Chapter 2 of 12

Tension & Compression Members

In the DSSSB JE Civil syllabus under Steel Structures · 2 parts

Tension Members · Compression Members & Built-up Columns

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📑 Contents (17 sections)

Part 1 of 2

Tension Members

Last reviewed 16 Sept 2026 · 5 min read

Tension members

A tension member carries axial pull: ties of roof trusses, bottom chords of bridge trusses, hangers, bracing members, cables and suspension rods. Because tension straightens a member, buckling is not a concern; the strength depends on the area, connection and material.

Common sections: flats and plates, round bars and rods, single and double angles (on one or both sides of a gusset), channels, tees, built-up sections, wire ropes.

Design strength (IS 800:2007)

The design tensile strength $T_{d}$ is the least of:

Formula1. Yielding of the gross section

T_{d g} = \frac{A _{g} f _{y}}{γ _{m 0}}, γ_{m 0} = 1.10

Excessive elongation of the whole member makes it unserviceable.

Formula2. Rupture of the critical net section

Plates: $T_{d n} = \frac{0.9 A _{n} f _{u}}{γ _{m 1}}$ , $γ_{m 1} = 1.25$

Threaded rods: $T_{d n} = \frac{0.9 A _{n} f _{u}}{γ _{m 1}}$ with $A_{n}$ = net root area at the threads.

Single angle connected through one leg (accounts for shear lag — the outstanding leg is not fully effective near the connection):

T_{d n} = \frac{0.9 A _{n c} f _{u}}{γ _{m 1}} + \frac{β A _{o} f _{y}}{γ _{m 0}}

$A_{n c}$ = net area of the connected leg; $A_{o}$ = gross area of the outstanding leg; $β = 1.4 - 0.076 (\frac{w}{t}) (\frac{f _{y}}{f _{u}}) (\frac{b _{s}}{L _{c}})$ , with $0.7 \leq β \leq \frac{0.9 f _{u} γ _{m 0}}{f _{y} γ _{m 1}}$ .

Simplified (preliminary) form: $T_{d n} = \frac{α A _{n} f _{u}}{γ _{m 1}}$ , with $α$ = 0.6 for one or two bolts, 0.7 for three bolts, 0.8 for four or more bolts in the end connection or equivalent welded length.

Formula3. Block shear

A block of the connected plate tears out: shear along the line of bolts and tension across the end. The block shear strength is the smaller of

T_{d b 1} = \frac{A _{v g} f _{y}}{3 γ _{m 0}} + \frac{0.9 A _{t n} f _{u}}{γ _{m 1}}

T_{d b 2} = \frac{0.9 A _{v n} f _{u}}{3 γ _{m 1}} + \frac{A _{t g} f _{y}}{γ _{m 0}}

$A_{v g}$ , $A_{v n}$ = gross and net areas in shear along the bolt line; $A_{t g}$ , $A_{t n}$ = gross and net areas in tension perpendicular to the load.

Part 2 of 2

Compression Members & Built-up Columns

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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