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Homework Help: Angle of twist on web flange steel member

  1. Dec 22, 2009 #1
    A 3.5 m long steel member with a W310 x 143 cross- section is subjected to 4.5KNm torque. Knowing that G=77GPa, determine (a) the maximum shearing stress along the line a-a, (b) the maximum shearing stress along the line b-b, (c) the angle of twist

    http://lh4.ggpht.com/_H4Iz7SmBrbk/Sysfg6WJmLI/AAAAAAAACBI/SsE4jsJMYAE/22.jpg [Broken]

    i know that

    Tau=M*t/J

    while J=1/3*sigma(h*b^3)

    i get J=1/3*(287.2*14^3 + 2*309*22.9)*10^-12
    =2.736e-6 m^4

    therefore in a-a the shear stress will be

    4500*0.0229/(2.736e-6)=37.66MPa

    and for b-b

    4500*0.014/(2.736e-6)=23.03MPa

    now for the angle

    phi=M*L/(G*eta*J)
    =4500*3.5/(77e9*1.29*2.736e-6)

    and i get 0.058rad=3.32degrees

    but the correct answers are meant to be
    a-a 39.7Mpa
    b-b 24.2Mpa
    phi 4.72degrees


    where have i gone wrong??


    someone told me i need to consider the web and the flanges separately and obtain a proportion between the torque exerted on the web and a flange, respectively, by assuming that the resulting angles of twist are equal

    how can i do this??
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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