NapkinCalc

Mechanics of Materials — Stress & Strain

Thermal stress — heat with nowhere to go

continues from lesson 4 — values defined earlier in the course stay live here

ELI5: materials expand when heated. Stop that expansion — clamp both ends — and the material pushes back with a stress σ = E·α·ΔT, no external load required. It depends only on stiffness, the expansion coefficient α, and the temperature change.

αsteel:=12e−6/K\alpha _{steel} := 12e-6 / K = 0.000012 K^-1 steel's thermal expansion coefficient
dTheat:=60KdT_{heat} := 60 K = 60 K temperature rise
σthermal:=Esteel∗αsteel∗dTheatinMPa\sigma _{thermal} := E_{steel} * \alpha _{steel} * dT_{heat} in MPa = 144 MPa locked-in stress = 144 MPa
✓ pass abs(σthermal−144MPa)<0.5MPaabs(\sigma _{thermal} - 144 MPa) < 0.5 MPa enormous — and from heat alone

Real-world hook: this is why bridges have expansion joints, railway tracks buckle in heatwaves, and pipelines are laid with deliberate bends.