Stress, Strain, and Elastic Modulus
Stress is force per unit area; strain is the dimensionless deformation. Together they define how a material responds to load.
Key Formulas
Normal Stress: σ = F / A (Pa, MPa, PSI)
Strain: ε = ΔL / L₀ (dimensionless)
Young's Modulus: E = σ / ε (GPa)
Shear Stress: τ = V·Q / (I·t) (structural)Pressure Unit Conversions
1 MPa = 145.04 PSI = 0.1450 ksi
1 PSI = 0.006895 MPa
1 ksi = 6.895 MPa = 1000 PSI
Example: 60,000 PSI steel bolt → 413.7 MPaMaterial Yield Strengths
- Mild steel (A36): 250 MPa (36 ksi)
- Stainless 304: 215 MPa (31 ksi)
- Aluminium 6061-T6: 276 MPa (40 ksi)
- Concrete (compressive): 20-40 MPa
- Oak wood: ~40 MPa parallel to grain
Convert stress units: Free Stress Calculator
Key Definitions
- Stress (σ): Force per unit area. σ = F/A (Pa or N/m²). Tensile, compressive, or shear.
- Strain (ε): Relative deformation. ε = ΔL/L (dimensionless). No units.
- Young's Modulus (E): Stiffness. E = σ/ε (Pa). Steel ≈ 200 GPa, aluminium ≈ 70 GPa, concrete ≈ 30 GPa, rubber ≈ 0.01 GPa.
- Yield strength: Stress at which permanent (plastic) deformation begins. Steel: 250–550 MPa; aluminium: 270–500 MPa.
- Ultimate tensile strength (UTS): Maximum stress before fracture.
The Stress-Strain Curve
A material's stress-strain curve reveals its mechanical behaviour: the linear elastic region (stress proportional to strain, reversible), the yield point (onset of permanent deformation), the plastic region (material flows with little additional stress increase), strain hardening, and final fracture. Engineers design structures to operate well within the elastic region, using safety factors of 2–4. Brittle materials (ceramics, glass) fracture with minimal plastic deformation — their stress-strain curve has no plateau. Ductile materials (steel, copper) show a clear yield point and extensive plastic deformation before fracture — they deform visibly before failing, giving warning.
Frequently Asked Questions
What is Poisson's ratio?
When a material is stretched in one direction, it contracts in the perpendicular directions. Poisson's ratio ν = -lateral strain / axial strain. Most structural materials have ν ≈ 0.25–0.35 (steel: 0.30, concrete: 0.20, rubber: ~0.50). ν = 0.5 means incompressible (constant volume), which applies to rubber and biological tissues.
What is the safety factor and how is it applied?
Safety factor = material strength / actual stress. A beam with yield strength 250 MPa designed to carry 50 MPa has a safety factor of 5. Codes specify minimum safety factors: structural steel bridges use ~1.6–2.0, pressure vessels use 3–4, aircraft structures use 1.5. Higher safety factors are used when material properties are uncertain, loads are variable, or consequences of failure are severe.
What causes fatigue failure?
Fatigue failure occurs when repeated cyclic loading causes crack growth and eventual fracture at stresses well below the static yield strength. The fatigue limit (endurance limit) is the stress below which a material can theoretically endure infinite cycles. Steel has a fatigue limit ~40–50% of UTS; aluminium has no true fatigue limit. Most mechanical failures in service are fatigue-related.