Thermal Strain with Mechanical Loading
In one-dimensional linear thermoelasticity, total strain is alpha Delta T plus sigma/Y with a consistent tensile sign convention; constraints determine the stress needed for compatibility.
Why this shows up in the exam
Thermally loaded rods · Expansion restraints · Temperature compensation in structures
Learn the idea
Thermal and elastic strains add algebraically under small deformation. A free heated rod expands, but an applied compression or a rigid constraint can reduce, cancel, or reverse that expansion.
🧠 Memory hook: Free heat strain plus signed force strain.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- epsilon_total = alpha Delta T + sigma/Y — signed sum of free thermal and elastic strains
- sigma_constraint = -Y alpha Delta T — stress for completely prevented expansion
- Delta L = L(alpha Delta T - F/(AY)) — heated rod under a stated compressive axial force
How to approach it
- 1Choose tension and elongation signs
- 2Write thermal and elastic strain contributions
- 3Apply the length or constraint condition
Common slip-ups that cost marks
- •Adding magnitudes when thermal and mechanical strains oppose
- •Using Celsius temperature instead of temperature change
- •Assuming zero stress for a constrained rod
🌟 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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