# A structural member of rectangular cross-section $10 \mathrm{~mm} \times 6 \mathrm{~mm}$ and length $1 \mathrm{~m}$ is made of steel (Young's modulus is $200 G P a$ and coefficient of thermal expansion is $\left.12 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right) .$ It is rigidly fixed at both the ends and then subjected to a gradual increase in temperature. Ignoring the three dimensional effects, the structural member will buckle if the temperature is increased by $\Delta T^{\circ} \mathrm{C}$ which is (A) 19.74 (B) 9.87 (C) 78.96 (D) 39.48

## Question ID - 1 :- A structural member of rectangular cross-section $10 \mathrm{~mm} \times 6 \mathrm{~mm}$ and length $1 \mathrm{~m}$ is made of steel (Young's modulus is $200 G P a$ and coefficient of thermal expansion is $\left.12 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right) .$ It is rigidly fixed at both the ends and then subjected to a gradual increase in temperature. Ignoring the three dimensional effects, the structural member will buckle if the temperature is increased by $\Delta T^{\circ} \mathrm{C}$ which is (A) 19.74 (B) 9.87 (C) 78.96 (D) 39.48

3537

(B) 9.87

Next Question :

A gas cylinder (closed thin-walled cylindrical pressure vessel) of diameter $30 \mathrm{~cm}$ and wall thickness $1 \mathrm{~mm}$ is subjected to a design maximum internal pressure of 5 bar $(0.5 \mathrm{MPa})$. The material used for manufacturing this cylinder has a failure stress of $260 M P a$. Assuming von Mises failure criterion, the factor of safety (with respect to maximum allowable stress) for this cylinder is
(A) 2.8
(B) 2.0
(C) 6.9
(D) 4.0 