Member Capacity & KL/r Slenderness for Lattice Tower Members

How each leg, diagonal, horizontal and redundant in a lattice tower is checked for tension, compression buckling and slenderness under IS 17740:2022 and IS 800:2007.

Once the analysis has given you the force in every member for every load combination, the design comes down to one question repeated hundreds of times: is this member adequate for its worst force? Getting the capacity rules right — especially slenderness — is what separates a safe, economical tower from one that is either unsafe or badly over-steel.

Two failure modes: yield and buckling

A tower member is an axially-loaded element. It can fail in only two ways:

• Tension — the section yields across its area.
• Compression — the member buckles before it yields (for anything but very stubby members, buckling governs).

Both are checked with the partial safety factor on material γm0 = 1.10.

Tension capacity

The design tensile strength governed by yielding of the gross section is:

Td = Ag · fy / γm0

where Ag is the gross area and fy the yield strength. (Net-section rupture at bolt holes is a connection-level check, covered separately.)

Compression capacity & buckling curves

Compression capacity uses the Perry-Robertson column formulation of IS 800. The design compressive stress fcd depends on the non-dimensional slenderness and an imperfection factor α that reflects the section's shape and residual-stress pattern. IS 800 (Table 10) assigns a buckling curve per section type:

Section	Buckling curve	Imperfection α
Tubular / CHS (hot-finished)	Curve a	0.21
Angle sections	Curve c	0.49

The higher α of curve 'c' means an angle carries noticeably less compression than a tube of the same slenderness — one reason tubular legs are attractive on taller towers. The design capacity is Pd = Ag · fcd.

Slenderness (KL/r) and why it governs

The single most important number for a compression member is its slenderness ratio:

λ = KL / r

where L is the unbraced length, r the radius of gyration about the governing axis, and K the effective-length factor. A slender member buckles at a small fraction of its yield load, so slenderness both reduces capacity and is capped by an absolute upper limit — regardless of the force, a member that is too slender is not permitted, because it will be damaged in handling and will rattle under wind.

Choosing the right r matters: an angle's minor (v-v) axis is far weaker than its geometric axes, and for a single-bolted diagonal that minor axis often governs.

KL/r limits by member role

IS 17740 sets maximum slenderness by the role a member plays, not one blanket value (Annex E-4 / Annex F notes):

Member role	Max KL/r
Legs and leg-to-leg diagonals (primary)	150
Horizontal struts	200
Redundant / secondary members	250

Redundants carry little direct force — their job is to shorten the unbraced length of the primary members — so they are allowed to be more slender.

Bracing: IS 17740 Annex F equivalent slenderness

Bracing members are rarely pin-ended and concentric in reality; they are bolted eccentrically, often through one leg of an angle. IS 17740 Annex F (Table 6) captures this with an equivalent (effective) slenderness that depends on the end fixity, replacing the older IS 800 Table 12 approach. In broad terms:

• Eccentric connection at both ends, for L/r ≤ 120: λeff = 60 + 0.5·(L/r)
• Single-bolt (pinned, unrestrained) ends, for 120 < L/r ≤ 200: λeff = L/r
• Multi-bolt (partially restrained) ends, for 120 < L/r ≤ 250: λeff = 46.2 + 0.615·(L/r)

The floor of ~60 on well-restrained short braces reflects that even a "stocky" eccentrically-loaded angle behaves as if more slender than its bare L/r suggests. This λeff is what feeds the compression curve — not the raw geometric slenderness.

Tension and compression, enveloped separately

A member reverses under wind from different directions — the same diagonal is in tension for one wind case and compression for another. It is a mistake to track only the largest-magnitude force: a large tension can hide a smaller compression that actually governs (because compression capacity is far lower). Track the peak tension and the peak compression independently, per member and per role, and check each against its own limit state.

Crossover X-braces: the out-of-plane trap

Where two diagonals cross and are connected at the crossover, each half-diagonal is restrained in the plane of the face at that point — so its in-plane buckling length is the sub-panel. But out-of-plane, the crossover alone does not restrain it. The out-of-plane length is only shortened to a sub-panel when genuine plan bracing (or a hip member) frames into the crossover node; otherwise the full diagonal length governs out-of-plane. Checking a fully plan-braced X-brace over its whole length (or an unbraced one over just a sub-panel) is a common and consequential error — the two give KL/r ratios that can differ by a factor of three or four.

Minimum bracing resistance

Finally, even a lightly-loaded brace must be sized for a sensible minimum. IS 17740 (Cl. 10.4.2 / Annex C) floors every bracing member's design force at a small percentage (order of 2.5%) of the compression in the leg it braces. This guards against the case where the analysis says a redundant carries almost nothing, yet it must still be stiff and strong enough to actually provide the restraint the primary member is relying on.

Member checking is mechanical but unforgiving — the rules are simple individually, but there are a lot of them, applied to every member across a dozen load combinations, and the slenderness subtleties (which axis, which effective length, which end fixity) are exactly where hand-checks slip. For the surrounding steps — loads, combinations and analysis — see the full design guide.

This guide is general engineering information, not a substitute for the codes themselves or for professional judgment. Always design to the current published standards and have work reviewed by a qualified structural engineer.