Steel Truss Bridge Design — Warren, Pratt, Howe, Parker Trusses
Steel truss bridges are among the most efficient long-span bridge structures. This guide covers design of through truss, deck truss, and pony truss bridges.
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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
What are the main types of steel truss bridges? Three configurations: (1) Deck truss — truss below the deck, traffic rides on top, common for longer spans, (2) Through truss — truss above the deck, traffic passes through the truss, limited to shorter spans due to lateral clearance, (3) Pony truss — through truss without top lateral bracing, limited span due to lack of top chord bracing. Common truss patterns: Pratt (verticals in tension, diagonals in compression), Warren (continuous triangles), Parker (curved top chord), Howe (verticals in compression). Truss depth-to-span ratio: typically 1/6 to 1/10.
How are truss gusset plates designed? Per AASHTO LRFD Section 6.14 and FHWA/TA/92-019: (1) Gusset plates must be checked for: yielding on Whitmore section (30° load dispersion angle), block shear rupture, and buckling of the unsupported edge, (2) Whitmore section width = 2×gusset_plate_thickness × tan(30°) + connection_length, (3) Gusset plate thickness minimum 1/2 inch (12 mm), typically 5/8-3/4 inch (16-19 mm) for highway bridges, (4) Buckling check per Section 6.14.2.8 — factored compressive stress ≤ φcFcr, (5) Fatigue — detail Category E for gusset plate edges per AASHTO Table 6.6.1.2.3-1.
How are truss bridge bearings designed? Per AASHTO LRFD Section 14: (1) Fixed bearings — transfer horizontal forces (braking, wind, seismic) through shear keys or anchor bolts, designed for factored horizontal force, (2) Expansion bearings — allow longitudinal movement through PTFE/stainless steel sliding surface or roller nests, movement capacity = thermal + creep + shrinkage, (3) Rocker bearings — pinned connection for rotation, base plate for vertical load distribution, (4) Design loads — vertical reaction + horizontal force + rotation, (5) Fatigue — bearing components designed for 75-year fatigue life per AASHTO Table 6.6.1.2.3-3, (6) Horizontal force at fixed bearings: typically 5-15% of dead load reaction.
How are steel truss bridge members designed for tension and compression? Truss member design follows the fundamental axial member provisions of AASHTO LRFD Section 6. The following worked example illustrates a typical design for a 200 ft span Warren through truss.
Truss configuration. A Warren truss with 200 ft span, 25 ft depth (depth/span = 1/8), 10 panels at 20 ft each. Panel point loads from dead load (12 kips) and live load (40 kips HL-93 loading per AASHTO LRFD Table 3.6.1.2-1): Pu = 1.25(12) + 1.75(40) = 85 kips per panel point (top chord), 70 kips per panel point (bottom chord).
Top chord design (compression). The maximum compression is in the top chord at the center panel. From the truss analysis: Pu = 1,020 kips compression, L = 20 ft (panel length). (1) Try a built-up box section: two MC18×42.7 channels laced together. Ag = 2 × 12.6 = 25.2 in². Ix = 2 × 554 = 1,108 in⁴. Iy = 2 × (12.6 × (9 - 0.87)² + 422) = 2,520 in⁴. rx = √(1,108/25.2) = 6.63 in, ry = √(2,520/25.2) = 10.0 in. (2) KL/r = 1.0 × 20 × 12/6.63 = 36.2 (governed by x-axis). (3) Per AASHTO 6.9.4: Fe = π²E/(KL/r)² = π² × 29,000/36.2² = 218 ksi. For Fy = 50 ksi: λ = (Fy/Fe)^0.5 = (50/218)^0.5 = 0.479. (4) Per AASHTO 6.9.4.1: for λ ≤ 2.25, Fcr = 0.658^(λ²) × Fy = 0.658^(0.229) × 50 = 0.877 × 50 = 43.9 ksi. (5) φcPn = 0.9 × 43.9 × 25.2 = 995 kips < 1,020 kips — increase section. Try MC20×45 (Ag = 2 × 13.2 = 26.4 in², Ix = 2 × 688 = 1,376 in⁴, rx = 7.22 in). KL/r = 240/7.22 = 33.2. Fe = 260 ksi. Fcr = 0.658^(50/260) × 50 = 44.6 ksi. φcPn = 0.9 × 44.6 × 26.4 = 1,060 kips > 1,020 kips — OK. (6) Check lacing per AASHTO 6.8.8: lacing must resist 2.5% of the axial force = 0.025 × 1,020 = 25.5 kips each side.
