Stress — Compressive, Tensile, and Shear
Stress is the internal force per unit area inside a material when external forces are applied. It looks like pressure (same units — psi, MPa), but it describes what’s happening inside the material, not on its surface.
The Three Types
σ = F / A
Tensile Stress (pulling apart)
A rope, cable, or bolt in tension. The material is being stretched. If a 1,000 lbf load hangs from a rod with 0.5 in² cross-section:
σ = 1000 / 0.5 = 2,000 psi tensile
Compressive Stress (pushing together)
A column supporting a roof, concrete under a footing. Same equation, opposite direction. A 50,000 lb column load on a 10 in² base plate:
σ = 50,000 / 10 = 5,000 psi compressive
Shear Stress (sliding)
A bolt in single shear, a pin connection, scissors cutting paper. The force acts parallel to the cross-section, not perpendicular:
τ = V / A
A ⅜” bolt (area = 0.110 in²) carries 1,000 lbf in single shear:
τ = 1000 / 0.110 = 9,091 psi shear
Yield Strength vs. Ultimate Strength
Yield strength is where permanent deformation begins — the material won’t spring back. For A36 steel: 36,000 psi (36 ksi).
Ultimate strength is where the material actually breaks. For A36 steel: 58,000-80,000 psi.
In structural engineering, we design to yield with a safety factor. In mechanical engineering, we often design to fatigue life or ultimate strength depending on the application.
Why Shear Strength ≈ 60% of Tensile
For most ductile metals, shear yield ≈ 0.577 × tensile yield (from von Mises theory). So A36 steel:
- Tensile yield: 36 ksi
- Shear yield: ~21 ksi
This is why bolts in shear can carry less than bolts in tension — and why you’ll see larger or more bolts in shear connections.
Bearing Stress
When a bolt presses against the side of a hole, the stress on the contact area is:
σbearing = F / (d × t)
where d = bolt diameter and t = plate thickness. This is often the limiting factor in thin plates — the bolt won’t break, but it’ll elongate the hole.
Combined Loading
Real parts rarely see pure tension or pure shear. A shaft under torque and bending sees combined stress. Von Mises equivalent stress combines them:
σvm = √(σ² + 3τ²)
If σvm exceeds yield strength, the part yields. This is the basis of most FEA (finite element analysis) color plots — that rainbow scale is usually von Mises stress.
Key Takeaways
- Stress = internal force / area, same units as pressure
- Tension pulls, compression pushes, shear slides
- Design to yield strength with safety factors, not ultimate
- Shear strength ≈ 58% of tensile for ductile metals
- Von Mises stress combines tension + shear for real-world loading
- Try our Beam Calculator to see shear and moment diagrams for real loading scenarios