10/1/2018
Strut-and-Tie Method for Analysis and
Design of Concrete Members
This Webinar is sponsored by ACI. The ideas expressed, however, are those of the speakers and do not necessarily reflect the views of ACI or its committees. The audience is expected to exercise judgment as to the appropriate application of the information.
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Questions related to specific materials, methods, and services will be addressed at the conclusion of this presentation.
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American Concrete Institute is a Registered Provider with The American
Institute of Architects Continuing Education Systems (AIA/CES). Credit(s) earned on completion of this online course will be reported to AIA/CES for
AIA members.
The online course based on this webinar is registered with AIA/CES for continuing professional education. As such, it does not include content that may be deemed or construed to be an approval or endorsement by the AIA of any material of construction or any method or manner of handling, using, distributing, or dealing in any material or product.
The American Institute of Architects has approved this course for 1 AIA/CES
LU Learning Unit.
The American Institute of Architects has approved this course for 1 AIA/CES LU learning unit.
ACI is an AIA/CES registered provider.
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Strut-and-Tie Method for Analysis and Design of Concrete Members
Course Description:
This webinar will present the background information and basic design rules for the strut-and-tie method prescribed in the ACI 318-
14 Building Code Requirements for Structural Concrete. Guidance will be given for the development of a strut-and-tie model (truss model) to be used for analysis and design of either D-regions
(disturbed regions) within a member or the entire member. Design rules and strength limits will be given for the elements of a strutand-tie model, namely the struts, ties and nodes. A deep beam example is included to show the steps required to design a member using the strut-and-tie method.
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Strut-and-Tie Method for Analysis and Design of Concrete Members
Learning Objectives
Summarize the background for the development of the strut-and-tie method
Explain design rules and geometric restraints for development of strut-and-tie models
Describe the Code-defined nominal strengths of struts, ties and nodes
Review how to finalize and check the design of either a whole member or a critical region within a member.
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Insert Photo here
James K. Wight, FACI and FASCE, is the F.E. Richart, Jr. Collegiate
Professor of Civil Engineering at the University of Michigan. He is well-known both nationally and internationally for his work in earthquake-resistant design of concrete structures. Professor Wight has been an active member of the American Concrete Institute where he has held several important positions including President of
ACI, Chair of the ACI Building Code Committee, Chair of Building
Code Subcommittee E during the development of the strut-and-tie method, Chair of the Technical Activities Committee, Member of the
Board of Direction, and President of the Greater Michigan Chapter.
He has received numerous awards for his teaching, including the
ASCE Student Chapter Teacher of the Year Award, the College of
Engineering Teaching Excellence Award and the ACI Joe Kelly
Award. He has also won several awards from ACI for his research and service, including the Structural Research Award, the Delmar Bloem
Award, the Alfred Lindau Award, and the Wason Medal. He has received Distinguished Alumnus Awards from the University of Illinois and Michigan State University. He is the lead-author of a widely used textbook on design of reinforced concrete structures and is a registered engineer in the State of Michigan.
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10/1/2018
James K. Wight
University of Michigan
October 2, 2018
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Strut-and-Tie Method for Analysis and Design of Concrete
Members
My introduction to the need for the strut-and-tie method:
Roof member collapse for a Combined Sewer
Overflow (CSO) basin in Michigan
Roof consisted of precast double-tee sections with dapped ends designed following the PCI Design
Handbook. Approximately 3 ft (1 m) of soil was placed over top of basin. Collapse occurred as small earth-mover was smoothing soil fill.
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Strut-and-Tie Method for Analysis and Design of
Concrete Members
Failed roof beam of CSO basin: Double-Tee with dapped end
Placeholder Photo
Photo for Position Only
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Strut-and-Tie Method for Analysis and Design of
Concrete Members
Placeholder Photo
Photo for Position Only
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Strut and Tie Models; Chapt. 23 of ACI 318-14
Members or regions of members may be designed for flexure and shear by idealizing the concrete and reinforcement as an assembly of axially loaded members, inter-connected at nodes, to form a truss capable of carrying loads across a region or member.
