
ground
motion.
Two
trends
are
readily
apparent.
First,
the
vast
majority
of
the
roof
displacement
is
due
to
residual
deformation
in
the
first
story.
Second,
the
P-delta
effect
increases
residual
deformations
by
about
50
percent.
Such
extreme
differences
in
behavior
do
not
appear
in
plots
of
base
shear,
as
provided
in
Figure
2.
The
residual
deformations
shown
in
Figure
1
may
be
real
(due
to
actual
system
behavior)
or
may
reflect
accumulated
numerical
errors
in
the
analysis.
Numerical
errors
are
unlikely
because
the
shears
computed
from
member
forces
and
from
inertial
forces
are
similar.
Strustural
Analysis:
Part
2 -55
If
the
analysis
is
accurate,
the
input
energy
will
coincide
with
the
total
energy
(sum
of
kinetic,
damping,
and
structural
energy).
DRAIN
2D
produces
individual
energy
values
as
well
as
the
input
energy.
As
seen
in
Figure,
the
total
and
input
energy
curves
coincide,
so
the
analysis
is
numerically
accurate.
Where
this
accuracy
is
in
doubt,
the
analysis
should
be
re-run
using
a
smaller
integration
time
step.
Strustural
Analysis:
Part
2 -56
It
is
interesting
to
compare
the
response
computed
for
Ground
Motion
B90
with
that
obtained
for
ground
motion
A00.
While
there
is
some
small
residual
deformation
in
Figure
1
(B90
motion),
it
is
not
extreme,
and
it
appears
that
the
structure
is
not
in
danger
of
collapse.
(The
corresponding
plastic
rotations
are
less
than
those
that
would
be
associated
with
significant
strength
loss.)
As
may
be
seen
in
Figure
2,
when
MCE
type
A00
motion
is
used,
residual
deformations
again
dominate
(as
the
DBE
case),
and
in
this
case
the
total
residual
roof
displacement
with
P-delta
effects
included
is
five
times
that
without
P-delta
effects.
This
behavior
indicates
dynamic
instability
and
eventual
collapse.
Strustural
Analysis:
Part
2 -57
The
characteristic
of
the
ground
motion
(A00)
that
produces
the
residual
deformations
is
not
evident
from
the
ground
acceleration
history
or
from
the
acceleration
response
spectrum.
The
source
of
the
behavior
is
quite
obvious
from
plots
of
the
ground
velocity
and
ground
displacement
histories.
The
ground
velocity
history
shows
that
a
very
large
velocity
pulse
occurs
approximately
10
seconds
into
the
earthquake.
This
leads
to
a
surge
in
ground
displacement,
also
occurring
approximately
10
seconds
into
the
response.
The
surge
in
ground
displacement
is
more
than
8feet,
which
is
somewhat
unusual.
Strustural
Analysis:
Part
2 -58
The
unusual
characteristics
of
Ground
Motion
A00
may
be
seen
in
Figure
which
is
a
tripartite
spectrum.
Strustural
Analysis:
Part
2 -59
The
circles
on
the
figure
represent
yielding
at
any
time
during
the
response;
consequently,
yielding
does
not
necessarily
occur
at
all
locations
simultaneously.
The
circles
shown
at
the
upper
left
corner
of
the
beam-column
joint
region
indicate
yielding
in
the
rotational
spring,
which
represents
the
web
component
of
panel
zone
behavior.
There
is
no
yielding
in
the
flange
component
of
the
panel
zones,
as
seen
in
Figure.
Yielding
patterns
for
the
other
ground
motions
and
for
analyses
run
with
and
without
P-
delta
effects
are
similar
but
are
not
shown
here.
As
expected,
there
is
more
yielding
in
the
columns
when
the
structure
is
subjected
to
the
A00
ground
motion.
The
maximum
plastic
hinge
rotations
are
shown
where
they
occur
for
the
columns,
girders,
and
panel
zones.
Strustural
Analysis:
Part
2 -60
Table
compares
the
results
obtained
from
the
response
history
analysis
with
those
obtained
from
the
ELF
and
the
nonlinear
static
pushover
analyses.
Recall
that
the
base
shears
in
the
table
represent
half
of
the
total
shear
in
the
building.
As
it
was
discussed
before,
2%
damped
MCE
based
spectrum
was
used
for
the
pushover
analysis.
To
be
consistent,
the
results
of
2%
damped
MCE
scaled
B90
motion
was
used
for
the
nonlinear
dynamic
analysis
part
of
the
table.
In
addition,
the
lateral
forces
used
to
find
the
ELF
drifts
in
Slide
7
were
multiplied
by
1.5
to
make
them
consistent
with
the
MCE
level
of
shaking.
The
ELF
analysis
drift
values
include
the
deflection
amplification
factor
of
5.5.
The
results
tabulated
as
results
of
pushover
analysis
are
obtained
at
the
load
level
of
target
displacement.
Strustural
Analysis:
Part
2 -61
Figure
shows
the
inertial
forces
from
the
nonlinear
response
history
analyses
at
the
time
of
peak
base
shear
and
the
loads
applied
to
the
nonlinear
static
analysis
model
at
the
target
displacement.
Strustural
Analysis:
Part
2 -62
Slide
summarizes
results
of
response
history
analysis.
Strustural
Analysis:
Part
2 -63
Base
shear
increases
with
added
damping,
so
in
practice
added
damping
systems
usually
employ
nonlinear
viscous
fluid
devices
with
a
“softening”
relationship
between
the
deformational
velocity
in
the
device
and
the
force
in
the
device,
to
limit
base
shears
when
deformational
velocities
become
large.
This
value
of
.device
is
for
the
added
damper
element
only.
Different
dampers
may
require
different
values.
Also,
a
different
(global)
value
of
.is
required
to
model
the
stiffness
proportional
component
of
damping
in
the
remaining
nondamper
elements.
Modeling
the
dynamic
response
using
Type
1
elements
is
exact
within
the
typical
limitations
of
finite
element
analysis.
Using
the
modal
strain
energy
approach,
DRAIN
reports
a
damping
value
in
each
mode.
These
modal
damping
values
are
approximate
and
may
be
poor
estimates
of
actual
modal
damping,
particularly
where
there
is
excessive
flexibility
in
the
mechanism
that
connects
the
damper
to
the
structure.
Strustural
Analysis:
Part
2 -64
Four
different
added
damper
configurations
are
used
to
asses
their
effect
on
story
drifts
and
base
shear.
These
configurations
increase
total
damping
of
the
structure
from
2percent
(inherent)
to
10
and
20
percent.
In
the
first
configuration
added
dampers
are
distributed
proportionally
to
approximate
story
stiffnesses.
In
the
second
configuration,
dampers
are
added
at
all
six
stories,
with
larger
dampers
in
lower
stories.
Since
the
structure
seems
to
be
weak
at
the
bottom
stories
(where
it
exceeds
drift
limits),
dampers
are
concentrated
at
the
bottom
stories
in
the
last
two
configurations.
Added
dampers
are
used
only
at
the
first
and
second
stories
in
the
third
configuration
and
at
the
bottom
four
stories
in
the
fourth
configuration.
Based
on
this
supplemental
damper
study,
it
appears
to
be
impossible
to
decrease
the
story
drifts
for
the
A00
ground
motion
below
the
limits.
This
is
because
of
the
incremental
velocity
of
Ground
Motion
A00
causes
such
significant
structural
damage.
The
drift
limits
could
be
satisfied
if
the
total
damping
ratio
is
increased
to
33.5
percent,
but
since
that
is
impractical
the
results
are
not
reported
here.
The
third
configuration
of
added
dampers
reduces
the
first-story
drift
from
10.40
inches
to
4.40
inches.
Strustural
Analysis:
Part
2 -65
All
of
the
configurations
easily
satisfy
drift
limits
for
the
B90
ground
motion.
While
the
system
with
10
percent
total
damping
is
sufficient
for
drift
limits,
systems
with
20
percent
damping
further
improve
performance.
Although
configurations
3
and
4
have
the
same
amount
of
total
damping
as
configuration
2,
story
drifts
are
higher
at
the
top
stories
since
dampers
are
added
only
at
lower
stories.
