Mechanical Engineering - Strength of Materials - Discussion

Here's the right answer. When any body is cooled then its is contracted. Now the stress is a resisting force, therefore if any body goes under shrinkage (suppose that in longitudinal direction) then force needed to resist that is in opposite direction.

So for that area stress is developed in opposite direction and so for compression or shrinkage tensile stress is developed. Similarly if a body is heated, it tries to expand and so in order to resist that compressive stress is developed in opposite direction.

But in question it is not mentioned whether the bar is allowed to expand freely or it is held rigidly.

@taniya.

The stress never be applied. It developed only.

When a body is cooled then it contracts. In the above question, it is asked that what stress will be developed when a body is cooled, but not induced stresses, assume that both the ends are connected to a spring when the bar is cooled it contracts to make the spring deform under tensile load.

So tensile stress is correct.

How can we relate the stress to the temperature?

Please explain.

The bar is fixed in both ends, when cooling bar to -5 the bar will shranking because change in temperatue this will produce a reaction forces in both ends will trying to opposite the action of shrinking so those forces will produce tensile stress in the body. Thank you.

Yes, by compressing the material. The compressive force is induced but tensile stress is developed.

The answer is correct. Actually, when the bar is held at -5 degrees. Temp than it's material tends to shrink but the molecule will resist this deformation and hence apply a tensile stress (stress in opposite direction of the shrink).

Here, stress = alpha*E*deltaT.

Since delta T will be positive, stress is positive, so is a tensile stree will be developed. Hope it helped.

Stress is the resistance offered by a material to resist the deformation caused by the force acting. Over here since it is cooling, compressive stress will be acting on the body and the body opposes by tensile force hence TENSILE force is induce in the body. Hence the answer is correct.