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Angle of twist due to linear varying torque

  1. Dec 27, 2009 #1
    in the following question
    http://stommel.tamu.edu/~esandt/Teach/Summer00/CVEN305/Examples/Set3/prob3413.jpg

    while G and J are parameters and the moment changes by the function M(x)=t*x
    i am asked to find the angle of twist from one end to another

    i know

    dθ/dx=M/(GJ)

    therefore

    dθ=M/(GJ)dx

    dθ=tx/(GJ)*dx

    since t,G,J are independant of X

    [tex]\int[/tex]dθ=t/(GJ)[tex]\int[/tex]xdx from 0 to L

    θ=tL^2/(2GJ)


    but the correct answer
    θ=tL^3/(6GJ)

    i can see that they have integrated twice, i can only imagine that they integrated once to find the total torque and the second time to find the angle,,,
    but surely this should come from the differential equation? surely if M is a function of X and i integrate dx i souldnt need to sum up the torqe seperately??
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
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