Strustural
Analysis:
Part
2 -66
Added
dampers
reduce
the
roof
displacement
for
both
A00
and
B90
ground
motions.
As
Figure
2
shows
added
dampers
reduce
roof
displacement
significantly
but
do
not
prevent
residual
displacement
for
the
A00
ground
motion.
Strustural
Analysis:
Part
2 -67
As
should
be
expected,
adding
discrete
damping
reduces
the
hysteretic
energy
demand
in
the
structure
(designated
as
structural
energy
in
Figures).
A
reduction
in
hysteretic
energy
demand
for
the
system
with
added
damping
corresponds
to
a
reduction
in
structural
damage.
Strustural
Analysis:
Part
2 -68
Again,
adding
discrete
damping
reduces
the
hysteretic
energy
demand,
which
results
in
a
reduction
in
structural
damage
for
B90
motion.
As
may
be
seen,
added
dampers
are
more
efficient
in
terms
of
energy
dissipation
for
B90
motion
than
A00
motion
(See
previous
slide).
Strustural
Analysis:
Part
2 -69
Figures
show
how
added
damping
increases
base
shear.
Especially,
for
A00
motion,
the
maximum
base
shear
increases
more
than
50%.
Strustural
Analysis:
Part
2 -70
This
slide
shows
a
movie
which
is
obtained
using
the
snapshot
tool
of
NonlinPro.
Displaced
shape
of
the
4th
combination
added
damper
frame
under
B90
motion
is
displayed.
Strustural
Analysis:
Part
2 -71
Summary
and
Conclusions.
Strustural
Analysis:
Part
2 -72
Slide
prompts
participants
to
ask
questions.
Strustural
Analysis:
Part
2 -73
system
with
various
geometric
irregularities.
The
building
is
located
in
Stockton,
California,
an
area
of
relatively
high
seismic
activity.
The
example
is
based
on
the
requirements
of
ASCE
7-05.
However,
ASCE
7-10
is
referred
to
in
several
instances.
Complete
details
for
the
analysis
are
provided
in
the
written
example,
and
the
example
should
be
used
as
the
“Instructors
Guide”
when
presenting
this
slide
set.
Many,
but
not
all
of
the
slides
in
this
set
have
“Speakers
Notes”,
and
these
are
intentionally
kept
very
brief.
Finley
Charney
is
a
Professor
of
Civil
Engineering
at
Virginia
Tech,
Blacksburg,
Virginia.
He
is
also
president
of
Advanced
Structural
Concepts,
Inc.,
located
in
Blacksburg.
The
written
example
and
the
accompanying
slide
set
were
completed
by
Advanced
Structural
Concepts.
Adrian
Tola
was
a
graduate
student
at
Virginia
Tech
when
the
example
was
developed,
and
served
as
a
contractor
for
Advanced
Structural
Concepts.
Structural
Analysis:
Part
1 -2
This
building
was
developed
specifically
for
this
example.
However,
an
attempt
was
made
to
develop
a
realistic
structural
system,
with
a
realistic
architectural
configuration.
Structural
Analysis:
Part
1 -3
These
are
the
three
linear
analysis
methods
provided
in
ASCE
7.
The
Equivalent
Lateral
Force
method
(ELF)
is
essentially
a
one-mode
response
spectrum
analysis
with
corrections
for
higher
mode
effects.
This
method
is
allowed
for
all
SDC
B
and
C
buildings,
and
for
the
vast
majority
of
SDC
D,
E
and
F
buildings.
Note
that
some
form
of
ELF
will
be
required
during
the
analysis/design
process
for
all
buildings.
The
Modal
Response
Spectrum
(MRS)
method
is
somewhat
more
complicated
than
ELF
because
mode
shapes
and
frequencies
need
to
be
computed,
response
signs
(positive
or
negative)
are
lost,
and
results
must
be
scaled.
However,
there
are
generally
fewer
load
combinations
than
required
by
ELF.
MRS
can
be
used
for
any
building,
and
is
required
for
SDC
D,
E,
and
F
buildings
with
certain
irregularities,
and
for
SDC
D,
E,
and
F
buildings
with
long
periods
of
vibration.
The
linear
Modal
Response
History
(MRH)
method
is
more
complex
that
MRS,
mainly
due
to
the
need
to
select
and
scale
at
least
three
and
preferably
seven
sets
of
motions.
MRS
can
be
used
for
any
building,
but
given
the
current
code
language,
it
is
probably
too
time-
consuming
for
the
vast
majority
of
systems.
Structural
Analysis:
Part
1 -4
The
vast
majority
of
the
written
example
and
this
slide
set
is
based
on
the
requirements
of
ASCE
7-05.
The
requirements
of
ASCE
7-10
are
mentioned
when
necessary.
When
ASCE
710
is
mentioned,
it
is
generally
done
so
to
point
out
the
differences
in
ASCE
7-05
and
ASCE
7-10.
Structural
Analysis:
Part
1 -5
The
structure
analyzed
is
a
3-Dimensional
Special
Steel
Moment
resisting
Space
Frame.
Structural
Analysis:
Part
1 -6
In
this
building
all
of
the
exterior
moment
resisting
frames
are
lateral
load
resistant.
Those
portions
of
Frames
C
and
F
that
are
interior
at
the
lower
levels
are
gravity
only
frames.
Structural
Analysis:
Part
1 -7
The
gravity-only
columns
and
girders
below
the
setbacks
in
grids
C
and
F
extend
into
the
basement.
Structural
Analysis:
Part
1 -8
This
view
show
the
principal
setbacks
for
the
building.
The
shaded
lines
at
levels
5
and
9
represent
thickened
diaphragm
slabs.
Structural
Analysis:
Part
1 -9
Note
that
the
structure
has
one
basement
level.
This
basement
is
fully
modeled
in
the
analysis
(the
basement
walls
are
modeled
with
shell
elements),
and
will
lead
to
complications
in
the
analyses
presented
later.
All
of
the
perimeter
columns
extend
into
the
basement,
and
are
embedded
in
the
wall.
(The
wall
is
thickened
around
the
columns
to
form
monolithic
pilasters).
Thus,
for
analysis
purposes,
the
columns
may
be
assumed
to
be
fixed
at
the
top
of
the
wall.
Structural
Analysis:
Part
1 -10
All
analysis
for
this
example
was
performed
on
SAP2000.
The
program
ETABS
may
have
been
a
more
realistic
choice,
but
this
was
not
available.
Structural
Analysis:
Part
1 -11
These
views
show
that
the
basement
walls
and
the
floor
diaphragms
were
explicitly
modeled
in
three
dimensions.
It
is
the
author’s
opinion
that
all
dynamic
analysis
should
be
carried
out
in
three
dimensions.
When
doing
so
it
is
simple
to
model
the
slabs
and
walls
using
shell
elements.
Note
that
a
very
coarse
mesh
is
used
because
the
desire
is
to
include
the
stiffness
(flexibility)
of
these
elements
only.
No
stress
recovery
was
attempted.
If
stress
recovery
is
important,
a
much
finer
mesh
is
needed.
Structural
Analysis:
Part
1 -12
The
goal
of
this
example
is
to
present
the
ASCE
7
analysis
methodologies
by
example.
Thus,
this
slide
set
is
somewhat
longer
than
it
would
need
to
be
if
only
the
main
points
of
the
analysis
were
to
be
presented.
Structural
Analysis:
Part
1 -13
The
steps
presented
on
this
slide
are
common
to
all
analysis
methods.
The
main
structural
analysis
would
begin
after
step
10.
Note,
however,
that
a
very
detailed
“side
analysis”
might
be
required
to
establish
diaphragm
flexibility
and
to
determine
if
certain
structural
irregularities
exist.
One
point
that
should
be
stressed
is
that
regardless
of
the
method
of
analysis
selected
in
step
8
(ELF,
MRS,
or
MRH),
an
ELF
analysis
is
required
for
all
structures.
This
is
true
because
ASCE
7-05
and
ASCE
7-10
use
an
ELF
analysis
to
satisfy
accidental
torsion
requirements
and
P-Delta
requirements.
