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.
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 1Support coordinates become exact solver nodes. The symbols describe the idealised beam model, not connection detailing. 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 RHS / SHS box CHS tube 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.
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
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 2Distributed actions may cover all or part of the member. Self-weight follows the actual varying section area when enabled. 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 3Use the left-end x coordinate consistently when locating supports, segment boundaries and actions. 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
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
Custom Steel Beam & Plate Girder calculation report
Tapered welded beam example · Rev A
2026-07-21 00:13:08 UTC
SI (mm · kN · MPa)
EN 1993-1-1:2005 · EN 1990:2002+A1:2005 actions
Scope and inputs summary
Calculation reference
CSB-27E43D64
Structural system
Simply supported
Beam length
6000.0 mm
Beam type
Tapered / haunched (linearly varying depth)
Section family
Welded I-section
Material
S355 — user-confirmed design yield strength; fy 345.0 MPa
Elastic modulus
210000.0 MPa
Lateral restraint
Confirmed adequate
Design standard
Eurocode 3 (EN 1993-1-1)
Design basis
EN 1993-1-1:2005 · EN 1990:2002+A1:2005 actions
Resistance factor
γM0 = 1.00 (EN 1993-1-1 §6.1 recommended value)
Load combinations
EN 1990:2002+A1:2005 recommended actions · EN 1993-1-1:2005 resistance · γM0 = 1.00 · conservative η = 1.00.
Verification status
Eurocode 3 clause references and recommended factors are applied as documented; project use requires review by a qualified engineer against the governing project requirements.
Self-weight
Included from varying area
Schematic
Governing summary
Governing check
Major-axis bending resistance
Utilisation
0.069
Overall status
pass
FEA recommended
No
Section classification and ULS checks
Demand and resistance are evaluated along the full member for every ULS combination.
| Check | Demand | Capacity | U | Status |
|---|---|---|---|---|
| Cross-section classification | Class 1 | Class 3 | — | Pass |
| ||||
Equations used (EN 1993-1-1:2005 Table 5.2) | ||||
| Major-axis bending resistance | 85.63 kN·m | 1240.36 kN·m | 0.069 | Pass |
| ||||
Equations used (EN 1993-1-1:2005 6.2.5) | ||||
| Web shear resistance | 57.23 kN | 1099.51 kN | 0.052 | Pass |
| ||||
Equations used (EN 1993-1-1:2005 6.2.6) | ||||
| Bending–shear interaction | 85.63 kN·m | 1240.36 kN·m | 0.069 | Pass |
| ||||
Equations used (EN 1993-1-1:2005 6.2.8) | ||||
Serviceability check
| Check | Demand | Capacity | U | Status |
|---|---|---|---|---|
| Project deflection criterion | 1.16 mm | 24.00 mm | 0.049 | Pass |
| ||||
Equations used (Project serviceability criterion) | ||||
Geometry and cross-section properties
Depth or diameter is interpolated linearly within each segment. Widths and wall / plate thicknesses remain constant inside a segment. The diagrams show the cross-section at the start, governing and end locations.
| Segment geometry | ||||
|---|---|---|---|---|
| Segment | Section | Range | Depth start → end | Dimensions |
| 1 | Welded I-section | 0.0 mm → 6000.0 mm | 500.0 mm → 650.0 mm | bf 250.0 mm · tf 20.0 mm · tw 12.0 mm |
| Evaluated cross-sections | |||
|---|---|---|---|
| Location | Depth / area | Iy / Wel / Wpl | Class |
| Start (0.0 mm) | 500.0 mm / 15520 mm² | 6.7367e+8 mm⁴ / 2.6947e+6 mm³ / 3.0348e+6 mm³ | Class 1 |
| Governing (2812.5 mm) | 570.3 mm / 16364 mm² | 9.0658e+8 mm⁴ / 3.1793e+6 mm³ / 3.5953e+6 mm³ | Class 1 |
| End (6000.0 mm) | 650.0 mm / 17320 mm² | 1.2196e+9 mm⁴ / 3.7525e+6 mm³ / 4.2663e+6 mm³ | Class 1 |
Load cases and combinations
| Load cases | |||
|---|---|---|---|
| ID | Name | Type / category | Actions |
| G | Permanent imposed load | permanent | 4.00 → 4.00 kN/m, 0.0 mm to 6000.0 mm |
| Q | Office imposed load | variable / B | 8.00 → 8.00 kN/m, 0.0 mm to 6000.0 mm |
| Generated combinations | |||
|---|---|---|---|
| Combination | Limit state | Case factors | Convergence |
| ULS — Office imposed load leading | ULS | G 1.350; Q 1.500 | Converged; n=8; error 1.46e-3 |
| SLS characteristic — Office imposed load leading | SLS | G 1.000; Q 1.000 | Converged; n=8; error 1.46e-3 |
| SLS — quasi-permanent | SLS | G 1.000; Q 0.300 | Converged; n=8; error 9.80e-4 |
Analysis results and diagrams
Sign convention: positive shear is upward on the left cut face; positive bending is sagging; negative deflection is downward.
