Pull on any bar and two things happen: an internal stress builds up to resist the load, and the bar strains — it stretches. Stress is simply the force spread over the cross-section (σ = F/A); strain is the stretch as a fraction of the original length (ε = ΔL/L). While the material behaves elastically the two are locked together by Young's modulus, the material's stiffness, through σ = E·ε. That single relationship lets you predict exactly how much a part will stretch — or how much stress a known stretch implies — without ever loading it to failure.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Hooke's law / mechanics-of-materials fundamentals.
The stress–strain equations
Keep units aligned: force in newtons, area in mm² and E in MPa (N/mm²) give stress in MPa and elongation in mm. Strain is dimensionless, often quoted as a percentage or in microstrain (µε). The axial stiffness k = A·E/L behaves exactly like a spring constant — a stubbier, stiffer, shorter bar resists stretch more — which is why a loaded bolt and a spring obey the same F = k·x rule.
Worked example — a steel tie rod
Scenario: A 20 mm-diameter steel rod, 2 m long, carries a 50 kN tensile load (E = 200 GPa).
At 159 MPa the rod is well below mild steel's ~250 MPa yield, so it behaves elastically and stretches a reversible 1.59 mm. Its axial stiffness is k = A·E/L = 31,400 N/mm. Swap the steel for aluminium (E = 69 GPa) and the same rod under the same load would stretch almost three times as far — about 4.6 mm — because aluminium is roughly a third as stiff.
Frequently Asked Questions
Stress is internal force per area (σ = F/A, in MPa); strain is deformation per length (ε = ΔL/L, dimensionless). Stress causes strain.
σ = F/A and ε = ΔL/L. In the elastic range σ = E·ε, so elongation ΔL = F·L/(A·E).
Material stiffness, E = σ/ε. ~200 GPa steel, 69 GPa aluminium, 117 GPa copper, 114 GPa titanium. Higher E = less stretch.
Stress ∝ strain while elastic: σ = E·ε. Valid below the proportional/yield limit; beyond it deformation becomes permanent.
ΔL = F·L/(A·E). Longer/thinner = more stretch; stiffer material = less. A 2 m steel rod, 314 mm², at 50 kN stretches ~1.6 mm.