Additionally,
an
ELF
analysis
would
almost
always
be
needed
in
preliminary
design.
Structural
Analysis:
Part
1 -14
This
structure
is
used
for
an
office
building,
so
the
Occupancy
Category
is
II.
Note
that
analysts
usually
need
to
refer
to
the
IBC
occupancy
category
table
which
is
somewhat
different
than
shown
on
this
slide.
It
is
for
this
reason
that
Table
1-1
as
shown
above
has
been
simplified
in
ASCE
7-10.
It
should
also
be
noted
that
assigning
an
Occupancy
Category
can
be
subjective,
and
when
in
doubt,
the
local
building
official
should
be
consulted.
Structural
Analysis:
Part
1 -15
These
coefficients
are
not
particularly
realistic
because
they
were
selected
to
provide
compatibility
with
an
earlier
version
of
this
example.
It
is
for
this
reason
that
Latitude-
Longitude
coordinates
are
not
given.
Students
should
be
advised
that
Latitude-Longitude
is
preferable
to
zip
code
because
some
zip
codes
cover
large
geographic
areas
which
can
have
a
broad
range
of
ground
motion
parameters.
Structural
Analysis:
Part
1 -16
Note
that
the
site
coefficients
are
larger
in
areas
of
low
seismicity.
This
is
because
the
soil
remains
elastic
under
smaller
earthquakes.
For
larger
earthquakes
the
soil
is
inelastic,
and
the
site
amplification
effect
is
reduced.
Note
that
for
site
classes
D
and
E
the
factor
Fv
can
go
as
high
as
3.5
for
smaller
earthquakes.
Thus,
for
such
sites
in
the
central
and
eastern
U.S.,
the
ground
motions
can
be
quite
large,
and
many
structures
(particularly
critical
facilities)
may
be
assigned
to
Seismic
Design
Category
D.
Structural
Analysis:
Part
1 -17
In
this
slide
the
intermediate
coefficients
SMS
and
SM1
are
not
separately
computed.
Note
that
the
subscript
M
stands
for
Maximum
Considered
Earthquake
(MCE),
and
the
subscript
D
in
SDS
and
SD1
stands
for
Design
Basis
Earthquake
(DBE).
The
MCE
is
the
earthquake
with
a
2%
probability
of
being
exceeded
in
50
years.
In
California,
the
DBE
is
roughly
a
10%
in
50
year
ground
motion.
In
the
Eastern
and
central
U.S.
the
DBE
is
somewhere
between
a
2%
and
10%
in
50
year
event.
Structural
Analysis:
Part
1 -18
Note
that
the
SDC
is
a
factor
of
BOTH
the
seismicity
and
intended
use.
For
important
buildings
on
soft
sites
in
the
central
and
Eastern
U.S.
it
is
possible
to
have
an
assignment
of
SDC
D,
which
requires
the
highest
level
of
attention
to
detailing.
A
few
code
cycles
ago
the
same
building
would
have
had
only
marginal
seismic
detailing
(if
any).
Structural
Analysis:
Part
1 -19
We
entered
this
example
knowing
it
would
be
aspecial
moment
frame,
so
system
selection
was
moot.
However,
this
table
can
be
used
to
illustrate
height
limits
(which
do
not
apply
to
the
Special
Steel
Moment
Frame).
The
required
design
parameters
are
also
provided
by
the
table.
The
values
of
R
=
8
and
.....0
are
the
largest
among
all
systems.
The
ratio
of
Cd
to
R
is
one
of
the
smallest
for
all
systems.
Structural
Analysis:
Part
1 -20
The
diaphragm
is
modeled
using
shell
elements
in
SAP2000.
Only
one
element
is
required
in
each
bay
as
all
that
is
needed
in
the
analysis
is
a
reasonable
estimate
of
in-plane
diaphragm
stiffness.
If
diaphragm
stresses
are
to
be
recovered
a
much
finer
mesh
would
be
required.
Structural
Analysis:
Part
1 -21
Torsional
irregularities
must
be
determined
by
analysis,
and
this
is
discussed
later
in
the
example.
The
structure
clearly
has
a
re-entrant
corner
irregularity,
and
the
diaphragm
discontinuity
irregularity
is
also
likely.
Note,
however,
that
the
consequences
of
the
two
irregularities
(2
and
3)
are
the
same,
so
these
are
effectively
the
same
irregularity.
The
structure
has
a
nonparallel
system
irregularity
because
of
the
nonsymmetrical
layout
of
the
system.
Note
that
in
ASCE
7-10
the
words
“or
symmetric
about”
in
the
description
of
the
nonparallel
system
irregularity
have
been
removed,
so
this
structure
would
not
have
a
nonsymmetrical
irregularity
in
ASCE
7-10.
This
is
a
consequential
change
because
requirements
for
three
dimensional
analysis
and
orthogonal
loading
are
tied
to
the
presence
of
a
type
5
irregularity.
Structural
Analysis:
Part
1 -22
The
structure
in
question
clearly
has
the
two
irregularities
noted.
One
thing
that
should
be
illustrated
on
this
slide
(and
the
previous
slide)
is
that
the
there
are
no
“consequences”
if
certain
irregularities
occur
in
SDC
B
and
C
systems.
For
example,
Vertical
Irregularities
1,
2,
and
3
have
consequences
only
for
SDC
D,
E,
and
F,
thus
the
possible
occurrence
of
the
irregularities
need
not
be
checked
in
SDC
B
and
C.
Structural
Analysis:
Part
1 -23
The
ELF
method
is
allowed
for
the
vast
majority
of
systems.
The
main
reason
that
ELF
is
not
allowed
for
this
system
is
that
(1)
it
is
in
SDC
D,
and
(2)
it
has
Reentrant
Corner
and
Diaphragm
Discontinuity
Irregularities.
It
is
interesting
to
note
that
ELF
is
allowed
in
higher
SDC
even
when
there
are
stiffness,
weight,
and
weak
story
irregularities.
It
seems
that
this
would
be
more
of
a
detriment
to
the
accuracy
of
ELF
than
than
would
a
reenrtant
corner.
Note
that
Table
12.6-1
as
shown
in
the
slide
is
from
ASCE
7-05.
The
table
has
been
simplified
somewhat
for
ASCE
7-10
(see
the
next
slide),
but
the
basic
configurations
where
ELF
are
allowed/disallowed
are
essentially
the
same.
Structural
Analysis:
Part
1 -24
This
is
Table
12.6-1
from
ASCE
7-10.
The
main
difference
with
respect
to
ASCE
7-05
is
that
building
height
is
the
trigger
for
making
decisions,
rather
than
the
use
of
T
<
3.5Ts.
The
change
was
made
because
there
are
scenarios
under
the
ASCE
7-05
table
that
produced
illogical
results.
For
example,
there
were
scenarios
where
a
tall
building
on
soft
soil
in
Seattle
could
use
ELF,
whereas
a
shorter
building
on
stiff
soil
in
New
York
could
not.
Structural
Analysis:
Part
1 -25
Title
slide.
Structural
Analysis:
Part
1 -26
It
is
important
to
note
that
ALL
seismic
analysis
requires
ELF
analysis
in
one
form
or
another.
The
statement
that
ELF
may
not
be
allowed
as
a
“Design
Basis”
analysis
means
that
the
design
drifts
and
element
forces
may
need
to
be
based
on
more
advanced
analysis,
such
as
Modal
Response
Spectrum
or
Response
History
analysis.
Structural
Analysis:
Part
1 -27
There
is
a
significant
inconsistency
in
the
requirement
that
P-Delta
effects
be
represented
in
the
mathematical
model.
In
fact,
such
effects
should
NOT
be
included
in
the
model
because
they
are
evaluated
separately
in
Section
12.8.7.
Additionally,
direct
modeling
of
the
strength
of
the
elements
is
not
required
in
linear
analysis,
but
of
course,
would
be
needed
in
any
form
of
nonlinear
analysis.
Structural
Analysis:
Part
1 -28
Three
dimensional
analysis
is
required
for
this
system,
and
the
diaphragms
must
be
modeled
as
semi-rigid
because
the
reentrant
corners
prohibit
classification
of
the
diaphragms
as
rigid.
