1 Composite Steel/Concrete
2 Introduction
Outline For The Presentation
Background and Overview
Example Building
PR Composite Connection Design
Loads and Load Combinations
Analysis
ASCE 7-10 and AISC Design Checks
Questions
3 Background & Overview
Composite Partially Restrained Moment Frame (C-PRMF)
Typically Consists Of:
Standard W-Shape Steel Columns
Composite W-Shape Steel Beams
Partially Restrained Composite Connections (PRCC)
4 Background & Overview
Different From A Typical Moment Frame
The PRCC is what makes the difference
Not as strong (Partial Strength Vs. Full Strength)-Typically designed as partial strength
Not as stiff (Angle between beam end and column does not stay at right angle)
Cant neglect the connection behavior through simplifying assumptions in the analysis
5 Background & Overview
Different From A Typical Moment Frame
The connections become the seismic fuses for seismic energy dissipation (need ductile connections)
Limited yielding of beams and columns
Required to engage more frames because of the reduced stiffness and strength
Highly redundant lateral force resisting system
Typically simple fabrication and erection details are used allowing quicker fabrication and erection
Cannot delegate the design to the fabricator
PRCC connections are not fully effective until the concrete hardens similar to waiting for moment connections to get welded
6 Background & Overview
ASCE 7-10 Provisions
7 Background & Overview
ASCE 7-10 Provisions
14.3 Composite Steel and Concrete Structures
14.3.1 Reference Documents
The design, construction, and quality of composite steel and concrete members that resist seismic forces shall conform to the applicable requirements of the following:
1. AISC 341
2. AISC 360
3. ACI 318, excluding Chapter 22
14.3.2 General
Systems of structural steel acting compositely with reinforced concrete shall be designed in accordance with AISC 360 and ACI 318, excluding Chapter 22. Where required, the seismic design of composite steel and concrete systems shall be in accordance with the additional provisions of Section 14.3.3.
8 Background & Overview
ASCE 7-10 Provisions
14.3 Composite Steel and Concrete Structures
14.3.3 Seismic Requirements for Composite Steel and Concrete Structures
Where a response modification coefficient, R, in accordance with Table 12.2-1 is used for the design of systems of structural steel acting compositely with reinforced concrete, the structures shall be designed and detailed in accordance with the requirements of AISC 341.
9 Background & Overview
AISC 341-05 Provisions
Part II Section 8. COMPOSITE PARTIALLY RESTRAINED (PR) MOMENT FRAMES (C-PRMF)
8.1. Scope
This Section is applicable to frames that consist of structural steel columns and composite beams that are connected with partially restrained (PR) moment connections that meet the requirements in Specification Section B3.6b(b). Composite partially restrained moment frames (C-PRMF) shall be designed so that under earthquake loading yielding occurs in the ductile components of the composite PR beam-to-column moment connections. Limited yielding is permitted at other locations, such as column base connections. Connection flexibility and composite beam action shall be accounted for in determining the dynamic characteristics, strength and drift of C-PRMF.
10 Background & Overview
AISC 341-05 Provisions
Part II Section 8
8.2. Columns
Structural steel columns shall meet the requirements of Part I Sections 6 and 8 and the
Specification.
8.3. Composite Beams
Composite beams shall be unencased, fully composite and shall meet the requirements of
Specification Chapter I. For purposes of analysis, the stiffness of beams shall be determined with an effective moment of inertia of the composite section.
8.4. Moment Connections
The required strength of the beam-to-column PR moment connections shall be determined considering the effects of connection flexibility and second-order moments. In addition, composite connections shall have a nominal strength that is at least equal to 50 percent of Mp, where Mp is the nominal plastic flexural strength of the connected structural steel beam ignoring composite action. Connections shall meet the requirements of Section 7 and shall have a total interstory drift angle of 0.04 radians that is substantiated by cyclic testing as described in Part I Section 9.2b.
11 Background & Overview
Other Design Guidance
AISC Design Guide 8 1996
ASCE Design Guide for Partially Restrained Composite Connections 1998 (Journal of Structural Engineering)
12 Example Building
Building Plan
13 Example Building
Building Elevations
14 Example Building
Building 3-D SAP 2000 Model
15 PR Composite Connection Design
Typical W18x35 PRCC
16 PR Composite Connection Design
Typical W18x35 PRCC
17 PR Composite Connection Design
Connection Moment-Rotation Curves
Two Curves Required:
Service Analysis Curves From ASCE TC Paper
18 PR Composite Connection Design
Connection Moment-Rotation Curves
Two Curves Required:
Strength Analysis Curves Based on Modifications of the Service Analysis Curves to Account for Direct Analysis Approach to Design
19 PR Composite Connection Design
Connection Moment-Rotation Curves
W18x35 PRCC Moment Rotation Curves
20 PR Composite Connection Design
Connection Moment-Rotation Curves
W18x35 PRCC Key Connection Curve Values
21 PR Composite Connection Design
Longitudinal Reinforcing Steel
22 PR Composite Connection Design
Longitudinal Reinforcing Steel
Minimum 6 Bars Distributed Evenly Over An Effective Width of 7 Column Flanges
Choose Sufficient Reinforcing To Reach Desired Strength Goals
Limit Reinforcing To Ensure Ductile Failure of Reinforcing Before Other Possible Non-Ductile
Connection Failures
Use #6 or Smaller Bar Size
