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8.1

Strut-and-Tie Model

Background AASHTO LRFD Provisions

Design Example

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8.2

Background

STM is a Truss Analogy

Truss Analogy Used in Standard and

LRFD SpecificationsVn = Vc+ Vs Vs = [Asfy/s]d(cot)

-AASHTO Standard

Vs 45 Truss

-AASHTO LRFD

Vs Variable Angle Truss

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8.3

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8.4

STM in Codes

CSA 23.3-84

OHBDC Third Edition, 1991

AASHTO LRFD - First Edition, 1994

CHBDC - 2000

ACI 318-02 Appendix A

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8.5

Quiz

A Three-Span Concrete Beam Is Built

Monolithically, with Continuous

Reinforcement Placed Only in the

Bottom of the Beam

How Will this Beam Perform UnderService Loads? and at Ultimate?

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8.6

As Built

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8.7Under Service Loads

- Uncracked Condition -

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8.9

Observations

Reinforcement Becomes Active After

Concrete Cracks

Redistribution of Internal Stresses

Occurs After Concrete Cracks

After Cracking, Concrete StructuresBehave the Way they Are Reinforced

For Best Serviceability, theReinforcement Must Follow the Flow

of Elastic Tensile Stresses

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8.10

Strut-and-Tie Model (STM)

Valuable tool for the analysis and

design of concrete members,especially for regions where the

plane sections assumption of beam

theory does not apply

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8.11

Deep Beam Stress Trajectories

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8.12

STM for D-Regions

Tee Beam

Dapped Beam

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8.13

Past Practice

D-Regions Designed Based On:

Experience

Empirical Rules

Rules of Thumb

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8.14Basic Description of the

Strut-and-Tie Model

A design tool for disturbed regions

where the flow of stresses is non-uniform

and the usual rules of analysis do notapply

A rational approach to visualize the flow of

forces at the strength limit state based onthe variable-angle truss analogy

A unified approach that considers all load

effects simultaneously

A highly flexible and conceptual method

that recognizes that several possiblesolutions may exist for any problem

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8.15

STM Basic Principle

Concrete is Strong in Compression

Compression Struts Steel is Strong in Tension

Tension Ties

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8.16

P

2

>

P

2

P

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8.17

Nodal

ZonesP

2

P

P

2

CC

T T

C CStrut

Fill

Fill

Tie

Fill

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8.18

T

C

T

C

C C

P

P

2

>A f Ts y

P

2

>

A f

C

c

cu

>A f Ts y

>

A f

C

c

cu

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8.19

Basic Concepts

Visualize a truss-like system to transfer load

to the supports where:

Compressive forces are resisted byconcrete struts

Tensile forces are resisted by steel

ties

Struts and ties meet at nodes

For best serviceability, the model should

follow the elastic flow of forces

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8.20Strut-and-Tie Model for Simple Span Beam

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8.21Examples of Strut-and-Tie Models

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8.22Methods for Formulating

Strut-and-Tie Models

Stress trajectories from elastic analysis

Load path approach

Experimentally

Standard models

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8.23

Deep Beam Stress Trajectories

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8.24

Examples of Strut-and-Tie Models

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8.25

Examples of Strut-and-Tie Models

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8.26

Procedures for Load Path Approach

Find reactions

Subdivide loads and internal forces

- Replace stresses with resultants

- Replace asymmetrical stresses with

couple and resultant Provide struts and ties to provide load

path

Locate ties using practical dimensions