Beam Load

Load a simply supported beam. Reactions, bending moment and deflection.

0/3challenges

Span Lm

Point load PkN

Load position am

Uniform load wkN/m

Material

Section

Width bmm

Depth hmm

I = 1.406e+7 mm⁴

Reaction A: 4.50kN
Reaction B: 4.50kN
Max moment: 7.00kN·m
Max deflection: 3.56mm
Span / deflection: L/1125
Peak bending stress: 37.3MPa

The model

A simply supported beam: pinned at the left, on a roller at the right. Taking moments about each support gives the reactions; shear is the running sum of forces, and bending moment is the area under the shear diagram.

Deflection uses Euler-Bernoulli beam theory, EI y″ = -M, with the standard point-load and uniform-load solutions added together. Peak bending stress is σ = M c / I at the outer fibre.

Reading it

Span over deflection is a common serviceability check: floors often aim for L/360 or better. Doubling the depth of a rectangle cuts deflection by eight, which is why beams are tall and thin.

Assumes linear elastic material, small deflections, no self-weight, no shear deformation, no buckling and no yield. Do not use it to size a real member. Educational model, not an engineering design or validation tool.

Achievements0/3

Building code +40Carry 20 kN over 6 m or more and stay within L/360.
Aluminium spec +30Span 3 m in aluminium with a 5 kN load under 1/250 deflection.
Hollow victory +30Get a rectangular tube under L/500 with at least 10 kN on it.

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