----------------------------- | ---------------------------- | -------------------------------- | ----------------------------- | ----------------------- | | Tension yielding | D2 (F_y * A_g) | Cl 7.2 (N_t = A_g * f_y) | Cl 6.2.3 (N_pl,Rd) | Cl 13.2(a) | | Tension rupture (net section) | D2 (F_u * A_e) | Cl 7.3 (N_t = 0.85k_tA_n*f_u) | Cl 6.2.2.2 | Cl 13.2(b) | | Compression buckling | E3 (flexural buckling) | Cl 6.3.3 (alpha_b) | Cl 6.3.1 (chi reduction) | Cl 13.3.1 | | Torsional/flexural-torsional | E4 | Cl 6.3.4 | Cl 6.3.1.4 | Cl 13.3.2 | | Built-up member | E6 | Cl 6.4 | Cl 6.4.4 | Cl 13.4 | | Slenderness limit | E2 (KL/r <= 200) | Cl 6.3.1 (L/r <= 200) | EN 1993-1-1 Cl 6.3.1 (<= 250) | Cl 10.4.2 (KL/r <= 200) | | Gusset plate — block shear | J4.3 | Cl 9.1.10 | Cl 3.10.2 | Cl 13.11 | | Gusset plate — compression | Whitmore (DG29) | Cl 6 (column analogy) | Annex K (effective width) | Cl 13.12 (Whitmore) | | HSS joint — chord plastification | K2.3 (T-, Y-, K-connections) | Cl 9.5 (K- and T-joints) | Table 7.10 (CHS joints) | Cl 12.7 | | Weld — fillet | J2.4 (phi=0.75, 0.6*F_EXX) | Cl 9.7.3 (phi=0.8, 0.6*f_uw) | Cl 4.5.3 (beta_w) | Cl 13.13 |

Key difference: EN 1993-1-8 has the most comprehensive hollow section joint provisions (Tables 7.10, 7.11, 7.12 covering CHS, RHS, and multiplanar joints). AISC 360 K2 provides separate equations for T/Y, K, and cross connections in CHS and RHS but is more limited in scope. CIDECT design guides fill the gap where codes are silent.

Step-by-Step Example

Problem: Design a simply-supported Warren truss spanning 60 ft with depth 6 ft, 6 panels (each 10 ft). Top chord slope: flat (parallel chords). Uniform factored panel point loads P = 20 kips at each bottom chord joint (5 loaded joints). Top chord: HSS 6x6x3/8 (A500 Gr. B, F_y = 46 ksi, A_g = 8.08 in^2, r = 2.28 in). Bottom chord: HSS 6x6x3/8 (same). Web members: HSS 4x4x1/4 (A500 Gr. B, F_y = 46 ksi, A_g = 3.59 in^2, r = 1.52 in). Design code: AISC 360-22 LRFD.

Step 1 — Reactions and member forces: Total load = 5 _ 20 = 100 kips. Reactions = 50 kips each end. Panel moment (at midspan) = 50 _ 30 - 20 * (20 + 10) = 1500 - 600 = 900 kip-ft. Max top chord compression = M/d = 900/6 = 150 kips. Max bottom chord tension = 900/6 = 150 kips.

Web member force (first panel diagonal, angle from horizontal = arctan(6/10) = 31.0 deg): Shear at first panel = 50 kips. F_diagonal = 50 / sin(31.0 deg) = 50 / 0.515 = 97.1 kips (tension for typical Warren layout).

Step 2 — Top chord compression check (HSS 6x6x3/8): Member length L = 10 ft = 120 in. KL/r = 1.0 _ 120 / 2.28 = 52.6. F_e = pi^2 _ 29000 / (52.6)^2 = 103.5 ksi. Fy = 46 ksi. 0.44 * Fy = 20.24 ksi. F_e > 20.24, so inelastic buckling. F_cr = 0.658^(46/103.5) * 46 = 0.658^0.444 _ 46 = 0.821 _ 46 = 37.8 ksi. phi*P_n = 0.90 * 37.8 * 8.08 = 274.7 kips. Utilization = 150 / 274.7 = 0.546 PASS.

