Suppose the ends of a 27-m-long steel beam are rigidly clamped at 0°C to prevent expansion.The rail has a cross-sectional area of 35 cm².What force does the beam exert when it is heated to 39°C? (α_steel = 1.1 × 10−⁵/C°,Y_steel = 2.0 × 10¹¹ N/m²).

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Quizplus · Accepted Answer

The force exerted by the steel beam when heated can be calculated using the formula for thermal stress, which is $F = \alpha \cdot Y \cdot A \cdot \Delta T$, where $\alpha$ is the coefficient of thermal expansion, $Y$ is the Young's modulus, $A$ is the cross-sectional area, and $\Delta T$ is the change in temperature. Given $\alpha = 1.1 \times 10^{-5} /°C$, $Y = 2.0 \times 10^{11} N/m^2$, $A = 35 \times 10^{-4} m^2$ (since $35 cm^2 = 35 \times 10^{-4} m^2$), and $\Delta T = 39°C - 0°C = 39°C$, substituting these values gives $F = 1.1 \times 10^{-5} \times 2.0 \times 10^{11} \times 35 \times 10^{-4} \times 39$, which calculates to approximately $3.0 \times 10^5 N$.

Suppose the Ends of a 27-M-Long Steel Beam Are Rigidly