Suppose the ends of a 20-m long steel beam are rigidly clamped at 0°C to prevent expansion.The rail has a cross-sectional area of 15 cm².What force does the beam exert when it is heated to 40°C? (α_steel = 1.1 × 10−⁵/C°,Y_steel = 2.0 × 10¹¹ N/m²) A) 2.6 × 10⁵ N B) 5.6 × 10⁴ N C) 1.3 × 10⁵ N D) 6.5 × 10² N

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Quizplus · Accepted Answer

The force exerted by the beam can be calculated using the formula F = Y * A * α * ΔT, where Y is Young's modulus, A is the cross-sectional area, α is the coefficient of linear expansion, and ΔT is the change in temperature. Substituting the given values, F = (2.0 × 10^11 N/m²) * (15 × 10^-4 m²) * (1.1 × 10^-5 /°C) * (40°C) = 1.32 × 10^5 N, which is approximately 1.3 × 10^5 N.

Suppose the Ends of a 20-M Long Steel Beam Are