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Problems on Temperature Stresses

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Given data:

$E_{steel}=2*10^5 N/mm^2$ (not given to be remembered)

$T_1=16 ^{\circ} C T_2=66 ^{\circ}$

$L=15m=15*1000mm$

$\alpha_{steel}=12*10^{-6}$ (Not given which mean to be remembered)

co-efficient of linear expansion

Now, change in temperature= $T=T_2-T_1=66-16=50^{\circ}$

Free expansion of rod is$ \delta=\alpha TL$

$=12*10^{-6}*50*15*1000$

=9mm

When the expansion is prevented of the rod,

temperature stress $P_{steel}=\alpha TE$

$=12*10^{-6}*50*2*10^{-5}$

$P_{steel}=120 N/mm^2$

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