Question

Suppose that a steel bridge, 1000 m long, were built without any expansion joints. Suppose that only one end of the bridge was held fixed. What would the difference in the length of the bridge be between winter and summer, taking a typical winter temperature as 0°C, and a typical summer temperature as 40°C? The coefficient of thermal expansion of steel is 10.5 × 10-6 K-1.

Answer 1

The difference in the length of the bridge is 0.42 m.

Step-by-step explanation:

Given that,

Length = 1000 m

Winter temperature = 0°C

Summer temperature = 40°C

Coefficient of thermal expansion
`\alpha= 10.5*10^(-6)\ K^(-1)`

We need to calculate the difference in the length of the bridge

Using formula of the difference in the length

`\Delta L=L\alpha\Delta T`

Where,
`\Delta T`= temperature difference

`\alpha`=Coefficient of thermal expansion

L= length

Put the value into the formula

`\Delta L=1000*10.5*10^(-6)(40^(\circ)-0^(\circ))`

`\Delta L=0.42\ m`

Hence, The difference in the length of the bridge is 0.42 m.