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Homework Help: Transverse loading with varing cross section

  1. Jan 3, 2010 #1
    Capture.JPG

    i know that

    τ=VQ/(Ib)

    now im looking for the maximum stress so i will find that at the point at the centre of the rectangle

    Q=A*[tex]\bar{y}[/tex]
    A=0.5*d*b
    [tex]\bar{y}[/tex]=0.25*d
    ===> Q=0.125d2b

    I=(b*d3)/12


    τ=VQ/(Ib)
    τ=V*0.125d2b*12/((b2*d3)

    τ=1.5V/(bd)

    now d changes as a function of X

    i know that τ is constant from x=0 to x=L
    but V is constant throughout and so is b, so how can this be?

    i tried making a differential equation where i know d(0)=do and d(L)=0 using dτ/dx=0 but really didnt manage
     
  2. jcsd
  3. Jan 3, 2010 #2

    PhanthomJay

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    Science Advisor
    Homework Helper
    Gold Member

    You are calculating max shear stress, but the problem is asking for the variation in d such that max flexure stress (bending stress) under the transverse load P is constant throughout the beam. Try again using the formula for max bending stress.
     
  4. Jan 3, 2010 #3
    am i meant to be using -y*(M/I)

    i know the following

    Ymax=d/2
    M=PL-Px=P(L-x)
    I=(bd3)/12

    therefore

    max stress=(d/2)*P(L-x)/((bd3)/12)

    and i get
    6P(L-x)/(bd2)

    from here i got it thanks
     
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