Compression Members & Built-up Columns Notes

Last reviewed 16 Sept 2026 · 7 min read

Compression members in steel

Columns in buildings and industrial sheds, struts and top chords of trusses, and bracing members carry axial compression. Unlike tension members, their strength is governed mainly by buckling, so the slenderness and the shape of the section matter as much as the area.

Common sections: rolled I and H sections (ISHB, ISWB), circular and rectangular hollow sections (most efficient), single and double angles (truss members), channels back-to-back, and built-up sections of channels or angles connected by lacing or battens.

Effective length and slenderness

λ_{e} = \frac{K L}{r}

$K L$ = effective length (depends on end restraint); $r$ = radius of gyration about the relevant axis. Buckling happens about the axis with the larger $K L / r$ .

Code ProvisionIS 800 — effective length (selected, as in Table 11)

End conditions (translation / rotation)	Effective length
Both ends restrained in translation and rotation	$0.65 L$
Both ends restrained in translation; one end restrained in rotation	$0.80 L$
Both ends restrained in translation, free in rotation (pinned)	$1.00 L$
One end fixed; other end restrained in rotation but free in translation	$1.20 L$
One end fixed; other end free	$2.00 L$

Slenderness limit for members carrying dead and imposed compression: 180 (250 for wind/earthquake-only compression). Truss members: effective length of discontinuous angle struts is taken as 0.7–1.0 of the centre-to-centre length depending on end connections (two or more bolts / welded vs single bolt).

Why real columns fall below Euler's load

Euler's elastic critical stress is $f_{cc} = \frac{π ^{2} E}{( K L / r ) ^{2}}$ . Real columns carry less because of initial crookedness, eccentricity of load, residual stresses from rolling and welding, and yielding before elastic buckling for stocky members. IS 800:2007 adopts the Perry–Robertson approach with imperfection factors.

IS 800 design compressive strength

FormulaDesign compressive stress

P_{d} = A_{e} f_{c d}, f_{c d} = \frac{f _{y} / γ _{m 0}}{ϕ + ϕ ^{2} - λ ^{2}} \leq \frac{f _{y}}{γ _{m 0}}

ϕ = 0.5 [1 + α (λ - 0.2) + λ^{2}], λ = \frac{f _{y}}{f _{cc}} = \frac{f _{y} ( K L / r ) ^{2}}{π ^{2} E}

$λ$ = non-dimensional slenderness; $α$ = imperfection factor.

Code ProvisionIS 800 — buckling classes

Buckling class	a	b	c	d
Imperfection factor $α$	0.21	0.34	0.49	0.76

Section	Buckling about z–z	about y–y
Rolled I-section, $h / b > 1.2$ , $t_{f} \leq 40$ mm	a	b
Rolled I-section, $h / b \leq 1.2$ , $t_{f} \leq 100$ mm	b	c
Welded I-section ( $t_{f} \leq 40$ mm)	b	c
Hot-rolled hollow sections	a	a
Cold-formed hollow sections	b	b
Channels, angles, tees, solid sections	c	c
Built-up sections (lacing/battens)	c	c

For $λ \leq 0.2$ , buckling does not reduce strength: $f_{c d} = f_{y} / γ_{m 0}$ . IS 800 also tabulates $f_{c d}$ against $K L / r$ for each class, so hand design usually reads values from tables.

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Compression Members & Built-up Columns