Guide · structural

Custom Steel Beam & Plate Girder Calculator guide

Model a normal or tapered steel beam, see the structural response and governing cross-section check, then carry the complete calculation into a standards-traceable professional report.

Built for engineers checking restrained doubly symmetric welded I-sections, plate girders, rectangular hollow sections and circular hollow sections in one vertical bending plane.

Built-in tapered welded-beam example
Live model
S1L = 6.000 mPositive loads downward · schematic not to scale
Span
6.000 m
Depth
500 → 650 mm
Standard
Eurocode 3
Units
SI / US
Section presets
140 nominal profiles
Structural systems
5 support idealisations
Design routes
EC3 · AISC · CSA · AS
Deliverable
Traceable calculation PDF

Section 01

What the calculator does

One input model drives the schematic, structural analysis, code checks, governing result and final report. Nothing has to be redrawn or transcribed between those stages.

The solver evaluates reactions, shear, bending moment, rotation and deflection, then applies the selected standard's section classification, major-axis bending, web shear and deflection routes. Eurocode 3 also applies its documented high-shear bending reduction. Unsupported stability or plated-element paths stop a PASS result instead of estimating a resistance.

Model

Normal/prismatic or linearly tapered segments, five support systems and three doubly symmetric section families.

Load

Named permanent and variable cases with point forces, point moments, full or partial varying line loads and self-weight.

Review

Reactions, shear, moment, deflection, key cross-sections and a utilization envelope at recovered stations.

Document

Governing summary, equations, geometry, charts, design-basis matrix, sources, assumptions and disclaimer.

Section 02

How to use it: the built-in tapered example

The default model is a complete worked example: a 6 m simply supported, fully restrained welded I-beam whose depth increases from 500 mm to 650 mm. Follow the same sequence for a catalogue seed or a fully custom member.

  1. Define the structural system

    Choose the support idealisation first, then enter the total length. A two-span continuous beam also needs the intermediate support coordinate measured from the left end. The example uses a 6,000 mm simply supported beam.

    Available support systemsFigure 1
    Simply supportedA beam with a pin-like support at each end.Simply supportedCantileverA beam fixed at the left end and free at the right end.Cantileverfree endFixed–fixedA beam fixed against translation and rotation at both ends.Fixed–fixedPropped cantileverA beam fixed at the left end and simply supported at the right end.Propped cantileverContinuous two-spanA continuous beam with end supports and one intermediate support.Continuous two-span
    Support coordinates become exact solver nodes. The symbols describe the idealised beam model, not connection detailing.
  2. Build the section and taper

    Select Normal (prismatic) for constant depth or Tapered / haunched for a linearly varying depth or diameter within a segment. Both use the same analysis and cross-section checks. In the example, one welded-I segment runs from 0 to 6,000 mm with a 250 × 20 mm flange, 12 mm web and 500 → 650 mm depth.

    Welded I / plate girder
    Welded Id 500 · bf 250 mmClass 1
    RHS / SHS box
    RHSh 400 · b 200 · t 12.0 mmClass 1
    CHS tube
    CHSD 300 · t 16.0 mmClass 1
  3. Enter material and confirm restraint

    Enter the design yield strength that applies to the actual grade and governing thickness; the calculator does not infer it from a profile name. The example uses the built-in user-confirmed design value of 345 MPa, an elastic modulus of 210,000 MPa and confirmed compression-flange restraint.

  4. Choose the governing standard

    The standard selector changes classification limits, resistance or capacity factors and automatic gravity load combinations. It does not change the shared Euler–Bernoulli direct-stiffness analysis. The example uses Eurocode 3 with automatic combinations.

    Eurocode 3

    EN 1993-1-1 · documented clauses and recommended factors

    AISC 360-22

    LRFD or ASD · official-text verification pending

    CSA S16-19

    Canadian gravity combinations · official-text verification pending

    AS 4100:2020

    Australian gravity combinations · official-text verification pending

  5. Create named load cases

    The example includes self-weight from the varying area, a 4 kN/m permanent imposed load and an 8 kN/m office imposed load. Add actions to named permanent or variable cases so the selected route can generate the applicable combinations. Positive transverse force acts downward; positive point moment acts clockwise.

    Load types and entry signsFigure 2
    Point forceA positive point force acts downward at coordinate x.Point force+P ↓Point momentA positive point moment acts clockwise at coordinate x.Point moment+M ↻Uniform or partial line loadA distributed load can cover the full member or only the entered start-to-end interval.Uniform or partial line loadq₁ = q₂Linearly varying loadStart and end intensities define a linearly varying distributed load.Linearly varying loadq₁q₂
    Distributed actions may cover all or part of the member. Self-weight follows the actual varying section area when enabled.
  6. Review diagrams at meaningful stations

    Supports, section changes, point actions and distributed-load boundaries are inserted as exact nodes. Tapered segments are refined from 2 to 32 elements until the selected convergence tolerance is met. The same recovered stations feed the diagrams and the cross-section checks.

