Question

The New River Gorge Bridge in West Virginia is a steel arch bridge 518 m in length. How much does the total length of the roadway decking change between temperature extremes of –20.0°C and 35.0°C? The result indicates the size of the expansion joints that must be built into the structure.

Answer 1

The change in length of the roadway decking between temperature extremes can be calculated using the formula for linear thermal expansion.

Step-by-step explanation:

The change in length of the roadway decking between temperature extremes can be calculated using the formula for linear thermal expansion:

ΔL = L₀ α ΔT

Where:

ΔL is the change in length

L₀ is the original length of the roadway decking

α is the coefficient of linear thermal expansion for steel

ΔT is the change in temperature

To solve for the change in length, we need to know the original length of the roadway decking, the coefficient of linear thermal expansion for steel, and the change in temperature between –20.0°C and 35.0°C.

Answer 2

`\Delta l=93.24\ mm`

Step-by-step explanation:

Given:

length of steel arch bridge,
`l=518\ m`

temperature difference,
`\Delta T=35-20=15^(\circ)C`

We have,

coefficient of linear expansion of steel,
`\alpha = 12* 10^(-6)\ ^(\circ)C^(-1)`

So, the change in length of the bridge:

`\Delta l=l.\alpha.\Delta T`

`\Delta l=518* 12* 10^(-6)* 15`

`\Delta l=93240* 10^(-6)\ m`

`\Delta l=93.24\ mm`

Above value must be the size of expansion joints.