Steel Lattice Column Design — Built-Up Members, Lacing, and Batten Plates

Built-up (lattice) columns consist of two or more main components (typically channels, angles, or W-shapes) connected by lacing bars, batten plates, or perforated cover plates. They are used when a single rolled section cannot provide the required radius of gyration, or when architectural/functional considerations demand an open cross-section (such as columns supporting crane runways). AISC 360-22 Section E6 provides the modified slenderness ratio approach for their design.

Modified slenderness ratio per AISC 360-22 Section E6

The key principle: a built-up column is weaker than a solid column of the same overall slenderness because the lacing or battens introduce shear flexibility. AISC accounts for this through a modified slenderness ratio:

(KL/r)_m = sqrt[(KL/r)_o^2 + (a/r_i)^2]

where:

• (KL/r)_o = slenderness ratio of the overall built-up member about the built-up axis
• a = distance between connectors (lacing/batten spacing) along the member length
• r_i = minimum radius of gyration of an individual component between connectors

This formula penalizes wide connector spacing. The term (a/r_i) represents the local slenderness of each component between lacing points. AISC requires a/r_i <= 3/4 * (KL/r)_o to prevent local buckling of individual components from governing before global buckling of the built-up member.

Worked example — double-channel lattice column

Given: Built-up column made from two C12x20.7 channels, back-to-back with 12 in. separation (face-to-face). Lacing bars at 45 degrees, single-lacing system. Column length = 24 ft, pinned-pinned (K = 1.0). A36 steel (Fy = 36 ksi).

Step 1 — Individual channel properties: A = 6.09 in.^2 per channel, I_x = 129 in.^4, I_y = 3.88 in.^4, r_y = 0.799 in. x-bar (distance from web back to centroid) = 0.698 in.

Step 2 — Built-up section properties about the lacing axis (y-y, the built-up axis):

Separation center-to-center = 12 + 2 * 0.698 = 13.40 in. (distance between channel centroids in the y-direction, assuming back-to-back with 12 in. gap)

Wait — for back-to-back channels with a 12 in. face-to-face gap:

• Channel web thickness = 0.282 in.
• Center-to-center of channels = 12 + 0.282 = 12.28 in. (approximate, measured centroid to centroid = 12 + 2 * (t_w/2) is not correct)
• Actually: distance from back of web to centroid = x-bar = 0.698 in. The back-to-back gap is 12 in. So centroid-to-centroid = 12 - 2 * 0.698 = 10.60 in. No — if the channels face outward (toes out), the backs face each other across the 12 in. gap:

Centroid distance = 12 + 2 _ x-bar = 12 + 2 _ 0.698 = 13.40 in. (from centroid of left channel to centroid of right channel, measured perpendicular to webs).

I*y,built-up = 2 * [I_y + A _ (13.40/2)^2] = 2 _ [3.88 + 6.09 _ 6.70^2] = 2 * [3.88 + 273.4] = 554.6 in.^4

A_total = 2 * 6.09 = 12.18 in.^2 r_y,built-up = sqrt(554.6 / 12.18) = sqrt(45.5) = 6.75 in.

Step 3 — Overall slenderness about built-up axis: (KL/r)_o = 1.0 _ 24 _ 12 / 6.75 = 288 / 6.75 = 42.7

Step 4 — Lacing spacing and local slenderness: For single lacing at 45 degrees: lacing bar spacing along the column = separation _ tan(45) = 13.40 _ 1.0 = 13.40 in. Use a = 13.5 in. (practical rounding).

r_i = r_y of individual channel = 0.799 in. a/r_i = 13.5 / 0.799 = 16.9

Check: a/r*i <= 3/4 * (KL/r)_o = 0.75 _ 42.7 = 32.0. Since 16.9 < 32.0, OK.

