Beam Analysis

How it calculates

The Beam Analysis calculator uses the finite element method (FEM) matrix stiffness approach to solve for internal forces, reactions, and deflections in simple or continuous beams.

FEA solver

The solver assembles the global stiffness matrix from member bending stiffness EI and axial stiffness EA, applies boundary conditions at each support, and solves the system = [K] for nodal displacements. Internal forces (moment, shear, axial) and deflections are then recovered from the displacement solution at a dense mesh of points along the beam length.

A single unfactored load combination is used - all loads pass through at 1.0× magnitude. For factored load combination analysis, use the Beam Analysis with Load Combinations (ASD) or (LRFD) calculators instead.

Reported results

The governing demand outputs are envelope maxima across the full beam:

• M = max(|positive moment|, |negative moment|)* across all spans
• V = max|shear|* across the beam length
• δ = max|deflection| across the beam length

Per-span analysis reports positive moment, Q1, midpoint, Q3, and negative moment peaks for each bay between supports. Per-support analysis reports the vertical reaction, moment reaction (for fixed supports), and shear at each bearing point.

Supported configurations

Supports can be fixed, pinned, roller, or spring (linear or rotational). Continuous rigid supports and guided (translational-only) boundary conditions are also available. Beams can be horizontal or inclined (Simple Slope or Hip/Corner Slope). Loads include distributed (uniform or linearly varying), point loads, moment loads, and axial loads - at any position along the span.