Steel Roof Truss Design — Fink, Howe, Pratt, Warren Trusses

Steel roof trusses provide efficient long-span roof structures for industrial, commercial, and recreational buildings. This guide covers truss design, analysis, and detailing.

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Core calculations run via WebAssembly in your browser with step-by-step derivations across AISC 360, AS 4100, EN 1993, and CSA S16 design codes. Results are preliminary and must be verified by a licensed engineer.

Frequently Asked Questions

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.

What are the common steel roof truss types? Common truss types: (1) Fink truss — most common for residential and light commercial, subdivided panels, efficient for spans up to 80 ft (24 m), (2) Howe truss — diagonals in tension, verticals in compression, good for shorter spans, (3) Pratt truss — diagonals in compression, verticals in tension, widely used for medium spans 60-120 ft (18-36 m), (4) Warren truss — equilateral triangles, no verticals, efficient for uniform loading, (5) Bowstring truss — curved top chord, efficient for long spans up to 200 ft (60 m), (6) Scissors truss — for buildings requiring a vaulted ceiling.

How are steel truss members designed? Per AISC 360 Chapters D-J: (1) Top chord — compression member with unbraced length between panel points, designed per Chapter E (flexural buckling), (2) Bottom chord — tension member per Chapter D (yield + rupture), (3) Diagonals and verticals — designed for either tension or compression based on truss type, (4) Slenderness — KL/r ≤ 200 for compression, L/r ≤ 300 for tension (AISC D1/E1), (5) Joint eccentricity — connections should be concentric within 1/4 inch (6 mm) per AISC J1.6. Truss depth-to-span ratio: typically 1/8 to 1/12.

How are truss deflections checked? Truss deflection: (1) Live load deflection — typically L/360 for roofs (similar to beams), (2) Camber — provided for spans > 60 ft (18 m), typically 1/2 to 3/4 of the calculated dead load deflection, (3) Second-order effects — P-Δ analysis required for compression chords if axial loads cause significant additional moments, (4) Thermal effects — for long-span trusses (> 120 ft / 36 m), expansion/contraction must be accommodated at one end through slotted connections or PTFE bearings, (5) Vibration — natural frequency > 3 Hz to avoid perceptible motion.

How are truss connections designed at panel points? Truss connections at panel points are among the most detailed design aspects, as multiple members converge at each joint. Per AISC 360 Chapter J and AWS D1.1: (1) Gusset plate design — the plate thickness is determined by the force in the critical member and the Whitmore section yield check. For a typical roof truss with 2L6×6×3/8 angles for chords and diagonal forces of 120 kips, a 3/8 inch gusset plate (A36) is typical. (2) Bolt design at panel points — for a diagonal delivering 80 kips at the connection: 6 bolts (3/4 inch A325-N, φRn = 15.9 kips/bolt, 2 rows × 3 columns): capacity = 6 × 15.9 = 95.4 kips > 80 kips — OK. (3) Weld design for welded trusses — fillet weld between diagonal and gusset: required weld size for 80 kips with 12 inches of weld on each side: D = 80,000/(1.392 × 24) = 2,394 → use 1/4 inch fillet weld (E70XX). (4) Block shear check on gusset plate at the connection: for the Whitmore section, φRn_per AISC J4.3 = 0.75 × (0.6FuAnv + UbsFuAnt). With plate thickness 3/8 inch, Anv = 4.5 in², Ant = 1.2 in²: φRn = 0.75 × (0.6 × 58 × 4.5 + 1.0 × 58 × 1.2) = 170 kips > 80 kips — OK.

Truss Analysis Methods and Worked Example

Accurate determination of member forces is essential for economical truss design. Several analysis methods are available, from hand calculations to sophisticated FEA.

Method of joints — worked example. Consider a simple Pratt roof truss with 80 ft span, 10 ft depth, 8 panels at 10 ft each, 4:12 roof slope. Panel point loads (DL+LL) = 25 kips at each top chord panel point. Dead load from truss self-weight estimated at 8 psf × 20 ft tributary width = 0.16 kips/ft, plus roofing at 5 psf = 0.10 kips/ft. Total uniform load = 0.26 kips/ft on the top chord converted to panel point loads of 2.6 kips per panel. Live load (snow) at 30 psf ground snow load: 0.9 × 30 × 20 = 0.54 kips/ft → 5.4 kips per panel point. Combined panel point load (1.2D + 1.6S): Pu = 1.2(2.6) + 1.6(5.4) = 11.76 kips per panel point.

(1) Reactions: R = 8 × 11.76/2 = 47.0 kips at each support. (2) Top chord force at panel point 1 (nearest support): from vertical equilibrium at the heel joint: the force in the top chord T = R/sinθ, where θ = roof slope angle = atan(4/12) = 18.4°. T = 47.0/sin(18.4°) = 149 kips compression. (3) Bottom chord at first panel: H = T × cosθ = 149 × cos(18.4°) = 141 kips tension. (4) Web member (first diagonal): from equilibrium at the first interior panel point, the diagonal force D = (47.0 - 11.76)/sin(θ_d), where θ_d = atan(10/10) = 45°, D = 35.24/0.707 = 49.8 kips compression (or tension, depending on truss configuration — in a Pratt truss, diagonals are in tension for gravity loading).

