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.
• A tension-only or compression-only member can deactivate when its axial force has the wrong sign, but it cannot reactivate during the same load-combination solve. Different members may deactivate over successive active-set passes.
• 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 integrates geometric stiffness over the recovered axial-force distribution. Wittrick-Williams uses exact member stability functions for uniform axial force; subdivision improves its representation when axial force varies along a member. The setup dialog steers 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.

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
• Gravity-direction nodal, member point, distributed, and plate loads included in the selected mass-source pattern

Moment loads and forces outside the selected gravity direction do not contribute to mass.

Formulation and outputs

Members use a consistent mass matrix and are automatically refined into four sub-elements for the eigensolve. 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 ordinary members when accurate modal behaviour of the bracing system is required.
• Mode shapes are normalised shapes, not physical displacement amplitudes.
• 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. Torsion-dominated numerical modes are filtered and reported in 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.