Distribute As Close to Equal on Each Side of Column Center Line As Possible
Minimum Of 33% of Reinforcing On One Side Of Column
Minimum Of 3 Bars On One Side Of Column
All Bars Should Extend Ό Of The Beam Span Or 24 Bar Diameters Past the Inflection Point
For Seismic Design Detail 50% of Bars As Continuous
Continuous bars should be spliced with Class B lap per ACI 318
Minimum cover per ACI 318
23 PR Composite Connection Design
Transverse Reinforcing Steel
24 PR Composite Connection Design
Transverse Reinforcing Steel
Provided To Promote The Force Transfer From Longitudinal Steel To Column And To Beam
Flange
Allows Development Of Strut And Tie Fields For Force Transfer To Column Basis For
Selection Of Reinforcing
Prevents Longitudinal Splitting Over Beam To Allow Force Transfer To Studs Then To Beam
Flange Reason To Keep Transverse Steel Below Top Of Shear Studs
Use #6 Or Smaller Bars
Typically Same Number As
Longitudinal Steel
Extend 12 bar diameters or 12 Past Outside Longitudinal Bars
25 PR Composite Connection Design
Concrete to Column Force Transfer
Transfer Slab Compression Force From One Side Of Connection Combined With Slab Tension Force From Other Side Of Connection Through Bearing Of Concrete On Column Flanges
Typically Taken As The Combination Of Mc- And Mc+ Of The Connection
Limit Bearing Stress to 1.8 fc
Check Flange Local Bending
Check Web Local Yielding
Concrete Between Flanges
Provide Sufficient Studs To Develop Slab Forces Within Inflection Points Each Side Of Column
26 PR Composite Connection Design
Connection Moment Capacity Limits
AISC 341 Part II Section 8.4 Requires A Minimum Nominal Connection Capacity Of 50% Of
Nominal Bare Steel Beam, Mp
ASCE TC Recommends 75% As The Target With 50% Lower Limit And 100% Upper Limits
Determine Nominal Connection Strengths At Target Rotations:
20 mrad For Negative Connection Moment Capacity
10 mrad For Positive Connection Moment Capacity
Not Clear If This Requirement Applies To Both Negative And Positive Capacity When A Connection Has Different Capacity In Each Direction Commentary of AISC 341 10
Suggests That Limit Is Applicable To Both Directions
Example:
W21x44 Negative Ratio 0.92
W21x44 Positive Ratio 0.60
27 PR Composite Connection Design
Seat Angle Design
Minimum Width Of 9 To Allow Typical Bolt Gage Of 5.5 and 1.75 Minimum Edge Distance
For Sheared Edges At 1 Bolts
Minimum Horizontal Angle Leg Area:
Asamin = 1.33 Χ Fyrd Χ Arb / Fya
Minimum Horizontal Leg Length Of 8 To Allow 4 1 Diameter Bolts
Vertical Leg Length Chosen To Allow Ductile Hinging Of The Seat Angle When Connection Is
In Full Positive Bending
Limit tsa / b To < 0.5 To Allow Development Of Proper Hinges And To Ignore Shear Bending Interaction
28 PR Composite Connection Design
Seat Angle Bolts
Bolts In Vertical Leg:
Oversize Holes For Mill Tolerance
Bolts In Vertical Leg Should Be Designed For Maximum Bolt Tension
Including Prying Action (See Paper) Magnified By Ry From AISC 341
Table I-6-1.
Ry Χ Bsa
Bolts In Horizontal Leg:
Generally This Is The Limiting Factor In The PRCC Design
Maximize Bolt Capacity By Using A490-X Bolts
1 Diameter Is A Practical Upper Limit On Bolt Size For The Typical
Angle Size and Connected Beams
Check Against Full Plastic Capacity Of
Longitudinal Steel And Web Angles Magnified
By Appropriate Ry Factors
Ry Χ Twa + Ry Χ Fyrd Χ Arb
29 PR Composite Connection Design
Double Angle Web Connection
Primary Purpose To Carry The Connection Shear Demand
Seismic Shear Demand Associated With Full Connection Strength At Each End Should Be Added To Gravity Shear Demand With Appropriate Load Factors To Determine Total Shear Demand
Detail Gage With Same Ductility Concept As Seat Angle Of twa / b To < 0.5 To Allow Web
Angles To Hinge As The Connection Rotates
30 Loads And Load Combinations
Gravity Loads and Seismic Weight
31 Loads And Load Combinations
Seismic Loads
Equivalent Lateral Force Procedure Permitted Per Table 12.6-1
32 Loads And Load Combinations
Seismic Loads ELF Building Period Determination
Approximate Period Per Equation 12.8-7 & Table 12.8-2
Ta = 0.66 sec
33 Loads And Load Combinations
Seismic Loads ELF Building Period Determination
Upper Limit Period Per Table 12.8-1
SD1 = 0.14 so Cu = 1.62
Tmax = 0.66 x 1.62 =1.07 sec
34 Loads And Load Combinations
Seismic Loads ELF Building Period Determination
Dynamic Analysis Period From 3-D SAP Model
Use Kci For Connection Stiffness To Estimate Shortest Possible Analytical Building Period
Tdynamic = 2.13 sec North-South And 1.95 sec East-West
Summary of Periods:
Ta = 0.66 sec
a
Tmax = 1.07 sec
Tdynamic = 2.13 sec North-South And 1.95 sec East-West
Use T = 1.07 sec To Determine Strength Level Forces
Could Use Tdynamic For Drift Check Forces If Need Be
35 Loads And Load Combinations
Notional Loads
AISC 360 Requires The Application Of Notional Loads To the Gravity-Only Load Combination
For This Example Building
Notional Loads Are Taken As 0.2% Of Gravity Loads
Example Building
NDnc = 4,258 kips Χ 0.002 = 8.516 kips / 4 floors = 2.13 kips/floor NDc = 2,393 kips Χ 0.002 = 4.786 kips / 4 floors = 1.20 kips/floor NL = 4,469 kips Χ 0.002 = 8.938 kips / 4 floors = 2.23 kips/floor
Because The Center Of Building Loading Corresponds To The Centroid Of The Building For
This Example, These Notional Loads Can Be Applied At Building Centroid
Typically Notional Loads Are Determined On A Column By Column Basis Thus Capturing
The Actual Gravity Load Distribution
36 Loads And Load Combinations
Load Combinations
37 Loads And Load Combinations
Load Combinations
Two-Stage Connection Behavior Requires Two-Stage Building Analysis And Thus Different Load Combinations For Each Phase And Separate Applications Of Dead Loads To Beams And Columns
38 Loads And Load Combinations
