engineering recuitment GATE ME 2023-24 Test Series Strength of Materials Simple Stress and Strain Thermal Stress and Strain
In the figure shown, a bar AB of length L is held between rigid supports and heated non uniformly in such a manner that the temperature increase at distance x from end A. The temperature increase is given by the expression \(\Delta T = \Delta {T_B}\frac{{{x^3}}}{{{L^3}}}\), where \(\Delta {T_B}\) is the increase in temperature at end B of the bar. If the material has modulus of elasticity E and coefficient of thermal expansion \(\alpha \),
1
The expression for the compressive stress \({\sigma _c}\) in the bar is \(\frac{{E\alpha \left( {\Delta {T_B}} \right)}}{4}\)
2
The expression for the compressive stress \({\sigma _c}\) in the bar is \(\frac{{E\alpha \left( {\Delta {T_B}} \right)}}{6}\)
3
The thermal deformation constrained = \(\frac{1}{4}\alpha \left( {\Delta {T_B}} \right)L\)
4
The thermal deformation constrained = 0