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Components of Strut and Tie Models:
Node
Strut
Tie
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Steps to build a strut and tie model:
Isolate member or D(disturbed) - region
Compute forces or distribution of stresses on boundary - convert stress distributions to equivalent forces
Select a truss model to transmit these forces across the member or D-region
Not a unique solution – multiple truss models could be used
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Concept of D-regions – geometric discontinuities: h
1 h
2 h
1 h
2
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Basic Requirements for strut-and-tie models:
Model should approximate stress flow across member or region
Define truss and component dimensions
Use constant φ -value (0.75) for all truss components (struts, ties and nodes)
Define β factors for struts and nodes
Select reinforcement details, including anchorage
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Modeling Stress Distributions:
FE Analysis Truss Model
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Minimum angle between struts and ties:
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Strength of Struts; what to consider:
Longitudinal cracking (splitting)
Transverse tension (stresses or strains)
Sustained compression
Reinforcement grid crossing strut
Confinement by concrete or reinforcement
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Effective compressive strength of struts:
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ACI values of β s for struts:
1.0 – prismatic shape (constant width) over its length, similar to flexural compression zone in B-region
0.75 – inclined strut crossed by minimum reinforcement grid
0.60 – inclined strut not crossed by minimum reinforcement grid
0.40 – struts in flexural tension zone
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Struts in a flexural tension zone:
C
T
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Minimum reinforcement grid of D-regions:
Reinf. Configuration
Orthogonal Grid
Reinf. in one direction crossing strut at angle α
1
Min. Dist. Reinf. Ratio
0.0025 each direction
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Minimum reinforcement of D-regions:
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Tie Dimensions:
Tie dimensions are governed by dimensions of nodal zones, which are controlled by allowable stresses in nodal zones (next)
Spread reinforcement throughout dimensions of tie
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Spread of tie reinforcement:
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Strength of ties:
Nominal strength = φ A s f y
, where φ = 0.75
Anchorage of ties at nodes is a major design concern
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Anchorage of tie reinforcement – same rules as normal members.
Extended Nodal Zone
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Nodal Zone Dimensions:
Nodal zone dimensions are governed by allowable stress in node, except
At intersection of strut and nodal zone, the lower allowable stress in strut or node will control that dimension of the node
Force/(all. stress) = dimension
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Node dimensions:
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Allowable stress in Nodes:
Function of type of members connecting at the node
Possible combinations are CCC, CCT and
CTT
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Examples of CCC and CCT Nodes:
Examples of CCT and CTT Nodes:
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Effective compressive strength of nodes:
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ACI values of β n for nodes :
CCC Node, use 1.0
CCT Node, use 0.8
CTT Node, use 0.6
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Example: CI Magazine, May 2003
640 k (includes member weight)
All member widths = 20 in.
20 in.
60 in.
428 k
16 in.
53 in.
16 in.
107 in.
212 k
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Initial Truss Model
20 in.
640 k
All member widths = 20 in.
60 in.
428 k
16 in.
53 in.
d v
16 in.
107 in.
212 k
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Final truss geometry and member forces
428 k 212 k
217 k 3
2
1
α
1
= 44.6
o
434 k
α
2
= 44.3
o
49.7 in.
428 k
10 in.
50.2 in.
4
217 k
α
2
50.2 in.
5
212 k
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Equilibrium at Node 1:
F
12
F
14
428 k
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Dimensions of Node 1 and Strut 1-2: w
14
α
1 ℓ b1
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Calc. width and check strength of Strut 1-2:
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Reinforcement for Tie 1-4:
Select 13 No. 8 bars,
A s
= 10.3 in.
2
20 in.
3 in.
3 in.
3 in.
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Req’d. min. reinf. crossing Strut 1-2 for use of
β s
= 0.75:
Min. reinf. percentage vert. and horiz. = 0.0025; satisfies deep requirement in 9.9.3.
Because h > 36 in., must satisfy “skin reinf.” requirement of 9.7.2.3.
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Req’d. min. reinf. crossing Strut 1-2:
Vert. reinf.: # 4 stirrups with four legs at s = 12 in.
Horiz. reinf.: 2 #4 bars at s = 8 in.
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Final design left span:
2 #4 per layer
#4 legs
3 in.
6 at 8 in.
13 #8
20 in.
3 at 3 in.
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Comments on right side of truss:
428 k 212 k
217 k 3
2
1
α
1
= 44.6
o
434 k
α
2
= 44.3
o
49.7 in.
428 k
10 in.
50.2 in.
4
217 k
α
2
50.2 in.
5
212 k
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Fan struts 2-4 and 3-5; distributed tie 3-4:
22in.
2
60in.
3
25 o
49in.
25 o
22in.
4 six stirrups at s = 10 in.
104 in.
5
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Final design of longitudinal and transverse steel:
2 in.
5 at 12 in.
15 at 6 in.
2 in.
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Strut-and-Tie Method for Analysis and
Design of Concrete Members
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Strut-and-Tie Method for Analysis and
Design of Concrete Members
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