Statics, Materials and Motion
Stress, Strain & Stiffness
14 min · 2 worked examplesFree
Why a part fails, the difference between strong and stiff, and why doubling a beam's depth is worth eight times as much as widening it.
After this lesson you can
- Tell stress from strain, and strength from stiffness
- Read a stress-strain curve
- Explain why geometry usually beats material choice
Stress and strain
Stress is force per unit area, in pascals: σ = F/A. It is what a material actually experiences, which is why a thin rod fails under a load a thick one carries easily despite the force being identical.
Strain is the resulting fractional change in length, extension divided by original length, and therefore dimensionless.
Up to a point the two are proportional, and the constant relating them is Young's modulus, E = σ/ε. That region is elastic: remove the load and the part returns to its original shape.
Beyond the yield stress it does not. The material deforms permanently, and past the ultimate tensile stress it fractures. Design normally keeps the working stress well below yield, that gap is the safety factor from the foundations track.
In the full lesson
- Stress and strain
- Strong is not stiff
- Why geometry beats material
Free with an account. Read it, work the examples, answer the questions, then build it in the simulator.