Design of members from analysis. (1) Top chord (149 kips compression, 10 ft panel length): try 2L4×4×3/8 (Ag = 2.86 in² per angle × 2 = 5.72 in², rx = 1.22 in, ry = 1.81 in). KL/r = 1.0 × 120/1.22 = 98.4 ≤ 200 — OK. Fe = π² × 29,000/98.4² = 29.6 ksi. Fcr = 0.658^(50/29.6) × 50 = 0.447 × 50 = 22.4 ksi. φcPn = 0.9 × 22.4 × 5.72 = 115 kips < 149 kips — insufficient. Try 2L5×5×1/2 (Ag = 4.75 in² × 2 = 9.5 in², rx = 1.53 in). KL/r = 120/1.53 = 78.4. Fe = 46.6 ksi. Fcr = 0.658^(50/46.6) × 50 = 0.649 × 50 = 32.5 ksi. φcPn = 0.9 × 32.5 × 9.5 = 277 kips > 149 kips — OK. (2) Bottom chord (141 kips tension): try 2L3×3×3/8 (Ag = 2.86 in² × 2 = 5.72 in²). Check yielding: φtPn = 0.9 × 50 × 5.72 = 257 kips > 141 kips — OK. Check rupture: An = 5.72 - 2 × 1.0 × 0.375 = 4.97 in² (assume 2 hole deductions). Ae = 4.97 × 0.85 = 4.22 in² (U = 0.85 for 2 angles). φtPn = 0.75 × 65 × 4.22 = 206 kips > 141 kips — OK. (3) First diagonal (49.8 kips compression): try 2L3×3×1/4 (Ag = 1.44 in² × 2 = 2.88 in²). L = 14.1 ft. rx = 0.93 in, ry = 1.36 in. KL/r = 1.0 × 14.1 × 12/0.93 = 182 > 200 — exceeds slenderness limit. Try 2L4×4×5/16 (Ag = 2.40 in² × 2 = 4.80 in², rx = 1.22 in). KL/r = 169/1.22 = 139 ≤ 200 — OK. Fe = 14.8 ksi. Fcr = 11.1 ksi. φcPn = 0.9 × 11.1 × 4.80 = 48.0 kips < 49.8 kips — marginally insufficient. Use 2L4×4×3/8 (Ag = 5.72 in²): φcPn = 54.8 kips > 49.8 kips — OK.

Purlins and sag rods. Purlins span between trusses at 5 ft spacing. For an 80 ft building with trusses at 20 ft spacing: (1) Purlin span = 20 ft. Loads: dead = 5 psf roofing + 2 psf purlin = 7 psf × 5 ft tributary = 35 lb/ft. Snow = 30 psf × 5 ft = 150 lb/ft. Combined w_u = 1.2(35) + 1.6(150) = 282 lb/ft. (2) M_u = 0.282 × 20²/8 = 14.1 kip-ft. A C8×11.5 purlin (Zx = 10.3 in³): φbMn = 0.9 × 50 × 10.3/12 = 38.6 kip-ft > 14.1 kip-ft — OK. (3) Sag rods at midspan: 5/8 inch diameter rods at the quarter points of the span, designed for 2% of the purlin reaction.

Lateral bracing of truss compression chord. Per AISC 360 Chapter E and Appendix 6: (1) The top chord (compression) must be braced at intervals not exceeding the calculated unbraced length. In this example, the purlins brace the top chord at each panel point (10 ft spacing) if the truss is restrained laterally at the supports. (2) The bracing force per AISC Appendix 6: P_br = 0.01 × P_u = 0.01 × 149 = 1.49 kips per panel point. (3) The roof diaphragm (metal deck) typically provides sufficient lateral bracing for the purlins, which in turn brace the truss top chord.

Deflection check. For the 80 ft Pratt truss: (1) Live load deflection can be estimated as Δ = (5wL⁴)/(384EI_equivalent). For a truss, an equivalent moment of inertia I_eq = A_chord × d²/2, where A_chord = 9.5 in² (top chord area), d = 10 ft = 120 in (truss depth). I_eq = 9.5 × 120²/2 = 68,400 in⁴. (2) Δ_L = (5 × 0.3 × 960⁴)/(384 × 29,000,000 × 68,400) = 1.93 inches. L/360 = 960/360 = 2.67 inches > 1.93 inches — OK. (3) Camber recommendation: 50% of DL deflection = 0.5 × (5 × 0.13 × 960⁴)/(384 × 29,000,000 × 68,400) = 0.42 inches — provide 1/2 inch camber.

Use the beam capacity calculator to verify purlin sections and the bolted connections calculator for gusset plate connection design.

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Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice. All results must be independently verified by a licensed Professional Engineer.