Documentation · structural

Custom Steel Beam & Plate Girder — methodology & sources

This calculator separates a single, standard-agnostic linear beam analysis from code-specific cross-section verification. It evaluates reactions, shear, bending moment, rotation and deflection for piecewise constant or linearly tapered welded I-sections, rectangular hollow sections and circular hollow sections, then checks compact / Class 1–3 resistance paths at stations along the full member under the design standard you select — Eurocode 3, AISC 360-22, CSA S16-19 or AS 4100:2020. Unsupported stability and plated-element paths stop a PASS result.

Sourcing note. The Eurocode 3 route applies clause references and recommended factors as documented. The AISC 360-22, CSA S16-19 and AS 4100:2020 routes are implemented from established engineering references and validated against published worked examples; their coefficients are pending independent verification against the official published standard text, and every report states this. All results require review by a qualified engineer.

Supported design scope

Implemented

Straight beams in one vertical bending plane; linear elastic small-displacement Euler–Bernoulli analysis.
Simply supported, cantilever, fixed–fixed, propped and two-span continuous systems.
Normal (prismatic, constant-depth) or tapered / haunched members — both use the same analysis and cross-section checks.
Doubly symmetric welded I-sections, rectangular hollow sections and circular hollow sections, with piecewise constant or linearly tapered depth / diameter.
A standard-profile picker (IPE, HEA, HEB, RHS, SHS, CHS) that fills nominal catalogue dimensions, or fully custom dimensions.
Point forces, point moments, full/partial linearly varying loads and self-weight from varying area.
A user-selectable governing standard — Eurocode 3, AISC 360-22, CSA S16-19 or AS 4100:2020 — driving classification, resistance factors and automatic gravity load combinations.
Compact / Class 1–3 classification, bending and shear resistance with adequate lateral restraint; Eurocode adds its Class 1–2 high-shear interaction reduction.
User-selected project deflection criteria; characteristic and quasi-permanent SLS results.

Explicitly unsupported

Class 4 effective sections and EN 1993-1-5 shear-buckling resistance.
Unrestrained lateral-torsional buckling of tapered members.
Axial force, beam-column interaction, biaxial bending, torsion and global portal-frame analysis.
Patch loading, local support bearing, stiffeners, welds, splices and connection design.
Composite, curved, cellular or perforated beams; fire, fatigue, seismic and dynamic verification.
Verified rolled-section property tables: the standard-profile picker fills nominal catalogue dimensions, but properties are computed from the modelled welded-equivalent geometry (no root fillet), so published rolled-section Iy / Wpl are not reproduced exactly.

Design-basis matrix

Each row records the exact edition and reference, applicability, method and validation basis. The matrix below shows the Eurocode 3 default; the report's matrix reflects whichever standard is selected. Standard text is paraphrased and no standard PDF is served by the application.

Check	Standard / 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

Check registry

Check	Status	Description
Cross-section classification	Implemented	Classifies flange and web (or wall) slenderness at recovered stations under the active design standard.
Major-axis bending resistance	Implemented	Cross-section bending resistance for fully restrained beams under the active design standard.
Web shear resistance	Implemented	Shear resistance with a shear-buckling applicability screen under the active design standard.
Bending–shear interaction	Implemented	High-shear bending reduction where the active design standard applies one.
Project deflection criterion	Implemented	Characteristic deflection against a selected project span-ratio limit.

Sources and factors

Under Eurocode 3, actions use the EN 1990:2002+A1:2005 recommended partial factors (γG = 1.35, γQ = 1.50), the recommended ψ values from Table A1.1 and the recommended consequence factor KFI from Annex B; resistance uses γM0 = 1.00 per EN 1993-1-1:2005 §6.1 with conservative η = 1.00. The AISC 360-22 (ASCE 7 combinations, φ or Ω), CSA S16-19 (NBCC combinations, φ = 0.90) and AS 4100:2020 (AS/NZS 1170.0 combinations, φ = 0.90) routes apply their own factors, reconstructed and validated against published worked examples pending official-source verification. Every listed source records its edition, clause and note.

