Tool

Beam Analysis

Single-span beam analysis using a matrix-stiffness (finite element) solution of Euler–Bernoulli beam theory. Select the support arrangement, define the section stiffness and build up any combination of point loads, distributed loads and applied moments. The tool reports reactions, shear, bending moment and deflection with full diagrams.

Mode

Full analysis: all support arrangements, up to five point loads, three distributed loads and two applied moments.

Disclaimer

This report contains indicative structural analysis results generated from information and idealised conditions entered by the user. It does not constitute structural design, certification, approval for construction or confirmation of regulatory compliance. Support conditions, stiffness, loading, load combinations, member capacity, stability, connections, robustness, durability, fire resistance and all project-specific requirements must be assessed and independently verified by a suitably qualified structural engineer.

I understand these results are indicative and require independent verification. Acknowledgement will be required before downloading a calculation report in a future release.

Model

All positions are measured from the left-hand end, x = 0.

Step 1

Define beam and supports

Beam reference (optional)

Beam span

Span units

Support arrangementVertical restraint at both ends, free rotation at both ends. The usual idealisation for a beam sitting on padstones or simple end connections.Vertical restraint at both ends, free rotation at both ends. The usual idealisation for a beam sitting on padstones or simple end connections.

Vertical restraint at both ends, free rotation at both ends. The usual idealisation for a beam sitting on padstones or simple end connections. Actual structural connections may behave semi-rigidly; idealised support conditions must be selected using engineering judgement.

Step 2

Define section stiffness

Section

Section properties

I_y = 21,600 cm⁴
Mass = 60.1 kg/m
Depth h = 406.4 mm
E = 210,000 N/mm² (structural steel)

Include beam self-weight as a permanent full-span UDL (Gk). Leave this off if self-weight has already been included in the loads entered below.

Flexural rigidity EI = 45.360 × 10¹² N·mm² (45,360 kN·m²).

Section properties compiled from SCI publication P363 (Blue Book), Eurocode edition, and BS EN 10210 for hot-finished hollow sections. Values are nominal and provided for preliminary sizing only.

Step 3

Add loads

Reference

Select serviceability limit

Deflection limit

Check deflection at position x (m) — optional

The appropriate deflection limit depends on the structural material, finishes, partitions, glazing, cladding, use of the building and project-specific requirements.

Worked example

Step 5

Review analysis results

Complete the steps above and select “Analyse beam” to calculate results.

Tool version 1.0 · Last reviewed Not yet recorded — pending engineering validation

Disclaimer

Indicative result only. The calculation depends on the assumptions and information entered and does not constitute structural design or professional advice. Do not use the result for construction, procurement, Building Regulations submissions or safety-critical decisions. All results must be independently verified by a suitably qualified structural engineer before being used for design, construction or regulatory purposes. Bebbington Engineering Studio Ltd accepts no responsibility for reliance placed on unverified results.

Looking for the original single-case calculator? The Basic Beam Deflection Check remains available.