Regardless
of
this
requirement,
it
would
be
virtually
impossible
to
model
the
example
structure
in
2
dimensions.
In
most
cases
is
is
easier
to
model
a
structure
in
three
dimensions
than
in
two.
This
is
due
to
the
fact
that
most
modern
software
makes
it
easy
to
generate
the
model,
and
assumptions
do
not
need
to
be
made
as
to
the
best
way
to
separate
out
the
various
elements
for
analysis.
Additionally,
the
use
of
rigid
diaphragms
as
a
way
to
reduce
the
number
of
DOF
is
not
needed
because
the
programs
can
analyze
quite
complex
3D
systems
in
only
a
few
seconds.
Semi-rigid
diaphragms
are
easy
to
model
using
shell
elements,
and
very
coarse
meshes
may
be
used
if
it
is
not
desired
to
recover
diaphragm
stresses.
Structural
Analysis:
Part
1 -29
No
comment
required.
See
the
notes
on
the
following
slide.
Structural
Analysis:
Part
1 -30
Most
of
these
points
are
self-explanatory.
It
should
be
noted
that
the
use
of
centerline
analysis
in
steel
moment
frames
is
used
because
it
has
been
shown
that
offsetting
errors
lead
to
reasonable
results.
The
errors
in
centerline
analysis
are
that
(a)
shear
deformations
in
the
panel
zones
are
underestimated,
and
(b)
flexural
deformations
in
the
panel
zones
are
overestimated.
Many
programs
have
models
that
can
directly
include
panel
zone
beam
column
joint
deformations.
Several
programs
allow
the
use
of
rigid
end
zones,
but
this
should
never
be
done
because
it
drastically
overestimates
the
lateral
stiffness
of
the
structure.
Structural
Analysis:
Part
1 -31
The
basement
was
modeled
because
it
was
desired
to
run
the
interior
columns
down
to
the
basement
slab.
Structural
Analysis:
Part
1 -32
These
are
the
basic
steps
required
for
equivalent
lateral
force
analysis.
Each
of
these
points
are
discussed
in
the
following
several
slides.
It
should
be
noted
that
there
is
a
lot
of
detail
in
the
ELF
analysis,
and
thus
this
is
not
a
trivial
task.
There
are
numerous
requirements
scattered
throughout
ASCE
7,
and
sometimes
these
requirements
are
somewhat
ambiguous.
Anyone
attempting
an
ELF
analysis
(or
any
other
ASCE
7
analysis
for
that
mater)
should
read
the
entire
relevant
chapters
(11
and
12
in
this
case)
before
beginning
the
analysis.
Structural
Analysis:
Part
1 -33
Slide
provides
comments
on
computing
period
of
vibration.
Structural
Analysis:
Part
1 -34
Here
the
height
for
period
calculations
is
taken
as
the
height
above
grade.
This
is
reasonable
because
the
basement
walls
are
very
stiff,
and
because
the
perimeter
columns
are
embedded
in
pilasters
that
are
cast
with
the
walls.
Structural
Analysis:
Part
1 -35
The
Cu
adjustment
to
period
is
allowed
only
if
a
rational
(Eigenvalue
or
Rayleigh)
analysis
is
used
to
compute
a
period.
This
adjustment
removes
an
inherent
conservatism
in
the
statistics
used
to
derive
the
empirical
formula,
and
adjusts
for
seismicity
(recognizing
that
structures
in
lower
hazard
areas
are
likely
to
be
more
flexible
than
structures
in
high
hazard
areas).
The
period
used
in
base
shear
calculations
can
not
exceed
CuTa,
but
drifts
may
be
computed
on
the
basis
of
the
period
determined
from
rational
analysis.
Structural
Analysis:
Part
1 -36
If
a
computer
model
is
available
it
is
easy
to
estimate
the
period
using
this
approach.
The
lateral
load
pattern
should
be
of
the
same
approximate
shape
as
the
first
mode
shape.
An
upper
triangular
pattern
or
the
ELF
load
pattern
will
usually
suffice.
Structural
Analysis:
Part
1 -37
Both
of
the
rationally
computed
periods
exceed
CuTa,
so
CuTa
will
be
used
in
the
ELF
analysis.
Structural
Analysis:
Part
1 -38
The
periods
from
the
Eigenvalue
analysis
are
the
most
mathematically
precise.
As
seen,
these
are
very
close
that
those
produced
by
the
Rayleigh
method
(see
previous
slide).
Periods
computed
using
the
Rayleigh
method
should
generally
be
close
to,
but
slightly
less
than
those
computed
from
Eigenvalue
analysis.
Structural
Analysis:
Part
1 -39
This
slide
simply
summarizes
the
periods
found
by
the
three
different
methods.
The
distribution
of
periods
shown
is
not
uncommon.
It
is
the
author’s
experience
that
the
computed
period
is
almost
always
greater
than
CuTa
for
moment
frames.
Structural
Analysis:
Part
1 -40
This
slide
provides
asimple
summary
for
choosing
the
period
to
use
for
ELF
analysis.
Structural
Analysis:
Part
1 -41
This
slide
is
simply
a
key
for
use
in
describing
masses
computation
(see
following
slide).
Both
line
masses
and
area
masses
were
considered.
Structural
Analysis:
Part
1 -42
Slide
shows
calculations
for
computing
area
and
line
weights.
Structural
Analysis:
Part
1 -43
The
calculations
for
determining
total
seismic
weight
are
shown.
The
equivalent
lateral
forces
will
be
based
on
the
weight
of
the
structure
above
grade
(30,394
kips)
even
though
the
full
structure,
including
the
basement,
is
modeled.
The
location
of
the
CM
is
needed
because
the
equivalent
lateral
forces
are
applied
to
the
CM
at
each
level.
Structural
Analysis:
Part
1 -44
This
slide
shown
the
equations
that
are
needed
for
computing
the
design
base
shear.
Equation
12.8-4
is
not
needed
because
the
structures
period
is
less
than
TL.
Equation
12.66
is
not
needed
because
S1
<
0.6g.
Equation
12.8-5
controls
the
base
shear.
Note
that
this
equation
was
originally
not
used
in
ASCE
7-05
(where
the
the
minimum
was
instead
taken
as
0.01W).
Equation
12.8-5
as
shown
above
is
included
in
a
supplement
to
ASCE
7-05,
and
is
provided
as
shown
in
ASCE
7-10.
Structural
Analysis:
Part
1 -45
This
slide
shows
that
the
“Effective”
R
value
for
this
structure
is
4.54.
Thus,
the
anticipated
economy
inherent
in
the
use
of
R
=
8
has
not
been
realized.
Structural
Analysis:
Part
1 -46
Although
base
shear
may
be
controlled
by
Equation
12.8-5,
the
drifts
can
be
based
on
the
base
shear
computed
from
Eqn.
12.8-3,
and
furthermore,
the
computed
period
of
vibration
may
be
used
in
lieu
of
CuTa
for
drift
calculations.
This
means
that
a
separate
set
of
lateral
forces
may
be
computed
for
the
purposes
of
calculating
deflections
in
the
structure.
The
exception
shown
for
ASCE
7-10
did
not
exist
in
ASCE
7-05,
although
many
analysts
used
this
exception
anyway.
The
reason
is
shown
on
the
following
slide,
where
the
deflections
based
on
Eqn.
12.8-3
and
12.5-5
are
compared.
Structural
Analysis:
Part
1 -47
This
slide
shows
Equations
12.8-3
and
12.8-5
in
the
form
of
a
displacement
spectrum.
The
two
periods
are
from
the
Eigenvalue
analysis.
If
Equation
12.8-5
is
used
to
compute
forces
for
determining
drift,
the
drifts
would
increase
exponentially,
which
is
not
rational.
The
irrationality
is
due
to
the
fact
that
12.8-5
is
a
minimum
base
shear
formula,
and
is
NOT
a
true
branch
of
the
response
spectrum.
Structural
Analysis:
Part
1 -48
When
Eqn.
12.8-6
controls,
the
drifts
must
be
based
on
the
lateral
forces
computed
from
12.8-6.
Note
that
this
formula
is
not
dependent
on
period.
