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Beam Deflection Calculator

Calculate maximum deflection and bending moment for simply supported and cantilever beams under UDL or point load.

Beam Formulas
Simply Supported - UDL
δmax = 5wL4 / 384EI
Mmax = wL2 / 8 (at centre)
Simply Supported - Point Load (centre)
δmax = PL3 / 48EI
Mmax = PL / 4 (at centre)
Cantilever - UDL
δmax = wL4 / 8EI
Mmax = wL2 / 2 (at fixed end)
Cantilever - Point Load (free end)
δmax = PL3 / 3EI
Mmax = P × L (at fixed end)
Beam Parameters
m
Max Deflection
Max Bending Moment
Allowable Deflection
Status
Calculation Steps
This calculator uses elastic beam theory for single-span beams with uniform cross-section. Results are for preliminary analysis only. Consult a qualified structural engineer for final design and code compliance.

Simply supported beam with UDL w (N/m): Max deflection = 5wL4/(384EI) at midspan. Max bending moment = wL2/8 at midspan. All values in consistent SI units (N, m, Pa, m4).

Cantilever UDL: deflection at free end = wL4/(8EI), moment at fixed end = wL2/2. Cantilever point load at free end: deflection = PL3/(3EI), moment at fixed end = P x L. Cantilevers deflect much more than simply supported beams for the same load and span.

IS 456 permits total deflection = L/250. Post-construction deflection should not exceed L/350 or 20 mm. For live load only, L/360 is commonly used. If deflection exceeds the limit, increase beam depth or use a material with higher E.

Steel: E = 200 GPa. For 200x200 mm square: I = bd3/12 = 133.3 x 106 mm4 = 13333 cm4. Concrete M20: E = 22360 MPa (= 5000 x sqrt(20)). For 230x450 mm rectangular section: I = 230 x 4503/12 = 1751 x 106 mm4 = 175100 cm4.