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If a steel rod of length 1 m rests on a smooth horizontal base is heated from $T_1$ to $T_2$, what is the longitudinal strain developed?
I think that due to thermal expansion/contraction, the length of the rod should change, so strain should be developed. However, after googling my doubt it turns out the strain developed is zero.
Can I get an explanation as to why it is zero?
Here's a link to one of the pdfs I found on the Internet about this topic:
See page no. 5, figure 9.1.
It says that mechanical strain is zero. The author considers mechanical strain and thermal strain separately. The mechanical one is zero if there is no external force. He never say that the thermal strain, due to thermal expansion, is zero.
Edit According to the article: Thermal strain is due to the change in temperature of the bar. Mechanical strain is due to external forces acting on the bar. Both strains measure the change in dimensions, here focus being on length of the bar. If the temerature is fixed and you pull the ends of the bar, the bar expands and you have a mechanical strain. If the temperature is changed but no forces act on the bar, the bar again expands and this is thermal strain. This is what free expansion means. The bar may be on a frictionless table and the ends are free from any obstacle. So there are no horizontal forces on the bar. In general, you can hae both strains at the same time and they can cancel out in the right conditions. If you heat the bar but you aplly some compression at the ends, you may have no change in length. You can imagine this as having the two strains with opposite signs and cancelling each other. But the net effect is no change in length so no strain. But there is a stress in the bar. You can consider this situation in two steps, if you want. You heat the bar, it expands. Then you apply some compression force and you bring it back to the initial length.
Thermal strain is strain that develops when a material is heated or cooled. So the strain should not be zero.
In addition to the site you provided, thermal strain for a non-constrained object is not zero as long as the coefficient of thermal expansion is not zero, per the following:
http://emweb.unl.edu/NEGAHBAN/Em325/05-Thermal-strain/Thermal%20strain.htm
http://www.ce.memphis.edu/3322/Pdfs/PaulsPDFs/Thermal%20Strain.pdf
https://www.engineeringtoolbox.com/stress-restricting-thermal-expansion-d_1756.html
https://en.wikipedia.org/wiki/Thermal_expansion#Effects_on_strain
https://www.britannica.com/science/thermal-strain
Thermal stress (though a misnomer) is the internal stress that occurs if the object being heated or cooled is constrained. That would be the case if the steel rod was wedged between two rigid walls prior to heating.
When the heated rod is constrained from increasing in length, its thermal strain is cancelled by the compressive mechanical stress of the walls. If it was fixed to the rigid walls (i.e., unable to separate from them) and cooled so that it is constrained from decreasing in length, its thermal strain is cancelled by the mechanical tensile stress of the walls.
Hope this helps.
