Question

The length of the steel base on a bridge is 200m at 300C (when installed). If the temperature extremes that he can experience are 00 C and 500 C, determine how much the bridge is shrinking and expanding. Coefficient of expansion for steel length: 12x10-6 /°C.

Answer 1

Expansion or shrinking in length due to temperature is given by,

dL = L0*alpha*dT

here, L0 = initial length = 200 m

alpha = coefficient of linear expansion of steel = 12.0*10^-6

When temperature is lowest 0 C, then

dT = change in temperature = 0 C - 30.0 C = -30 C

So, dL = 200*(12.0*10^-6)*(-30)

dL = -0.072 m = 72.0*10^-3 m = 72.0 mm

So length of bridge will shrink by 72.0 mm

When temperature is lowest 50 C, then

dT = change in temperature = 50 C - 30.0 C = 20 C

So, dL = 200*(12.0*10^-6)*(20)

dL = 0.048 m = 48.0*10^-3 m = 48.0 mm

So length of bridge will expand by 48.0 mm

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