I-Section Design Theory - UB, UC, IPE, HE (Eurocode 3)

I-sections (UK Universal Beams/Columns and European IPE/HE) are the workhorse of steel design - efficient in bending and, for the wider H-sections, in compression. Their behaviour to Eurocode 3 (EN 1993-1-1) is summarised below.

📐See it applied - full worked exampleA complete EC3 capacity calculation for a representative section, across the full design range.Worked example →

Why the I-shape is efficient

An I-section concentrates material in the flanges, far from the neutral axis, where it does the most work resisting bending. This maximises the major-axis second moment of area $I_y$ for a given weight - which is why beams are deep and narrow.

The trade-off is a small minor-axis $I_z$ : I-beams are weak about the weak axis and prone to lateral-torsional buckling unless restrained. Wide-flange H-sections (UC, HE) widen the flanges to improve minor-axis and axial performance, making them the natural choice for columns.

Plastic vs elastic bending

A compact (Class 1 or 2) I-section can develop its full plastic moment, using the plastic modulus $W_{pl}$ - about 10–15% more than the elastic value for a typical I-shape. A Class 3 section is limited to first yield (elastic modulus $W_{el}$ ). The flange outstand $c/t_f$ and web $c/t_w$ slenderness decide the class.

M_{c,Rd} = \frac{W_{pl}\,f_y}{\gamma_{M0}}\ (\text{Class 1, 2})

Lateral-torsional buckling (LTB)

Because the minor axis is weak, an unrestrained I-beam in bending tends to buckle sideways and twist before reaching $M_{c,Rd}$ . The design resistance $M_{b,Rd}$ applies a reduction $\chi_{LT}$ that depends on the unrestrained length, the moment shape $(C_1)$ , and the warping/torsional stiffness. Restraining the compression flange (e.g. with a slab or purlins) dramatically raises capacity.

M_{b,Rd} = \chi_{LT}\,\frac{W_y\,f_y}{\gamma_{M1}}

Combined axial + bending (interaction)

A real beam-column carries axial force and bending together, so two interaction checks apply - the same ones the worked example derives in full. First the cross-section check (§6.2.9): the coexistent axial load reduces the available moment to $M_{N,Rd}$ , and for a Class 1/2 I-section the plastic biaxial form governs, with exponents $\alpha=2$ and $\beta=\max(5n,1)$ where $n=N_{Ed}/N_{pl,Rd}$ :

\left(\frac{M_{y,Ed}}{M_{N,y,Rd}}\right)^{\alpha} + \left(\frac{M_{z,Ed}}{M_{N,z,Rd}}\right)^{\beta} \le 1.0

Then the member stability check (§6.3.3) combines compression buckling with lateral-torsional buckling through the interaction factors $k_{yy}, k_{yz}, k_{zy}, k_{zz}$ . Both Expressions (6.61) and (6.62) must be satisfied:

\frac{N_{Ed}}{N_{b,y,Rd}} + k_{yy}\frac{M_{y,Ed}}{M_{b,Rd}} + k_{yz}\frac{M_{z,Ed}}{M_{c,z,Rd}} \le 1.0\quad(6.61)

\frac{N_{Ed}}{N_{b,z,Rd}} + k_{zy}\frac{M_{y,Ed}}{M_{b,Rd}} + k_{zz}\frac{M_{z,Ed}}{M_{c,z,Rd}} \le 1.0\quad(6.62)

The k-factors come from EN 1993-1-1 Annex B (Method 2) - the method this tool implements, valid for all section types. With the axial ratios $n_y=N_{Ed}/N_{b,y,Rd}$ and $n_z=N_{Ed}/N_{b,z,Rd}$ and the equivalent-uniform-moment factors $C_{my}, C_{mz}$ (Table B.3):

Annex B (Method 2) interaction factors for I/H sections

Factor	$\bar\lambda \le 1.0$	$\bar\lambda > 1.0$
$k_{yy}$	$C_{my}\,[1+(\bar\lambda_y-0.2)\,n_y]$	$C_{my}\,[1+0.8\,n_y]$
$k_{zz}$	$C_{mz}\,[1+(2\bar\lambda_z-0.6)\,n_z]$	$C_{mz}\,[1+1.4\,n_z]$
$k_{yz}$	$0.6\,k_{zz}$	$0.6\,k_{zz}$
$k_{zy}$	$0.6\,k_{yy}$ (or a three-branch $\bar\lambda_z$ form if susceptible to torsion, Table B.2)	-

The worked example evaluates all four factors and both expressions for a representative load - see it applied with real numbers.

UB vs IPE - UK vs European

UB (Universal Beams, BS EN 10365) and IPE (European, EN 10365) are both I-beams but from different size series with different flange tapers and dimension steps. IPE/HE dominate continental Europe, the Middle East and much of Asia; UB/UC dominate the UK and Commonwealth. The Eurocode design method is identical - only the section dimensions differ.

Section tables

UB UC UBP UJ IPE HE MBMC

Back to the steel section theory overview or open the interactive tool.

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