Checks a rolled I or H section under a moment and an axial force in compression or tension, to SIA 263:2013: the section resistance, flexural and lateral-torsional buckling, and their interaction. Every step shows its formula and the clause it comes from.

What it checks

Section properties from the five profile dimensions: A = 2b · t_f + (h − 2t_f) · t_w + (4 − π) · r², with I_y, I_z, W_y,el and W_y,pl.
Section class under these forces, tables 5a and 5b: the compressed flange c/t_f, with c = (b − t_w)/2 − r, against the limits for uniform compression, and the web c/t_w, with c = h − 2t_f − 2r, against limits set by α (plastic, from N and M) and ψ (elastic).
Section resistance: N_pl,Rd = A · f_y,k/γ_M1 (clause 4.1.3), n = N_Ed/N_pl,Rd, and the reduced plastic moment M_y,N,Rd = M_y,pl,Rd · (1 − n)/(1 − 0.5a), not more than M_y,pl,Rd, with a = (A − 2b · t_f)/A, not more than 0.5. The check is M_y,Ed ≤ M_y,N,Rd.
Flexural buckling, clause 4.5.1, about both axes: λ̄_K = (l_K/i)/λ_E, with λ_E = π · √(E/f_y,k), and N_K,Rd = χ_K · A · f_y,k/γ_M1 on the buckling curve of each axis. The elastic critical load N_cr = π² · E · I/l_K² sets the amplification 1/(1 − N_Ed/N_cr) of the moment.
Which interaction applies: out-of-plane buckling is prevented while λ̄_K,z < 0.5 and N_Ed < N_K,z,Rd; lateral-torsional buckling (clause 4.5.2) is judged by l_D against l_cr.
Stability in the plane of bending: N_Ed/N_K,y,Rd + ω_y · M_y,Ed/((1 − N_Ed/N_cr,y) · ξ · M_y,Rd) ≤ 1, with the shape factor ξ = 1/(1 − a/2), not more than 1 + 0.2 · N_Ed/N_K,y,Rd. Where out-of-plane and lateral-torsional buckling are both prevented, the moment term uses the section resistance.

What you enter and what you get

You enter f_y,k from table 1 of your copy of SIA 263, for the grade and the plate thickness, E and G (clause 2.2), h, b, t_w, t_f and r, γ_M1 (clause 4.1.3), the sense and magnitude of N_Ed, the largest moment M_y,Ed, the moment diagram with M_min and the signs of the end moments, and bending about the strong axis only or about both axes. For the member: the buckling lengths l_K,y and l_K,z, entered or derived from the end conditions and intermediate supports, and whether lateral-torsional buckling is considered, with l_D.

You get the section properties, the class under these forces, every resistance and the utilisation of each check with a pass or fail. With the Basic plan, it prints as an A4 calculation note.

Assumptions and limits

Compression brings in the member checks. Tension leaves the section check and lateral-torsional buckling of the bending alone.
M_y,Ed is the largest moment in absolute value along the member; with end moments only, the larger end moment.
With end moments only, ω_y = 0.6 + 0.4 · M_min/M_max, at least 0.4. A transverse load between the ends, or an end not held laterally, takes ω = 1.0.
Lateral-torsional buckling may be left out only where the compressed flange is held laterally all along. l_D is not necessarily l_K,z: purlins may hold the member against weak-axis buckling without holding its compressed flange.
Shear is not included. Where V_Ed exceeds half the shear resistance, the moment resistance has to be reduced as well.

Worked example

A rolled section with h = 270 mm, b = 280 mm, t_w = 8 mm, t_f = 13 mm and r = 24 mm in f_y,k = 235 N/mm², under a compression N_Ed = 310 kN and end moments of 200 kNm and zero about the strong axis, with buckling lengths of 3,750 mm about y and 1,250 mm about z, and lateral supports of the compressed flange 5,000 mm apart. These are the module's own results for its worked example, computed when this page was built.

Inputs
Input	Value	Ref.
Characteristic yield strength f_y,k	235 N/mm²	§ t.1
Modulus of elasticity E	210000 N/mm²	§ 2.2
Overall depth h	270 mm
Flange width b	280 mm
Web thickness t_w	8 mm
Flange thickness t_f	13 mm
Root radius r	24 mm	§ t.5b
Resistance factor γ_M1	1.05	§ 4.1.3
The axial force is	Compression
Design axial force N_Ed	310 kN
Largest moment about y along the member M_y,Ed	200 kN·m
Moment diagram	End moments only — the diagram is linear
Smaller end moment \|M_min\|	0 kN·m
The two end moments have	The same sign at both ends
Bending	About the strong axis only
Buckling lengths	Buckling lengths entered
Buckling length, strong axis l_K,y	3750 mm
Buckling length, weak axis l_K,z	1250 mm
Lateral-torsional buckling	Considered	§ 4.5.2
Distance between lateral supports of the compressed flange l_D	5000 mm
Shear modulus G	81000 N/mm²	§ 2.2

