Example 1
A simply supported, hollow shaft with R1=12� and R2=10� carries a load of 300 lb. What is the maximum stress in the cylinder?
a) 0.5 psi
a) 2150 psi
a) 3.2 psi
a) 1.7 psi
Solution:
This is a very straightforward bending problem. If prepared for the PE exam the correct solution should be almost immediate. In this case our governing equation is:
We are concerned with the maximum stress in this problem; therefore your value for M is the 300 lb force as stated in the problem multiplied by the largest moment arm. In this case that is 15 inches. The cross section of the beam is a simple circle so the area moment of inertia can be found from standard tables to be:
The cross section is symmetrical and there are no axial loads applied to the beam to the neutral axis can be taken to be the center of the circular cross section, therefore c = 6 inches. Substituting these values into the original equation gives:
NOTES ON THIS PROBLEM
The PE exam often includes answers that reflect common mistakes. The problems on this site will often utilize the same tactics in an effort to prepare you for the real thing. As such, let�s go over some of the wrong answers to understand some of the more common mistakes one can make.
a) 0.5 psi
If you chose a), it�s probably because you took the moment � M as 300, NOT 300 times the appropriate moment arm of 15�.
b) 2150 psi
You'd get approximately 2150 psi if you incorrectly wrote the term for moment of inertia. The formula for the cross section of a hollow tube is:
I've seen many hasty or preoccupied test takers wrongly write this as:
This is WRONG and will net you extremely incorrect answers.