Chapter 10, Problem 62AP

A 250-m-long bridge is improperly designed so that it cannot expand with temperature. It is made of concrete with α = 12 × 10⁻⁶ (°C)⁻¹. (a) Assuming the maximum change in temperature at the site is expected to be 20°C, find the change in length the span would undergo if it were free to expand. (b) Show that the stress on an object with Young’s modulus Y when raised by ΔT with its ends Firmly fixed is given by a αY ΔT. (c) If the maximum stress the bridge can withstand without crumbling is 2.0 × 10⁷ Pa, will it crumble because of this temperature increase? Young’s modulus for concrete is about 2.0 × 10¹⁰ Pa.