Analisis Momen by kukuhkurniawands

VIEWS: 20 PAGES: 11

									                          3/20/2009




 RESPONSE OF MEMBER
SUBJECTED TO FLEXURE
       Iswandi Imran




  Section Subjected to
 Flexure and Axial Load




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Moment Curvature Response




     Compability Conditions



Concrete Strain at any level y :
      ε c = ε cen − φy
Steel Strain at any level y = the strain at
surrounding concrete:
      ε s = ε cen − φy
      ε p = ε cen − φy + Δε p




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             Equibrium Conditions




∫
Ac
     f c dA c + ∫
                As
                      f s dA s + ∫
                                   Ap
                                        f p dA p = N

∫
Ac
     f c ydA c + ∫
                     As
                          f s ydA s + ∫
                                        Ap
                                             f p ydA p = − M
Note :
• Tensile stresses are taken as positive
• Tensile force (N) is taken as positive
• Moment M is positive if it causes tensile stresses on bottom face




    Determining Sectional Forces
    Using layer-by-layer Evaluation




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                    Stress Block Factors
Stress-block factors α1 and β1 are determined so that the magnitude and
location of the resultant force are the same in the equivalent uniform
stress distribution as in the actual distribution :
               c

               ∫ f bdy = α           f β1cb
                                       '
                     c              1 c
               o
                         c

                         ∫ f bydy
                              c

               y=        o
                          c
                                         = c − 0.5β1c
                         ∫ f bdy
                         0
                              c


For a parabolic stress-strain curve and a constant width b:
                                                       2
                       ε 1⎛ε                       ⎞
               α 1 β1 = t' − ⎜ t'                  ⎟
                       εc 3⎜εc
                             ⎝
                                                   ⎟
                                                   ⎠
                         4 − ε t / ε c'
                   β1 =
                        6 − 2ε t / ε c'




         Rectangular Stress – Block
                  Factors

                                                                            Effective embedment
                                                                            zone = 2*7.5 db




    ∈t / ∈’c       0.25           0.50      0.75           1.00    1.25    1.50    1.75    2.00


    α1             0.336          0.595     0.779          0.888   0.928   0.900   0.810   0.667

    β1             0.682          0.700     0.722          0.750   0.786   0.833   0.900   1.000




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Comparison of Calculated and Observed
    Moment-Curvature Response




Comparison of Short-Term and Long-
 Term Moment-Curvature Response




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                    Elastic Uncracked Response
     Compability                                               Stress – Strain Rel
     ε c = ε cen − φy                                          f c = E c ε cf
     ε s = ε cen − φy                                          f s = E c ε sf
     ε p = ε cen − φy + Δε p                                   f p = E p ε pf

     Where :
     ε cf = ε c − ε co
     ε sf = ε s − ε so
     ε pf = ε p − ε po




                                       Equilibrium
N = ∫ f c dAc + ∫ f s dAs + ∫ f p dAp
          Ac                As                   Ap

           N − N0                                          Es      Ep
ε cen =              ;                Atrans = Ac +           As +    Ap
           Ec Atrans                                       Ec      Ec
N 0 = ∫ E p Δε p dAp − ∫ Ecε co dAc − ∫ Esε so dAs − ∫ E pε po dAp
          Ap                          Ac                   As                   Ap




−M =
           Ac
               ∫f   c   ydAc +   ∫f
                                 As
                                       s   ydAs +     ∫f
                                                      Ap
                                                           p   ydAp

     M − M0
φ=
     Ec I trans
M 0 = − ∫ E p Δε p ydAp + ∫ Ecε co ydAc + ∫ Esε so ydAs + ∫ E pε po ydAp
               Ap                           Ac                     As                Ap




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         Thermal Stress




Suggested Temperature Distribution for
   Bridge Sections (from Priestley)




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 Fatigue Resistance




Suggested S-N Curve




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Compatibility Conditions for
Bonded and Unbonded Beam




Axial Load-Moment Interaction Diagram




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   Influence of Axial Load on
   Moment-Curvature Response




    Comparison of Long-Term and
Short-term M-N Interaction Diagrams




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   Axial Load and Moment
   at Midheight of Column




    Moments, Curvatures and
Deformations of Slender Wall Panel




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