Load Combinations
Seismic And Wind Drift Checks Based On Non-Linear Analysis Thus You Need Full Load
Combinations In Order To Capture Connection Behavior And Building Second Order Effects:
39 Analysis
Preliminary Design
Design All Framing For Pure Gravity Loading Assuming All PR Connections As Pins
PR Frame Beams To Be Designed As 100% Composite
Filler Beams Designed As Typical
Perform 1st Order Lateral Analysis Assuming All PR Connections As Rigid
Review Beam End Moments From EQ And Wind And Compare To Previously Determined Connection Design Capacity (Would Like To Be Below About 75% Of Connection Design Capacity)
Review Building Drift Assuming PR Building Drift Will Be Approximately 2 x Above Model
Drift
If Fail:
Increase Number Of Frames
Increase Column / Beam Sizes (& Thus Connections)
40 Analysis
Application of Load
Pre-Composite PR Connection Behavior Assumed As Pinned
Stage 1 Analysis Applies Pre-Composite Gravity Loads To Beams Only
Post-Composite PR Connection Behavior Based On Previously Determined Curves
Stage 2 Analysis Applies Pre-Composite Gravity Loads To Columns Only And Post- Composite Gravity Loads To Beams (With Exception Of Seismic Vertical Loading Associated With Pre-Composite Loads)
41 Analysis
Application of Load
Stage 2 Load Combination 5
42 Analysis
Application of Load
Stage 2 Load Combination 7
43 Analysis
Beam & Column Moment of Inertia
Beam Moment Of Inertia
Ieq = 0.6ILB+ + 0.4ILB- For Drift
ILB = Lower Bound Moment Of Inertia Of Composite Beam
ILB+ Positive Bending From AISC Manual
ILB- Negative Bending Typical Assume Bare Steel
0.8 x Ieq For Strength (Direct Analysis)
Column Moment Of Inertia
Icol For Drift
0.8 x tb x Icol For Strength (Direct Analysis)
tb Only Applies If Pr/Py > 0.5
44 Analysis
Connection Behavior Modeling
For Each Connection There Are 4 Connection Models
Linear Spring Using Kci For Dynamic Analysis For Determining Building Period
Non-Linear Spring Using Nominal Connection Behavior Curve For Service Level Analysis
Pin For Stage 1 Gravity Analysis Of Beams
Non-Linear Spring Using Reduced Connection Behavior Curve For Stage 2 Strength Level
Analysis
SAP 2000 Allows 2 Connection Behavior Definitions One For Linear Analysis And One
For Non-Linear Analysis When Using The Multi-Linear Elastic Link Option
Conduct A Path Independent Analysis Where Connection Behavior Always Remains On
Connection Curve
45 Analysis
Connection Behavior Modeling
Path Independent Vs. Path Dependent
46 ASCE 7-10 & AISC Design Checks
Building Drift and P-D Checks
Use Service Moment-Rotation Curves and Full Member Moment of Inertia
Nonlinear Analysis Required Because of Connection Curves (Requires Non-Linear Load
Combinations)
Check Wind and Seismic Drift Using P-D Analysis
Wind Drift: hsx/400 Limit Applied
Torsional Irregularity Check ASCE 7-10 Table 12.3-1
Seismic Drift Check ASCE 7-10 Table 12.12-1
Check P-D Effect and Story Stability Coefficient (q) By Comparing and Contrasting Analysis
Results With and Without P-D.
Check For P-D Effect to Be Less Than 1.5 to Meet AISC 360 Requirement For Using
Notional Loads As Minimum Lateral Load (Factored Load Check)
Check For q per Section 12.8.7 of ASCE 7-10 (No Load Factor > 1.0)
47 ASCE 7-10 & AISC Design Checks
Beam Design
Design As Composite Beam For 100% Composite Action
Shear Stud Distribution Needs To Allow For Development of Slab Reinforcing Between Column and Inflection Point But Does Not Need to Develop 100% Composite Action Between These Points
AISC 341 Part II Section 8 Does Not Specifically Address Beam Compactness Criteria Suggest Using AISC 360 Compact Criteria (Note AISC 341-10 Will Require Seismic Compact Criteria)
48 ASCE 7-10 & AISC Design Checks
Beam Design
Because Beam Is Now Part Of Lateral System, It May Go Into Negative Moment At One End Resulting In Possibly Considering The Entire Beam As Un-braced For Lateral-Torsional Buckling Checks Consider Using Alternative Cb Equations For Special Beam Cases (Yura, Helwig Beam Buckling and Bracing)
49 ASCE 7-10 & AISC Design Checks
Column Design
AISC 341 Part II Section 8.2 Requires Columns Meet Requirements Of AISC 341 Part I Section 6 and 8
Material Requirements of Section 6 Are Met By All W10 Columns of A992 Steel
AISC 341 Part I Section 8.3 Requires Special Load Combination If Pu/fcPn Exceeds 0.4.
AISC 360 Allow Use Of K = 1.0 By Direct Analysis Method
AISC 341 Part II Section 8 Does Not Address Required Compactness Criteria (AISC 341-10
Will Address This); But Suggest Requiring Seismic Compact Criteria Because of High R Value
(AISC 341 Part I Table I-9-1). Can Check Using AISC SDM Table 1-2.
Strong Column Weak Beam Concept For C-PRMF Not Addressed By AISC 341 Currently But
ASCE TC Recommends:
50 ASCE 7-10 & AISC Design Checks
Connection Checks
Because Using Non-Linear Curve, A Check Against Connection Capacity Is Not Really Necessary;However,It Is Of Interest To Understand How Hard The Connections Are Being Pushed.
s1g Questions
This is an introductory slide
Explain that Chapter 9 is dealing with Composite Steel and Concrete seismic lateral
force resisting systems; but, that the only system covered in the examples at this
point is the C-PRMF system. Other systems are viable and recognized by the
Provisions and AISC Seismic; but, none have the maturity of the C-PRMFsystem as
of yet. The 2012 AISC Seismic Manual has examples of other composite systems
such as steel link beam coupled shear walls.
Composite Steel and Concrete -1
This is a slide with the outline of the presentation
Going to convey the major design issues involved in the design of a C-PRMF
system by introducing some background material and then walking through each of
the major design considerations via an example building design.
