Docstoc

structureshandouts unomaha edu CIVE Concre

Document Sample
structureshandouts unomaha edu CIVE Concre Powered By Docstoc
					   STRUT-AND-TIE
      MODEL
        based on
AASHTO LRFD Specifications

        Week 13

                             1
               Outline

   Background
   AASHTO LRFD Provisions
   Design Example




                             2
              Background

   STM is a Truss Analogy
   Truss Analogy Used in Standard and
    LRFD Specifications
    Vn = Vc + Vs    Vs = [Asfy/s]d(cot)
    - AASHTO Standard
              Vs  45º Truss
    - AASHTO LRFD
         Vs  Variable Angle Truss

                                           3
        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
                                           4
    P




P       P
2       2
            5
                        P
Strut
                    C   C
        Fill                      Fill
                    Fill
    C                                    C
        T                          T
            Nodal
P                           Tie              P
            Zones
2                                            2
                                                 6
                             P

                         C   C
                     C
                   >
                fc
                 u

         A   c

    C                                  C
        T             As fy > T   T

P                                          P
2                                          2
                                               7
     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



                                         8
STM for D-Regions




   Flanged Section




                     9
STM for D-Regions




Dapped Beam with Opening




                           10
             Past Practice

   D-Regions Designed Based On:
    » Experience
    » Empirical Rules
    » Rules of Thumb




                                   11
Strut-and-Tie Model




                      12
             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
                                            13
           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
                                          14
Examples of Strut-and-Tie Models




                                   15
              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 *
                                             16
     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


                                         17
Examples of Good and Poor STM




                                18
 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
                                                       19
    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)



                                          20
            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

                                                     21
Limiting Compressive Stress in Strut
                      LRFD 5.6.3.3.3
                 fc
    fcu                  0.85fc
            0.8  170 ε1

 where:

     ε1  ε s  ε s  0.002  cot 2 α s
    fcu  the limiting compressive stress
     α s  the smallest angle between the
           compressive strut and adjoining
           tension ties (DEG)
     ε s  the tensile strain in the concrete
           in the direction of the tension tie (IN/IN)
                                                         22
Development of Ties (ACI 318)




                                23
             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

                                              24
Limiting Stresses for STM Elements
                LRFD 5.6.3.3 - 5.6.3.5




         Element             Limiting Stress
      1 - CCC Node              0.85  fc
      2 - CCT Node              0.75  fc
      3 - CTT or TTT Node       0.65  fc
      4 - Strut                    fcu
      5 - Tie               fy or ( fpe  fy )   25
    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



                                               26
DESIGN EXAMPLES

   See PCI BDM




                  27

				
DOCUMENT INFO