Stress and Strain Calculator
Stress (MPa)
10
Strain
0.01
How it works
Stress is force per unit area (σ = F / A), measured in Pascals (N/m²) or psi. Strain is the fractional deformation (ε = ΔL / L₀), dimensionless. These two quantities describe the mechanical state of a material under load.
**Types of stress** Normal stress (tension/compression): force perpendicular to the cross-section. Shear stress (τ): force parallel to the cross-section. Bearing stress: compressive stress at a contact surface (bolt through a hole, pin in a bracket). Bending creates combined normal stresses: tension on one side, compression on the other.
**Stress concentration** Holes, notches, and sharp corners concentrate stress locally. The stress concentration factor K_t (typically 2–4 for common geometries) multiplies the nominal stress. A shaft with a keyway or shoulder has significantly higher local stress than the calculated nominal value — fatigue cracks initiate at these locations. Smooth fillet radii reduce stress concentration.
**Yield stress and safety factors** Yield stress (σ_y) is the stress at which permanent deformation begins. Ultimate tensile stress (UTS) is the maximum stress before fracture. Safety factor = σ_y / σ_applied. Typical safety factors: 2–4 for static loads, 4–8 for dynamic/impact loads. Codes specify minimum safety factors for structural applications.
**Thermal stress** Constrained thermal expansion creates thermal stress: σ_thermal = E × α × ΔT, where E is Young's modulus and α is thermal expansion coefficient. A steel pipe anchored at both ends heated by 100°C develops σ = 200 GPa × 12×10⁻⁶/°C × 100°C = 240 MPa — approaching yield stress of mild steel. Expansion joints in pipelines and bridge expansion gaps prevent this.
Frequently Asked Questions
- Mild steel (ASTM A36): yield 250 MPa, UTS 400 MPa. High-strength steel (ASTM A572 Grade 50): yield 345 MPa, UTS 450 MPa. 6061-T6 aluminum: yield 276 MPa, UTS 310 MPa. 304 stainless steel: yield 215 MPa, UTS 505 MPa. Structural engineering designs to yield strength (permanent deformation begins). Aerospace design uses UTS with appropriate safety factors. The ratio UTS/yield is the 'strain hardening ratio' — high ratios indicate ductile materials with reserve capacity beyond yield.
- When a material is stretched in one direction, it contracts in the perpendicular directions: ε_lateral = -ν × ε_axial, where ν (Poisson's ratio) is typically 0.25–0.35 for metals (steel ≈ 0.29, aluminum ≈ 0.33). A 1% axial strain in steel produces 0.29% lateral contraction. This lateral strain matters in: biaxial stress states (pressure vessels), composite materials (anisotropic Poisson ratios), precision machining (accounting for dimensional changes during stress relief), and finite element analysis (biaxial stress effects on yield criterion).
- Normal stress (σ) acts perpendicular to a cross-section — it's the stress that causes tension/compression. Shear stress (τ) acts parallel to the cross-section — it's the stress that causes sliding. In a beam, bending creates normal stresses (maximum at top and bottom flanges), while shear force creates shear stresses (maximum at the neutral axis). At 45° to the principal stress directions, shear stress is maximum (τ_max = σ_max/2 for uniaxial stress). This is why ductile materials fail in shear at 45° in tension tests, and brittle materials fail perpendicular to tension (at the plane of maximum normal stress).
- Modulus of resilience = σ_yield²/(2E) = area under the stress-strain curve up to yield. It represents the energy per unit volume the material can absorb elastically (without permanent deformation). Materials with high yield strength and low E have high resilience — spring steel, titanium alloys. Modulus of toughness (area under entire stress-strain curve to fracture) represents total energy absorption including plastic deformation. For impact resistance: tough materials (high toughness, high % elongation) absorb more energy than strong but brittle materials. 'Strong' and 'tough' are not the same property.