The
argument
for
requiring
that
Eqn.
12.8-6
be
used
for
drift
calculations
is
that
it
represents
the
the
“true”
spectral
shape…
it
is
not
a
minimum
base
shear
formula.
However,
for
longer
period
buildings,
Eqn.
12.8-6
can
lead
to
irrationally
large
displacements
because
the
deflections
will
increase
exponentially
with
period.
Structural
Analysis:
Part
1 -49
This
slide
summarizes
the
use
of
Equations
12.8-3and
12.8-5
when
computing
base
shear
and
drift.
Structural
Analysis:
Part
1 -50
This
slide
summarizes
the
use
of
Equations
12.8-3and
12.8-6
when
computing
base
shear
and
drift.
Structural
Analysis:
Part
1 -51
These
are
the
equations
for
determining
the
distribution
of
lateral
force
along
the
height.
The
exponent
k
is
determined
by
interpolation.
Structural
Analysis:
Part
1 -52
The
lateral
forces
are
computed
using
a
spreadsheet.
Note
that
the
forces
in
the
Xand
Y
directions
are
the
same
because
both
directions
are
controlled
by
the
same
minimum
base
shear
formula,
and
both
have
the
same
period
of
vibration
CuTa.
Structural
Analysis:
Part
1 -53
The
basic
analysis
assumptions
for
ELF
are
summarized
here.
And
on
the
following
slide.
Structural
Analysis:
Part
1 -54
Assumptions
on
ELF
analysis,
continued.
Structural
Analysis:
Part
1 -55
Previous
versions
of
ASCE
7
required
that
both
accidental
and
inherent
torsion
be
amplified
in
higher
SDCs
when
there
were
significant
torsional
irregularities.
Thus,
the
inherent
torsion
needed
to
be
separated
out
from
the
results
of
a
3D
analysis.
In
ASCE
7-05
and
ASCE
7-10,
the
inherent
torsion
need
not
be
amplified,
so
inherent
torsion
need
not
be
separated
out
when
a
3D
analysis
is
used.
If
a
planar
analysis
is
performed,
it
will
be
necessary
to
determine
the
inherent
torsion
loading
and
transform
it
into
in-plane
loads
on
the
frames.
Such
calculations
are
not
straightforward,
thus
3D
modeling,
which
may
seem
to
be
complex,
may
in
fact
be
simpler
than
2D
analysis.
Structural
Analysis:
Part
1 -56
The
structure
analyzed
will
require
accidental
torsion
analysis
because
the
diaphragms
are
not
flexible.
Structural
Analysis:
Part
1 -57
Excerpt
of
ASCE
7
showing
requirements
for
accidental
torsion.
Structural
Analysis:
Part
1 -58
Three
dimensional
structural
analysis
is
required
to
determine
if
the
structure
has
torsion
irregularities.
In
the
analysis,
the
ELF
loads
determined
earlier
are
applied
at
a
5%
eccentricity
as
required.
Note
that
the
torsion
irregularity
calculations
are
based
on
interstory
DRIFT,
not
story
displacement.
On
the
other
hand,
torsional
amplification
(when
required)
is
based
on
story
displacement,
not
drift.
Structural
Analysis:
Part
1 -59
In
the
analysis
the
direct
lateral
load
and
the
torsional
loads
are
applied
separately.
The
direct
loading
is
shown
here.
These
forces
have
been
computed
to
represent
center
of
mass
loading
on
the
diaphragms.
A
similar
set
of
forces
(not
shown)
were
computed
in
the
Y
direction.
Structural
Analysis:
Part
1 -60
These
forces
represent
the
accidental
torsion
due
to
X-direction
forces
applied
at
a
5%
eccentricity.
A
similar
set
of
forces
(not
shown)
were
computed
for
the
Y
direction
loading.
Structural
Analysis:
Part
1 -61
This
slide
shows
the
stations
for
which
displacements
were
calculated
to
determine
torsional
irregularity
due
to
lateral
forces
applied
in
the
Y
direction.
Structural
Analysis:
Part
1 -62
There
is
no
torsional
irregularity
for
loading
in
the
X
direction.
Structural
Analysis:
Part
1 -63
There
is
a
very
minor
torsional
irregularity
a
level
9
for
loads
applied
in
the
Y
direction.
It
would
probably
be
best
to
redesign
the
structure
to
eliminate
the
irregularity.
However,
the
consequences
of
the
irregularity
are
not
severe.
Note
that
the
double
entries
for
displacements
in
some
locations
(Levels
5
and
9)
is
due
to
the
setbacks.
This
was
discussed
on
a
previous
slide
that
showed
the
deflection
monitoring
stations
for
this
loading.
Structural
Analysis:
Part
1 -64
No
torsional
amplification
is
required
for
this
structure.
Structural
Analysis:
Part
1 -65
This
is
directly
from
ASCE
7.
No
additional
commentary
required.
Structural
Analysis:
Part
1 -66
ASCE
7
states
that
for
structures
with
“Significant
Torsional
Deflections”,
the
maximum
drift
shall
include
torsional
effects.
This
language
is
vague,
because
it
is
not
clear
what
“significant”
is,
and
it
is
not
clear
how
torsional
effects
should
be
included
(inherent
torsion,
inherent
plus
accidental
torsion,
inherent
plus
amplified
accidental
torsion?).
The
authors
assumed
that
this
structure
did
not
have
significant
torsional
deflections,
and
thereby
did
not
include
accidental
torsion
loading
in
the
analysis.
Inherent
torsion
was,
of
course,
included
in
the
analysis.
Deflections
were
computed
at
center
of
mass,
not
at
the
edges
of
the
building.
As
shown
later,
this
building
is
relatively
stiff,
and
the
drifts
are
significantly
less
than
allowed.
Had
the
drifts
been
closer
to
the
allowed
drifts,
it
might
have
been
appropriate
to
determine
the
drifts
at
the
edge
of
the
building.
Structural
Analysis:
Part
1 -67
This
issue
was
discussed
in
earlier
slides.
In
the
present
analysis
drift
is
computed
on
the
basis
of
lateral
forces
computed
using
Eqn.
12.8-3
with
T
=
CuTa.
Has
the
drifts
from
this
analysis
exceeded
the
allowable
drift,
a
reanalysis
would
have
been
permitted
using
the
periods
for
Rayleigh
or
Eigenvalue
analysis.
Structural
Analysis:
Part
1 -68
The
drifts
have
been
determined
on
the
basis
of
lateral
loads
from
Eqn.
12.8-5,
and
have
been
modified
to
be
consistent
with
Eqn
12.8-3,
which
uses
CuTa
as
the
period
of
vibration.
Note
that
the
computed
periods
from
Eigenvalue
analysis
could
have
been
used
instead,
and
the
resulting
drifts
would
be
even
lower.
If
the
drifts
had
been
based
on
lateral
forces
consistent
with
Eqn.
12.8-5,
the
drifts
would
have
been
excessive.
However,
the
computed
drifts
are
significantly
less
than
the
limits
when
the
adjustment
is
made.
Structural
Analysis:
Part
1 -69
The
comments
on
the
previous
slide
apply
to
this
slide
as
well.
Structural
Analysis:
Part
1 -70
This
slide
provides
the
basic
expressions
used
in
P-Delta
analysis.
Note
that
the
deflections
“Delta”
in
equation
12.8-16
are
for
the
analysis
without
P-Delta
effects
included.
Structural
Analysis:
Part
1 -71
For
this
structure
the
maximum
stability
factor
of
0.091
is
marginally
exceeded
for
the
bottom
three
levels
of
the
structure.
However,
this
is
based
on
conservative
estimates
of
live
load,
and
the
“Beta”
factor
used
to
compute
.max
was
taken
conservatively
as
1.0.
Actual
values
of
this
factor
are
likely
to
be
significantly
less
than
1.0,
so
the
analysis
will
proceed
as
if
P-Delta
provisions
are
satisfied.
Structural
Analysis:
Part
1 -72
This
structure
has
a
type
5
horizontal
irregularity
under
the
provisions
of
ASCE
7-05,
but
not
under
ASCE
7-10.