Bottom chord design (tension). Maximum tension in the bottom chord at center: Pu = 960 kips tension. (1) Try four L6×6×1 angles (Ag = 4 × 5.77 = 23.1 in²). (2) Check yielding: φtPn = 0.95 × 50 × 23.1 = 1,097 kips > 960 kips — OK. (3) Check rupture: effective net area Ae = U × An. U = 0.85 for four angles with bolted connections at 4 inch gage. Net area = 23.1 - 4 × (1.0 × 0.5) = 21.1 in² (removing 4 bolt holes of 7/8 inch diameter at 1/8 oversize). Ae = 0.85 × 21.1 = 17.9 in². φtPn_rupture = 0.80 × 65 × 17.9 = 931 kips < 960 kips — increase section. Try L6×6×1-1/8 (Ag = 4 × 6.56 = 26.2 in², net = 26.2 - 4 × 1.0 × 0.5 = 24.2 in², Ae = 0.85 × 24.2 = 20.6 in²). φtPn_rupture = 0.80 × 65 × 20.6 = 1,070 kips > 960 kips — OK.
Diagonal member design. For the end diagonal (maximum force in diagonals): Pu = 410 kips compression (from truck live load at the end panel), L = √(20² + 25²) = 32.0 ft. (1) Try WT8×28.5 (A = 8.37 in², rx = 2.49 in, ry = 2.03 in). KL/r = 1.0 × 32 × 12/2.03 = 189. (2) AASHTO slenderness limit for compression members in trusses: KL/r ≤ 140 per Section 6.9.3 — exceeds limit. (3) Try WT10×45 (A = 13.2 in², rx = 2.67 in, ry = 2.32 in). KL/r = 384/2.32 = 165 — still exceeds 140. (4) Use double-angle section 2L6×6×5/8 (A = 2 × 7.11 = 14.22 in², rx = 1.86 in, ry = 2.72 in). KL/r = 384/1.86 = 207 — exceeds 140. (5) Conclusion: the diagonal is too slender for compression. In a Warren truss with long diagonals (32 ft), the diagonals act primarily in tension. Re-design as a tension-only member: Pu = 310 kips tension. Check yielding: 0.95 × 50 × 14.22 = 675 kips > 310 kips. Check rupture with 2 bolt holes per angle (7/8 inch bolts): An = 14.22 - 4 × 1.0 × 0.625 = 11.72 in². Ae = 0.80 × 11.72 = 9.38 in². φtPn = 0.80 × 65 × 9.38 = 488 kips > 310 kips — OK.
Bridge truss erection methods. The method of erecting a steel truss bridge significantly affects member stresses during construction. Per AASHTO LRFD Section 2.5 and AASHTO/NSBA G13.1: (1) Cantilever erection — the truss is built out from each abutment/pier by adding members progressively. During construction, the partially completed truss experiences stresses that may exceed final service stresses by 15-30%. (2) Temporary stay cables — for spans exceeding 300 ft, temporary stay cables from the pier mast support the cantilever during erection. A 400 ft span may require 4 stay cables per cantilever arm, each with 300-500 kips of temporary pretension. (3) Lift-in-place — for spans under 200 ft, the truss can be fully assembled on the ground and lifted into position by multiple cranes. For a 180 ft truss weighing 120 tons: four cranes at 30 tons each (with 1.25 dynamic factor = 37.5 tons capacity required per crane). (4) Incremental launching — the truss is assembled behind one abutment and launched across the span. The launching nose (a lightweight truss 60% of the span length) guides the main truss onto the far pier. Friction between the steel and PTFE launch bearings: μ = 0.05-0.08, requiring jacks with 150-300 ton capacity for a 500 ft truss.
Fatigue design of truss connections. Per AASHTO LRFD Table 6.6.1.2.3-2: (1) Bolted connections in tension members — Category B, constant amplitude threshold (CAFT) = 16 ksi. (2) For 75-year design life with 2×10⁶ cycles of HL-93 loading: the allowable stress range for Category B at N = 2×10⁶: ΔF_TH = (A/N)^(1/3) = (120×10⁸/2×10⁶)^(1/3) = 18.2 ksi, but capped at CAFT = 16 ksi. (3) The stress range in the bottom chord at the splice: Δσ = (M_LL+I × c)/I — for the HL-93 truck at midspan, Δσ ≈ 8-12 ksi at the splice location, below the 16 ksi CAFT. (4) Gusset plate design at the panel point: the Whitmore section check per FHWA/TA/92-019. At the connection of the diagonal (310 kips) to the gusset plate: Whitmore width = 2 × 0.625 × tan(30°) + 9 = 9.72 inches. Section area = 9.72 × 0.625 = 6.08 in². Stress = 310/(2 × 6.08) = 25.5 ksi (two gusset plates). φFy = 0.95 × 50 = 47.5 ksi > 25.5 ksi — OK.
Use the beam capacity calculator for floorbeam and stringer design within the truss panel, and refer to 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.