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 walls. The cross section area of the rod is A. If the temperature of the rod is increased by theta , then the compressive force developed in rod can be written as-

Answer 1

The compressive force developed in rod is $T = AY (\alpha)(\Delta \theta)$

Explanation:

As we know that the rod is fixed between two rigid walls

When temperature of free rod is increased by some value then it will show thermal expansion

So we will have

$\Delta L = L_o \alpha \Delta \theta$

now we know that

$\frac{\Delta L}{L_o} = \alpha \Delta \theta$

as we know that rod is fixed between rigid walls and then temperature is raised so here rod is in compression strain

Now we have

$\frac{T}{A} = Y(strain)$

$T = AY\frac{\Delta L}{L_o}$

$T = AY (\alpha)(\Delta \theta)$

#Learn

Topic : Thermal stress

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Answer 2

Answer:

Explanation: see the pic