Channel Section Design Theory - PFC, UPN (Eurocode 3)

The shear centre - why channels twist

A channel's shear centre lies outside the web, on the opposite side from the flanges. If a load is applied through the web (the usual assumption) rather than through the shear centre, it creates a torque - so a channel loaded as a simple beam will tend to twist as well as bend. This is the single most important thing to understand about channel design.

In practice channels are often used where this torsion is restrained (purlins fixed to roof sheeting, channels paired back-to-back, or used as bracing) so the twisting is suppressed.

Mono-symmetric bending & LTB

Because a channel is symmetric about only the y-y axis, its lateral-torsional buckling is more complex than an I-beam's - the section's response couples bending and torsion asymmetrically. SCI P363 provides the buckling parameter $u$ and torsional index $x$ that simplify the $M_{cr}$ calculation for these sections.

Built-up channels

Pairing two channels - back-to-back or laced - produces a doubly-symmetric or near-symmetric built-up member that cancels the torsion problem and roughly doubles capacity, commonly used for columns and heavy bracing.

Combined axial + bending (interaction)

A channel carrying axial load and bending together is verified by the same two interaction checks as an I-section. The cross-section check (§6.2.9) reduces the moment resistance to $M_{N,Rd}$ as the axial ratio $n=N_{Ed}/N_{pl,Rd}$ increases. The member stability check (§6.3.3) then combines compression buckling with lateral-torsional buckling - both Expressions (6.61) and (6.62) must be satisfied:

The interaction factors $k_{yy}, k_{yz}, k_{zy}, k_{zz}$ are taken from Annex B (Method 2). For a single channel the shear-centre offset means the engineer must also confirm the load path does not introduce unaccounted torsion. The worked example evaluates the factors and both expressions for a representative PFC.