What will happen if a rod is tied with fixed | vedclass

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(B) When a rod is fixed rigidly at both ends,it cannot expand freely upon heating. As the temperature increases,the rod attempts to expand by $\Delta

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The rod will experience compressive stress and may bend.

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(B) When a rod is fixed rigidly at both ends,it cannot expand freely upon heating. As the temperature increases,the rod attempts to expand by $\Delta l = l \alpha \Delta T$. Since the supports are rigid,they exert an inward force on the rod,preventing this expansion. This constraint results in the development of compressive strain and,consequently,thermal stress within the material. The thermal stress is given by $\sigma = Y \alpha \Delta T$. If the internal compressive force exceeds the structural limit of the rod or its supports,the rod may buckle or bend. For example,if a steel rod of cross-sectional area $40 	ext{ cm}^2$ is constrained,a temperature change of $10^{\circ}C$ produces a compressive strain of $\epsilon = \alpha \Delta T = 1.2 	imes 10^{-5} 	imes 10 = 1.2 	imes 10^{-4}$. The resulting force $F = Y A \epsilon = (2 	imes 10^{11} 	ext{ Pa}) 	imes (40 	imes 10^{-4} 	ext{ m}^2) 	imes (1.2 	imes 10^{-4}) = 96,000 	ext{ N}$,which is sufficient to cause bending or buckling in many structures.

What will happen if a rod is tied with fixed supports rigidly at both ends and its temperature is increased?

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