| Combination extrema | |||
|---|---|---|---|
| Combination | Reaction max | V max / min | M max / min; |v|max |
| ULS — Office imposed load leading | 57.41 kN | 57.23 kN / -57.41 kN | 85.98 kN·m / 0.00 kN·m; 1.7 mm |
| SLS characteristic — Office imposed load leading | 39.86 kN | 39.72 kN / -39.86 kN | 59.69 kN·m / 0.00 kN·m; 1.2 mm |
| SLS — quasi-permanent | 23.06 kN | 22.92 kN / -23.06 kN | 34.49 kN·m / 0.00 kN·m; 0.7 mm |
| Support reactions — governing ULS combination | ||
|---|---|---|
| Support x | Vertical reaction | Reaction moment |
| 0.0 mm | 57.23 kN | 0.00 kN·m |
| 6000.0 mm | 57.41 kN | 0.00 kN·m |
Design-basis matrix
Implemented routes are limited to the stated applicability. A source screen is not a substitute for an unimplemented resistance method.
| Check | Reference | Applicability | Method / verification |
|---|---|---|---|
| Linear beam analysis | Public-domain structural mechanics; Euler–Bernoulli two-node beam element; consistent nodal loading | Straight beams, one bending plane, linear elastic small displacement | Direct-stiffness beam solver with convergence-controlled mesh refinement; Simply supported, cantilever, fixed-fixed and continuous closed-form cases |
| ULS/SLS combinations | EN 1990:2002+A1:2005; eq. 6.10, 6.14b, 6.16b; Tables A1.1 and A1.2(B); Annex B | Persistent building situations; non-geotechnical STR; CC1–CC3 | Recommended γ, ψ and KFI factors applied per named permanent and variable case; Factor and ψ-value unit tests |
| Section classification | EN 1993-1-1:2005; 5.5 and Table 5.2 sheets 1–3 | Doubly symmetric welded I, rectangular and circular hollow sections in bending | Element slenderness against the Class 1/2/3 limits for each section family; Boundary tests at Class 1/2/3 limits |
| Cross-section bending resistance | EN 1993-1-1:2005; 6.2.5 equations (6.12)–(6.15) | Class 1–3, no fastener holes, fully laterally restrained | Plastic (Class 1–2) or elastic (Class 3) modulus times fy over γM0; Independent section-modulus hand checks |
| Plastic shear resistance | EN 1993-1-1:2005; 6.2.6 equations (6.17)–(6.22) | Shear parallel to the depth; section-specific shear area Av | Av·fy/(√3·γM0) with the clause 6.2.6(3) shear area for each family; Independent shear-area hand checks |
| Bending-shear interaction | EN 1993-1-1:2005; 6.2.8 equations (6.29)–(6.30) | Equal-flange Class 1–2 I-sections; other cases reported without reduction | Reduced plastic modulus once VEd exceeds 0.5·Vpl,Rd; High-shear reduced plastic modulus hand check |
| Shear-buckling applicability screen | EN 1993-1-1:2005; EN 1993-1-5:2006; EN 1993-1-1 6.2.6(6) equation (6.22) | Unstiffened web screen only; full EN 1993-1-5 resistance is not implemented | Web slenderness compared with the 72ε/η screening limit; Slenderness threshold boundary test |
| Project deflection criterion | Project serviceability criterion; User-selected span-ratio limit | User-selected total characteristic deflection criterion | Recovered SLS deflection against the selected span ratio limit; Closed-form deflection cases and unit invariance |
Assumptions
- Linear elastic, small-displacement Euler–Bernoulli bending in one vertical plane; shear deformation is neglected.
- Every segment is a doubly symmetric section bent about its major axis — an equal-flange welded I-section, a rectangular hollow section, or a circular hollow section. Wall and plate thicknesses and the width are constant within a segment; the depth or diameter varies linearly.
- The compression flange is continuously or otherwise adequately restrained so lateral-torsional buckling does not govern.
- The entered design yield strength is applicable to the actual steel grade and governing plate thickness; no catalogue grade/thickness lookup is inferred. The resistance / capacity factor shown for the active design standard is applied unless a project input is deliberately changed.
- Support bearing, load introduction, patch loading, stiffeners, welds, splices and connections require separate design.
- The selected deflection ratio is a project serviceability criterion and must be agreed for the building use and finishes.
Source traceability
- CSB_MECH_BEAMEuler–Bernoulli beam theory and direct stiffness methodLinear two-node bending elements with two degrees of freedom per node, consistent nodal loads, explicit support constraints and equilibrium recovery.
- CSB_DEFLECTION_PROJECTProject serviceability criterionVertical deflection is checked against the project span-ratio criterion selected by the user; the limit is not presented as a universal code limit.
- CSB_EN1990_COMBINATIONSEN 1990:2002+A1:2005 · 2002+A1:2005 · eq. 6.10, 6.14b, 6.16b; Tables A1.1 and A1.2(B); Annex BPersistent building STR combinations using the Eurocode-recommended partial factors (, ), recommended values for imposed-load categories A–H, and the recommended consequence factor .
