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eng.structural-beam Calculator
Calculates beam reactions, bending moment diagram, and maximum deflection for simply supported, cantilever, and fixed beams under uniform or point loads. The Euler-Bernoulli beam theory assumes plane sections remain plane — valid for beams where span is at least 10× depth.
Inputs
W
Applied force or weight (N or kN). Divide into dead load (permanent) and live load (variable — people, wind, etc.).
L
Linear measurement. Ensure consistent units: 1 m = 1,000 mm = 3.281 ft.
E
Material stiffness (GPa). Stress divided by strain in the elastic range. Steel: 200 GPa. Aluminium: 70 GPa. Rubber: 0.01–0.1 GPa.
I
Resistance to rotational acceleration. Mass farther from the axis of rotation increases it — like a spinning skater extending their arms.
Results
mid-span deflection
Maximum lateral displacement of the beam under load. Codes typically limit to L/360 for floors (to avoid cracking finishes) or L/240 for roofs. Excessive deflection signals the beam is undersized.