Posted by **Claire** on Saturday, March 6, 2010 at 6:55am.

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!

- Mechanics of Materials -
**drwls**, Saturday, March 6, 2010 at 8:09am
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.

- Mechanics of Materials -
**MathMate**, Saturday, March 6, 2010 at 9:34am
An inversion of digits caused the answers to differ.

2.42/8.42*64.3 gives 18.5 MPa.

- Mechanics of Materials -
**drwls**, Saturday, March 6, 2010 at 11:07am
Thanks, MathMate!

- Mechanics of Materials -
**Claire**, Saturday, March 6, 2010 at 11:11am
Thanks a lot!! :)

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