Analysis Types

AutoCalcs offers different analysis methods for static response, second-order effects, elastic stability, and vibration. Choose the method that matches the behaviour and results you need.

Comparison Guide

Linear Analysis

Best for: Most routine structures where displacements are small and material behaviour remains elastic. This is the default analysis type.

How it works

The solver assembles the global stiffness matrix and solves [K]{D} = {F} on the undeformed model. Members use 12-degree-of-freedom cubic-Hermite beam-column elements. Plate and shell elements contribute their membrane and bending stiffness.

Models with tension-only or compression-only members or supports use an active-set process. The active-set selection is nonlinear even though each active structural state is solved with the linear elastic stiffness matrix.

Limitations

• The equilibrium equations use the undeformed geometry.
• Tension-only or compression-only members and supports can deactivate or reactivate over successive active-set passes. Inactive one-way elements are checked using their trial elastic force, so convergence requires a sign-consistent active set. A solve that cannot reach a stable active set reports non-convergence instead of publishing that state.
• Yielding, plastic hinges, cracking progression, and material softening are not modelled.

See Verification Tests for the linear benchmark set.

P-Delta Analysis (Second Order)

Best for: Slender, sway-sensitive, or drift-sensitive structures where axial loads can materially amplify forces and displacements. Use it when the applicable design standard and chosen stability method require second-order effects.

How it works

P-Delta uses a bounded two-pass elastic solution:

1. A first-order solve recovers the member and plate force state.
2. The solver assembles geometric stiffness from that force state and solves ([K] + [K_g]){D} = {F}.

For members, this captures member-level P-δ bowing and frame-level P-Δ sway effects. Plate and shell elements also contribute geometric stiffness. If tension-only or compression-only behaviour is present, the two-pass solve repeats until the active set stabilises.

Limitations

• This is a linearised second-order formulation. It does not update element geometry or provide a large-rotation, co-rotational solution.
• Materials remain elastic; yielding, plastic hinges, and material softening are not captured.
• Results become highly sensitive as the selected load approaches an elastic instability. Review solver warnings and run buckling analysis as a separate stability check.

See Verification Tests for the P-Delta benchmark set.

Solver options

Classic is the general-purpose option. Wittrick-Williams uses an exact member solution when axial force is constant. When axial force changes along an ordinary member, turn on Refine members; the analysis compares successively finer results and returns no result if they do not agree closely enough. The setup dialog directs unsupported model configurations to Classic.

What it outputs

• Critical load factors (λ): elastic multipliers for the selected reference load pattern
• Mode shapes: normalised eigenvectors showing the form of each instability mode
• Equivalent K-factors: Mode 1 diagnostic values derived from λ, member axial force, length, E, and I

The reported K-factors are diagnostic equivalents based on the governing global Mode 1 result. They do not establish that a particular member or axis participates in that mode and should not be transferred automatically into design inputs without reviewing the mode shape and applicable design method.

Important limitations

• There is no universal λ threshold that proves design adequacy or classifies a frame as braced. Apply the requirements of the selected material standard and stability method.
• Very low factors can indicate a modelling mechanism or missing restraint rather than a meaningful structural buckling mode.
• Detailed open-section warping, lateral-torsional, and flexural-torsional buckling are not represented by the frame eigenmodes. Likely numerical twist modes may be omitted and are identified in a warning.
• Wittrick-Williams supports member-only beam, frame, and truss models, including 3D space frames. Use Classic for plates or shells, rigid diaphragms or node links, member offsets, and changing-force tension-only or compression-only members. Open-section torsional and flexural-torsional buckling require a separate design check.

Tier limits

• Free tier: up to 3 buckling modes per run
• Pro tier: up to 10 buckling modes per run

See Verification Tests for the Classic and Wittrick-Williams benchmark sets.

Mass source

Select a load case or combination containing self-weight in the modal setup dialog. The mass matrix includes:

• Member and plate self-weight from material density and geometry
• The locally net force acting with gravity from nodal, member point, distributed, and plate loads in the selected mass-source pattern

Applied loads are netted at each physical location. A locally net-upward load is omitted and reported as a warning; loads at different locations do not cancel each other. Moment loads and forces outside the selected gravity direction do not contribute to mass.

Physical mass and reported modes

Modal analysis uses the physical mass of the model: element mass from density and geometry, plus gravity-direction applied loads from the selected mass source. Extra mass is not added to massless degrees of freedom. Those coordinates still move with the structure through stiffness, and they are omitted from the reported frequency list.

A 0 Hz result means the model can translate or rotate as a rigid body while still carrying mass. That usually indicates a missing support. Those modes have no period. Add the missing restraints unless unsupported rigid-body vibration is intended. A direction with neither stiffness nor mass is a mechanism; correct connectivity, releases, or restraints before relying on the frequencies.

The mode count you request is a maximum. The solver reports finite-frequency modes it can verify, which can be fewer than requested. A short result set does not mean every remaining mode of the structure has been ruled out. Read any shortfall warning and check cumulative effective mass in X, Y, and Z. Reported total mass includes mass at supported nodes, and participation percentages use that complete physical mass.

Formulation and outputs

Distributed member mass uses consistent element mass matrices. Plate and shell mass is consistent by default; the solver also supports row-sum-lumped translational shell mass. This option does not change member or nodal mass. Concentrated mass remains at its application location. The analysis returns:

• Natural frequencies in ascending order
• Normalised mode shapes
• Directional participation factors and effective modal mass
• Total assembled mass for the selected mass source

Important limitations

• Tension-only and compression-only members contribute two-way elastic stiffness and mass during the eigenvalue solve. For X-braced systems, this can overestimate lateral stiffness and frequency because both diagonals participate. Use a documented linear equivalent that represents the intended bracing stiffness, and independently verify its suitability for the dynamic response being assessed.
• Mode shapes are normalised shapes, not physical displacement amplitudes. Modal analysis uses elastic stiffness; a prior static or P-Delta solve does not make it a prestressed modal analysis. Numerical subdivision leaves generated nodes fully 3D unless a planar idealisation is explicitly requested.
• Natural frequency alone is only a preliminary floor-vibration screen. Occupant comfort requires appropriate forcing, damping, acceleration, and response checks.
• Detailed open-section warping and flexural-torsional vibration are outside the frame formulation. Effectively pure Saint-Venant torsional candidates carried by known unsupported open sections are filtered with a warning. Supported Saint-Venant torsion and coupled modes are retained; pure torsional candidates with unknown section topology are retained with a warning.

Tier limits

• Free tier: up to 12 modes per run
• Pro tier: up to 30 modes per run

See Verification Tests for the modal benchmark set.