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October 16, 2017
Analysis and Design of Reinforced Cast-in-Place
Concrete Diaphragms
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1. Background
2. Case Study Introduction
3. Example ‘traditional’ diaphragm design
4. Example of Alternate design approach using strut
and tie
5. Conclusions
Diaphragm Designusing strut- and-tie analysis
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Background
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Uncertainty in Current Diaphragm Stiffness and Design
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Euler-Bernoulli Beam Theory
Plane Sections Remain Plane
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St. Venant’s principaleMechanics of Materials, Fourth Edition
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▪ The Strut-and-Tie considers all load effects (Moment, Axial, Shear)
simultaneously
▪ The model provides a rational approach by representing a complex structural
behavior with an appropriate simplified truss of 1-D members
▪ MacGregor’s 1992 book on Concrete Design provide one of the early and
detailed examples of how to implement Strut-and-Tie.
▪ The method was incorporated into the 2002 version of ACI-318 in Appendix A
Strut-and-Tie method
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DESIGN RECOMMENDATIONS AND METHODS
FOR REINFORCED CONCRETE FLOOR
DIAPHRAGMS
SUBJECTED TO SEISMIC FORCES, PhD Thesis,
Debra Gardiner, University of Canterbury,
February, 2011.
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CaseStudy
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Perla on Broadway4th & Broadway, Downtown Los Angeles
▪ Guided by strict
planning constraints in
the historic core of
downtown Los Angeles
▪ 35-story tower with
▪ Tall 11-story Podium
▪ Large 4-story Atrium
▪ Creates unique
challenges for
diaphragm design.
▪ Including large
openings and transfer
forces
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Historic 4th and Broadway
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Historic 4th and Broadway
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Tower Section
Tow
er
He
igh
t =
38
0’
Po
diu
m H
eig
ht
= 1
15
’
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Tower Floor Plate
CENTER CORE
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Podium Floor Plate
CENTER CORE
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DiaphragmDesign
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Tower Section
Rig
id D
iap
hra
gm
sS
em
i R
igid
or
S&
T
Dia
ph
ragm
s
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Rigid Diaphragm
CENTER CORE
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Semi Rigid or S&T Diaphragm
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Rigid Diaphragm
Forces extracted at vertical elements and a diaphragm load path is
assumed or modeled outside of the primary analysis program
Rigid Diaphragm vs
Semi Rigid or Simple Truss Diaphragm
Semi Rigid or S&T
Diaphragm forces are extracted from within the diaphragm using
section cuts or axial S&T forces
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TraditionalDiaphragm
Design
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AlternateApproach
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Sketch the flow of forces
through the D-region
Calculate Strut and Tie
Forces
Select steel for Ties and
Determine its Location
Steel fits in
Assumed
STM
Geometry
Stress
levels
Okay
Change a location of Ties and
Modify STM
Modify STM by Changing Tie
Locations or increasing
Bearing Areas or Increasing
Member Geometry
Detail Steel Anchorage and
Additional Crack Control
Steel
Check stress levels in Struts
and Nodes
Yes
No
No
Yes
Develop a sufficiently
dense grid of struts and
ties that is
compatible with the flow
of forces
Procedure for Strut-and-Tie Modeling
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Diaphragm Tie Forces at Level 11
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Tension Steel in L11 Diaphragm Ties - H1 Direction
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Tension Steel in L11 Diaphragm Ties - H2 Direction
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Compression Width Required in L11 Diaphragm Diagonal Struts
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Conclusions
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Conclusion
1. This approach provides a simplified analysis model that can account for shear,
axial, and moment forces through a resultant one dimensional element in
tension or compression.
2. Provides a graphical representation of the diaphragm load path.
3. Allows for the extraction of diaphragm forces without having to define explicit
section cuts.
4. Provides explicit modeling of collectors to assist the designer in the
determination of collector reinforcing and extents.
5. Provide explicit deformation in long collector elements where the stiffness of
the collector can be calibrated to the amount of steel provided.
6. Future studies - Allows for nonlinear analysis of diaphragm elements
7. Future studies – provides a detailed distribution of diaphragm forces that can
lead to more economical, safe designs.
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