Answer:
[tex]\Delta l=93.24\ mm[/tex]
Explanation:
Given:
length of steel arch bridge, [tex]l=518\ m[/tex]
temperature difference, [tex]\Delta T=35-20=15^{\circ}C[/tex]
We have,
coefficient of linear expansion of steel, [tex]\alpha = 12\times 10^{-6}\ ^{\circ}C^{-1}[/tex]
So, the change in length of the bridge:
[tex]\Delta l=l.\alpha.\Delta T[/tex]
[tex]\Delta l=518\times 12\times 10^{-6}\times 15[/tex]
[tex]\Delta l=93240\times 10^{-6}\ m[/tex]
[tex]\Delta l=93.24\ mm[/tex]
Above value must be the size of expansion joints.
