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When composite rod is free, composite le...

When composite rod is free, composite length increase to `2.002m` from temperature `20^(@)C` to `120^(@)C`. When composite rod is fixed between the support, there is no change in component length. Find `Y` and `alpha` of steel if
`Y_(cu) = 1.5 xx 10^(13) N//m^(2)` and `alpha_(cu) = 1.6 xx 10^(-5//@)C`

Text Solution

Verified by Experts

`Deltal = l_(s)alpha_(s)DeltaT + l_(c)alpha_(c)DeltaT`
`.002 = [1.5 alpha_(s) + 0.5 xx 1.6 xx 10^(-5)] xx 100`
`alpha_(s) = (1.2 xx 10(-5))/(1.5) = 8 xx 10^(-6)//^(@)C`
there is no change in component in length
For steel
`x = l_(s) alpha_(s) DeltaT - (Fl_(s))/(AY_(s)) = 0`

`(F)/(AY_(s)) = alpha_(s)Delta_(s) ....(A)`
for copper
`x = (Fl_(c))/(AY_(c)) - l_(c)alpha_(c)DeltaT = 0`
`(F)/(AY_(c)) = alpha_(c)DeltaT ...(B)`
`B//A rArr (Y_(s))/(Y_(c)) = (alpha_(c))/(alpha_(s))`
`Y_(s) = Y_(c) (alpha_(c))/(alpha_(s)) = (1.5 xx 10^(13) xx 16 xx 10^(6))/(8 xx 10^(-6)) = 3 xx 10^(13N//m^(2)`
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