1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Torsion in a beam

  1. Jan 3, 2009 #1
    1. The problem statement, all variables and given/known data

    The question is shown in the attached picture. I know how to do the first part fine,and i know how to do the second part but i keep getting the wrong answer (answers are on the back of the sheet)

    2. Relevant equations

    tau/r=T/J (tau = shear stress, r = radial distance from centre, T = Torque, J = Polar second moment of area)

    J = (pi/2)*r^4 for a solid circular cross section

    3. The attempt at a solution

    T = 12k*0.75 = 9k Nm

    J = (pi/2)*(37.5x10^-3)^4 = 3.106x10^-6 m^4

    tau = (9x10^3*37.5x10^-3)/3.106x10^-6
    tau = 108.7 MPa (answer given is tau = 45.8 MPa)

    sigma = My/I

    I = (pi/4)*r^4 = 1.553x10^-6

    M = 18kNm
    y = 37.5mm
    sigma = 18x10^3*37.5x10^-3/1.553x10^-6
    sigma = 434.6 MPa (answer given is sigma = 188 MPa)

    both answers are wrong but if you use r and y = 15.8mm (but not when calculating second moments) the right answer comes out. Where does this 15.8mm come from or am I going wrong somewhere else?

    Thanks for any help

    Attached Files:

    Last edited: Jan 3, 2009
  2. jcsd
  3. Jan 3, 2009 #2


    User Avatar
    Homework Helper

    Well, first of all, isn't J given with [tex]J = \frac{d^4 \pi}{32} = \frac{r^4 \pi}{2}[/tex]?
  4. Jan 3, 2009 #3
    oh yeah thats a typo
  5. Jan 3, 2009 #4


    User Avatar
    Homework Helper

    Very interesting, I get the same answer for the shear stress due to the torsion moment. I'll have to consult my mechanics of materials book, I'll be back later.
  6. Jan 3, 2009 #5


    User Avatar
    Science Advisor
    Homework Helper

    jaderberg: Nice work. You did not do anything wrong. You got all answers correct. Both of the given answers from the back of the sheet are wrong.
  7. Jan 3, 2009 #6
    cheers man, was beginning to wonder whether that was the case :p
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook