Beam deflection calculator

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Result

Maximum deflection10.55 mm

Maximum bending moment45 kN·m

Maximum shear force30 kN

Span/deflection568.9

Step-by-step solution

Bending stiffness

EI = 200 GPa · 80 × 10⁶ mm⁴ = 1.6 × 10⁷ N·m²

Standard formulas

δ = 5wL⁴/(384EI) = 10.55 mm

M = wL²/8 = 45 kN·m

Key formulas

Point load at midspan: δ = PL³/(48EI)
Uniform load, simply supported: δ = 5wL⁴/(384EI)
Cantilever, end load: δ = PL³/(3EI)
Cantilever, uniform load: δ = wL⁴/(8EI)
Superposition: δ = δ₁ + δ₂

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