Mechanical engineering formula sheet
| Formula | Equation | Symbols | Conditions |
|---|---|---|---|
| Statics | |||
| Normal Stress | σ = F / A | σ Stress (Pa); F Force (N); A Area (m²) | Valid for uniform stress distribution over the cross-section |
| Normal Strain | ε = Δ L / L₀ | ε Strain; ΔL Change in Length (m); L₀ Original Length (m) | Valid for small deformations in elastic region |
| Hooke's Law | σ = E ε | σ Stress (Pa); E Young's Modulus (Pa); ε Strain | Valid only in elastic region, below yield strength |
| Shear Stress | τ = V / A | τ Shear Stress (Pa); V Shear Force (N); A Shear Area (m²) | Average over the specified shear area |
| Torque | τ = F · r | τ Torque (N·m); F Force (N); r Moment Arm (m) | Magnitude assumes the force is perpendicular to the moment arm |
| Moment of Inertia (Rectangle) | I = bh³ / 12 | I Moment of Inertia (m⁴); b Width (m); h Height (m) | About the centroidal axis parallel to the base (width b) |
| Moment of Inertia (Circle) | I = π d⁴ / 64 | I Moment of Inertia (m⁴); d Diameter (m) | About the centroidal axis |
| Torsional Shear Stress | τ = Tr / J | τ Shear Stress (Pa); T Torque (N·m); r Radial Distance (m); J Polar Moment of Inertia (m⁴) | Circular cross-section, elastic range, small deformations |
Equations are rendered from the library's own typeset source with no term reordered, dropped or simplified. Symbol legends and validity conditions are the library's; an equation is a model, not a guarantee — confirm its assumptions hold before you rely on a result.
- The formula library records no validity conditions for this entry. An absent condition line is not a statement that the formula is unconditional — check the source before applying it outside the obvious case.
Reference values are provided for study and quick reference. Verify against current standards and manufacturer data before safety-critical design.