Question

The steel bed of a suspension bridge is 200m long at 20°C. If the extreme of temperatures to which it might be exposed are -30°C to 40°C,how much will it contract and expland? The coefficient of linear expansion for steel is 12×10⁶°C/s.

Answer 1

To determine the amount of contraction and expansion of the steel bed, we can use the formula for linear thermal expansion:

ΔL = α * L * ΔT

Where: ΔL is the change in length α is the coefficient of linear expansion L is the original length ΔT is the change in temperature

Given: L = 200 m (original length) α = 12 × 10^(-6) °C^(-1) (coefficient of linear expansion) ΔT = (40°C - (-30°C)) = 70°C (change in temperature)

First, let's calculate the expansion at the maximum temperature of 40°C:

ΔL_expansion = α * L * ΔT ΔL_expansion = 12 × 10^(-6) °C^(-1) * 200 m * 70°C ΔL_expansion = 0.168 m (rounded to three decimal places)

Therefore, the steel bed will expand by approximately 0.168 meters at the maximum temperature.

Next, let's calculate the contraction at the minimum temperature of -30°C:

ΔL_contraction = α * L * ΔT ΔL_contraction = 12 × 10^(-6) °C^(-1) * 200 m * (-30°C) ΔL_contraction = -0.072 m (rounded to three decimal places)

Therefore, the steel bed will contract by approximately 0.072 meters at the minimum temperature.

In summary:

• The steel bed will expand by approximately 0.168 meters at the maximum temperature of 40°C.
• The steel bed will contract by approximately 0.072 meters at the minimum temperature of -30°C.