NapkinCalc

Mechanics of Materials — Stress & Strain

Stress, strain, Hooke's law and Young's modulus, factor of safety, shear, thermal stress, and pressure-vessel hoop stress — the math that decides if a part survives.

Statics told you the force in a part. This course asks the question that actually matters: will it break? The answer lives in stress (force packed into area) and strain (how much it stretches) — and the link between them is the single most useful line in engineering, Hooke's law.

  1. 01 Stress — force divided by area ELI5: the same pull is gentle on a thick rod and brutal on a thin wire. Stress σ = F / A measures the intensity: newtons per square metre, which engineers call…
  2. 02 Strain & Hooke's law — stiffness is a material property ELI5: strain ε = ΔL / L is the fractional stretch — pure ratio, no units. For most metals, stress and strain rise together in lockstep: σ = E·ε. The constant E…
  3. 03 Factor of safety — the engineer's margin ELI5: you never load a part to the edge of failure. The factor of safety = strength / actual stress tells you how much headroom you have. A FoS of 1 means…
  4. 04 Shear stress — forces that slice, not stretch ELI5: a bolt holding two plates feels a force trying to shear it across, not pull it apart. Shear stress τ = V / A uses the same force-over-area idea, but the…
  5. 05 Thermal stress — heat with nowhere to go 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.…
  6. 06 Pressure vessels — the hoop stress that ties to this app's roots ELI5: pressure inside a cylinder pushes the wall outward everywhere. The seam running around the circumference (hoop stress, σ = P·r / t) carries twice the…

next course: Beams & Columns — Bending & Buckling →