Mechanical Engineering - Strength of Materials - Discussion

The answer to this question depends upon the past temperature of the bar. The formula for thermal stress is

(σ)thermal = (Eα . dT).
dT = Final Temp - Initial Temp.

So if the initial temperature of the bar was below -5° (like -10°), then -5° will obviously be considered as a rise in the temperature and therefore it will result into a compressive stress(positive thermal strain, expansion of the bar) as the difference between the temperatures will be positive. If the initial temperature was greater than -5° (like +10°), then cooling it down to -5° will result into a negative value of temperature difference and generate a tensile stress(negative thermal strain, contraction of the bar) in the bar.

Now, as the word "cooled to -5° is written in the question, it shows that the initial temp was more than -5°. Hence the stress will be tensile. The Answer is [C]. I assume that the bar is held at the ends from expanding. If not, then the answer

Ans:- no stress.

If the bar is cooled to 5 degrees C, Contraction takes place. Or If the bar is heated, expansion takes place, based on temperature differences.

But no stress here developed. Because it's free expansion. There is no opposing force/resisting area is there.

Remembering stress formula.

"Total resistance per unit area of cross-section". In the given question "area is varying like a contraction but no resistance".

In order to prevent the free expansion. The bar must be fixed on both ends or pulling or pushing load must act on it. The only possibility of stress was developed either it may compressive or tensile based on type load acting on it.

So, please change the answer to ***no stress***.

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.

It depends on the configuration of a bar. If the bar is free at both ends and no restriction whatsoever, then no stresses will be developed.

If it is constrained, when we cool the bar it tends to shrink which develops tensile stress inside the bar.

Similarly, when we heat the bar it tends to expand and due to constraint compressive stresses are developed.

When a bar is cooled to - 5° C, it will develop.

Actually, this question denoted 'a bar '.

It is not Mentioned as the bar is fixed, hinged, both sides fixed it. So the bar is free, not fixed and hinged.

That's why the answer is ' no stress '.

(If it is mentioned as "one side is fixed" then the answer is compressive stress generate).

Thank you.

If any force applied on a bar then the resisting force developed in the body against the applied force. When the bar is cooled, it will compress. So against compression, the internal force against compression developed. So the force developed is the Tensile force which is trying to resist compression.

So, the tensile stress is the right answer.

I think the answer should be no stresses, as the bar is contracting freely.

Suppose the bar is fixed at both the ends and it is being cooled, then in order to maintain it's true state tensile stresses will be induced in bar.

In similar manner if a fixed bar is being heated it won't expand and compressive stresses will be induced in bar.

Correct answer is tensile stress.

Here -5 degrees denotes that there will be an initial temperature
Thermal stress= E alpha ΔT,
ΔT= T2-T1.

If T2 is -10 degrees that means ΔT =-10-(-5)=-5 degree which means compressive,
If T2 =10 degree.

ΔT= 10-(-5)=15 which means tensile stress . So the answer will be tensile.

If body fixed at both ends then tensile stress will develop, due to cooling contraction will be developed and compressive stress will occur. But because of a bar fixed at both end their tensile stress will be developed.

See the question is not asking about which stress will apply, it is asking about which will develop.

Thanks

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.