This
is
because
the
symmetry
requirement
included
in
the
nonparallel
system
irregularity
has
been
eliminated
(see
Table
12.3-1).
As
this
example
was
written
principally
for
accordance
with
ASCE
7-05,
orthogonal
loading
is
included.
Additionally,
this
structure
uses
a
perimeter
moment
frame,
and
the
corner
columns
will
be
affected
by
loading
from
two
directions.
Structural
Analysis:
Part
1 -73
The
100/30
percent
loading
is
used
for
this
structure.
Structural
Analysis:
Part
1 -74
The
modification
in
ASCE
7-10
is
significant,
because
many
structures
deemed
irregular
due
to
nonsymmetric
systems
in
ASCE
7-05
are
longer
irregular.
Thus,
orthogonal
loading
may
no
longer
be
required
for
may
SDC
D,
E,
and
F
structures.
Structural
Analysis:
Part
1 -75
This
slide
shows
the
16
basic
seismic
loadings
that
are
required
when
accidental
torsion
and
orthogonal
loading
requirements
are
met.
When
the
two
basic
gravity
loadings
are
included,
it
is
seen
that
32
seismic
load
cases
are
required.
Structural
Analysis:
Part
1 -76
These
are
the
basic
gravity
plus
seismic
load
combinations.
The
snow
and
hydrostatic
loads
are
not
applicable,
and
are
crossed
out.
There
would
be
no
requirement
to
use
the
similar
load
combinations
including
the
overstrength
factor
.....0,
so
this
is
not
shown.
The
two
gravity
loadings
in
combination
with
the
16
seismic
loads
produce
a
total
of
32
seismic
load
combinations.
This
is
in
addition
to
the
gravity
only
and
gravity
plus
wind
combinations
that
would
be
required.
Structural
Analysis:
Part
1 -77
The
structure
is
not
regular,
so
only
subparagraph
(a)
applies.
Structural
Analysis:
Part
1 -78
It
is
very
clear
that
the
removal
of
a
single
beam
in
this
highly
redundant
perimeter
moment
frame
structure
would
not
cause
an
extreme
torsional
irregularity
or
a
reduction
in
strength
of
more
than
33
percent.
These
redundancy
calculations
would
only
be
required
for
systems
with
only
one
or
two
bays
of
resisting
frame
in
each
direction.
Thus,
for
the
Stockton
building,
the
.factor
is
taken
as
1.0.
Structural
Analysis:
Part
1 -79
This
slide
provides
the
maximum
beam
shears
in
Frame
1
of
the
structure.
These
include
lateral
loads
only,
without
gravity
and
without
accidential
torsion.
Accidental
torsional
forces
are
included
separately
(see
next
slide).
Separation
of
the
torsional
forces
facilitates
the
comparison
of
the
results
from
the
three
methods
of
analysis.
Additionally,
the
torsional
forces
determined
in
the
ELF
analysis
would
be
used
(with
possibly
some
reduction)
in
the
response
spectrum
and
response
history
calculations.
Structural
Analysis:
Part
1 -80
These
are
the
accidental
torsion
forces
on
Frame
1.
See
also
the
comments
for
the
previous
slide.
Note
that
these
forces
are
applicable
to
all
three
analysis
methods
because
both
the
MRS
and
the
MRH
methods
apply
accidental
torsion
using
the
ELF
procedure.
Structural
Analysis:
Part
1 -81
Title
slide.
No
commentary
provided.
Structural
Analysis:
Part
1 -82
These
are
the
basic
steps
in
a
modal
response
spectrum
analysis.
Many
of
the
steps
are
required
for
ELF
analysis,
so
the
amount
of
additional
work
is
not
substantial,
and
the
additional
work
that
is
required
(steps
6,
7,
and
8)
is
generally
done
by
the
computer.
Structural
Analysis:
Part
1 -83
Note
that
P-Delta
effects
are
handled
in
exactly
the
same
manner
as
for
ELF.
Thus,
P-Delta
effects
should
not
be
included
when
computing
the
mode
shapes
and
frequencies.
ASCE
7
requires
that
drift
be
checked
at
the
center
of
mass,
but
this
is
not
easily
done
when
the
masses
are
not
vertically
aligned.
The
new
ASCE
7-10
provision
addresses
the
problem.
Drifts
computed
at
the
corners
of
the
building
would
be
conservative
(exceeding
the
requirements
for
center
of
mass
calculations)
and
are
much
easier
to
calculate.
The
vertical
alignment
approach
described
in
ASCE
7-10
was
used
in
the
example.
Structural
Analysis:
Part
1 -84
This
procedure
would
be
used
for
a
system
with
significant
torsional
displacements.
It
was
not
required
for
the
building
under
consideration.
Structural
Analysis:
Part
1 -85
One
of
the
complications
to
response
spectrum
analysis
is
that
member
forces
must
generally
be
scaled
up
such
that
the
base
shear
from
the
response
spectrum
analysis
is
not
less
than
85
percent
of
the
ELF
shears.
Accidental
torsional
forces
would
be
scaled
using
the
same
factor.
This
85
percent
rule
provides
some
incentive
for
performing
MRS
analysis
because
the
15
percent
reduction
in
base
shear
is
usually
allowed.
This
is
due
to
the
fact
that
the
computed
periods
based
on
Eigenvalue
analysis
are
generally
much
longer
than
periods
computed
using
CuTa.
Note,
however,
that
in
the
unlikely
case
that
the
MRS
analysis
produces
shears
greater
than
those
from
ELF,
there
are
no
provisions
for
scaling
the
results
down
to
the
ELF
forces.
Deflections
computed
from
MRS
analysis
may
be
used
directly,
without
scaling.
This
is
consistent
with
allowing
deflections
to
be
based
on
the
computed
period,
without
the
CuTa
limit,
in
ELF
analysis.
Structural
Analysis:
Part
1 -86
This
plot
simply
shows
the
first
four
mode
shapes
and
associated
periods
from
the
SAP
2000
analysis.
Structural
Analysis:
Part
1 -87
The
next
four
mode
shapes
are
shown
here.
There
is
significant
lateral-torsional
interaction
because
of
the
setbacks.
Structural
Analysis:
Part
1 -88
This
provision
is
based
on
the
assumption
that
the
heavy
basement
walls
and
ground
level
slab
are
not
modeled
in
the
system.
The
basement
has
significant
mass,
and
that
mass
does
not
appear
until
modes
100
and
above
in
this
structure.
Had
the
structure
been
modeled
as
fixed
at
the
base
of
the
first
story
columns,
only
the
first
dozen
or
so
modes
would
be
required
to
capture
85
percent
of
the
mass
in
each
direction.
The
authors
believe
that
the
ASCE
7
language
should
be
modified
to
account
for
such
problems.
Furthermore,
a
sufficient
modes
should
be
used
to
capture
85
percent
of
the
torsional
mass.
Structural
Analysis:
Part
1 -89
Only
82
percent
of
the
total
lateral
mass
is
captured
by
mode
12.
The
third
mode
is
principally
torsion,
and
with
12
modes
only
75
percent
of
the
torsional
mass
is
captured.
Structural
Analysis:
Part
1 -90
At
mode
108
the
lateral
mass
has
only
marginally
increased.
At
mode
112
the
mass
associated
with
the
basement
finally
appears
in
the
Y
direction.
This
mass
shows
up
at
mode
118
in
the
X
direction.
The
torsional
mass
has
still
not
reached
85
percent,
even
at
mode
119.
Structural
Analysis:
Part
1 -91
Only
the
first
12
modes
were
used
in
the
analysis,
as
this
captured
more
than
90
percent
of
the
mass
in
each
direction.
Structural
Analysis:
Part
1 -92
These
are
the
response
spectrum
ordinates
used
in
the
analysis.
The
R
factor
is
included
in
the
spectrum.
Structural
Analysis:
Part
1 -93
A
question
arises
when
the
ELF
base
shear
is
based
on
the
absolute
minimum
of
0.01W.
The
Standard
is
not
clear
on
whether
the
scaling
would
effectively
lower
this
minimum
to
0.0085W.
In
the
author’s
opinion,
the
scaling
of
the
MRS
results
should
not
produce
a
base
shear
less
than
the
absolute
minimum
of
0.01W.
