Civil engineering formula sheet
| Formula | Equation | Symbols | Conditions |
|---|---|---|---|
| Beams | |||
| Cantilever Beam Deflection (Point Load) | δ = FL³ / (3EI) | δ Deflection (m); F Force (N); L Length (m); E Elastic Modulus (Pa); I Moment of Inertia (m⁴) | Point load at free end; small deflection, linear elastic, prismatic beam |
| Simply Supported Beam Deflection | δ_max = FL³ / (48EI) | δₘₐₓ Max Deflection (m); F Force (N); L Span (m); E Elastic Modulus (Pa); I Moment of Inertia (m⁴) | Point load at center; small deflection, linear elastic, prismatic beam |
| Bending Stress | σ = My / I | σ Bending Stress (Pa); M Bending Moment (N·m); y Distance from NA (m); I Moment of Inertia (m⁴) | Linear elastic, pure bending; plane sections remain plane |
| Section Modulus 1 | S = I / c | S Section Modulus (m³); I Moment of Inertia (m⁴); c Distance to Extreme Fiber (m) | not defined |
| Shear Stress in Beams | τ = VQ / (It) | τ Shear Stress (Pa); V Shear Force (N); Q First Moment of Area (m³); I Moment of Inertia (m⁴); t Width at Point (m) | Transverse shear in a prismatic beam |
| Simply Supported Beam (Uniform Load) | δ_max = 5wL⁴ / (384EI) | δₘₐₓ Max Deflection (m); w Load per Unit Length (N/m); L Span (m); E Elastic Modulus (Pa); I Moment of Inertia (m⁴) | Simply supported, uniform load over entire span |
| Cantilever Beam (Uniform Load) | δ_max = wL⁴ / (8EI) | δₘₐₓ Max Deflection (m); w Load per Unit Length (N/m); L Length (m); E Elastic Modulus (Pa); I Moment of Inertia (m⁴) | Cantilever, uniform load over entire length |
| Maximum Moment (Simply Supported, Uniform) | M_max = wL² / 8 | Mₘₐₓ Maximum Moment (N·m); w Load per Unit Length (N/m); L Span (m) | Simply supported beam with uniform load |
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.