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A steel rod of length 6.0 m and diameter...

A steel rod of length 6.0 m and diameter 20 mm is fixed between two rigid supports. Determine the stress in the rod, when the temperature increased by `80^(@)C` if ends do not yield. Take `Y=2.0xx10^(5)kg//cm^(2) and alpha=12xx10^(-6)"per ".^(@)C`.

Text Solution

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Given,

Length of the rod l = 6 m = 600 cm
Diameter of the rod d = 20 mm = 2 cm
Increase in temperature `DeltaT=80^(@)C`
Young's modulus `Y=2xx10^(6)kg//cm^(2)`
Thermal coefficient of linear expansion `alpha=12xx106(-6)" per ".^(@)C`
When the ends of rod do not yield
Let `sigma` be the stress in the rod
Using the relation,
`sigma=alpha Y DeltaT`
`sigma=12xx10^(-6)xx2xx10^(6)xx80`
`=1920kg//cm^(2)`
Stress in the rod = `1920 kg//cm^(2)`
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