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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 increases by `80^@`C if
(a)the ends do not yield (b) the ends yield by 1mm
Take `Y=2.0xx10^(6) kg//cm^(2)`and `alpha=12xx10^(-6) per ^@C.`

Text Solution

Verified by Experts

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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