CONTINUOUS BEAM ANALYSIS

SIMPLE SUPPORTS — UNIFORM LOAD — kN / m

⬡ BEAM CONFIGURATION

Number of Bays

Bay Lengths

Equal Unequal

Bay Length (m)

⬡ SECTION & LOADING

Moment of Inertia I (cm⁴)

Young's Modulus E (N/mm²)

Uniform Load w (kN/m)

Tool information

What this page computes

The calculator solves a continuous multi-span beam by the finite-element method (the FEALiTE2D engine) and plots the internal-force diagrams and the deflected shape. Unlike the single-span beam formulas, which cover only canonical cases, here you can define any number of supports and spans, with arbitrary loads on each span.

Why continuity changes everything

A beam continuous over several supports behaves fundamentally differently from a simply supported one. Over the intermediate supports, negative moments appear (tension on the top face), and the span moments are reduced compared with a simply supported beam of the same span.

The distribution of moments between span and supports depends on the ratio of the spans and on the load of each span — hence the need for an analysis, not a formula. The system is statically indeterminate: the reactions and moments do not follow from equilibrium alone, but from the compatibility of deformations, which the finite-element method solves directly.

What the analysis returns

The bending moment diagram \(M\) — with the span and support moments
The shear force diagram \(V\)
The deflected shape — the deflection of each span
The support reactions

The peak values are then the loading for the section check (steel or concrete).

Input data

Geometry — the support positions, hence the span lengths.
Support types — pin, roller, fixed.
The section — the stiffness \(EI\) (from a profile or entered), which enters the deflected shape and the moment distribution.
The loads — point forces and distributed loads on each span.

Assumptions and limitations

A linear-elastic first-order analysis; plasticity, buckling and second-order effects are not treated.
A plane (2D) model: the beam and the loads are in the same plane.
It gives the internal forces and deformations; the section resistance and stability check is done separately.
For frames (columns + beams) use the frame analysis.

Single-span beams — the closed-form formulas for simple cases
Fixed-base frame (finite element) — for structures with columns and beams
Bending resistance (steel) — the section check at the obtained moment
Reinforced section (concrete) — the concrete equivalent