A steel rod is clamped rigidly at both ends. At 20^ ^ ^ C , the rod experiences zero tension. If the temperature increases to 100^ ^ ^ C , determine the force exerted by the rod on one of the clamps. The cross-sectional

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Quantrex Academy · Accepted Answer

Correct answer: C. 384 N

The thermal stress developed in a rigidly clamped rod due to a change in temperature is given by

\sigma = Y \alpha \Delta T

.

The force exerted by the rod on the clamps is

F = \sigma A = Y A \alpha \Delta T

.

Substituting the given values

Y = 2.00 \times 10^{11} \text{ N m}^{-2}

,

A = 2.00 \times 10^{-6} \text{ m}^2

,

\alpha = 12.0 \times 10^{-6} ^{{}^{{}^{\circ}}}\textC^{-1}

, and

\Delta T = 100^{{}^{{}^{\circ}}}\text{C} - 20^{{}^{{}^{\circ}}}\text{C} = 80^{{}^{{}^{\circ}}}\text{C}

:

F = (2.00 \times 10^{11}) \times (2.00 \times 10^{-6}) \times (12.0 \times 10^{-6}) \times 80

F = 4 \times 12 \times 80 \times 10^{-1}

F = 384 \text{ N}

A steel rod is clamped rigidly at both ends. At 20^ ^ ^ C , the rod...

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