Step 3 — Bottom chord tension check (HSS 6x6x3/8): Tension yielding: phi*P_n = 0.90 * 46 * 8.08 = 334.5 kips. Utilization = 150 / 334.5 = 0.448 PASS.

Step 4 — Web diagonal compression check (HSS 4x4x1/4): Member length L = sqrt(10^2 + 6^2) = 11.66 ft = 140 in. KL/r = 1.0 _ 140 / 1.52 = 92.1. F_e = pi^2 _ 29000 / (92.1)^2 = 33.8 ksi. 0.44 _ F_y = 20.24 ksi. F_e > 20.24, inelastic buckling. F_cr = 0.658^(46/33.8) _ 46 = 0.658^1.361 _ 46 = 0.572 _ 46 = 26.3 ksi. phi*P_n = 0.90 * 26.3 * 3.59 = 85.0 kips. Assuming the diagonal carries compression in the alternate load case: utilization = 97.1 / 85.0 = 1.14 FAIL — increase web size to HSS 4x4x5/16 or reduce panel load.

Step 5 — Joint check (bottom chord panel point, K-joint with gap): Chord: HSS 6x6x3/8, web: HSS 4x4x1/4. Angle theta = 31 deg. Per AISC 360 K2.3, check chord face plastification: gamma = B/(2t) = 6/(20.349) = 8.6. beta = 4/6 = 0.667. Rn sin(theta) = F_y * t^2 _ [9.8 * beta * sqrt(gamma)] / sin(theta) _ Qf = 46 * 0.349^2 _ [9.8 _ 0.667 _ sqrt(8.6)] / sin(31) _ 1.0 = 46 _ 0.122 _ [9.8 * 0.667 * 2.933] / 0.515 = 5.61 * 19.17 / 0.515 = 208.8 kips. phi = 0.90. phi*R_n = 187.9 kips. Demand = 97.1 kips. Utilization = 0.517 PASS.

Result: Top chord and bottom chord OK. Web diagonal needs upgrade for compression case. Joint capacity adequate for K-joint at panel points. Total truss weight (approximate): top + bottom chords: 2 _ 60 ft _ 27.5 lb/ft = 3,300 lb; webs: ~70 ft * 12.2 lb/ft = 854 lb; total ~4,154 lb.

Common Design Mistakes

• Assuming all web members carry only tension: In a Warren truss under gravity load, diagonal web members alternate between tension and compression. Under asymmetric loading (partial span load, wind uplift), the force reversal can put a tension-designed member into compression. Always check both signs.
• Neglecting effective length for compression chord buckling: The top chord is continuous across panel points in most trusses. The effective length factor K for in-plane buckling is typically 0.9 (not 1.0) for continuous chords. However, K = 1.0 is conservative. For out-of-plane buckling, the chord is laterally braced only at purlin/girt locations, which may be at larger spacing.
• Using the gross section for net section checks at bolted connections: Web members connected with one leg of an angle (or one face of an HSS) experience shear lag. The net effective area A_e = U * A_n, where U is the shear lag factor (AISC Table D3.1). For angles connected by one leg, U can be as low as 0.60, dramatically reducing tension capacity.
• Overlooking gusset plate buckling: A gusset plate loaded in compression by a web member can buckle out of plane if the free edge length behind the Whitmore section is excessive. The effective column length is the average of the Whitmore width distances to the connected edges, and if the free edge exceeds ~2x the plate thickness, buckling controls.
• Welding HSS branches to HSS chords without checking chord plastification: Hollow section joints fail by chord face deformation before the brace itself yields. The CIDECT/AISC K-connection equations are geometry-sensitive — small changes in chord wall thickness dramatically change capacity because capacity varies with t^2.
• Not accounting for secondary bending moments from joint eccentricity: When the working lines of truss members do not intersect at a single point at the joint, an eccentricity moment is introduced. For gusset plate connections, limiting the eccentricity to the Whitmore section width is common practice. For HSS joints, a gap (positive eccentricity) or overlap (negative) in K-joints shifts the moment into the chord, which should be included in the chord interaction check.

