In strength of materials: when a bar experiences a temperature change but its thermal expansion or contraction is fully prevented, what do we call the stress that develops in the bar?

Introduction / Context:
Engineers frequently encounter members that heat up or cool down while being restrained by connections or surrounding materials. If a bar tries to expand or contract due to temperature change but is prevented from deforming, internal forces develop. The name and nature of this stress are central to thermal stress analysis in bridges, piping, rails, and machine components.

Given Data / Assumptions:

• Uniform, homogeneous bar.
• Temperature change occurs uniformly along the member.
• All free thermal expansion or contraction is fully prevented by rigid supports.
• Material behaves elastically within the stress range considered.

Concept / Approach:
A free bar subjected to a temperature rise ΔT would expand by ΔL_free = α * L * ΔT, where α is the coefficient of linear expansion. When expansion is fully restrained, the bar cannot change length, so mechanical stress develops to counter the thermal strain. This internally induced stress due only to restrained thermal strain is termed thermal stress.

Step-by-Step Solution:

Verification / Alternative check:
The same conclusion arises from energy methods: the restraint does work against the tendency to thermally deform, storing strain energy associated with the induced thermal stress.

Why Other Options Are Wrong:
Tensile stress / Compressive stress: These may describe the sign in a given case but do not name the phenomenon; the proper general term is thermal stress.Shear stress: Not produced by purely axial thermal restraint in a straight prismatic bar.Residual stress: A broader term usually related to manufacturing or non-uniform processes; here the cause is temperature change with restraint—specifically thermal stress.

Common Pitfalls:
Assuming no stress if supports are “flexible”; partial restraint still induces thermal stress. Forgetting that sign depends on whether heating or cooling occurs.

Final Answer:

thermal stress