    Coordinates, nodes and recovered stationsFigure 3
    Beam coordinate and station systemThe x coordinate starts at the left end. Supports, segment changes, point actions and distributed-load boundaries become exact nodes. Recovered stations between nodes are used for diagrams and checks.x = 0x = LExact node at a support, segment or load boundarySmall dots are recovered check stations; tapered elements refine until convergence.All input coordinates are measured from the left end.
    Use the left-end x coordinate consistently when locating supports, segment boundaries and actions.
  7. Confirm the governing result, then review the report

    Start with the overall state and governing utilization, then inspect the selected combination's reactions, shear, moment, deflection and utilization envelope. Check the start, governing and end sections before treating the report as ready for independent review.

Section 03

Read the built-in result

These values are calculated on the server from the current default input object. They are evidence for this worked example, not suggested values for another beam.

Pass within stated scope

Major-axis bending resistance

The result contains no warning or out-of-scope flag for the built-in model.

Governing utilisation

0.069

Governing station
2.8125 m
Moment demand
85.63 kN·m
Moment resistance
1240.36 kN·m
Downward deflection
1.165 / 24 mm
Calculated bending-moment diagramFigure 4
Bending moment
M
Bending moment for the built-in example. Maximum 85.98 kilonewton metres.M: x 0.000 m, y 0.000 kN·mM: x 0.000 m, y 0.000 kN·mM: x 0.188 m, y 10.396 kN·mM: x 0.375 m, y 20.123 kN·mM: x 0.563 m, y 29.181 kN·mM: x 0.750 m, y 37.570 kN·mM: x 0.938 m, y 45.290 kN·mM: x 1.125 m, y 52.340 kN·mM: x 1.313 m, y 58.721 kN·mM: x 1.500 m, y 64.432 kN·mM: x 1.688 m, y 69.473 kN·mM: x 1.875 m, y 73.843 kN·mM: x 2.063 m, y 77.543 kN·mM: x 2.250 m, y 80.573 kN·mM: x 2.438 m, y 82.931 kN·mM: x 2.625 m, y 84.618 kN·mM: x 2.813 m, y 85.634 kN·mM: x 2.896 m, y 85.871 kN·mM: x 3.000 m, y 85.979 kN·mM: x 3.002 m, y 85.979 kN·mM: x 3.188 m, y 85.652 kN·mM: x 3.375 m, y 84.653 kN·mM: x 3.563 m, y 82.982 kN·mM: x 3.750 m, y 80.638 kN·mM: x 3.938 m, y 77.622 kN·mM: x 4.125 m, y 73.933 kN·mM: x 4.313 m, y 69.572 kN·mM: x 4.500 m, y 64.537 kN·mM: x 4.688 m, y 58.829 kN·mM: x 4.875 m, y 52.447 kN·mM: x 5.063 m, y 45.391 kN·mM: x 5.250 m, y 37.662 kN·mM: x 5.438 m, y 29.258 kN·mM: x 5.625 m, y 20.180 kN·mM: x 5.813 m, y 10.427 kN·mM: x 6.000 m, y 0.000 kN·mM: x 6.000 m, y 0.000 kN·m85.980.0000.006.00 mkN·m
ULS — Office imposed load leading. The real recovered station array is passed to the same chart component used by the calculator.
How the governing check is selectedFigure 5
Demand, resistance and utilization envelopeDemand and resistance are evaluated at recovered stations. Their ratio forms an utilization envelope, and its highest supported value identifies the governing station and check.Demand|E(x)|Analysis resultResistanceR(x)Section + standardUtilisationU(x) = |E| / RChecked at every stationU = 1.0Highest supported ratio governs
Demand and resistance are evaluated along the member. The largest supported utilization controls the governing summary; a missing required method produces an outside-scope state instead.

Section 04

Review the real professional report

This is the actual report renderer, populated by the built-in input object and calculation engine. It is intentionally unblurred so you can inspect the deliverable before running your own project.

Governing proof

Overall state, governing check, utilization and FEA recommendation stay prominent.

Check traceability

Demand, resistance, equations, status and notes remain together in each check table.

Analysis record

Geometry, key sections, combinations, convergence, reactions and vector charts are included.

Review context

Design-basis matrix, sources, warnings, assumptions and the professional disclaimer complete the record.

Complete example report

Built-in tapered welded beam · unblurred · engine v1.0.0

Open full-page report ↗

Project calculations use the same document structure. Free project previews blur deliverable values; a platform subscription unlocks the clean PDF across all calculators.

