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