- CSB_EC3_CLASSIFICATIONEN 1993-1-1 · 2005 · 5.5 and Table 5.2Cross-section classification in major-axis bending using : outstand flanges and internal webs of welded I-sections, internal walls of rectangular hollow sections, and the limit () of circular hollow sections. Class 4 is blocked.
- CSB_EC3_BENDINGEN 1993-1-1 · 2005 · 6.1 and 6.2.5, equations (6.12)–(6.15)Major-axis cross-section bending resistance uses for Class 1–2 and for Class 3, divided by .
- CSB_EC3_SHEAREN 1993-1-1 · 2005 · 6.2.6, equations (6.17)–(6.22)Plastic shear resistance with the clause 6.2.6(3) shear area: for welded I-sections (), for rectangular hollow sections loaded parallel to the depth, and for circular hollow sections.
- CSB_EC3_INTERACTIONEN 1993-1-1 · 2005 · 6.2.8, equations (6.29)–(6.30)For Class 1–2 equal-flange I-sections with , bending resistance is reduced using .
- CSB_EC3_LTB_SCOPEEN 1993-1-1 · 2005 · 6.3.2.1(2)The implemented cross-section route requires sufficient restraint to the compression flange; unrestrained tapered-member LTB is not inferred.
- CSB_EC3_15_SCOPEEN 1993-1-5 · 2006 · Section 5 (applicability referenced by EN 1993-1-1 6.2.6(6))The release screens when shear-buckling verification is required but does not calculate EN 1993-1-5 shear-buckling resistance; such a section is outside scope.
- CSB_DEFLECTIONEN 1990:2002+A1:2005 · 2002+A1:2005 · A1.4.2 and A1.4.3Vertical deflection is checked against the project criterion selected by the user; the limit is not presented as a universal Eurocode limit.
- CSB_AISC_COMBINATIONSASCE 7-22 / AISC 360-22 · 2022 · ASCE 7-22 §2.3 (LRFD) / §2.4 (ASD)Basic gravity strength combinations 1.4D and 1.2D + 1.6L (LRFD), or D and D + L (ASD). Wind, snow and seismic actions are not modelled. Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_AISC_CLASSIFICATIONAISC 360-22 · 2022 · Chapter B, Table B4.1bWidth-to-thickness classification (compact / non-compact / slender) for flexure: I-flange , I-web , HSS wall and round limits. Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_AISC_BENDINGAISC 360-22 · 2022 · Chapter F (F2, F3, F7, F8)Flexural strength: for compact sections, with flange-local-buckling interpolation for non-compact sections and the F8 round-HSS branches. Design strength (LRFD, ) or (ASD, ). Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_AISC_SHEARAISC 360-22 · 2022 · Chapter G (G2, G4, G5)Shear strength with for stocky webs; the web shear-buckling range is blocked rather than computed. Design strength () or (). Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_AISC_LTB_SCOPEAISC 360-22 · 2022 · F2.2 (assumed Lb ≤ Lp)Full lateral restraint is assumed so lateral-torsional buckling does not govern; unrestrained members are outside the supported scope. Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_CSA_COMBINATIONSNBCC 2020 / CSA S16-19 · 2020 / 2019 · NBCC 2020 Table 4.1.3.2Gravity strength combinations 1.4D and 1.25D + 1.5L. Wind, snow and seismic actions are not modelled. Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_CSA_CLASSIFICATIONCSA S16-19 · 2019 · Clause 11 / Table 2Class 1–4 width-to-thickness limits: I-flange , I-web , HSS and round-HSS limits, with in MPa. Class 4 is blocked. Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_CSA_BENDINGCSA S16-19 · 2019 · Clause 13.5Factored moment resistance (Class 1–2) or (Class 3), with . Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_CSA_SHEARCSA S16-19 · 2019 · Clause 13.4.1.1Factored shear resistance with for stocky webs; the shear-buckling range is blocked. . Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_AS_COMBINATIONSAS/NZS 1170.0:2002 · 2002 · Clause 4.2.2Gravity strength combinations 1.35G and 1.2G + 1.5Q. Wind, snow and earthquake actions are not modelled. Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_AS_CLASSIFICATIONAS 4100:2020 · 2020 · Clause 5.2 / Table 5.2Plate-element slenderness against giving the section slenderness ; slender sections are blocked. Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_AS_BENDINGAS 4100:2020 · 2020 · Clause 5.2.1–5.2.6Section moment capacity with for compact sections and linear interpolation to for non-compact sections. . Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
- CSB_AS_SHEARAS 4100:2020 · 2020 · Clause 5.11Shear capacity for stocky webs; the shear-buckling range is blocked. . Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
This standards-traceable engineering calculation is generated from user inputs. It is not certified, approved or engineer-stamped, and it requires review by a qualified engineer for the project context, load introduction, stability, connections and all excluded checks.
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.
| Route | Implemented basis | Verification status |
|---|---|---|
| Eurocode 3 · EN 1993-1-1 | Class 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 360-22 | Compactness, 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 S16-19 | Class 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 4100:2020 | Section 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. |
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.