Steel Section Capacity Check to EN 1993-1-1 - Theory
The theory behind the calculator: how a rolled steel I or H section is classified (Class 1-4), and how its bending resistance, lateral-torsional-buckling resistance, axial (flexural and torsional) buckling resistance and shear resistance are computed to Eurocode 3, then compared with the design demands to give a utilisation and a PASS/FAIL.
Run this method in the free calculator and export the result to Excel (.xlsx) or PDF.
Cross-section classification
Every check starts with classifying the section (Class 1 to 4) from the width-to-thickness ratios of the compression flange and the web, compared with limits that scale with the material factor ε=235/fy. The section class is the worse of the web class and the flange class. Class 1 and 2 sections reach the plastic moment; Class 3 reaches the elastic (yield) moment; Class 4 buckles locally first and needs effective section properties (not computed here).
Cross-section resistances (§6.2)
The axial, bending and shear resistances of the gross section are:
where W=Wpl for Class 1-2 and W=Wel for Class 3, andAv is the shear area. With the UK National AnnexγM0=γM1=1.0.
Lateral-torsional buckling (§6.3.2)
A beam bent about its major axis and unrestrained laterally may buckle sideways and twist. The buckling resistance moment reduces the bending resistance by χLT:
Mb,Rd=χLTWγM1fy,λˉLT=McrWfy
The elastic critical moment Mcr depends on the unrestrained length and the moment-diagram factor C1 (1.00 for uniform moment, higher for peaked diagrams - 1.13 for a UDL, 1.35 for a central point load, up to 2.70). A short unrestrained length makesχLT→1.0 so the cross-section resistance governs instead.
Flexural and torsional buckling (§6.3.1)
A member in compression buckles about the axis with the lower resistance. The reduction factorχ follows the buckling curve for the non-dimensional slendernessλˉ=(Lcr/i)/(93.9ε):
Nb,Rd=χγM1Afy=min(Nb,y,Rd,Nb,z,Rd,Nb,T,Rd)
Utilisation and verdict
Each design action is divided by its resistance to give a utilisation; the section is adequate when every utilisation - and the combined linear interaction when two or more actions act together - is at most 1.0.
Npl,RdNEd+Mc,y,RdMy,Ed+Mc,z,RdMz,Ed≤1.0
Frequently asked questions
A rolled I or H section is first classified (Class 1 to 4) from the slenderness of its web and flange. The cross-section resistances are then computed: bending M_c,Rd = W·fy/gM0 (with the plastic modulus for Class 1-2 or the elastic modulus for Class 3), axial N_pl,Rd = A·fy/gM0, and shear V_pl,Rd = Av·fy/(sqrt3·gM0). If a member length is given, the lateral-torsional-buckling resistance M_b,Rd and the flexural/torsional buckling resistance N_b,Rd are found from the relevant buckling curves. Each design action is divided by its resistance to give a utilisation, and the section passes when every utilisation is at most 1.0.
Classification tells you whether a section can reach its plastic moment, only its elastic moment, or will buckle locally first. Class 1 can form a plastic hinge with rotation capacity; Class 2 can reach the plastic moment but with limited rotation; Class 3 can reach the elastic (yield) moment; Class 4 buckles locally before yield and needs effective section properties. The class is the worse of the web class and the flange class, each found from a width-to-thickness ratio compared with limits that scale with epsilon = sqrt(235/fy).
A beam bent about its major axis can buckle sideways and twist before reaching its in-plane bending resistance - this is lateral-torsional buckling. The reduced resistance M_b,Rd = chi_LT·W·fy/gM1 depends on the non-dimensional slenderness, which grows with the unrestrained length between lateral restraints. LTB governs long, laterally unrestrained beams; a short span or closely spaced restraints (small LTB length) makes chi_LT approach 1.0 so the cross-section bending resistance governs instead. Enter the LTB length in the calculator to include this check.
The calculator loads the exact Blue Book properties for the section you pick, so an unedited check matches the published tables. When you change a dimension - depth, width, web or flange thickness, or root radius - the area, second moments, section moduli, radii of gyration, torsion constant and warping constant are re-derived from the geometry (including the root fillets) so you can check a trimmed, built-up or non-standard I-section that is not in the catalogue. The torsion constant is derived approximately, which affects only the buckling checks.
This tool covers rolled I and H sections - Universal Beams (UB), Universal Columns (UC) and Universal Bearing Piles - in grades S275 and S355, to BS EN 1993-1-1 with the UK National Annex (gM0 = gM1 = 1.0). Channels, hollow sections and angles use different resistance models and are not covered here yet.
Ready to check a section? Pick a UB or UC, override any dimension, enter your demands and get the classification, resistances and utilisation with a live diagram.
