A railroad is laid so that there is no stress in the rails at 20 degrees celcius. Calculate the stress in the rails at -6 degrees celcuis if all the contraction is prevented. Take E=206GPa and linear coefficient of expansion is 12 x 10^(-6) /deg celcius. If, however, there is 6mm allowance for contraction per rail, what is the stress at -6 deg celcius if the rails are 27m long.

Question

The answers should be 64.3 MPa, and 18.5 MPa.

I managed to get the first answer. However, I don't know how to continue. Can someone please help me? Thanks!

Answer 1

If the rail is free to contract, the 26 degree cooling shortens a 27 m rail by 8.42 mm. If no stress develops for the first 6 mm of contraction, somehow, then you only get 2.24/8.24 or 27% of the stress you get with no freedom to contract. That would be 27.2% of 64.3 MPa, your first answer, ot 17.5 MPa.
This problem should not expect answers correct to three significant figures, since the input data only has two.

Answer 2

An inversion of digits caused the answers to differ.
2.42/8.42*64.3 gives 18.5 MPa.

Answer 3

Thanks, MathMate!

Answer 4

Thanks a lot!! :)