What will be the stress at -20^∘ C, if a steel rod with a cross-sectional area of 150 mm^2 is s

step 1 Hello students in this question we have to calculate the stress sigma at temperature suppose the

What will be the stress at -20^∘ C, if a steel rod with a...

What will be the stress at $-20^{\circ} \mathrm{C}$, if a steel rod with a cross-sectional area of $150 \mathrm{~mm}^{2}$ is stretched between two fixed points? The tensile load at $20^{\circ} \mathrm{C}$ is $5000 \mathrm{~N}:$ (Assume $\alpha=11.7 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $Y=200 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ ) (a) $12.7 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ (b) $1.27 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ (c) $127 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ (d) $0.127 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$

What will be the stress at $-20^{\circ} \mathrm{C}$, if a steel rod with a cross-sectional area of $150 \mathrm{~mm}^{2}$ is stretched between two fixed points? The tensile load at $20^{\circ} \mathrm{C}$ is $5000 \mathrm{~N}:$ (Assume $\alpha=11.7 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $Y=200 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ )
(a) $12.7 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
(b) $1.27 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
(c) $127 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
(d) $0.127 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$

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Key Concepts

Constrained Thermal Stress

When a material is prevented from freely expanding or contracting due to fixed boundaries, the thermal strain is counteracted by induced mechanical strain. This mismatch creates an additional stress in the material, calculated using Young's modulus multiplied by the prevented thermal strain, based on Hooke's Law.

Thermal Strain

Thermal strain is the deformation a material experiences because of a change in temperature if it were free to expand or contract. It is calculated by multiplying the coefficient of thermal expansion by the temperature change, representing the strain that would occur without any mechanical constraint.

Coefficient of Thermal Expansion

This material property quantifies how much a material's length changes with temperature for a unit change in temperature. It is defined as the fractional change in length per degree change in temperature and is essential for predicting dimensional changes in structures subjected to thermal variations.

Young's Modulus

Young's Modulus is a measure of a material's stiffness. It describes the relationship between stress (force per unit area) and strain (relative deformation) in a material under elastic conditions. A higher modulus means the material deforms less under a given load.

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