Structural
Analysis:
Part
1 -94
Drifts
need
be
scaled
only
if
the
ELF
base
shear
is
based
on
equation
12.8-6.
This
is
consistent
with
the
requirements
of
ELF.
Structural
Analysis:
Part
1 -95
The
MRS
analysis
automatically
accounts
for
inherent
torsion.
Accidental
torsion
is
generally
included
by
direct
addition
of
the
the
ELF
static
torsion
effects,
scaled
in
accordance
with
the
85
percent
rule,
if
applicable.
Note
that
when
static
accidental
torsions
are
used,
they
may
need
to
be
amplified
in
accordance
with
Section
12.8.4.3.
Accidental
torsion
need
not
be
amplified
if
is
is
included
in
the
dynamic
analysis,
presumably
by
physically
shifting
of
the
mass
eccentricities.
See
Section
12.9.5
of
ASCE
7.
Structural
Analysis:
Part
1 -96
This
is
one
of
two
approaches
to
handle
orthogonal
loading
in
MRS
analysis.
The
approach
shown
on
the
next
slide
is
preferred.
Structural
Analysis:
Part
1 -97
This
approach,
while
not
specifically
described
in
ASCE
7,
is
preferred.
This
method
is
somewhat
more
conservative
than
the
method
given
on
the
previous
slide
because
it
will
provide
a
uniform
resistance
for
“all
possible
angles
of
attack”
of
the
earthquake.
Programs
like
SAP2000
and
ETABS
can
automatically
implement
this
procedure
(or
the
procedure
shown
on
the
previous
slide).
Structural
Analysis:
Part
1 -98
This
slide
shows
the
modal
shears
for
each
level
as
computed
using
the
MRS
approach.
The
X
direction
base
shear
is
438.1
kips,
and
the
Y
direction
shear
is
492.8
kips.
Thus,
all
of
the
story
shears
and
related
member
forces
need
to
be
scale
up
to
0.85
times
the
ELF
base
shear
of
1124
kips.
The
scale
factors
are
2.18
and
1.94
in
the
X
and
Y
directions,
respectively.
Structural
Analysis:
Part
1 -99
The
modal
story
drifts
in
the
second
column
come
directly
from
the
analysis,
and
are
not
scaled.
These
drifts
already
include
the
effect
of
R,
which
was
included
in
the
response
spectrum.
The
story
drifts
are
generally
not
equal
to
the
difference
in
the
total
drifts,
as
these
are
determined
individually
in
each
mode
and
then
SRSSed.
The
story
drifts
are
multiplied
by
Cd
in
the
fourth
column.
The
final
Cd
scaled
drifts
are
significantly
less
than
the
allowable
drifts,
indicating
that
this
structure
is
probably
too
stiff
as
currently
designed.
These
displacements
will
be
compared
to
the
ELF
and
MRH
displacements
at
the
end
of
this
slide
set.
Structural
Analysis:
Part
1 -100
See
previous
slide
for
discussion
Structural
Analysis:
Part
1 -101
The
beam
shears
are
found
in
each
mode,
and
then
combined
by
SRSS.
The
shears
shown
on
this
slide
have
been
scaled
such
that
they
are
consistent
with
(85%
scaled)
scaled
base
shears.
These
shears
will
be
compared
to
the
ELF
and
MRH
shears
at
the
end
of
this
slide
set.
Structural
Analysis:
Part
1 -102
Title
slide.
Structural
Analysis:
Part
1 -103
This
slide
shows
the
basic
steps
in
the
Modal
Response
History
method.
Many
of
the
steps
are
the
same
as
required
for
ELF
or
MRS
analysis.
The
largest
“new”
item
is
the
selection
and
scaling
of
the
ground
motions,
and
the
running
of
the
dynamic
analysis.
Structural
Analysis:
Part
1 -104
This
slide
lists
the
steps
required
to
determine
drift.
Drifts
are
taken
directly
from
the
analysis,
and
need
not
be
scaled
other
than
by
the
ratio
of
Cd/R.
All
drifts
are
calculated
at
the
center
of
mass.
Note
that
P-Delta
effects
are
checked
using
the
same
procedure
as
used
for
the
ELF
and
MRS
analysis.
Therefore,
P-Delta
effects
should
not
be
included
in
the
dynamic
analysis.
Structural
Analysis:
Part
1 -105
The
only
difference
between
this
slide
and
the
previous
slide
is
that
when
there
are
significant
torsional
deflections,
the
drift
should
be
computed
at
the
corner
of
the
building.
This
was
not
done
here
as
the
structure
did
not
have
a
significant
torsional
response.
Structural
Analysis:
Part
1 -106
This
is
the
procedure
for
determining
design
seismic
member
forces.
The
significant
point
in
this
slide
is
that
the
scaling
to
85
percent
of
the
design
base
shear
will
be
required
if
the
dynamic
base
shears
are
less
than
the
85
percent
of
the
ELF
shears.
Structural
Analysis:
Part
1 -107
The
ASCE
7-10
requirements
for
selecting
ground
motion
are
shown
here.
Selecting
an
appropriate
number
of
records
that
satisfy
the
criteria
can
be
challenging
because
there
are
few
available
recordings
of
design
level
ground
motions.
There
is
a
general
consensus
that
“more
is
better”
when
running
response
history
analysis.
If
fact,
ASCE
7
rewards
the
engineer
when
seven
or
more
motions
are
used
as
the
average
response
among
the
seven
may
be
used
when
determining
design
values.
The
peak
response
must
be
used
if
less
than
seven
motions
are
included
in
the
analysis.
One
must
not
use
fewer
than
three
records
under
any
circumstances.
Structural
Analysis:
Part
1 -108
The
scaling
requirements
for
the
ground
motions
are
based
on
ASCE
7-10.
This
results
in
somewhat
lower
scale
factors
than
used
in
ASCE
7-05.
Here
it
is
important
to
note
that
that
there
are
several
sets
of
scale
factors
applied
in
the
analysis:
(1)
Scaling
by
ratio
of
I/R
(2)
Ground
motion
scaling
as
indicated
above
(3)
Scaling
to
85%
of
ELF
base
shear
Structural
Analysis:
Part
1 -109
Ground
motions
must
be
scaled
to
be
compatible
with
the
design
spectrum.
There
are
numerous
was
to
do
scaling,
and
there
is
no
consensus
as
to
which
is
the
best
approach.
In
ASCE
7-10,
the
first
step
in
scaling
(for
3D
analysis)
is
to
take
the
square
root
of
the
sum
of
the
squares
of
the
5%
damped
spectra
for
the
two
orthogonal
components
from
each
earthquake.
Next,
each
of
these
SRSS
spectra
are
multiplied
by
a
scale
factor.
Then,
the
average
of
the
three
Scaled
Spectra
is
computed.
The
chosen
scale
factors
must
be
established
such
that
the
average
spectra
lies
above
the
design
spectra
for
the
period
range
of
0.2T
to
1.5T,
where
T
is
the
period
of
vibration
of
the
structure.
In
the
example,
the
Match
Point
is
that
point
at
which
the
scaled
average
scaled
spectrum
and
the
target
spectrum
have
the
same
ordinate.
In
the
example
given,
note
how
the
average
scaled
spectral
ordinate
is
far
above
the
target
spectrum
at
the
structures
period
of
vibration.
This
is
one
of
the
consequences
in
the
ASCE
7
method.
Structural
Analysis:
Part
1 -110
These
points
are
in
addition
to
the
problem
discussed
in
the
commentary
in
the
last
slide.
Regarding
the
first
point,
the
authors
chose
to
scale
to
the
average
of
the
two
first
mode
fundamental
periods.
Another
choice
would
be
to
scale
over
the
range
of
0.2
times
the
smaller
period
to
1.5
times
the
larger
period.
To
some
the
second
point
is
not
important
because
it
is
unlikely
that
different
engineers
would
use
the
same
set
of
ground
motions.
However,
the
current
method
allows
the
designer
to
apply
scale
factors
in
a
arbitrary
manner,
and
this
allows
the
designer
to
scale
down
“offending”
ground
motions.
