Steel Truss Design — Member Sizing, Connections & Slenderness

Steel truss design: Pratt vs Warren configurations, chord and web member sizing, KL/r limits, gusset plate connections, secondary bending effects, and deflection control.

Truss fundamentals

A truss is an assembly of straight members connected at joints (nodes) to form a stable triangulated framework. Applied loads at the nodes produce only axial forces in the members (tension or compression) when the joints are idealized as pins. In reality, gusset plate connections provide partial fixity that generates secondary bending moments, but the primary load path remains axial.

Trusses are used for roof structures (spans 15-60 m), transfer girders, pedestrian bridges, and long-span floor systems. The main advantage over rolled beams is that trusses achieve very high span-to-depth ratios — typically span/10 to span/15 — using relatively light members.

Common truss types

• Pratt truss — verticals in compression, diagonals in tension. Efficient because the longer diagonal members carry tension (no buckling concern) and the shorter verticals carry compression. Standard for roof trusses with gravity load.
• Warren truss — no verticals; diagonals alternate between tension and compression. Fewer members than Pratt, so less fabrication cost. Under non-uniform loading, some diagonals reverse, so all diagonals must be designed for both tension and compression.
• Howe truss — diagonals in compression, verticals in tension. Less efficient than Pratt for gravity load because the long diagonal members must resist buckling. Sometimes used where uplift (reversal) governs.
• Vierendeel truss — rectangular panels with no diagonals. Moment-resisting joints carry the shear through frame action. Very heavy but provides unobstructed openings for ductwork. Members must resist significant bending.

Worked example — Pratt roof truss

Span = 24 m, depth = 2.4 m (span/10), 6 panels at 4 m each. Factored uniform load on top chord = 8 kN/m (from purlins at 2 m spacing). Steel grade: A992 (Fy = 345 MPa).

Total factored load W = 8 x 24 = 192 kN. Reactions = 96 kN each.

Maximum chord force (at mid-span): M_max = wL^2/8 = 8 x 24^2 / 8 = 576 kN-m. Chord force = M / depth = 576 / 2.4 = 240 kN. Top chord in compression, bottom chord in tension.

Top chord design (compression): unbraced length between panel points = 4.0 m. Out-of-plane bracing from purlins at 2.0 m, so Lx = 4.0 m (in-plane), Ly = 2.0 m (out-of-plane). Using 2L75x75x6 back-to-back (A = 17.4 cm^2, rx = 2.28 cm, ry = 3.52 cm with 10 mm gap).

KLx/rx = 4000/22.8 = 175. KLy/ry = 2000/35.2 = 57. In-plane slenderness governs. Fe = pi^2 x 200,000 / 175^2 = 64.4 MPa. Since Fe < 0.44Fy, Fcr = 0.877 x 64.4 = 56.5 MPa. phi*Pn = 0.9 x 56.5 x 1740 / 1000 = 88.5 kN. Insufficient for 240 kN.

Increase to 2L100x100x8 (A = 30.8 cm^2, rx = 3.04 cm): KLx/rx = 4000/30.4 = 132. Fe = pi^2 x 200,000 / 132^2 = 113 MPa. Fcr = 0.658^(345/113) x 345 = 97.5 MPa. phi*Pn = 0.9 x 97.5 x 3080 / 1000 = 270 kN > 240 kN. OK.

Bottom chord design (tension): Pu = 240 kN. Required Ag = 240,000 / (0.9 x 345) = 773 mm^2. Net section at gusset bolt holes also checked. 2L65x65x6 (Ag = 14.8 cm^2 = 1,480 mm^2) provides ample capacity with 50 percent utilization.

Maximum diagonal force (end panel): V = 96 kN (shear at support). Diagonal length = sqrt(4^2 + 2.4^2) = 4.66 m. Diagonal force = 96 x 4.66 / 2.4 = 186 kN (tension in Pratt truss).

Slenderness limits by code

AISC 360 Section E2 provides the compression capacity equation. AS 4100 Clause 6.3.3 uses the column curve approach with alpha_b based on section type. EN 1993 uses buckling curves a through d. CSA S16 Clause 13.3 mirrors the AISC approach.

Secondary bending

In practice, truss members are connected by gusset plates that provide partial moment fixity, not true pins. This generates secondary bending moments in the members, particularly:

• At loaded chords between panel points (local bending from purlin loads applied between nodes).
• At connections where member centroids do not intersect at a single working point (eccentricity).
• In Vierendeel panels where all shear is carried by member bending.

AISC Steel Construction Manual Part 14 recommends accounting for secondary bending when the ratio of secondary moment to member capacity exceeds 0.10. For most Pratt and Warren trusses with loads applied at panel points, secondary effects add 5-10 percent to member demand.

Common pitfalls

• Using single-plane effective length for out-of-plane buckling. If purlins brace the top chord out-of-plane but not in-plane, the in-plane unbraced length equals the full panel length while out-of-plane unbraced length equals the purlin spacing. Always check both axes.
• Neglecting eccentricity at gusset plates. If member centroids do not converge at a common working point, the gusset plate eccentricity creates a moment that the connection must resist. The Uniform Force Method in AISC Manual Part 13 handles this.
• Designing all web members for the maximum diagonal force. Web member forces decrease from the support toward mid-span. Using the same heavy section throughout wastes material. Size each member individually or group into zones (end third, middle third).
• Ignoring uplift reversal in Warren trusses. Under wind uplift, Warren diagonal forces reverse. A diagonal sized for gravity-only tension may buckle under uplift compression if its slenderness ratio is too high.

Run this calculation

• Section Properties Database
• Beam Calculator

Related references

• Gusset Plate Design
• Tension Member Design
• Column Buckling
• Steel Lattice Column
• How to Verify Calculations
• steel beam capacity calculator

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.