I have this example:

Image of shaft dimensions and forces (momentum)

  • $M_k$ = 80 Nm
  • $d_1$ = 30 mm
  • $d_2$ = 20 mm
  • $a$ = 600 mm
  • $b$ = 500 mm
  • $G$ = 8,5e4 MPa

I want to know the twist at free end of this shaft. I am using the formula:

$$\phi = \dfrac{M_k \cdot a}{G \cdot \dfrac{\pi d_1^4}{32}} + \dfrac{M_k \cdot b}{G \cdot \dfrac{\pi d_2^4}{32}}$$

It gives me 0,037 rad.

But the result in the book is 0,013 rad. Where is the error?

  • 1
    $\begingroup$ Whenever I end up with answers that contradict what my textbook states is the correct answer, I always double check that I am using the correct equation for the question. $\endgroup$
    – user16
    Apr 8, 2015 at 18:57
  • $\begingroup$ Also 'working backwards' to try an determine where the errors may be my help $\endgroup$
    – user1184
    Apr 8, 2015 at 21:46
  • 1
    $\begingroup$ I also get 0.037... $\endgroup$
    – BeyondLego
    Apr 8, 2015 at 22:59
  • $\begingroup$ Like series/parallel connections do they add up do their reciprocals add up? Compare contribution of each shaft whether it increases or decreases. $\endgroup$
    – Narasimham
    Apr 13, 2015 at 21:04

1 Answer 1


The problem is not your formula. If your diagram is correct and you have copied the values correctly, then the answer indeed is 0,037 rad.

Therefore, I suggest that you do the following:

  1. Check that you copied the diagram correctly
  2. Check that you copied the correct values
  3. Check that you didn't misread the answer key

If you still can't determine what is wrong, talk to your professor or TA. Textbooks have errors, and if you are in a class of students who are all working on this problem, they might already know about the issue. If they don't already know, they'll probably be grateful that you alerted them to the error.

  • $\begingroup$ 1) Check; 2) Check; 3) Check; I'm not student, so I can't ask classmates or professor. I will try to contact the author of this exercise. $\endgroup$
    – Lluser
    Apr 9, 2015 at 7:08

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