Euler–Bernoulli beam theory and direct stiffness method
Linear two-node bending elements with two degrees of freedom per node, consistent nodal loads, explicit support constraints and equilibrium recovery.
Project serviceability criterion
Vertical deflection is checked against the project span-ratio criterion selected by the user; the limit is not presented as a universal code limit.
EN 1990:2002+A1:2005 · 2002+A1:2005 · eq. 6.10, 6.14b, 6.16b; Tables A1.1 and A1.2(B); Annex B
Persistent building STR combinations using the Eurocode-recommended partial factors ( $γ_{G} = 1.35$ , $γ_{Q} = 1.50$ ), recommended $ψ$ values for imposed-load categories A–H, and the recommended consequence factor $K_{F I}$ .
EN 1993-1-1 · 2005 · 5.5 and Table 5.2
Cross-section classification in major-axis bending using $ε = 235/ f_{y}$ : outstand flanges and internal webs of welded I-sections, internal walls of rectangular hollow sections, and the $d / t$ limit ( $50/70/90 ε^{2}$ ) of circular hollow sections. Class 4 is blocked.
EN 1993-1-1 · 2005 · 6.1 and 6.2.5, equations (6.12)–(6.15)
Major-axis cross-section bending resistance uses $W_{pl}$ for Class 1–2 and $W_{e l}$ for Class 3, divided by $γ_{M 0}$ .
EN 1993-1-1 · 2005 · 6.2.6, equations (6.17)–(6.22)
Plastic shear resistance with the clause 6.2.6(3) shear area: $η h_{w} t_{w}$ for welded I-sections ( $η = 1.0$ ), $A h / (b + h)$ for rectangular hollow sections loaded parallel to the depth, and $2 A / π$ for circular hollow sections.
EN 1993-1-1 · 2005 · 6.2.8, equations (6.29)–(6.30)
For Class 1–2 equal-flange I-sections with $V_{E d} > 0.5 V_{pl, R d}$ , bending resistance is reduced using $ρ = (2 V_{E d} / V_{pl, R d} - 1)^{2}$ .
EN 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.
EN 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.
EN 1990:2002+A1:2005 · 2002+A1:2005 · A1.4.2 and A1.4.3
Vertical deflection is checked against the project criterion selected by the user; the limit is not presented as a universal Eurocode limit.
ASCE 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.
AISC 360-22 · 2022 · Chapter B, Table B4.1b
Width-to-thickness classification (compact / non-compact / slender) for flexure: I-flange $0.38/1.0 E / F_{y}$ , I-web $3.76/5.70 E / F_{y}$ , HSS wall and round $D / t$ limits. Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
AISC 360-22 · 2022 · Chapter F (F2, F3, F7, F8)
Flexural strength: $M_{n} = F_{y} Z_{x}$ for compact sections, with flange-local-buckling interpolation for non-compact sections and the F8 round-HSS branches. Design strength $ϕ_{b} M_{n}$ (LRFD, $ϕ_{b} = 0.90$ ) or $M_{n} / Ω_{b}$ (ASD, $Ω_{b} = 1.67$ ). Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
AISC 360-22 · 2022 · Chapter G (G2, G4, G5)
Shear strength $V_{n} = 0.6 F_{y} A_{w} C_{v 1}$ with $C_{v 1} = 1.0$ for stocky webs; the web shear-buckling range is blocked rather than computed. Design strength $ϕ_{v} V_{n}$ ( $ϕ_{v} = 0.90$ ) or $V_{n} / Ω_{v}$ ( $Ω_{v} = 1.67$ ). Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
AISC 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.
NBCC 2020 / CSA S16-19 · 2020 / 2019 · NBCC 2020 Table 4.1.3.2
Gravity 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.
CSA S16-19 · 2019 · Clause 11 / Table 2
Class 1–4 width-to-thickness limits: I-flange $145/170/200 F_{y}$ , I-web $1100/1700/1900 F_{y}$ , HSS and round-HSS limits, with $F_{y}$ 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.
CSA S16-19 · 2019 · Clause 13.5
Factored moment resistance $M_{r} = ϕZ F_{y}$ (Class 1–2) or $ϕS F_{y}$ (Class 3), with $ϕ = 0.90$ . Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
CSA S16-19 · 2019 · Clause 13.4.1.1
Factored shear resistance $V_{r} = ϕ A_{w} F_{s}$ with $F_{s} = 0.66 F_{y}$ for stocky webs; the shear-buckling range is blocked. $ϕ = 0.90$ . Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
AS/NZS 1170.0:2002 · 2002 · Clause 4.2.2
Gravity 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.
AS 4100:2020 · 2020 · Clause 5.2 / Table 5.2
Plate-element slenderness $λ_{e} = (b / t) f_{y} /250$ against $λ_{e p} / λ_{ey}$ giving the section slenderness $λ_{s}$ ; slender sections are blocked. Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
AS 4100:2020 · 2020 · Clause 5.2.1–5.2.6
Section moment capacity $M_{s} = f_{y} Z_{e}$ with $Z_{e} = Z_{c} = min (S, 1.5 Z)$ for compact sections and linear interpolation to $Z$ for non-compact sections. $ϕ = 0.90$ . Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.
AS 4100:2020 · 2020 · Clause 5.11
Shear capacity $V_{v} = 0.6 f_{y} A_{w}$ for stocky webs; the shear-buckling range is blocked. $ϕ = 0.90$ . Coefficients are reconstructed from established engineering references and validated against published worked examples, pending review against the official published standard.

Numerical controls and units

Supports, section changes, point actions and distributed-load boundaries are exact mesh nodes. Tapered stiffness is refined from 2 to 32 elements per segment until reactions, extrema and deflection meet the selected relative tolerance; failure to converge becomes an outside-scope result. Internal units are N, mm and MPa. SI/US switching changes display only.

Open the calculator Read the user guide View example report