Example 13.3 from College Physics, 13.2 Thermal Expansion of Solids and Liquids

Calculating Linear Thermal Expansion: The Golden Gate Bridge

The main span of San Francisco’s Golden Gate Bridge is 1275 m long at its coldest. The bridge is exposed to temperatures ranging from $- 15 º C$ to $40 º C$ . What is its change in length between these temperatures? Assume that the bridge is made entirely of steel.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Use the equation for linear thermal expansion $Δ L = αL ΔT$ to calculate the change in length , $Δ L$ . Use the coefficient of linear expansion, $α$ , for steel from Table 13.2, and note that the change in temperature, $Δ T$ , is $55 º C$ .
Solution
Plug all of the known values into the equation to solve for $Δ L$ .
$Δ L = αL Δ T = (\frac{12 \times 10^{- 6}}{º C}) (1275 m) (55 º C) = 0 . 84 m.$
13.8
Discussion
Although not large compared with the length of the bridge, this change in length is observable. It is generally spread over many expansion joints so that the expansion at each joint is small.

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