First we will go through the literature that forms the basis for the design
approach.
Second we will introduce you to the example building parameters.
Third we will focus on the Composite PR connection itself as it is the
fundamental building block used to design this lateral system.
Fourth we will look into special considerations that one has to take care with
regarding loads and their application.
Fifth we will focus on special aspects of analysis of a PR building
Sixth we will review a few of the basic code required design checks
Finally we will open it up for questions
Composite Steel and Concrete -2
This slide illustrates the basic structural components of a C-PRMF system
To date, most C-PRMF systems have been comprised of standard W-shape
columns, W-shape composite beams, and the PRCC itself.
The frames are typically strong axis only frames (no bi-axial columns)
Testing has been done on bi-axial PRCC connections; however, to date, they
are not widely used
HSS columns could be used and may be advantageous for the biaxial condition;
however, the author is not aware of PRCC tests with HSS columns at this time
The typical PRCC connection has the component shown in the figure; however,
there are other versions of this type of connection that have been tested.
Despite the testing of other versions, only the above version has been fully
developed in the literature to a point that truly allows for the connections design
Composite Steel and Concrete -3
This slide illustrates the Primary Differences Between C-PRMF and Typical
Moment Frame
The connection is not as strong as the beam it is attaching to the column (what is
known as partial strength).
Consequently the hinging occurs in the connection and not in the beam
PR (partially restrained) connections are not as stiff as FR (Fully restrained)
connections, they allow relative rotation between the beam end and the column
axis
The connection stiffness no longer allows us to conduct our analysis with the
idealized assumptions of fully rigid or fully pinned (simple).
A reasonable approximation of the connection stiffness has to be considered in
the frame analysis
The figure on the left illustrates the true connection moment-rotation behavior
(connection moment vs. relative rotation of the beam end relative to the column
face), it also illustrates several connection stiffness values that could be used
depending on where the connection is along its true behavior curve
The figure on the right illustrates the idea that if connections are stiff and strong
enough to fall into the FR zone then the little bit of relative rotation that does
occur has little affect on the analysis. At the other end, when a connection
rotates very freely then the little bit of moment developed has little affect on the
analysis. Between these two idealized zones of behavior lies the PR behavior
zone. In this zone the relative rotation and the connection moments cannot be
ignored.
Composite Steel and Concrete -4
This slide continues with the Primary Differences Between C-PRMF and
Typical Moment Frame
Because the connections become the hinges in the system it is important that
the connections be detailed in such a way to remain ductile through the expected
rotations cycles the connection will see
Little to any yielding will be seen in the actual beams and columns since the
connections are not capable of developing the yielding capacity of these
elements
Because of the additional flexibility in the system that results from the weaker
and less stiff PRCC connections it does become necessary to engage more
columns and beams in the overall lateral load resisting system
More lower strength frames results in a highly redundant lateral load resisting
system
Most traditional moment frame connections involve significant shop or field
welding; as compared to the PRCC connections which involve no welding only
bolting and the placing of reinforcing steel. This allows quick fabrication and
erection
Unlike most simple connections and even some lateral connections (such as
braced frame connections) the EOR cannot delegate the design of the PRCC
connection since the details of the connection directly influence the lateral load
resisting system response
The PRCC uses reinforcing steel and concrete in the slab as a major component
of the connection. Consequently, until the slab has cured the connections are
Composite Steel and Concrete -5
relatively weak and the building may require temporary guying
Composite Steel and Concrete -5
This slide illustrates the ASCE 7 provisions table as the basis for the system
The C-PRMF system is recognized in Section 12.2 of the Provisions
as a pre-
qualified seismic lateral load resisting system.
It is only allowed in seismic design categories (SDC A to D)
Note the height restrictions, these reflect limits of what has been theoretically
studied for this type of system as well as some practical limits when one
considers the increased connection demands for taller structures
Note that the system is assigned an R=6 which is between that for intermediate
and special steel moment frames, so it is expected to see a good bit of
deformation during a seismic event
Composite Steel and Concrete -6
This slide outlines some of the ASCE 7 provisions
ASCE 7 really does not address the design of this system other than to say that one
must design it in accordance with these reference standards
Composite Steel and Concrete -7
This slide outlines some of the ASCE 7 provisions
Under previous versions of ASCE 7, designers were designing the C-PRMF system
with an R=3 and not requiring all the rules of AISC 341 (Seismic Provisions) be
enforced.
Under the new ASCE 7 provisions, that is no longer allowed. This issue has also
been directly addressed in AISC 360-10. It specifically states that all composite
lateral systems have to be designed in accordance with AISC 341.
Composite Steel and Concrete -8
Slide outlines provisions of AISC 341-05
At the time the 2009 NEHRP Provisions were being developed and published
the AISC 341 in effect was the 2005 version. Consequently the AISC 341 rules
described here are from the 2005 version rather than the 2010 version.
First, the rules for this system are found in Part II of the AISC Provisions. This
section was dedicated to composite systems.
The primary issue to focus on from Section 8.1 is the fact that the connection
flexibility cannot be ignored, the designer has to account for this flexibility in the
frame design.
Composite Steel and Concrete -9
Slide outlines provisions of AISC 341-05
Section 8.2 invokes some of the typical seismic requirements on steel columns
Section 8.3 outlines the rules for the beams
100% composite is required at this time because of the limited
testing of beams with less than 100% composiite
The effective moment of inertia accounts for the averaging of the
negative and positive moments of inertia for a composite beam with
reinforcing steel at the ends, this will be gone into more detail later
in the presentation
Section 8.4 outlines the rules for the PRCC connections
Second order analysis required
The 50% requirement is an attempt to avoid having a building very
weak connections that might be fully yielded (i.e. tangent stiffness
of the connection near zero) under typical gravity loads
Because most of the story drift associated with a C-PRMF building
is concentrated at the connections itself, the interstory drift angle
requirement amounts to a connection rotational ductility
requirement. The idea is to provide a connection detail that can
sustain repeated cycles of up to 40 mrad without significant
degradation of strength and stiffness. Tests of the connections
outlined in this example have shown their ability to meet this
Composite Steel and Concrete -10
requirement
Composite Steel and Concrete -10
Slide gives additional resources used for the design of this system
As seen so far, there is really very little code guidance and very few rules found
in the actual design codes for this seismic lateral force resisting system (in direct
contrast to very specific rules for say a SMF)
To fill in the gap, the designer has to turn to the literature
The two primary pieces of literature that form the basis for the design of the
C_PRMF system are above.
