Analysis Types

AutoCalcs offers different analysis methods to suit various structural problems. Choosing the right analysis type is crucial for obtaining accurate results.

Linear Analysis

Best for: Most standard structures, beams, frames, and trusses where deformations are small.

This is the default analysis type. It assumes:

• Small Displacements: The structure's deformed shape does not significantly affect the equilibrium equations.
• Linear Material Behavior: Materials follow Hooke's Law (stress is proportional to strain).

Tension/Compression Only Support

Although termed "Linear", this solver is capable of handling Tension-Only or Compression-Only members and supports. It performs an iterative process to deactivate members or supports that are acting in their forbidden direction (e.g., a cable in compression).

P-Delta Analysis (Second Order)

Best for: Tall buildings, slender columns, and flexible structures where sway is significant.

P-Delta analysis accounts for geometric nonlinearity. It considers the additional forces and moments created when vertical loads (P) act on the laterally displaced (Delta) position of the structure.

Key effects captured:

• P-δ (small delta): Effect of axial loads on the bending stiffness of individual members (e.g., beam-column effect).
• P-Δ (large Delta): Effect of vertical resultants acting on the sway of the entire frame.

Note: This is an iterative non-linear analysis and may take longer to compute than Linear analysis.

Buckling Analysis (Linear Eigenvalue)

Best for: Determining critical load factors, effective length factors (K), and visualising buckling mode shapes.

Buckling analysis (also called Linear Buckling Analysis or LBA) computes the buckling load factor — the factor by which the applied loads need to be increased to reach the buckling load. A load factor less than 1.0 means the applied loads exceed the structure's buckling capacity.

An accurate buckling analysis looks at the interaction of every member in the structure and detects buckling modes that involve individual members, groups of members, or the structure as a whole. It is an essential component of structural design because it:

• Determines if the loads exceed the structure's buckling capacity and by how much
• Calculates member effective lengths for use in steel design checks
• Validates that the static analysis results are usable (if the buckling capacity has been exceeded, static analysis results are unreliable)

Solver

The solver uses the Wittrick-Williams sign-count algorithm with exact trigonometric stability functions. This is equivalent to the "Signcount Eigenvalue" method used by commercial software. Unlike the "Classic Eigenvalue" method (cubic Hermitian geometric stiffness) used by many FEA programs, exact stability functions give precise results with a single element per member — no mesh refinement is needed.

What Type of Buckling is Computed

The buckling modes considered involve flexural instability due to axial compression (Euler buckling). This should not be confused with:

• Flexural-torsional buckling — torsional instability due to bending moments
• Axial-torsional buckling — torsional instability due to axial loads

These torsional buckling modes require warping stiffness (I_w) in the element formulation, which is not included in the current beam element. Instead, torsional and flexural-torsional buckling is assessed separately by the steel design code checks (AS4100 §6.3.3, AISC 360 E4, Eurocode 3 cl.6.3.1.4, CSA S16 cl.13.3.2) using section properties including the warping constant directly.

Practical Modifications

The solver includes several practical enhancements beyond pure Wittrick-Williams theory:

• Max-end axial force: Members with varying axial force (e.g. columns carrying self-weight) use the maximum compression at either end rather than the average. This is conservative and matches commercial software within 0.1%.
• Torsional mode filtering: Because warping stiffness is not in the element, pure torsional modes appear at artificially low eigenvalues. These are automatically filtered (modes with less than 10% translational participation are skipped). A warning is displayed when modes are filtered.
• Pin-pin tension members: Tension-only members with pinned ends (e.g. braces) are treated as axial-only elements with zero geometric stiffness, consistent with industry practice. This avoids numerical artefacts from exact hyperbolic stability functions at high load multiples.

What It Outputs

• Critical load factors (λ) — the eigenvalues for each buckling mode
• Mode shapes — the deformed shape at each buckling mode, displayed on the model
• Effective length factors (K) — computed per member from the Mode 1 eigenvalue. K = π√(EI / (λ × P × L²)). Members with negligible compression are excluded. K-factors are automatically injected into the Ky and Kz fields in the Design Check tab when you run a subsequent Linear or P-Delta analysis.

Interpreting λ Values

• λ > 10 — Stable. Second-order effects are negligible (AS4100 cl.4.4, EC3 cl.5.2.1)
• 3 – 10 — Adequate. Use P-Delta analysis to capture second-order effects
• 1 – 3 — Low margin. P-Delta required, review design carefully
• λ ≤ 1 — Structure buckles under applied loads

Important Notes

• The results of a static analysis may be unreliable if the structure's buckling capacity has been exceeded (λ ≤ 1). A buckling analysis should always be performed unless you are certain the structure has adequate stability margin.
• Very low buckling factors (e.g. below 0.05) may indicate a model instability (missing supports, mechanisms) rather than a genuine buckling problem. Check deflections and support conditions.
• The magnitudes of K-factors alone cannot determine if buckling is a problem — only the buckling load factor (λ) indicates whether the applied loads exceed the structure's buckling capacity.
• K-factors are computed from the governing (lowest) eigenvalue only. They are not persisted to the project file and must be re-computed after re-running buckling analysis.

Comparison Guide

Which one should I use?

Start with Linear Analysis. It is faster and sufficient for the vast majority of low-rise structures.

Consider P-Delta if:

• You are designing a Moment Resisting Frame (MRF)
• Your structure has slender columns
• Lateral drift is a governing design criteria
• Axial loads are a significant fraction of the buckling load

Use Buckling Analysis to:

• Determine effective length factors (K) for steel design checks
• Classify your frame as braced or sway (AS4100 cl.4.4: λ ≥ 10 means braced)
• Verify that the structure has adequate stability margin under factored loads
• Visualise the governing buckling mode shape to understand the failure mechanism