Section 05

Standards basis

The structural analysis is standard-agnostic. The selected route supplies section classification, resistance or capacity factors, check equations and automatic gravity combinations.

RouteImplemented basisVerification status
Eurocode 3 · EN 1993-1-1Class 1–3 classification, major-axis bending, web shear, documented high-shear interaction, EN 1990 combinations and recommended factors.Documented clauses and recommended factors are applied as stated in the methodology.
AISC 360-22Compactness, restrained bending, shear, LRFD/ASD resistance basis and gravity combinations.Reconstructed from established engineering references and validated against published worked examples; pending independent verification against the official published standard text.
CSA S16-19Class limits, restrained bending, shear, capacity basis and gravity combinations.Reconstructed from established engineering references and validated against published worked examples; pending independent verification against the official published standard text.
AS 4100:2020Section slenderness, restrained bending, shear, capacity basis and gravity combinations.Reconstructed from established engineering references and validated against published worked examples; pending independent verification against the official published standard text.
Review the complete methodology, design-basis matrix and source registry →

Section 06

Supported scope and explicit limits

A credible result is as much about what stops as what runs. The calculator blocks unsupported paths rather than substituting an unverified resistance.

Implemented

  • Straight beams in one vertical bending plane using linear elastic, small-displacement Euler–Bernoulli analysis.
  • Simply supported, cantilever, fixed–fixed, propped cantilever and continuous two-span systems.
  • Normal/prismatic or piecewise linearly tapered welded I, RHS and CHS geometry.
  • Point forces, point moments, full or partial varying line loads and self-weight from varying area.
  • Class 1–3 or equivalent section paths, restrained bending, shear and a project-selected deflection criterion.
  • Reactions, shear, moment, deflection, utilization envelopes, convergence data and SI/US display.

Not implemented

  • Class 4 effective properties and web shear-buckling resistance.
  • Unrestrained lateral-torsional buckling of tapered members.
  • Axial force, beam-column interaction, biaxial bending, torsion or portal-frame analysis.
  • Patch loading, support bearing, stiffeners, welds, splices and connections.
  • Composite, curved, cellular or perforated beams; fire, fatigue, seismic or dynamic verification.
  • Catalogue-exact rolled-section properties, certification, approval or an engineer's stamp.

Before relying on the result

Confirm that the real member is doubly symmetric, the entered yield strength is applicable, the compression flange is adequately restrained, loads and combinations match the project, and every excluded local, stability and connection check is covered elsewhere. The final report supports that review; it does not perform it for you.

Section 07

Frequently asked questions

Short answers to the choices that most often change how the model or its result should be used.

Do Normal and Tapered modes use different analysis methods?

No. Normal mode is the constant-depth special case; Tapered / haunched mode allows the depth or diameter to vary linearly within each segment. Both use the same direct-stiffness analysis and the same selected-standard checks.

Does an IPE, HEA, HEB, RHS, SHS or CHS selection reproduce catalogue properties?

No. The picker fills nominal catalogue dimensions. Properties are calculated from the modelled welded-equivalent I-section without a root fillet, or a hollow section with square modelled corners, so Iy and Wpl can differ slightly from published rolled-section values.

Can the calculator check an unrestrained beam?

It can retain the inputs, but it will not report PASS when adequate compression-flange restraint is unconfirmed. Unrestrained lateral-torsional buckling for these tapered members is outside the implemented scope and is never guessed.

What does PASS mean?

PASS means every implemented check passes and no required path is outside the stated assumptions and exclusions. It does not mean the member, connections or project have been certified or approved.

Are all four standard routes verified against official standard text?

The Eurocode 3 route applies the documented clauses and recommended factors. The AISC 360-22, CSA S16-19 and AS 4100:2020 routes are reconstructed from established engineering references and validated against published worked examples, pending independent verification against the official published standard text.

What changes when I switch SI and US units?

Only displayed and entered units change. The calculation continues to use the same internal N, mm and MPa basis.

What is available without a subscription?

Free users can run a real calculation, see the overall state and basic diagrams, and review a blurred project-report preview. The platform subscription unlocks the clean professional PDF across the calculator catalogue. The built-in example report on this guide is intentionally unblurred so you can inspect the deliverable before subscribing.

Does the report replace an engineer's review?

No. It records the inputs, checks, sources, assumptions and exclusions, but it is not certified or engineer-stamped. A qualified engineer must review the calculation in the project context.

Ready to calculate

Build the beam, inspect what governs, and keep the calculation traceable.

Start from the built-in example, replace it with the project geometry and actions, then review the checks, assumptions and report before issuing the calculation.

Steel Beam & Plate Girder Calculator guide | Normal and tapered beams · Xarpis