Question

When a building is constructed at −10oC, a steel beam (cross-sectional area 45 cm2) is put in place with its ends cemented in pillars. If the sealed ends cannot move, what will be the compressional force in the beam when the temperature is 25oC. For steel αs = 1.1×10−5 oC−1 and Y = 2×1011 N/m2.

Answer 1

We know that the Youngs Modulus can be expressed as \[Y=(F/A)x(dL/L)\]In this case,\[(dL/L) = \alpha _{S} \Delta T = 1.1*10^{-5} * (25-(-10)) = 1.1*10^{-5} * 35 = 3.85*10^{-4}\] Therefore, the compressional force in the beam at 25oC will be\[F = \frac{ Y * A }{ 3.85 * 10^{-4} } = \frac{ 2 * 10^{11} * 45 }{ 3.85 * 10^{-4} } = 2.34 * 10^{16} N\]

Answer 2

Well...this question was meant to be in my exam ..and it really happened! Thanx a lot.. :p