Suppose that the 1.3-km main span of steel for the Golden

QUESTION:

To solve the next problems, you will need to know the average coefficient of linear expansion, a, which differs for different materials. We define a to be the change in length (L) per unit length—or the fractional change in length—for a temperature change of \({ }^{\circ} \mathrm{C}\); that is, \(\Delta L / L\) per \({ }^{\circ} \mathrm{C}\). For aluminum, \(\alpha=24 \times 10^{-6} /{ }^{\circ} C\), and for steel, \(\alpha=11 \times 10^{-6} /{ }^{\circ} \mathrm{C}\). The change in the length \(\Delta L\) of a material is given by \(\Delta L=L \alpha \Delta T\).

Suppose that the 1.3-km main span of steel for the Golden Gate Bridge had no expansion joints. Show that for an increase in temperature of \(20^{\circ} \mathrm{C}\), the bridge would be nearly 0.3 m longer.

Text Transcription:

^circ C

Delta L / L

alpha = 24 times 10^-6 / ^circ C

alpha = 11 times 10^-6 / ^circ C

Delta L

Delta L = L alpha Delta T

20^circ C