Mechanical Engineering - Strength of Materials - Discussion

There is no stress develop, because when we heated a metal then it receive the heat energy and the molecules nearer to it produce vibration and transfer the thermal energy to other.

This causes the rise in its temperature and as well as increases the intermolecular distances as there is no external forces applied on the metal who the metal resists it, and as we know that stress is restoring force per unit crossectional area so there is no stress developed in the material.

Basically stress is internal resistance of a body to applied load unlike pressure (Though both have same unit). Here there is no applied load rather there is no constraint for the bar which means no internal resistance to the deformation therefore the induced (internal force within a body) is zero, correspondingly the stress is zero.

Because free expansion of a bar stress will induce in the bar

As =σ = E ε

= E α dt ---- (1).

Where,

σ = Stress due to temperature expansion (N/m2, Pa).
E =Youngs Modulus (N/m2).
ε = Strain.
α = Temperature expansion coefficient (m/m°C).
dt = Temperature differance(°C).

Stress is nothing but the resisting force since due to temperature rise body will expand and if this expansion due to temperature change is restricted then only resisting stress (thermal stress) will come into play since expansion is not restricted that's why no stress is occurring.

No stress will be there because stress is the internal resistance per cross-sectional area. There is no such resistance to expansion. Also, no thermal stress will be there since there is free expansion and thermal stress is produced when there is resistance to expansion.

Since there is no young modulus in the question, stress cannot be calculated.

Thermal stress = young modulus * stain.
Or
Thermal stress = young modulus*temperature expansion coefficient*temperature difference.

For the free expansion of the bar, no stress is induced because there is no resistance to the free expansion.

It is free to expand, and we need the thermal coefficient of expansion, which is also not given in this problem.

When the steel is heated up to elevated temperatures increases in Ductility and Malleability properties.

So, here steel is heated up to 15 to 40-degree centigrade then Ductility is increased so the steel is no stress.

A body subjected heating under free expansion state doesn't produce stress because it is free to expand. Unless something stops or constrains the expansion due to heat, the body dies not produce stress.

Stress is what, when we apply some load, there will opposing internal resistance offered to material for not to deform, So in this case, there is no load is applied. It just leave as free expansion.