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Question related to Bending Stress and Shear Stress of a I shape beam

  1. Nov 9, 2014 #1

    1. The problem statement, all variables and given/known data

    The beam ABCD with the cross section has pin connections at B and C and is subjected to a uniformly distributed load w. If the allowable bending stress is 150MPa and the allowable shear stress is 80 Mpa. ( Hint : the horizontal reaction forces at A and D are both zero).

    the picture of beam is :
    https://fbcdn-sphotos-f-a.akamaihd...._=1425149738_3735a63d312d409ebc2ebe6405dca32c

    2. Relevant equations
    Bending stress = My/I
    Shear stress = VQ/It

    3. The attempt at a solution
    I tried in this way but cannot get the answer. answer : w = 57.1 kn/m

    6 Rd-5w*3=0
    6Rd = 15w
    Rd = 2.5w

    Ra=2.5 w
    then i draw shear force diagram to find Vmax.
    V max = 2500w N

    I also find neutral axis at 165mm
    Moment of Inertia I = 1/12 * 300^3*10 + 2 [ 1/12*15^3*70+15*170*157.5^2]
    = 1.491075*10^-4 m^4

    t= 0.01 m
    Q = y'A' = 150*10*75+170*15*157.5
    = 5.14125*10^-4 m^3

    So, we have 80*10^6 = 2500w * 5.14125*10^-4 / 1.491075*10^-4 *0.01
    w = 92.8 kN

    _________________________________________________________________

    For bending moment stress
    I draw bending moment diagram to find max bending moment = 4.375 kN.m
    150*10^6 = (4.375w * 165/1000) / 1.491075*10^-4
    w = 30.98 kN


    Can anyone tell me what's wrong that I cant get the solution w = 57.1 kN/m
    Thank you :cool:
     
  2. jcsd
  3. Nov 14, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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