The beam rests on a pin support (left, resists horizontal + vertical) and a roller support (right, vertical only) — a statically determinate simply supported span. A uniform distributed load (its own weight plus anything spread along it) and a movable point load act downward together. Reactions come from static equilibrium, and the bending moment M(x) and deflection curve follow directly from beam theory.
ΣFy=0, ΣM=0 → R_A, R_B
M(x) = R_A·x − w·x²/2 − P·max(0, x−a)
σ = M·c / I, I = b·h³/12, c = h/2
EI·y'' = −M(x) (integrated twice, y(0)=y(L)=0)
- Span / depth — a longer span or shallower beam raises stress and deflection for the same loads, since M grows with L² and I grows with h³.
- Material — steel, concrete and timber carry very different allowable bending stress and stiffness (E); the same beam that's safe in steel can fail in timber.
- Distributed / point load — the amber bars beneath the beam are the bending-moment diagram; taller bars mean higher local stress. The point load's position shifts where the peak moment lands.
- Stability — when the calculated bending stress exceeds the material's allowable capacity, the beam turns red and is flagged as failed — a simplified stand-in for a real structural safety check.
Deflection is drawn magnified for visibility (real structural deflections are a few millimetres over metres of span) — the numeric readout gives the true, unmagnified value.