Of these the 1998 Journal paper is the latest and forms the majority of the basis
for design; however, the 1996 design guide still provides information not in the
ASCE journal paper which is still pertinent to the design of this type of frame
While both of these documents provide guidance for design of PRCC, the
method presented in this design example deviates from that guidance based on
more recent code requirements for stability and on years of experience in
designing C-PRMF systems.
Composite Steel and Concrete -11
Slide shows example building plan
The example building is a four-story steel framed medical office building located
in Denver, Colorado.
The building is free of plan and vertical irregularities.
Floor and roof slabs are 4.5-inch normal-weight reinforced concrete on 0.6-inch
form deck (total slab depth of 4.5 inches.).
Typically slabs are supported by open web steel joists which are supported by
composite steel girders.
Composite steel beams replace the joists at the spandrel locations to help
control cladding deflections and provide the C-PRMF frames for the N-S lateral
direction
Note that every column is engaged in the lateral load resisting system in one
direction or the other
The PRCC connections are illustrated by the dots at the face of the column
beam interface in the figure
Stair/Elevator opening is ignored for computing seismic mass
Composite Steel and Concrete -12
Slide shows example building Elevations
The building is located in a relatively low seismic hazard region, but localized
internal storage loading and Site Class E are used in this example to provide
somewhat higher seismic design forces for purposes of illustration and to push
the example building into Seismic De
The floor and roof slabs serve as horizontal diaphragms distributing the seismic
forces and by inspection they are stiff enough to be considered as rigidsign
Category C
The typical bay spacing is 25 feet.
Architectural considerations allowed an extra column at the end bay of each side
in the north-south direction, which is useful in what is the naturally weaker
direction.
Note the pins of the east-west frames at the end columns (coming into the weak
axis of the end column)
Composite Steel and Concrete -13
Slide shows example building 3-D SAP Model
The example building was modeled using the SAO 2000 analysis program v. 14.0
(Computers and Structures, Inc., Berkeley, CA)
Only the primary frame beams and columns were included in the model
Beams were connected to the columns via rotational spring elements
Column bases were considered fixed for analysis purposes
Composite Steel and Concrete -14
Slide gives Details of a Typical PRCC at a W18x35 Beam to Column
This basic connection configuration is what has the most testing behind it in the
literature and is what is directly addressed in terms of design guidance in the
1998 Journal paper and the AISC Design Guide 8
The primary components of the connection include a reinforced composite slab,
a bolted-bolted double angle web connection, and a bolted seat angle
connection
In real partially restrained building design, it is advantageous to select and
design the complete PRCC simply based on beam depth and element
capacities.
Generally it is impractical to tune connections to beam plastic moment
capacities and/or lateral load demands.
This allows the designer to develop an in-house suite of PRCC details and
associated behavior curves for each nominal beam depth ahead of time.
Slight adjustments can be made later to account for real versus nominal beam
depth
The designer generally starts by maxing out the connection design capacity
based on the practical limits of the pieces involved. . For instance, the largest
angle leg commonly available is 8 inches, which can reasonably accommodate
four 1-inch-diameter bolts. As a result, the maximum shear that can be delivered
from the beam flange to the seat angle is limited by shear in four A490-X bolts.
Bolt shear failure is generally considered to be non-ductile, so the rest of the
connection design and detailing aims to maximize moment capacity of the
Composite Steel and Concrete -15
connection while avoiding this limit state.
Composite Steel and Concrete -15
Slide gives Details of the Reinforced Composite Slab
Reinforcing plays a key role in the behavior of the connection
Longitudinal bars (bars in line with the frame direction) are used to develop one
component of the connection moment couple
Transverse steel is required to help provide equilibrium in the load transfer path
from the slab to the column as well as to prevent transverse splitting of the slab
immediately over the frame beams
Composite Steel and Concrete -16
Slide gives the equations that are used to estimate the moment-rotation
behavior for the PRCC connections
The above equations are found in the ASCE Journal Paper
Two different curves are provided to characterize the negative and the positive
moment-rotation behavior
The above parametric moment rotation curves do not represent the results of
any single test
The above parametric equations were developed by fitting the curves to lots of
test data (both real and numerical)
Real test curves have jumps in them that result from bolt slip; however, these
curves have smeared out those deformations into a single smooth curve
The above curves are considered to represent the Nominal behavior of the
connection
This behavior is what we will use for service level design checks
Composite Steel and Concrete -17
Slide indicates what modifications have to be made to these curves when
using them for strength design
The nominal moment-rotation behavior has to be modified to account for the
requirements of the direct analysis procedure that is used for the design of the
frames
First a 20% stiffness reduction is required
In order to apply a stiffness reduction, one must know the predicted stiffness of
the connection. Because the connection behavior is non-linear from the start,
the ASCE Journal paper recommends using the Secant stiffness at 2.5 mrad as
the initial stiffness
Note that this will be different values for the positive and negative branches of
the PR curves
The second modification required is to reduce the strength. The ASCE Journal
paper recommends using a strength reduction factor of 0.85 (i.e. a 15%
reduction in strength) on the nominal behavior to account for variability in the
connection strength
Composite Steel and Concrete -18
Slide shows the Resulting Moment Rotation Curves
The resulting moment rotation curves for the typical PRCC on a W18x35 is
shown in this figure
The solid red line represents the nominal behavior
The dashed black line represents the modified behavior
Note the differences in positive and negative behavior (for example how much
stiffer the connection is in negative bending (slab in tension) than in positive
bending (angle in tension)
Composite Steel and Concrete -19
Slide shows the key values taken from the moment rotation curves for the
two typical connection types used in the example building
From the curves there are a few key quantities that we will need later on in the
design example for doing our analysis and for checking some of the code
required checks
Because the curves are non-linear, one has to pick a rational point along the
curve to identify as the moment capacity
The 10 mrad and 20 mrad points used above are what is recommended in the
ASCE Journal paper for positive and negative moment portions of the curve
Again note the significant difference in strength and stiffness depending on the
bending direction of the connection
Composite Steel and Concrete -20
Slide shows the composite slab reinforcing used in the example building
The typical reinforcing details for the example building are shown in the above
figure
Key is using several small diameter well distributed reinforcing bars rather than a
few large diameter bars
The primary negative moment resistance derives from tensile yielding of slab
reinforcing steel.
