Mechanics of Materials
posted by Claire on .
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.
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!

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

Thanks a lot!! :)