Question

The Humber Bridge in England has the world’s longest single span, 1410 m. Calculate the change in length of the steel deck of the span when the temperature increases from -5.0ºC to 18.0ºC.

Short answer

The change in length of the steel deck when temperature increases from -5.0ºC to 18.0ºC is +0.39 m.

Step-by-step solution

Concept of Linear Expansion in solids.

The linear change in length when the temperature change is given by the linear expansion expression,

$\mathbf{L}\mathbf{=}{\mathbf{L}}_{\mathbf{0}}\left(1+\alpha ∆T\right)$ ...(i)

Here, L is the expanded length, L₀ is the original length, α is the coefficient of expansion of the material and T is the absolute temperature.

 Determination of the change in length of the steel deck when temperature increases from -5.0ºC to 18.0ºC.

For steel, the coefficient of linear expansion,

$\alpha =1.2\times {10}^{-5}{\left(C°\right)}^{-1}$

Use the values in equation (i),

$$\begin{gathered} ∆L=\left(1.2\times {10}^{-5}{\left(C°\right)}^{-1}\right)\left(1410m\right)\left(18.0°C-\left(-5°C\right)\right) \\ =+0.39m \end{gathered}$$

Thus, the length increases with temperature by +0.39 m.