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Question on beams

  1. Apr 16, 2012 #1
    1. The problem statement, all variables and given/known data
    a solid rectangular section beam has a cross section: 0.1m x 0.2m, and length 2m is simply supported at each end. A load of 1100N is applied at the middle of the span.
    a) find the maximum bending stress and specify the location of the bending stress
    b) to reduce weight a hollow rectangular section beam having an outside horizontal dimension of 0.2m and a constant wall thickness of 0.02m is to be designed. determine a suitable vertical dimension so that the maximum bending stress is the same as a)


    2. Relevant equations
    I= (bd^3)/12 for a solid rectangular beam
    I = (BD^3)/12 -(bd^3)/12 for a hollow rectangular beam



    3. The attempt at a solution
    a) think ive done it, needs checking.
    Mmax = 1/4FL
    maximum stress = (Mmax/I)x 1/2 x d
    max stress = (0.25x1100x2)/(0.1x(0.2)^3/12) x0.5 x 0.2
    max stress = 825000

    b)have to use 825000(or if i have it wrong whatever the correct answer for stress is) and
    use I = (BD^3)/12 -(bd^3)/12 for the value of I this time and plug it back into maximum stress = (Mmax/I)x 1/2 x d , only thing is i'm having trouble rearranging everything to get the value of the vertical height, any help please?
     
  2. jcsd
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