Question

A steel bridge is 200 m long at 0 0C . The temperature has annual variation from -25 to 45 0C . What
is the difference in length of the bridge at these two temperature extremes? (coefficient of linear
expansion of steel= 12 × 10−6 / C
0

Answer 1

To find the difference in length of the bridge at the two temperature extremes, we can use the formula for linear expansion:
ΔL = αLΔT
Where:
ΔL = change in length
α = coefficient of linear expansion for steel (12 x 10^-6 / 0C)
L = original length of the bridge (200m)
ΔT = change in temperature
At -25 0C:
ΔT = -25 0C - 0 0C = -25 0C
ΔL1 = (12 x 10^-6 / 0C)(200m)(-25 0C)
ΔL1 = -0.06m
At 45 0C:
ΔT = 45 0C - 0 0C = 45 0C
ΔL2 = (12 x 10^-6 / 0C)(200m)(45 0C)
ΔL2 = 0.108m
The difference in length at the two temperature extremes is:
ΔL2 - ΔL1 = 0.108m - (-0.06m) = 0.168m
Therefore, the difference in length of the bridge at the two temperature extremes is 0.168 meters.