Question

A steel railroad track has a length of 24 m when the temperature is 8◦C.

What is the increase in the length of the rail on a hot day when the temperature is

36 ◦C? The linear expansion steel is 11 × 10−6 (◦C)−1.

Answer in units of m.

004 (part 2 of 2) 10.0 points

Suppose the ends of the rail are rigidly clamped at 8◦C to prevent expansion.

Calculate the thermal stress in the rail if its temperature is raised to 36◦C. Young’s modulus for steel is 20 × 1010 N/m2.

Answer in units of N/m2.

Answer 1

A)

Using relation,

L = Lo (1 + a dT)

dL = 24 x 11 x 10^-6 x (36 - 8)

dL = 0.0074 m

B)

Thermal stress = Y dL/L

Stress = 20 x 10^10 x 0.0074/24 = 6.16 x 10^7 N/m^2

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