Steel Beams — Laterally Supported & Unsupported — Steel Structures Notes

Last reviewed 16 Sept 2026 · 5 min read

Types and behaviour

Steel beams (joists, girders, lintels, purlins, stringers, spandrel beams) are usually rolled I-sections (ISMB, ISWB, parallel-flange beams), channels for light purlins, or built-up/plate girders for heavy loads.

A beam can fail by:

Flexural yielding (formation of a plastic hinge),
Shear yielding of the web,
Local buckling of the flange or web (thin elements),
Web buckling or web crippling under concentrated loads,
Lateral–torsional buckling (LTB) — the compression flange buckles sideways and the section twists, when it is not laterally restrained.
Excessive deflection (serviceability).

Laterally supported beams

A beam is laterally supported when its compression flange is restrained against lateral movement and twisting continuously (e.g. embedded in or connected to a concrete slab) or at close spacing. LTB then cannot occur.

FormulaDesign bending strength (IS 800 cl. 8.2.1.2)

When the factored shear $V \leq 0.6 V_{d}$ (low shear):

M_{d} = \frac{β _{b} Z _{p} f _{y}}{γ _{m 0}}

$β_{b}$ = 1.0 for plastic and compact sections; $β_{b} = Z_{e} / Z_{p}$ for semi-compact sections.

To avoid irreversible deformation at service load:

simply supported beams: $M_{d} \leq \frac{1.2 Z _{e} f _{y}}{γ _{m 0}}$
cantilever beams: $M_{d} \leq \frac{1.5 Z _{e} f _{y}}{γ _{m 0}}$

Shear

FormulaShear strength

V_{d} = \frac{A _{v} f _{y w}}{3 γ _{m 0}}

$A_{v}$ = shear area: $h t_{w}$ for rolled I and channel sections bent about the major axis; $d t_{w}$ for welded sections.

If $V > 0.6 V_{d}$ (high shear), the design moment is reduced: $M_{d v} = M_{d} - β (M_{d} - M_{f d})$ , with $β = (\frac{2 V}{V _{d}} - 1)^{2}$ and $M_{f d}$ = plastic moment of the flanges alone.

Shear buckling of the web need not be checked if $d / t_{w} \leq 67 ε$ (unstiffened web).

Web buckling and web crippling

At supports and under concentrated loads, the thin web may buckle like a column or cripple (yield locally).

Web crippling (bearing): $F_{w} = \frac{( b _{1} + n _{2} ) t _{w} f _{y w}}{γ _{m 0}}$ , where $b_{1}$ = stiff bearing length and $n_{2}$ = dispersion length through the flange and root at a slope of 1 : 2.5 ( $n_{2} = 2.5 (t_{f} + r)$ ).
Web buckling: the web below the load acts as a strut of effective length about $0.7 d$ (for flanges restrained against rotation), with width $b_{1} + n_{1}$ (load dispersed at 45° to the mid-depth); strength $= f_{c d} \times$ area, using buckling class c.

If either check fails, provide bearing (load-carrying) stiffeners.

Deflection

Check deflection under unfactored imposed loads against IS 800 Table 6 limits (e.g. span/300 for floor members supporting elements not susceptible to cracking; span/360 where elements are susceptible to cracking).

Laterally unsupported beams — lateral–torsional buckling

When the compression flange is free between supports (gantry girders, beams without slab, cantilevers), the beam can buckle laterally and twist at a moment below $M_{p}$ .

FormulaIS 800 cl. 8.2.2 — design bending strength with LTB

M_{d} = β_{b} Z_{p} f_{b d}, f_{b d} = χ_{L T} \frac{f _{y}}{γ _{m 0}}

χ_{L T} = \frac{1}{ϕ _{L T} + ϕ _{L T}^{2} - λ _{L T}^{2}} \leq 1, ϕ_{L T} = 0.5 [1 + α_{L T} (λ_{L T} - 0.2) + λ_{L T}^{2}]

λ_{L T} = \frac{β _{b} Z _{p} f _{y}}{M _{cr}}

$α_{L T}$ = 0.21 for rolled sections, 0.49 for welded sections.

Elastic critical moment for a doubly symmetric I-section (simplified):

M_{cr} = \frac{π ^{2} E I _{y} h}{2 L _{L T}^{2}} [1 + \frac{1}{20} (\frac{L _{L T} / r _{y}}{h / t _{f}})^{2}]^{0.5}

$M_{cr}$ increases with lateral stiffness ( $I_{y}$ ), torsional stiffness and shorter unbraced length. LTB is not a concern if $λ_{L T} \leq 0.4$ .

Effective length for LTB (simply supported, loads not destabilising)

Restraint at supports	$L_{L T}$
Torsionally restrained, compression flange fully restrained against rotation in plan	$0.70 L$
Torsionally restrained, compression flange partially restrained against rotation in plan	$0.85 L$
Torsionally restrained, both flanges free to rotate in plan	$1.00 L$

Increase effective length (e.g. by 20%) where the load acts on the top flange and is free to move laterally with it (destabilising load). Cantilevers have their own table.

Ways to improve LTB resistance: lateral bracing of the compression flange at intervals, choosing wider flanges or box/tubular sections, top-flange channels (as in gantry girders), torsional restraints at supports.

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Steel Beams — Laterally Supported & Unsupported

Types and behaviour

Laterally supported beams

Shear

Web buckling and web crippling

Deflection

Laterally unsupported beams — lateral–torsional buckling

Effective length for LTB (simply supported, loads not destabilising)

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