A steel rail, rigidly fixed at its ends is assumed to be stress free at 20°C. If the stress required to cause the buckling of the rail is −75 Mpa, at what temperature will the rail buckle? (E = 200 GPa and α = 12.5 × 10^-6/°C)

Question

Question

This question was previously asked in

ISRO VSSC Technical Assistant Mechanical 14 July 2021 Official Paper

Answer 1

Concept:

Thermal stress in a material that is rigidly fixed and unable to expand or contract is given by:

Where:

σ is the thermal stress

&E; is the Young's modulus of the material

α is the coefficient of linear thermal expansion

ΔT is the change in temperature

Calculation:

Given:

Initial temperature,

Stress required to cause buckling,

Young's modulus,

Coefficient of linear thermal expansion,

Rearranging the formula to solve for ΔT:

Substituting the given values:

Calculate the denominator:

Now, calculate ΔT:

Since the change in temperature is negative, indicating a decrease for compressive stress:

The temperature at which the rail will buckle is 50°C.

The correct answer is:
2) 50°C