1
GATE ME 2016 Set 2
Numerical
+2
-0
A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of 0.2 mm between the rod and the wall on the right side. If the temperature of the rod is increased by 200oC, the axial stress developed in the rod is __________ MPa.

Young’s modulus of the material of the rod is 200 GPa and the coefficient of thermal expansion is 10−5 per oC.

2
GATE ME 2016 Set 3
Numerical
+2
-0
A square plate of dimension L $$\times$$ L is subjected to a uniform pressure load P = 250 MPa on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus E = 200 GPa.

The deformed shape is a square of dimension 𝐿 − 2$$\delta .$$ If 𝐿 = 2 m and $$\delta$$ = 0.001 m, the Poisson’s ratio of the plate material is __________ .

3
GATE ME 2012
+2
-0.6
A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $$\Delta T.$$ If the thermal coefficient of the material is $$\alpha$$, young's modulus is $$E$$ and the Poisson's ratio is $$\upsilon$$, the thermal stress developed in the cube due to heating is
A
$$- {{\alpha \left( {\Delta T} \right)E} \over {\left( {1 - 2\upsilon } \right)}}$$
B
$$- {{2\alpha \left( {\Delta T} \right)E} \over {\left( {1 - 2\upsilon } \right)}}$$
C
$$- {{3\alpha \left( {\Delta T} \right)E} \over {\left( {1 - 2\upsilon } \right)}}$$
D
$$- {{\alpha \left( {\Delta T} \right)E} \over {3\left( {1 - 2\upsilon } \right)}}$$
4
GATE ME 2012
Numerical
+2
-0
A $$200$$ mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by $$250$$oC. If the Young's modulus and coefficient of thermal expansion are $$200$$ GPa and $$1 \times {10^{ - 5}}/{}^ \circ C,$$ respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is _________