STRUT-AND-TIE MODEL based on AASHTO LRFD Specifications Week 13

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STRUT-AND-TIE MODELbased onAASHTO LRFD
SpecificationsWeek 13

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Outline

• Background
• AASHTO LRFD Provisions
• Design Example

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Background

• STM is a Truss Analogy
• Truss Analogy Used in Standard and LRFD
  Specifications
• Vn Vc Vs Vs Asfy/sd(cot?)
• AASHTO Standard
• Vs ? 45º Truss
• AASHTO LRFD
• Vs ? Variable Angle Truss

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LRFD 5.2 - Definitions

• Strut-and-Tie Model - A model used principally in
  regions of concentrated forces and geometric
  discontinuities to determine concrete proportions
  and reinforcement quantities and patterns based
  on assumed compression struts in the concrete,
  tensile ties in the reinforcement, and the
  geometry of nodes at their points of intersection

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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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STM for D-Regions
Flanged Section
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STM for D-Regions
Dapped Beam with Opening
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Past Practice

• D-Regions Designed Based On
• Experience
• Empirical Rules
• Rules of Thumb

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Strut-and-Tie Model
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Basic Concepts

• Visualize a truss-like system to transfer load to
  the supports where
• Compressive forces are resisted by concrete
  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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Basic Concepts

• Reinforcement Becomes Active After Concrete
  Cracks
• Redistribution of Internal Stresses Occurs After
  Concrete Cracks
• After Cracking, Concrete Structures Behave the
  Way they Are Reinforced
• For Best Serviceability, the Reinforcement Must
  Follow the Flow of Elastic Tensile Stresses

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Examples of Strut-and-Tie Models
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Assumptions

• Ties yield before struts crush (for ductility)
• Reinforcement adequately anchored
• Forces in struts and ties are uniaxial
• Tension in concrete is neglected
• External forces applied at nodes
• Prestressing is a load
• Equilibrium must be maintained

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STM Design Procedure

• 1. Draw Idealized Truss Model and Solve for
  Member Forces
• 2. Check Size of Bearings
• 3. Choose Tension Tie Reinforcement
• 4. Check capacity of struts
• 5. Check anchorage of tension tie
• 6. Provide crack control reinforcement

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Examples of Good and Poor STM
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Factors Affecting Size of Strut

• Width of the strut is affected by
• Location and distribution of reinforcement (tie)
  and its anchorage
• Size and location of bearing

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Strength Limit State for STM

• Pr ? Pn (5.6.3.2-1)
• where
• Pr Factored resistance
• Pn Nominal resistance of strut or tie
• ? Resistance factor for tension or compression
  (5.5.4.2)

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Strength of Struts

• LRFD 5.6.3.3
• Unreinforced strut
• Pn fcu Acs (5.6.3.3.1-1)
• Reinforced strut
• Pn fcu Acs fy Ass (5.6.3.3.4-1)
• where
• ? 0.70 for compression in strut-and-tie models
  (LRFD 5.5.4.2.1)
• Acs effective cross-sectional area of strut
  (LRFD 5.6.3.3.2)
• Ass area of reinforcement in the strut

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Limiting Compressive Stress in Strut

• LRFD 5.6.3.3.3
• where

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Development of Ties (ACI 318)
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Strength of Tie

• LRFD 5.6.3.4.1
• Pn Ast fy Aps ( fpe fy )
• where
• Ast Total area of longitudinal mild steel
  reinforcement on the tie
• Aps Area of prestressing steel
• fy Yield strength of mild steel longitudinal
  reinforcement
• fpe Stress in prestressing steel due to
  prestress after losses

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Limiting Stresses for STM Elements

• LRFD 5.6.3.3 - 5.6.3.5

Element Limiting Stress 1 - CCC Node 2 - CCT
Node 3 - CTT or TTT Node 4 - Strut 5 - Tie
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Crack Control Reinforcement

• LRFD 5.6.3.6
• Provide orthogonal grid of reinforcement near
  each face of D-Region
• Maximum Bar Spacing 12 in.
• Ratio As / Ag ? 0.003 in each of the orthogonal
  directions
• Crack control reinforcement, located within tie,
  considered as part of tie

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DESIGN EXAMPLES

• See PCI BDM