Since ductile response of the connection requires that the reinforcing steel yield
and elongate prior to failure of other connection components, providing too much
reinforcing is not a good thing.
The following recommendations are from the ASCE Journal Paper
Composite Steel and Concrete -21
Slide outlines the Rules for Longitudinal Reinforcing Steel
Go through each of the above rules
Note that in this example building you are using 8 # 5 bars (4 of which are
continuous)
Distributing over 36 each side of the column (10 column x 7 = 70, 70/2 = 35,
say 36)
Composite Steel and Concrete -22
Slide shows the composite slab reinforcing used in the example building
The typical reinforcing details for the example building are shown in the above
figure
Key is using several small diameter well distributed reinforcing bars rather than a
few large diameter bars
The purpose of the transverse reinforcing steel is to help promote the force
transfer from the tension reinforcing to the column and to prevent potential shear
splitting of the slab over the beams, thus allowing the beam studs to transfer the
reinforcing tension force into the beam.
The following recommendations are from the ASCE Journal Paper
Composite Steel and Concrete -23
Slide outlines the Rules for Longitudinal Reinforcing Steel
Size transvers reinforcing based on the above strut-tie model of the force
transfer, or in the worst case, the transverse reinforcing can simply equal the
longitudinal reinforcing
Go through other rules presented here
Composite Steel and Concrete -24
Slide outlines the rules for checking concrete bearing stresses and illustrates
the mechanism at work via two figures
The primary means of turning the moment from the beam ends into the column is
through slab concrete bearing on the encased flanges and through the seat
angle bearing or pulling at the bottom of the beam.
The maximum moment that can be delivered from the system to the column is
simply the sum of the plastic moment capacities of the connections on each side
of the column.
For the W21x44 of our example this summation of moment capacities is 367 +
240 = 607 k-ft
Depth between compression centroid at slab and bottom of beam is
approximately 20.7 (depth of W21x44) + 4.5/2 = 22.95
Thus concrete bearing force at flange is approximately 607k-ft/22.95 = 317 kips
A W10x88 column has a 10.3-inch-wide flange. Assuming uniform bearing of
the concrete on each flange, the bearing stress would be 317 kips / 2 flanges /
4.5-inch-thick slab / 10.3-inch-wide flange = 3.42 ksi, which is less than the
recommended limit of .
It is also necessary to check this force against the flange local bending and web
local yielding limit states given in Chapter J of AISC 360.
It is important to have concrete filling the gap between column flanges;
otherwise, the force must be transferred by a single column flange.
Composite Steel and Concrete -25
Slide outlines the checking of connection moment capacity ratios
AISC 341 requires 50% min
However, ASCE Journal paper recommends targeting 75% with 50% as a lower
bound and 100% as an upper bound
The two values for negative and positive connection capacity (@ 20 mrad and 10
mrad respectively) divided by the bare beam Mp are presented above
Composite Steel and Concrete -26
Slide outlines the guidelines for proportioning the bottom seat angle
Most of the angle proportioning is dictated by geometric issues of fitting bolts
There is an As min required per the AISC Design Guide
You want as long an outstanding leg as possible to allow as many bolts in this
leg as possible in order to get the most moment capacity out of the connection.
This is typically the limiting factor for the moment capacity of the connection.
The vertical leg bolt location and thickness should allow a ductile hinge
mechanism to form without brittle shearing of the angle or tension failure of the
bolt. When the connection is in positive bending, this is the source of the
ductility.
By detailing to the above suggested limits, one can ensure a ductile failure mode
and also eliminate significant interaction between bending and shear failures of
the angle
This last rule is a guideline developed by the author and not found in any of the
research literature
Composite Steel and Concrete -27
Slide outlines the basic checks one has to make for the bolts in the bottom
seat angle
Vertical Leg Bolts
The bolts in the vertical leg need to be able to develop the tension
that can be delivered by the angle as it develops its hinge in the
portion of the leg above the bolt.
The example problem in the paper goes into detail on how one
would determine the hinging capacity of the angle and the
associated additional prying forces in the bolt.
In order to ensure the bolts are capable of handling potential
overstrength of the angle, an Ry factor is applied
Horizontal Leg Bolts
4 1 bolts is about as many as one can fit given standard angle
sizes
The source of shear comes from tension yielding of the reinforcing
steel and hinging of the web angles being pulled in tension away
from the column face (similar to the hinge mechanism of the seat
angle)
Ry factors are applied to ensure overstength issues are covered,
the Ry for rebar comes from the ASCE Journal paper
Composite Steel and Concrete -28
Slide outlines the guidelines for proportioning and detailing the double web
angle shear connection
Primary purpose is to carry beam shear; however, they do participate in the
connection moment rotation behavior as well so they still should be sized by the
EOR and not delegated
The shear to be considered would be the full gravity plus seismic. The seismic
shear is determined assuming full hinges at both ends of the beam
The gage for the bolts to the column should be detailed to allow ductile tension
hinging of the web angles as discussed when we talked about the seat angle
connection, again this guideline presented is not a rule; but, merely a guideline
that will ensure ductile failure
Composite Steel and Concrete -29
Slide summarizes all the gravity type loads applied to the example building
The design gravity loads and the associated seismic weights for the example
building are summarized above.
The seismic weight of the storage live load is taken as 50 percent of the design
gravity load (a minimum of 25 percent is required by Standard Section 12.7.2).