In
nonlinear
analysis
the
periods
elongate,
so
it
makes
sense
to
consider
this
when
scaling.
For
linear
analysis,
the
periods
do
not
change,
and
there
is
no
reason
to
scale
at
periods
above
T
(unless
one
is
trying
to
manage
uncertainties
related
to
computing
T).
The
final
point
is
related
to
the
problem
illustrated
in
the
previous
slide.
The
higher
modes
dominate
the
scaling,
even
though
they
may
contribute
very
little
to
the
dynamic
response.
Structural
Analysis:
Part
1 -111
As
already
mentioned,
the
third
approach
was
used
in
this
example.
Structural
Analysis:
Part
1 -112
In
this
example
a
two-step
scaling
approach
is
used.
First,
the
SRSS
of
each
component
pair
are
scaled
to
match
the
target
spectrum
at
the
period
Tavg.
This
factor
will
be
different
for
each
of
SRSS
spectra.
Structural
Analysis:
Part
1 -113
The
average
of
the
scaled
spectra
will
match
the
target
spectrum
at
Tavg.
Now
a
second
factor
is
applied
equally
to
each
motion
(already
scaled
once)
such
that
the
scaled
average
spectrum
lies
above
the
target
spectrum
from
0.2Tavg
to
1.5Tavg.
Structural
Analysis:
Part
1 -114
The
final
scale
factor
for
each
motion
is
the
product
of
the
two
scale
factors.
By
use
of
this
approach
all
engineers
will
arrive
at
the
same
scale
factors
for
the
same
set
of
motions.
Structural
Analysis:
Part
1 -115
The
actual
records
used
form
the
analysis
are
shown
in
this
slide.
These
records
came
from
the
PEER
NGA
database.
They
are
referred
to
as
sets
A,
B,
and
C
herein.
Structural
Analysis:
Part
1 -116
This
slide
shows
the
unscaled
SRSS
spectra
for
each
motion
pair,
together
with
the
target
spectrum.
Structural
Analysis:
Part
1 -117
This
slide
shows
the
average
of
the
S1
scaled
spectra
for
the
three
earthquakes.
Note
the
perfect
match
at
the
target
period.
Structural
Analysis:
Part
1 -118
This
slide
shows
the
ratio
of
the
target
spectrum
to
the
S1
Scaled
spectra
over
the
target
period
range.
Structural
Analysis:
Part
1 -119
The
spectrum
final
scaled
spectrum
is
compared
to
the
target
spectrum
here.
There
is
a
pretty
good
match
at
periods
between
0.5
seconds
and
5.0
seconds,
but
the
match
is
not
so
good
in
the
higher
modes.
Structural
Analysis:
Part
1 -120
This
plot
shows
the
individual
scaled
components
in
the
00
direction.
Note
that
the
component
spectra
fall
below
the
target
spectra
because
the
components
are
not
“amplified”
by
the
SRSS
procedure.
The
SRSS
of
the
component
pairs
would
be
closer
to
the
target
spectrum.
Structural
Analysis:
Part
1 -121
See
the
comment
on
the
previous
slide.
Structural
Analysis:
Part
1 -122
This
slide
shows
the
final
computed
scale
factors.
Note
that
each
component
pair
receives
its
own
S1
factor,
and
all
records
use
the
same
S2
factor.
Structural
Analysis:
Part
1 -123
Chapter
16
of
ASCE
7
does
not
provide
guidance
on
the
number
of
modes
to
use
in
modal
response
history
analysis.
It
seems
logical
to
follow
the
same
procedures
as
given
in
Chapter
12
for
modal
response
spectrum
analysis,
and
this
was
done
for
the
example
building.
Structural
Analysis:
Part
1 -124
Chapter
16
of
ASCE
7
does
not
provide
guidance
on
damping
in
response
history
analysis.
It
seems
logical
to
use
5%
damping
in
each
mode
as
this
was
used
in
the
development
of
the
response
spectra.
Thus,
5%
was
used
in
the
example.
Note,
however
the
that
use
of
5%
damping
in
nonlinear
response
history
analysis
is
probably
unconservative.
The
use
of
a
lower
value,
say
2%
critical,
is
generally
recommended
for
nonlinear
analysis.
Structural
Analysis:
Part
1 -125
These
points
are
explained
in
the
following
slides.
Structural
Analysis:
Part
1 -126
The
response
history
shears
should
be
scaled
up
to
85%
of
the
minimum
base
shear.
Structural
Analysis:
Part
1 -127
No
scaling
is
required
when
the
MRH
shear
is
greater
than
the
Minimum
Base
Shear.
Structural
Analysis:
Part
1 -128
This
slide
compares
response
spectrum
scaling
with
response
history
scaling.
Structural
Analysis:
Part
1 -129
These
are
the
individually
scaled
GM
used
in
the
analyses.
Structural
Analysis:
Part
1 -130
This
slide
shows
the
maximum
response
quantities
from
the
SS
scaled
ground
motions.
There
is
a
huge
variation
(considering
the
fact
that
all
records
were
scaled
in
a
similar
manner
to
the
same
target
spectrum),
with
base
shears
ranging
from
a
low
of
1392
kips
to
a
high
of
5075
kips.
The
variation
in
other
response
quantities
are
similar.
It
is
difficult
to
determine
the
source
of
these
variations,
which
include
the
scaling
method,
the
difference
between
components,
and
higher
mode
effects.
Structural
Analysis:
Part
1 -131
Here
the
individual
scale
factors
are
provided.
These
factors
“normalize”
the
responses
to
have
the
same
base
shear
as
given
by
85
percent
of
the
ELF
base
shear.
It
is
notable
that
all
of
the
ground
motions
had
to
be
scaled
up.
Structural
Analysis:
Part
1 -132
The
computed
drift
envelopes
are
shown
here.
The
drifts
shave
been
scaled
by
Cd/R,
but
no
“85%”
scaling
is
required.
As
with
the
other
methods,
the
drifts
appear
to
be
well
below
the
limits,
indicating
that
the
structure
is
probably
too
stiff.
Structural
Analysis:
Part
1 -133
This
slide
shows
the
various
load
combinations.
Note
that
100
percent
of
the
“85%”
scaled
motions
were
applied
in
each
direction.
Structural
Analysis:
Part
1 -134
This
slide
shows
the
envelopes
of
all
of
the
“85%”
scaled
beam
shears
on
Frame
1.
These
will
be
compared
to
the
results
from
the
other
methods
at
the
end
of
the
presentation.
Structural
Analysis:
Part
1 -135
Title
slide.
Structural
Analysis:
Part
1 -136
The
story
shears
are
comparable
due
to
the
scaling
of
the
MRS
and
MRH
results.
However,
it
seems
that
he
shears
in
the
upper
levels
are
relatively
greater
in
the
MRH
analysis.
This
is
probably
due
to
the
higher
spectral
acceleration
in
the
higher
modes
(when
compared
to
the
target
spectrum).
Structural
Analysis:
Part
1 -137
The
ELF
method
produces
the
largest
drifts.
However,
these
drifts
were
based
on
aperiod
of
CuTa,
and
not
on
the
computed
system
period.
The
response
history
drifts
are
larger
at
the
upper
levels,
reflecting
the
influence
of
the
higher
modes.
Structural
Analysis:
Part
1 -138
Again,
the
beam
shears
are
larger
in
the
upper
levels
when
computed
using
response
history.
As
with
drift
and
story
shear,
this
is
attributed
to
higher
mode
effects
accentuated
by
high
spectral
accelerations
at
lower
periods
(when
compared
to
the
target
spectrum).
Structural
Analysis:
Part
1 -139
Title
slide.
Structural
Analysis:
Part
1 -140
Slide
comparing
relative
effort
of
various
methods
of
analysis.
Structural
Analysis:
Part
1 -141
Slide
describes
accuracy
in
analysis.
Structural
Analysis:
Part
1 -142
These
are
the
author’s
opinion
and
do
not
necessarily
reflect
the
views
of
ASCE
or
BSSC.
Structural
Analysis:
Part
1 -143
This
slide
is
intended
to
initiate
questions
for
the
participants.
Structural
Analysis:
Part
1 -144