Frequently Asked Questions

What is the difference between a Warren truss and a Pratt truss for steel design? A Warren truss uses a series of equilateral or near-equilateral triangles, with diagonal web members alternating in tension and compression. It is materially efficient for symmetric loading because chord forces are nearly uniform along the length. A Pratt truss has vertical posts in compression and diagonal tension members, which works well under gravity loading where diagonals are always in tension (if oriented correctly). Warren trusses use fewer members and joints but require compression design of every diagonal; Pratt trusses have more members and joints but diagonals are designed for tension only, reducing buckling concerns for those elements. For long-span steel trusses (over 80 ft), Pratt trusses with counter-diagonals are often preferred because the tension-only diagonal scheme is lighter.

How do I determine effective length factors for truss compression members? For in-plane buckling of web members, K = 1.0 is standard for pin-connected trusses. For welded trusses with gusset plates, the end restraint provided by the gusset plate and chord can reduce the effective length — K = 0.9 is commonly used for welded web members in the plane of the truss. For out-of-plane buckling, K = 1.0 typically governs unless later bracing is provided at mid-length. For continuous chord members (compression), in-plane K = 0.9 (continuous through joints), out-of-plane K = 1.0 (laterally braced at panel points). Always check the actual restraint condition at each end — a single-bolt connection provides near-zero rotational restraint.

When should I use gusset plate connections versus direct welded hollow section joints? Gusset plate connections are preferred when: (a) member sections are open profiles (angles, channels, W-sections), (b) multiple members frame into a single joint at different angles, (c) site bolting is preferred over site welding, or (d) the truss depth is large enough that gusset plates do not proportionally dominate. Direct welded HSS connections are preferred when: (a) all members are hollow sections (architecturally exposed trusses), (b) shop fabrication and galvanizing are feasible, (c) the truss depth is moderate and chord wall thickness is sufficient to resist face plastification. HSS joints are generally stiffer and cleaner-looking but are more demanding on fabrication tolerance and quality control.

What slenderness limits apply to truss web members in tension? AISC 360 specifies a preferred slenderness limit of L/r <= 300 for tension members, though this is a serviceability recommendation (not a strength limit) to prevent sagging and vibration. For wind bracing and secondary members, L/r up to 300 is acceptable. For primary truss tension members, L/r <= 240 is commonly targeted. AS 4100 recommends L/r <= 300 for rods and 250 for other tension members. EN 1993-1-1 does not specify an explicit slenderness limit for tension members. In practice, slender tension members (L/r > 300) are prone to wind-induced vibration and accidental damage during erection.

Why does the truss joint capacity often control over member capacity? Truss joints concentrate forces from multiple members into a confined region of the chord or gusset plate. For HSS trusses, the chord face is loaded out-of-plane by the brace members, and the chord wall thickness (not the brace section) typically controls joint capacity — this is why strengthening a HSS truss joint often requires increasing the chord wall thickness rather than the brace section. For gusset plate connections, block shear along the bolt lines and buckling of the free gusset edge (Whitmore section) frequently control. The joint is the nexus of all member forces, and the complex triaxial stress state at the joint panel zone means simple member-level checks do not capture the governing mode.

How do I handle a truss with top chord slope (pitched roof truss)? A pitched truss (non-parallel chords) introduces a vertical component to the chord forces at each joint. The method of joints still applies, but the force resolution is more complex because chord members are not horizontal. The key additional checks are: (a) at the ridge joint, the top chord compression force has both horizontal and vertical components that must be resisted by the ridge connection detail, and (b) at the eaves (bearing), the inclined top chord reaction has a horizontal thrust component that must be resisted by the support (tie beam, buttress, or moment-resisting column). For steeply pitched trusses (slope > 30 deg), the horizontal thrust can be significant and must be included in the bearing and foundation design.

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