TheBridgeEng

Continuous Beam Analyzer

Multi-span beam — shear, moment & deflection

Direct-stiffness solution of a prismatic continuous beam. Set spans, end fixity, a uniform load per span and one moving point load — diagrams update live. Sagging moment positive, deflection positive down in the plot.

Spans2

Left end

Right end

EI2.0×10⁵ kN·m²

UDL w (all spans)20 kN/m

Point load P100 kN

P position—

Beam & loads

Shear V kN

Moment M kN·m (sagging +, plotted on tension side)

Deflection mm

Max sagging M

—

Max hogging M

—

Max |V|

—

Max deflection

—

Method: Euler–Bernoulli 2-node elements, banded LDLᵗ with equilibration and iterative refinement; V and M recovered by closed-form left-side equilibrium, so diagrams carry no quadrature error. Verified against 35 closed-form cases, a 300-model independent Python implementation (agreement ≤ 5×10⁻⁸), and global-equilibrium sweeps. Scope: prismatic EI, interior supports are rollers, no shear deformation (use care below L/d ≈ 10), load positions snap to a fine internal grid (≈L/1200). Results are for preliminary design — verify final designs independently.

Field notes — what to watch for

Before trusting any output, check the reactions sum against your total load — it is the fastest sanity check there is. Watch the hogging moment over interior supports: in real girders that is where the deck cracks and where you need top steel. If your span-to-depth ratio is under about 10, shear deformation (not included here) starts to matter.

Inputs are saved on this device · reset to defaults