Stress and Strain Calculator
Calculate normal stress, strain, and deformation for structural members.
Covers σ=F/A, strain ε=σ/E, elongation δ=FL/(AE), and factor of safety.
When a force is applied to a structural member, two things happen: the material develops internal stress, and the member deforms.
Normal stress
σ = F / A
σ is stress in MPa (megapascals = N/mm²). F is the applied force in Newtons. A is the cross-sectional area perpendicular to the force in mm².
Tension is positive, compression is negative. Steel can handle roughly 250 MPa in tension before yielding. Concrete handles only about 3-5 MPa in tension but 20-40 MPa in compression.
Strain
ε = σ / E = δ / L
Strain is dimensionless — it is the fractional change in length. E is Young’s modulus (stiffness), which varies by material:
Steel: 200 GPa, Aluminum: 69 GPa, Concrete: 30 GPa, Wood (along grain): 10-14 GPa
Elongation
δ = FL / (AE)
δ is the total deformation in mm. L is the original member length in mm. This combines the stress and strain equations.
Factor of safety
FoS = σ_yield / σ_applied
The yield strength is the stress at which the material begins to permanently deform. A FoS of 2 means you are applying half the yield stress. Structural codes typically require FoS ≥ 1.5 to 2.5 depending on the application and uncertainty in loads.
A bolt loaded in tension: F = 15,000 N, diameter = 12 mm, A = π(6²) = 113 mm². σ = 15,000/113 = 133 MPa. For steel with σ_yield = 250 MPa: FoS = 250/133 = 1.88.
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