Steel train rails are laid in 13.5-m-long segments placed end to end. The rails

Question

Steel train rails are laid in 13.5-m-long segments placed end to end. The rails are laid on a winter day when their temperature is -3.0. For steel, assume that the coefficient of linear expansion is and the Young's modulus is .How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 31.5? If the rails are originally laid in contact, what is the stress in them on a summer day when their temperature is 31.5? (Hint from the instructor: Enter a negative number.)

Explanation / Answer

since u got ur first answer that is co-eff of linear expansion of steel = 12e-6 temp change = 31.5-(-3) = 34.5 degC so change in length = 12e-6*34.5*13.5 = 5.589e-3m now the second part is bit of peculiar strain is (change in length)/(original length ) in this case of thermal expansion, if the rail is expanding without any stress its length will become (13.5 + 5.589e-3m) from this length it is constraint to be put in length of 13.5 so strain is (5.589e-3m)/ (13.5 + 5.589e-3m) now stress =young mod.* strain 8.59*10^7

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