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

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

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

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