Question

A concrete bridge is built of 325-cm-long concrete slabs with an expansion joint between them. The slabs just touch on a 115∘F day, the hottest day for which the bridge is designed.

A. What is the gap between the slabs when the temperature is 0∘F∘F?

Express your answer with the appropriate units.

Answer 1

The linear expansion of a solid material that undergoes a temperature change of ∆T is given by,

∆L = a* L * ∆T

where T is in Kelvin, a is the coefficient of linear expansion of the material, L the length and ∆L the linear expansion.

first convert temperature into Kelvin,

115 F = 319.3 K

0 F = 255.4 K

now, ∆T = 319.3 - 255.4 = 63.9 K

L = 325 cm = 3.25 m

a for concrete is = 12 * 10^-6 K^-1

using all known values,

∆L = 12 * 10^-6 * 3.25 * 63.9

∆L = 2492.1 * 10^-6 m

∆L = 2.49 mm

Thus the gap between slabs when temperature is 0 F is 2.49 millimetre.