Solid mechanics · Structural
Stress Calculator
Axial, shear, bending, torsion, and von Mises — enter loads and geometry, watch the diagram respond, and check margin against yield when you pick a material.
Result
Axial stress
σ = F / A
Pick a stress mode above — axial, shear, bending, torsion, or von Mises — then fill in the geometry and loads.
Formulas, failure criteria, and design margins — what this calculator solves.
Stress is the internal resistance of a material to external forces, expressed as force per unit area. It determines whether a component stays elastic, deforms permanently, or fractures. Most hand calculations assume linear-elastic behavior and compare results to yield strength through a safety factor.
- Axialσ = F/ATension or compression normal to the section
- Shearτ = F/AForce parallel to the shear plane
- Bendingσ = My/ILinear variation from neutral axis
- Torsionτ = Tr/JTwisting of shafts and closed sections
- von Misesσᵥ = √(σx² + σy² − σxσy + 3τxy²)Ductile yield under combined stress
| Range | Typical interpretation |
|---|---|
| SF < 1 | Stress exceeds yield — redesign required |
| 1 – 1.5 | Marginal — well-controlled static loads only |
| 1.5 – 2 | Typical for understood static machinery |
| 2 – 3 | Average conditions with some uncertainty |
| SF > 3 | Critical apps or poorly known loading |
SF = σyield / σinduced
- Maximum normal stress — brittle materials
- Maximum shear (Tresca) — conservative ductile estimate
- Distortion energy (von Mises) — most common for metals
- Mohr and Coulomb-Mohr — tension–compression asymmetry
- Cross-section properties (I, J, area) dominate stress magnitude.
- Stress raisers at holes and sharp corners are not included in nominal formulas.
- Temperature gradients add thermal stress on top of mechanical load.
- Cyclic loading needs fatigue analysis — static SF alone is insufficient.
- Stress is force per unit area — same units as pressure (Pa, MPa, psi).
- von Mises is the go-to criterion for ductile metals under multiaxial load.
- Stress concentrations at fillets and holes can multiply local stress several times over nominal.
- Fatigue failure can occur below yield when loads cycle — static SF does not cover that.
- Thermal expansion of a constrained member creates stress even without external load.
- Principal stresses σ₁ and σ₂ are the max/min normal stresses on planes with zero shear.
Worked example: Axial stress in a 20 mm steel rod under 10 kN
- Area A = π × (20/2)² = 314.16 mm²
- σ = F / A = 10,000 N / 314.16 mm²
σ ≈ 31.8 MPa (well below typical mild steel yield ~250 MPa)
What is engineering stress?
Engineering stress is force divided by the original cross-sectional area (σ = F/A). It is used to compare loading against a material's yield or ultimate strength.
When should I use von Mises stress?
Use von Mises (equivalent) stress for ductile materials under combined normal and shear loading. It gives a single scalar value to compare against yield strength.
What units does this stress calculator support?
You can enter dimensions in metric (mm, m) or imperial (in) and forces in N, kN, lbf, or kip. Results are shown in Pa, MPa, GPa, psi, or ksi.
Which torsion formula is used for non-circular sections?
Only solid and hollow circular shafts use the elementary τ = T·r/J. Solid rectangular sections use τmax = T/(α·a·b²), where α is interpolated from the standard shape-factor table (0.208 for a square, rising toward 1/3 for thin strips). Thin-walled closed rectangular tubes use Bredt's formula τ = T/(2·Aₘ·t), with Aₘ the mid-thickness enclosed area.
What are principal stresses and τmax?
For a combined stress state, the principal stresses σ₁ and σ₂ are the maximum and minimum normal stresses on any plane, found by rotating the element until shear vanishes. The maximum in-plane shear stress is τmax = (σ₁ − σ₂)/2. In von Mises mode the calculator reports both, and the Mohr's circle shows them graphically.
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