Beam Load Calculator determines the serviceability-based allowable load for beams using classic elastic deflection formulas (four cases: simply supported/cantilever × uniform/point), and also returns the corresponding maximum moment and shear. Use it to size members against a chosen L/ratio and compare support/load scenarios before running full code checks.
About support conditions. Support type changes the stiffness response and the shape of the deflection curve. This tool covers simply supported spans and cantilevers, which are the most common early-stage scenarios in building practice.
About load types. Uniformly distributed load (w) acts along the whole span; a point load (P) acts at a single location (here assumed at midspan for simply supported, and at the free end for cantilever). Each case has its own deflection, moment, and shear relationships.
About modulus of elasticity (E). E characterizes the material stiffness (e.g., steel ≈ 200–210 GPa, concrete’s effective E depends on strength and cracking). Enter E directly; the tool treats it as a constant along the span.
About second moment of area (I). I (also called moment of inertia) captures the section’s bending stiffness with respect to the neutral axis. It depends on geometry only. Use your section property (from catalogs or section-properties tools).
About deflection limit (L/ratio). Serviceability limits such as L/240, L/300, or L/360 are common practice. The smaller the allowable deflection, the lower the allowable load for a given span, E, and I.
Conversion / Calculation. The tool enforces a single computational state based on elastic-beam relationships for prismatic members. It computes the allowable load that produces the target midspan/free-end deflection (Δ_allow = L/ratio) for the selected support/load case, then derives Mmax and Vmax from the same case formulas.
Formulas:
- Δallow = L / (ratio) (target deflection)
- Simply supported, uniform w: Δ = (5 w L⁴) / (384 E I) ⇒ w = (384 E I Δallow) / (5 L⁴) (allowable uniform load)
- Simply supported, midspan point P: Δ = (P L³) / (48 E I) ⇒ P = (48 E I Δallow) / L³ (allowable point load)
- Cantilever, uniform w: Δ = (w L⁴) / (8 E I) ⇒ w = (8 E I Δallow) / L⁴ (allowable uniform load)
- Cantilever, free-end point P: Δ = (P L³) / (3 E I) ⇒ P = (3 E I Δallow) / L³ (allowable point load)
- Simply supported (uniform): Mmax = w L² / 8; Vmax = w L / 2 (section actions)
- Simply supported (point at midspan): Mmax = P L / 4; Vmax = P / 2 (section actions)
- Cantilever (uniform): Mmax = w L² / 2; Vmax = w L (section actions)
- Cantilever (point at free end): Mmax = P L; Vmax = P (section actions)
Examples:
- Simply supported, uniform load. L = 6 m, E = 200 GPa, I = 8 500 cm⁴, limit L/240.
Δallow = 6 / 240 = 0.025 m → w ≈ 25.19 kN/m, Mmax ≈ 113.33 kN·m, Vmax ≈ 75.56 kN. - Simply supported, midspan point load. Same L, E, I, L/240.
Δallow = 0.025 m → P ≈ 94.44 kN, Mmax ≈ 141.67 kN·m, Vmax ≈ 47.22 kN. - Cantilever, uniform load. Same L, E, I, L/240.
Δallow = 0.025 m → w ≈ 2.62 kN/m, Mmax ≈ 47.22 kN·m, Vmax ≈ 15.74 kN.
Corresponding tools. Use together with: Beam Deflection Calculator, Bending Stress Calculator, Moment of Inertia Calculator, Section Properties, and Column Buckling Calculator.
