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7/24/2019 Module 13 Wight

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Chapter 23 - Strut-and-Tie Models

ACI 318-14:

Reorganized for Design


Ch. 23 Strut-and-Tie Models

23.1 Scope

23.2 General

23.3 Design strength

23.4 Strength of struts

23.5 Reinforcement crossing bottle-shaped struts

23.6 Strut reinforcing detailing

23.7 Strength of ties 23.8 Tie reinforcement detailing

23.9 Strength of nodal zones


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Why strut-and-tie models?

Valuable tool where plane-sections

assumption of beam theory does not apply

Truss analogy used to analyze concretestructures


Strut and tie models

3 components

Struts

Ties

Nodal zones

P P

RR


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Struts

Compression elements

2 types

Prismatic

Bottle-shaped

P P

RR

Prismaticstrut

Bottleshapedstrut



Strut strength Without longitudinal reinforcement,

Fns = fceAcs

With longitudinal reinforcement, Fns = fceAcs + Asfs

= 0.75 for all struts

Where:

Acs = bwws ws based on width at node

fce = 0.85 sfcsTable 23.4.3

ws bw


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Strut coefficient, sTable 23.4.3


Struts in a flexural tension zone

T

C


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23.5 Reinf. crossing bottle-shaped struts

Distributed transverse reinforcement

(Asi / bssi)sin i0.003

for fc6000 psi

Only required if using s = 0.75

Not practical in all situations

Also meet deep beam minimumreinforcement in Section 9.9



3 components

Struts

Ties

Nodal zones

P P

RR


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23.7 Strength of ties

Tensile strength:

Simple tension element

Fnt = Atsfy (nonprestressed)

= 0.75 for all ties

Tie centroid coincides with reinforcement

centroid


23.8 Tie reinforcement detailing

Develop bars at the centroid within the

extended nodal zone

Develop difference between force on one

side and the other within the nodal zone

T

C

NodalzoneExtendednodal

zoneRd, min


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3 components

Struts

Ties

Nodal zones

P P

RR



Node strength

Depends on node type

CCC CCT CTT

T

C

R

C

C

P

T

C

T


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Node strength

Fnn = fceAnz fce = 0.85 nfcnTable 23.9.2

= 0.75 for all nodal zones

CCC

CCT

CTT

Typeofnode


Examples

Deep beam from SP-17(14)


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Examples



Examples



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Examples



Examples

Corbel from SP-17(14)

Strut

Tie


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may be reproduced copied distributed or transmitted in any form


Examples

Pile cap from SP-17(14)


Resources

SP-208: Examples for the Design of Structural

Concrete with Strut-and-Tie Models

SP-273 Further Examples for the Design of

Structural Concrete with Strut-and-Tie

Models

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