To simplify this design example, the roof design is assumed to be the same as
the floor design and floor loads are used rather than considering special roof and
snow loads
The reason for categorizing dead loads as non-composite and composite is
explained later.
Live loads are applied to beams in the analytical model, with corresponding live
load reductions appropriate for beam design.
Column live loads are adjusted to account for different live load reduction factors,
including the 20 percent reduction on storage loads for columns supporting two
or more floors per Standard
Section 4.8.2.
Composite Steel and Concrete -30
Slide shows the ASCE 7 table and the associated seismic design values
associated with a C-PRMF system
For Seismic Design Category C, the height limit is 160 feet, so the selected
system is permitted for this 52-foot-tall example building.
The building is regular in both plan and elevation; consequently, the Equivalent
Lateral Force Procedure of Section 12.8 is permitted in accordance with
Standard Table 12.6 1.
Other applicable parameters regarding site are given in the example problem
Composite Steel and Concrete -31
Slide illustrates the table from ASCE 7 where you choose the approximate
period coefficients
The approximate period is determined to be 0.66 seconds using Equation 12.8-7
and the steel moment-resisting frame parameters of Table 12.8-2.
Composite Steel and Concrete -32
Slide illustrates the table from ASCE 7 where you choose the upper bound
coefficient for the period determination
The coefficient for upper limit on calculated period, Cu,
from Table 12.8-1 is 1.62
(interpolated between values in table), resulting in Tmax
of 1.07 seconds for
purposes of determining strength-level seismic forces.
Composite Steel and Concrete -33
Slide outlines the basic thoughts on how one goes about finalizing the period
determination that will be used for determining seismic forces
A specific value for PRCC stiffness must be selected in order to conduct a
dynamic analysis to determine the building period. Cant do a dynamic analysis
to determine a single period when using a non-linear connection curve.
It is recommended that the designer use Kci
of the negative moment-rotation
behavior given in Section 9.2.2 above for this analysis.
This should result in the shortest possible analytical building period and thus the
largest seismic design forces.
For the example building, the computed periods of vibration in the first modes
are 2.13 and 1.95 seconds in the north-south and east-west directions,
respectively. These values exceed Tmax,
(given above) so strength-level seismic
forces must be computed using Tmax
(given above) for the period.
The final calculation of building base shear and the vertical distribution of forces
is exactly like any other building and is detailed in the example
Note that if seismic drift was becoming a problem you could use the calculated
period to determine a set of seismic forces for drift checking
Composite Steel and Concrete -34
Slide outlines rules for determining notional loads for the example building
Note that wind loads were considered; but, were substantially less than the
seismic loads so they are not discussed here and there is nothing unique about
calculating them associated with the C-PRMF system
AISC 360 now requires that notional loads be included in the building analysis.
This example building qualifies for application of notional loads to gravity-only
load combinations. This is typically the case.
Notional loads are taken as 0.2% of gravity loads
The notional loads are applied in the same manner as the seismic and wind
loads in each orthogonal direction of the building and they are factored by the
same load factors that are applied to their corresponding source (such as 1.2 or
1.4 for dead loads).
It is important to note that, in general, notional loads should be determined, at a
minimum, on a column-by-column basis rather than for an entire floor as done
above. This will allow the design to capture the effect of gravity loads that are
not symmetric about the center of the building.
The example building happens to have gravity loads that are concentric with the
center of the building, so it does not matter in this case.
Composite Steel and Concrete -35
Slide outlines the load combinations that control the design of the example
building
The above load combinations are the primary combinations controlling the
design of this example building
The loads have to be broken out into pre-composite and post composite loads
for proper application of the loads to the building due to the 2-stage behavior of
the connection that is discussed later. In addition, the seismic coefficients are
expanded to give the expanded combinations above.
Composite Steel and Concrete -36
Slide illustrates how the basic load combinations have to be expanded to
include two stages of analysis and breaking about pre-composite and post-
composite loads
Because the PRCC has two distinct stages of moment-rotation behavior, the
analysis and application of load has to be consistent with that.
This requires not only separating pre and post composite loads; but, also dead
loads on columns from dead loads on beams.
Further explanation of why these are broken out is still coming up.
Composite Steel and Concrete -37
Slide outlines loads combinations to be used for service level design checks
All drift checks are done from the results of a non-linear analysis
Linear superposition of non-linear results wont cut it
Drift from wind or seismic alone wont cut it because the gravity loads soften the
connections
Consequently, the above complete load combinations have to be run in order to
get a wind or seismic drift
The last note here is just to indicate that the above load combinations (and on
previous slides) would have to have all the normal east-west, north-south
directions and torsions applied.
Composite Steel and Concrete -38
Slide outlines a procedure that can be used for the initial proportioning of
frame members
The goal of an efficient partially restrained building design is to have a sufficient
number of beams, columns and connections participating in the lateral system so
that the forces developed in any of these elements from lateral loads is relatively
small compared to the gravity design.
Design for gravity as if the connections are pinned; add the connections and
check to see if any beams or columns must be upsized to handle the lateral
loads. The goal is that you wont have to.
The steps above are intended to get the designer close to their final result before
stepping into the full blown non-linear analysis that is required for the final design
confirmation of the building
Go through above steps
Composite Steel and Concrete -39
Slide outlines how the loads have to be applied in two stages because of the
two stage behavior that exists with the PRCC connections
The true behavior of a PRCC consists of two stages.
The first stage is the bare steel connection (double web angles and seat angle)
The second stage is the full composite connection
We typically assume the first stage behaves as a pinned connection and the
second stage behaves as our prediction curves have suggested
So we do a Stage 1 analysis of just pre-composite gravity loads on beams only
in order to get the proper moment distribution of these loads in these beams
assuming pin ended connections.
We then do a Stage 2 analysis which only has the post-composite loads on the
beams and all loads on the columns in order to capture the post-composite
moment distribution and frame analysis.
