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## Homework Statement

A steel rod having a cross-sectional area of 0.005 m^2and length 3 m is attached to supports at both ends. Find (a) the force exerted by the rod on the supports if the temperature falls 60ºC and the supports are unyielding, and (b) the force exerted by the rod on the supports if they yield 0.0002 m while the temperature raises 50ºC. Take E = 210 GPa, coefficient of thermal expansion =10.5 x 10^(-6) °C^(-1)

## Homework Equations

dl = length x temperature change x expansion coefficient

E = stress/strain

F = α x ΔT x A x E

## The Attempt at a Solution

a)

rod unrestrained : dl = original length x temperature change x expansion coefficient

= 3 x 60 x 10.5 x 10^(-6)

= 1.89 x10^-3 m

Tensile stress due to supports : E = stress/strain = (Force*cross-sect area)/(dl*orig length)

at this point I have no force, do I just neglect it in this equation?

Or do I just use the equation:

F = α x ΔT x A x E

Where E is the modulus of elasticity

α is the expansion coefficient

Am I on the right track? Would be grateful for any help of guidance.

Thanks.