Thermal Stress, Composite Rods, and Bimetallic Bending
In one-dimensional linear thermoelasticity the total strain is sigma/Y + alpha Delta T; constraints and interface compatibility determine sigma, while a bimetallic strip curves because its bonded layers have unequal free thermal strains.
Why this shows up in the exam
Rail and wire thermal stress · Temperature-invariant composite scales · Bimetallic thermostats and bonded strips
Learn the idea
Prevented or unequal free expansion creates elastic stress, while bonded unequal materials bend or share strain. A free rod simply changes length, but a restraint must supply the mechanical strain that cancels thermal strain; bonded materials compromise through force balance, compatibility, or curvature.
🧠 Memory hook: Free means expansion; fixed means stress.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- epsilon_total = sigma/Y + alpha Delta T — signed elastic plus thermal strain in a linear material
- |sigma| = Y alpha |Delta T| — stress magnitude for complete prevention of expansion or contraction
- U/V = sigma²/(2Y) = (1/2)Y alpha² Delta T² — elastic energy density for a fully constrained rod
How to approach it
- 1Write each member's free thermal strain
- 2Add the elastic strain with sign
- 3Apply length compatibility and force balance before solving
Common slip-ups that cost marks
- •Calling compressive stress tension after heating
- •Using force without cross-sectional area
- •Equating free expansions when compatibility requires equal final lengths
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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