Question

A cylindrical metal rod of length L Young's modulus of elasticity Y and thermal coefficient of linear expansion Alpha is fixed between two concrete was the cross section area of the rod is a if the temperature of the rod is increased by Delta theta the compressive force development can be written as

Answer 1

Answer:

YA(alpha)delta theta

Answer 2

$F=a.Y(\alpha.\Delta \theta)$ is the expression for force due to change in temperature in the given terms.

Explanation:

Given:

• length of rod, $L$

• young's modulus of the rod material, $Y$

• coefficient of linear thermal expansion, $\alpha$

• cross-section area of the rod, $a$

• increase in temperature, $\Delta \theta$

Now the tendency of change in length due to temperature change will induce strain:

$\epsilon=\frac{\Delta L}{L}$

$\epsilon=\frac{L.\alpha.\Delta \theta}{L}$

$\epsilon =\alpha.\Delta \theta$ .................................(1)

Now, we also have the stress considering this strain:

$\sigma=Y.\epsilon$

$\sigma=Y(\alpha.\Delta \theta)$

Therefore the force due to this stress:

$F=\sigma.a$

$F=a.Y(\alpha.\Delta \theta)$