Simply Supported Beam Calculator
Full analysis: reactions, max shear, max moment and max deflection for a point load + UDL.
INPUTS
m
kN
m
kN/m
GPa
×10⁶ mm⁴
RESULTS
Left reaction R₁
25 kN
Right reaction R₂
25 kN
Max shear |V|max
25 kN
Max moment (at x = 3.00 m)
52.5 kN·m
Max deflection δmax
17.438 mm
Span/deflection ratio
344 : 1
How it works
The simply supported beam is the fundamental case of structural analysis. Reactions come from static equilibrium, the moment diagram integrates the shear diagram, and deflections superpose the classic closed-form solutions for each load. Everything here follows Euler–Bernoulli beam theory with linear-elastic behaviour.
Worked example
L = 6 m, P = 20 kN at midspan, w = 5 kN/m, E = 200 GPa, I = 50×10⁶ mm⁴: R₁ = R₂ = 25 kN, Mmax = PL/4 + wL²/8 = 30 + 22.5 = 52.5 kN·m at midspan, δmax ≈ 9.6 mm (superposition of PL³/48EI and 5wL⁴/384EI).
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