The reason for getting all the loads on the columns in the Stage 2 analysis is to
ensure the second order effects from these loads are captured; however, we
dont put these loads on the beams in this stage because they occurred before
the concrete hardened
Composite Steel and Concrete -40
Slide presents an illustration to help clarify how the loads are applied to the
building frame in the second stage for load combination 5
This slides shows how the different load types are applied for the Stage 2
version of Load Combination 5
Note how the pre-composite loads that would normally be applied to the beams
are directly applied to the columns instead. This way the columns have the
correct total loading while the beams only have the post-composite loading
This is why the beams have to be designed for the linear combination of Stage 1
and Stage 2 results
Composite Steel and Concrete -41
Slide presents an illustration to help clarify how the loads are applied to the
building frame in the second stage for load combination 7
This slides shows how the different load types are applied for the Stage 2
version of Load Combination 7
Here you should note that there is actually a negative dead load applied to the
beams to account for the vertical component of the seismic force that comes
about during a seismic event which is considered to occur in the post-composite
stage of the structure life
Composite Steel and Concrete -42
This slide discusses the effective moment of inertia to be used for beam and
columns
The beam moment of inertia is a weighted average of the inertia in the positive
bending zone and the inertia in the negative bending zones. This equation
comes from the ASCE Journal Paper
The lower bound moment of inertia for the positive zone is reported in the steel
manual
The lower bound moment of inertia for the negative zone is typically taken as the
bare steel beam moment of inertia; but, it can be taken as the composite moment
of inertia including the area of reinforcing steel
The 20% reduction in the moment of inertia is required for the strength design
per the direct analysis rules
The column is simply the bare column for drift checks and has the same 20%
reduction for the strength design per the direct analysis rules
Composite Steel and Concrete -43
This slide discusses the 4 different ways that the PR spring at the beam to
column connection is modeled during the analysis
First we assign a linear spring so we can conduct a dynamic analysis
We assign the nominal nonlinear connection curve for service level type checks
We assign a pin behavior for the Stage 1 strength analysis
We assign the modified nonlinear connection curve for the Stage 2 strength
analysis
All of these analysis are done using a path independent approach. This simply
means that the sequence and timing of load application does not change the
answer. A path dependent approach takes into account the sequence and
magnitude level that the loads are applied.
Composite Steel and Concrete -44
This slide further illustrates the difference between path independent and
path dependent
A path independent analysis forces equilibrium to occur with the connection in a
moment-rotation state along the dotted curve
Reality is that when a connection starts to unload, it does not travel along the
curve; but, instead it takes an almost linear unloading path (as shown where the
connections go from Step 4 to Step 6 in the slide above)
.This path-dependent analysis is more accurate and allows consideration of
connection shakedown to be captured in the model; however, it is also much
more complicated when compared to the path-independent analysis.
Since the simpler, path-independent connection modeling approach does not
capture connection shakedown behavior, the author does not recommend
reducing beam sizes from the pure simple pinned gravity design discussed
previously
Composite Steel and Concrete -45
This slide outlines the approach to checking common service level code
checks
When checking drift, irregularity, and p-delta effects, we typically use the nominal
moments of inertia and connection curve.
These require a non-linear analysis with the load combinations that were
presented previously.
Discuss other limits outlined above
The specific values and checks for the example building are provided in the
example problem and are not reiterated here
Note: The example problem is not correct in its discussion of checking this
value, it was based on an earlier draft of the Standard before the final was
voted on. The final version kept this part of the standard un-changed.
Composite Steel and Concrete -46
This slide outlines the requirements for beam design and distribution of
shear studs
100% composite required because of the testing done on these connections to
date
Studs between column and inflection point need to be sufficient to off load the
tension in the reinforcing steel
Compact requirements are not currently addressed in the AISC 341; however,
the AISC 341-10 does address this issue and will require seismic compactness.
The example problem presumes that only typical compact requirements will be
needed since it was done before the AISC 341-10 was finalized.
Composite Steel and Concrete -47
This slide illustrates the issues associated with the potential of lateral
torsional buckling of beams that are part of the frame
Have to consider potential un-braced lengths of beams and potential lateral
torsional buckling that can occur because of the bottom flange going into
compression
Inflection point is not a brace point, so unless braces come into side of beam
have to consider entire length un-braced
Recommend using alternative Cb equations in order to avoid adding bracing or
bumping beam size to meet the LTB requirements
Composite Steel and Concrete -48
This slide outlines the current rules and guidance for checking the columns
in the C-PRMF
Part 1 of the AISC 341 has some material and over strength check requirements
for columns
The only columns in the example building that would be affected by the over
strength check are the interior columns where the axial load from seismic is
minor compared to the gravity load and would consequently make no difference
in the design checks
Since we used a direct analysis we get to use K=1
Again the compact requirements are not addressed in AISC 341-05; however,
they will be addressed in AISC 341-10 and they will require Seismic Compact
Can check compact limits by hand or by using tables found in the seismic design
manual
Strong column weak beam concept now takes the form of strong column weak
connection concept
This is not addressed in AISC 341-05 but is addressed in the ASCE Journal
paper and is addressed in the commentary of the AISC 341-10
Numerical checks for one sample column of the example building are provided in
the example
Composite Steel and Concrete -49
This slide outlines requirements for final checking of the PRCCs in the
building
There is really little to do with the connection design at this stage because the
full nonlinear connection behavior is being used in the analysis. This means that
the connection moments will never exceed the connection capacity during the
analysis. This is in contrast to any analysis method that models the connections
with linear behavior. When the connections are modeled with linear behavior, it
is up to the designer to confirm that the final connection results are consistent
with the expected connection behavior. This might be very easy for building
designs where connection moments are small; however, when the connections
are being pushed close to their capacity, that sort of independent connection
check by the designer can be problematic.
Although not entirely necessary, it is useful to check where the connections are
along the expected behavior curves for any given analysis so one can see just
how hard the connections are being pushed. The connection moment demand
versus design capacities (including phi) are presented in Table above. The
demand values are from different load combinations. A quick check of this table
indicates that this building design is not being pushed particularly hard and that
there is likely significant reserve capacity in the lateral system.
Composite Steel and Concrete -50
This slide is a placeholder for an opening the floor up to questions
Composite Steel and Concrete -51