The steel bed of a suspension bridge is 200m long at 20 C. If the extremes of temperature to which it might be exposed are -30 C to 40 C, how much will it contract and expand

The steel bed will contract by  0.13 m, and expand by 0.052 m

Explanation:

For contraction,

α = ΔL/(LΔθ) Equation 1

Where α = Linear expansivity of  steel, ΔL = decrease in length/ Increase in length, L = Original length, Δθ = Change in temperature

make ΔL the subject of the equation

ΔL = α(LΔθ) Equation 2

Given: α = 13×10⁻⁶/C, L = 200 m, Δθ = -30-20 = -50 °C

Substitute into equation 2

ΔL = 13×10⁻⁶(200)(-50)

ΔL = -0.13 m

Similarly, For expansion,

Using equation 2

ΔL =  α(LΔθ)

Given: α = 13×10⁻⁶/C, L = 200 m, Δθ = 40-20 = 20  °C

Substitute into equation 2

ΔL =  13×10⁻⁶(200)(20)

ΔL = 0.052 m.

Hence the steel bed will contract by  0.13 m, and expand by 0.052 m

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