Step 5 — Modified slenderness ratio: (KL/r)_m = sqrt(42.7^2 + 16.9^2) = sqrt(1,823 + 286) = sqrt(2,109) = 45.9

Step 6 — Column capacity using AISC Chapter E: F_e = pi^2 * 29,000 / 45.9^2 = 286,200 / 2,107 = 135.8 ksi

Since Fy/Fe = 36/135.8 = 0.265 < 2.25: F*cr = 0.658^(Fy/Fe) * Fy = 0.658^0.265 _ 36 = 0.896 * 36 = 32.3 ksi

phi _ P_n = 0.90 _ 32.3 * 12.18 = 354 kips

Without the modification: Fcr at KL/r = 42.7 would give phi * Pn = 0.90 * 33.0 * 12.18 = 362 kips. The modification reduces capacity by about 2% in this case because the lacing spacing is well-controlled.

Lacing bar design (the "2% rule")

Lacing bars must resist a shear force equal to at least 2% of the axial compression in the column (AISC 360 Section E6.2). For the example above:

V_lacing = 0.02 * P_u

If P_u = 300 kips: V_lacing = 0.02 * 300 = 6 kips

For single lacing at 45 degrees, the force in each lacing bar = V*lacing / (2 * cos(45)) = 6 / (2 _ 0.707) = 4.24 kips (two lacing planes, one on each side).

The lacing bar must be checked as a compression member with KL/r_lacing <= 140 (AISC Section E6.2). For a flat bar 2 in. x 3/8 in., L_lacing = 13.4 / sin(45) = 18.95 in.:

r_bar = t / sqrt(12) = 0.375 / 3.464 = 0.108 in. KL/r = 18.95 / 0.108 = 175 >> 140 (NOT OK)

Need a larger bar. Try 2.5 in. x 1/2 in.: r = 0.5/3.464 = 0.144 in., KL/r = 18.95/0.144 = 131.6 < 140 (OK).

Batten plates as an alternative

Batten plates (flat plates welded or bolted perpendicular to the column axis) can replace lacing. They create a Vierendeel (moment frame) action between the main components. AISC Section E6.2 requires:

• Batten plate length >= 2/3 of the distance between lines of fasteners
• Batten spacing <= 1.5 * distance between lines of fasteners
• End battens at each end of the member

Code comparison

EN 1993-1-1 uses a more refined approach, modeling the built-up member with initial bow imperfections and calculating the shear force from the imperfection. The 2% rule in AISC is a simplification of this concept.

Key clause references

• AISC 360-22 Section E6 — Built-up member design, modified slenderness ratio
• AISC 360-22 Section E6.2 — Lacing and batten plate requirements
• AISC 360-22 Section E6.1 — Connector spacing limits (a/r_i)
• EN 1993-1-1 Section 6.4 — Uniform built-up compression members
• AS 4100 Clause 6.5 — Laced and battened compression members

Topic-specific pitfalls

• Ignoring the a/r_i limit — if the lacing or batten spacing is too wide relative to the component's radius of gyration, the individual components buckle between connectors before the overall column buckles. The a/r_i <= 0.75 * (KL/r)_o rule exists specifically to prevent this failure mode.
• Designing lacing bars for tension only — in a single-lacing system, some bars are in compression. The KL/r <= 140 limit applies to these compression lacing bars. If only tension capacity is checked, the compression bars may buckle.
• Neglecting end batten plates — without end battens, the load transfer from the main components to the gusset plate or base plate is eccentric, introducing local bending. AISC requires battens at each end.
• Using the overall r for local checks instead of the individual component r_i — the individual channel's weak-axis r_y (0.799 in. in our example) controls the local buckling between lacing points, not the overall built-up section r_y (6.75 in.). Confusing these two is a common error.

Run this calculation

• Column Capacity Calculator
• Section Properties Database

Related references

• K-Factor Guide
• Column K-Factor
• How to Verify Calculations
• Column Design Guide
• Effective Length
• Steel Truss
• HSS Connections
• Column Buckling

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.