Calculation: Common values
Step	Value	Ref.
Characteristic yield strength	f_y,k = 235 N/mm²	§ t.1
Gross area2b·t_f + (h − 2t_f)·t_w + (4 − π)·r².	A = 9,726 mm²
Second moment of area, strong axis	I_y = 136,722,971 mm⁴
Second moment of area, weak axis	I_z = 47,616,403 mm⁴
Elastic section modulus, strong axis	W_y,el = 1,012,763 mm³
Plastic section modulus, strong axis	W_y,pl = 1,112,223 mm³
Plastic axial resistanceA·f_y,k/γ_M1.	N_pl,Rd = 2,176.9 kN	§ 4.1.3
Axial utilisationN_Ed/N_pl,Rd.	n = 0.1424
Compressed flangec = (b − t_w)/2 − r. Limits 9.0 · 10.0 · 14.0 in uniform compression: class 1.	c/t_f = 8.62	§ t.5b
Webc = h − 2t_f − 2r. Under these forces α = 0.921 (plastic, from N and M) and ψ = -0.636 (elastic): limits 36.1 · 41.6 · 91.3, class 1. The axial force decides how much of the web is compressed, so the class is found for these forces and not for bending alone.	c/t_w = 24.50	§ t.5a
Section class under these forces	– = Class 1	§ t.5a

Calculation: Check 1 — section resistance
Step	Value	Ref.
Plastic moment resistance, strong axisf_y,k·W_y,pl/γ_M1.	M_y,pl,Rd = 248.9 kN·m
Web share of the areaa = (A − 2b·t_f)/A, not more than 0,5.	a = 0.2515
Reduced plastic moment, strong axisM_y,pl,Rd·(1 − n)/(1 − 0,5a), not more than M_y,pl,Rd: the axial force is carried first by the web, which contributes little to the moment, so the moment falls more slowly than n.	M_y,N,Rd = 244.2 kN·m
Section, bending and axial forceM_y,Ed ≤ M_y,N,Rd	η = 0.819 · Pass82 % of the capacity used

Calculation: Common values — flexural buckling
Step	Value	Ref.
Buckling length, strong axisEntered.	l_K,y = 3,750 mm
Buckling length, weak axisEntered.	l_K,z = 1,250 mm
Relative slenderness, strong axis(l_K,y/i_y)/λ_E, i_y = 118.6 mm, λ_E = π·√(E/f_y,k) = 93.91.	λ̄_K,y = 0.3368
Relative slenderness, weak axis(l_K,z/i_z)/λ_E, i_z = 70.0 mm.	λ̄_K,z = 0.1902
Buckling resistance, strong axisχ_K·A·f_y,k/γ_M1, curve b, χ_K = 0.9505.	N_K,y,Rd = 2,069.0 kN	§ 4.5.1
Buckling resistance, weak axisχ_K·A·f_y,k/γ_M1, curve c, χ_K = 1.0000.	N_K,z,Rd = 2,176.9 kN	§ 4.5.1
Elastic critical load, strong axisπ²·E·I_y/l_K,y². It sets the amplification 1/(1 − N_Ed/N_cr) of the moment.	N_cr,y = 20,151 kN
Elastic critical load, weak axis	N_cr,z = 63,162 kN

Calculation: Common values — which interaction applies
Step	Value	Ref.
Moment factor, strong axisω = 0,6 + 0,4·M_min/M_max = 0,6 + 0,4·(0.000), at least 0,4.	ω_y = 0.6000
Out-of-plane bucklingPrevented while λ̄_K,z < 0,5 and N_Ed < N_K,z,Rd: here λ̄_K,z = 0.190.	– = Prevented
Lateral-torsional bucklingl_D = 5,000 mm against l_cr = 5,647 mm (EP, ψ = 0.000).	– = Prevented

Calculation: Check 2 — stability, buckling in the plane of bending
Step	Value	Ref.
Shape factor for stability1/(1 − a/2), not more than 1 + 0,2·N_Ed/N_K,y,Rd = 1.0300.	ξ = 1.0300
Amplification	1/(1 − N_Ed/N_cr,y) = 1.0156
Axial term	N_Ed/N_K,y,Rd = 0.1498
Moment term, amplified	ω_y·M_y,Ed/(ξ·M_y,Rd) = 0.4754
Stability, bending and compressionN_Ed/N_K,y,Rd + ω·M_Ed/((1 − N_Ed/N_cr,y)·ξ·M_y,Rd) ≤ 1	η = 0.625 · Pass63 % of the capacity used

How this module is verified

Verified clause by clause against SIA 263:2013 and against independent calculations used on real projects, before release.

Questions

Why is the class found for these forces and not for bending alone?

The axial force decides how much of the web is compressed. In the worked example the web limits come from α = 0.921 and ψ = −0.636, and the section is class 1.

Why does the moment resistance fall more slowly than n?

The axial force is carried first by the web, which contributes little to the moment. Hence the factor 1/(1 − 0.5a) on M_y,pl,Rd · (1 − n).

Can I print the calculation?

The full calculation is shown on screen, free and without an account. A print-ready A4 calculation note is part of the Basic plan.

Norm: SIA 263:2013 · Page updated: 28 October 2026

Rolled I or H section under bending and axial force to SIA 263

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