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A steel rod with a cross-sectional area ...

A steel rod with a cross-sectional area of `150 mm^(2)` is stretched between two fixed points. The tensile load at `20^(@)C` is `5000N`.
`(a)` What will be the stress at `-20^(@)C` ?
`(b)` At what temperature will the stress be zero ?
(Assume `alpha=11.7mu m//m^(@)C` and `Y=200GN//m^(2)`)

A

`12.7 xx 10^(6)N//m^(2)`

B

`1.27 xx 10^(6)N//m^(2)`

C

`127 xx 10^(6)N//m^(2)`

D

`0.127 xx 10^(6)N//m^(2)`

Text Solution

Verified by Experts

c) Let L = free length at `0^(@)`C
`L_(0)`=Final stretched length in each case.
`L_(1)` and `L_(2)` are free lengths at `+20^(@)`C and `-20^(@)`C, respectively.
We know, Here `s_(1)` and `s_(2)` are load deformation
`(F_(2)L)/(AY) = (F_(1)L)/(AY) + 2alphaLDeltaT`
`rArr sigma_(2) = (F_(2)/A =(F_(1))/A + 2alphaDeltaTY`
`=(5000)/(150 xx 10^(-6)) + (2)(11.7 xx 10^(-6)(20)(2 xx 10^(11))`
`(127 xx 10^(6)N//m^(2)`)
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