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Torsion question

  1. Dec 15, 2009 #1
    Each of the two aluminum bars shown is subjected to a torque of magnitude . Knowing that , determine for each bar the maximum shearing stress and the angle of twist at B.

    Untitled.jpg

    Answers: a) 40.1Mpa 0.6630 degrees
    b) 50.9Mpa 0.9510 degrees

    my equations


    τmax=[tex]\frac{T}{alpha*h*b^2}[/tex]


    [tex]\frac{dΦ}{dx}[/tex]=[tex]\frac{T}{G*beta*hb^3}[/tex]


    so to find the angle of twist at B i can integrate [tex]\frac{T}{Gβhb^3}[/tex]dx from 0 to 0.3, but since the moment is constant throughout, the integral comes to [tex]\frac{T}{Gβhb^3}[/tex]*0.3

    and i get

    a) ΦB=[tex]\frac{1000}{26e9*0.14*0.06*0.06^3}[/tex]*0.3=0.0211979 rad = 1.21455degrees

    b) ΦB=[tex]\frac{1000}{26e9*0.245*0.095*0.038^3}[/tex]*0.3=0.03011 rad = 1.725degrees

    where the actual answers are much much smaller

    for the shear strength used the equation

    τmax=[tex]\frac{T}{alpha*h*b^2}[/tex]

    and i get

    a)τmax=[tex]\frac{1000}{0.21*0.06*0.06^2}[/tex]=22Mpa
    b)τmax=[tex]\frac{1000}{0.26*0.095*0.038^2}[/tex]=28Mpa

    a seemingly simple question but i have managed to get 0/4 correct answers, can anyone see where im going wrong?
     
  2. jcsd
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