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A bridge to be fabricated of steel girders is designed to be 500 m long and 12 m wide at ambient temperature (assumed 20°C). Expansion joints will be provided to compensate for the change in length in the girders as the temperature varies. Each expansion joint can compensate for a maximum of 20 mm of change in length. From historical records it is estimated that the minimum and maximum temperatures in the region will be -35°C and 40°C, respectively. Determine (a) the minimum number of expansion joints required and (b) the length that each bridge section should be fabricated. The coefficient of thermal expansion α=12(10-6)/C for steel.

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Answer:

23

21.7391304348 m

Explanation:

L = Initial length = 500 m

[tex]\Delta T[/tex] = Change in temperature = 40-(-35)

[tex]\alpha[/tex] = Coefficient of thermal expansion = [tex]12\times 10^{-6}\ /^{\circ}C[/tex]

Change in length is given by

[tex]\Delta L=L\alpha \Delta T\\\Rightarrow \Delta L=500\times 12\times 10^{-6}\times (40-(-35))\\\Rightarrow \Delta L=0.45\ m[/tex]

The change in length is 0.45 m

The number of joints would be

[tex]n=\dfrac{0.45}{0.02}\\\Rightarrow n=22.5\\\Rightarrow n\approx 23[/tex]

The number of joints is 23

Each bridge section length would be

[tex]\dfrac{L}{n}=\dfrac{500}{23}=21.7391304348\ m[/tex]

The length of each bridge section would be 21.7391304348 m

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