Constrained thermal expansion creates stress σ=EαΔT.
If expansion is prevented, the stress is σ=EαΔT. Free expansion is δ=αLΔT. Steel α≈12×10⁻⁶ /K, aluminium 23×10⁻⁶ /K. Expansion joints in bridges and rails relieve this stress.
A fully restrained steel bar heated by 50 K develops about 120 MPa.
Thermal stresses can crack or buckle parts that are heated or cooled while constrained, so they must be designed for in pipes and rails.
Constrained thermal expansion creates stress σ=EαΔT.
Thermal stresses can crack or buckle parts that are heated or cooled while constrained, so they must be designed for in pipes and rails.
If expansion is prevented, the material must develop the stress that would have produced the same strain, which is E times the thermal strain.
They allow the length to change freely, which reduces the constraint and removes most of the thermal stress.
Typical applications include checking the compressive stress in a rail on a hot day, designing expansion joints for a long steel pipe and estimating the stress in a bonded joint of two metals with different expansion rates.
Study "Axial deformation" first (topic 49 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Mismatch of α in joined materials. Thermal shock in ceramics. Bimetallic strips bend.
A fully restrained steel bar heated by 50 K develops about 120 MPa.
The next topic is "Factor of safety", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 50 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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