Steel Truss Design Guide — Pratt, Howe, Warren Configurations and HSS Chord Design

Complete steel truss design reference covering truss typology (Pratt, Howe, Warren), member force analysis, HSS chord design, joint eccentricity limits, slenderness and buckling checks, and a full worked example for a 30-meter span Pratt roof truss. Based on AISC 360, Eurocode 3, and AS 4100.

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.

Truss Fundamentals and Applications

A truss is a triangulated structural system composed of axially loaded members connected at nodes (joints). Unlike beams, which carry loads through flexure, a truss resolves external loads into purely axial tension and compression forces within its members. This axial-only load path makes trusses extraordinarily efficient — a well-designed truss can span 30 to 100 meters using far less steel than an equivalent rolled beam.

Trusses are used wherever long spans meet the need for light structural depth: roof framing for warehouses, sports arenas, and airport terminals; bridge girders; transfer structures carrying columns above large openings; and temporary works like scaffolding and falsework. The key advantage of a truss is the separation of the compression chord (top) and tension chord (bottom) by a structural depth — typically span/10 to span/15 — enabling the moment couple to develop with minimal material.

Truss Typology: Pratt, Howe, Warren

Three classic truss configurations dominate structural steel design. Each has a distinct internal force pattern and is selected based on span, loading, and depth constraints.

Pratt Truss

The Pratt truss features diagonal members sloping downward toward the centre of the span. Under gravity load, the diagonals are in tension and the verticals are in compression. This arrangement is efficient because tension members are not subject to buckling, allowing the diagonals to be slender (rods, angles, or single HSS sections). The compression verticals are short — limited to the truss depth — which minimises their buckling length and weight.

The Pratt truss is the most common configuration for roof trusses spanning 15 to 60 meters. For a typical Pratt roof truss with 2-meter panel spacing, a 30-meter span requires 15 panels with a truss depth of approximately 2.0 to 2.5 meters (span/12 to span/15). The top chord carries compression, the bottom chord carries tension, and the diagonals alternate between tension (gravity) and compression (uplift), with uplift being the governing case for diagonal member design in light roof structures.

Howe Truss

The Howe truss reverses the diagonal orientation — diagonals slope upward toward the centre. Under gravity load, the diagonals are in compression and the verticals are in tension. This is less efficient than the Pratt configuration for steel because the compression diagonals are longer than the tension verticals, requiring larger sections to resist buckling.

The Howe truss is less common in steel but finds favour in timber construction (where compression joinery is easier than tension connections) and in bridge design where deeper sections are required for the diagonals. In steel, a modified Howe truss with counter-diagonals (X-bracing in the web panels) can create a stiff, redundant system suitable for heavy industrial loads.

Warren Truss

The Warren truss consists entirely of diagonal members forming a series of equilateral or isosceles triangles, with no verticals. Under gravity load, the diagonals alternate between tension and compression. The Warren truss is more efficient than the Pratt for spans under 25 meters because fewer members and joints are required, reducing fabrication cost.

For longer spans, a modified Warren truss with verticals at load points (often called a "Warren truss with verticals" or "subdivided Warren") provides intermediate support to the chords and reduces the unbraced length of compression diagonals. This modification is standard for bridge trusses and long-span roof trusses where the chord panel length would otherwise be excessive.

Member Force Analysis

The analysis of a truss begins with the assumption that all members are pin-connected and that loads are applied only at the joints. This idealisation is remarkably accurate for trusses with HSS or angle members where the joints are sufficiently flexible to approximate pinned behaviour.

Method of Joints: Solve for member forces by applying equilibrium (ΣFx = 0, ΣFy = 0) at each joint. Start at a joint with only two unknown forces. This method is systematic and well suited to hand calculation for trusses with up to about 30 members.

Method of Sections: For trusses with many members where only a few critical member forces are needed, cut the truss with an imaginary section through three members (not all concurrent or parallel) and solve using moment equilibrium about a convenient point. This is the fastest way to determine chord forces at mid-span and diagonal forces in the end panels.

Computer Analysis: For trusses with more than about 20 members, a computer stiffness analysis is standard practice. Most commercial structural analysis packages (SAP2000, ETABS, RISA-3D, SpaceGass, SCIA Engineer) include automated truss modelling with pin-ended members.

For preliminary sizing, the maximum chord forces can be estimated from the truss moment and depth:

• Top chord compression: C_max ≈ M_max / d ≈ (w × L² / 8) / d
• Bottom chord tension: T_max ≈ M_max / d

Where M_max is the maximum bending moment in an equivalent simply supported beam, w is the uniformly distributed load per unit length, L is the span, and d is the truss depth. For a 30 m span Pratt truss with depth d = 2.5 m and w = 15 kN/m: C_max = T_max = (15 × 30² / 8) / 2.5 = 675 kN.

HSS Chord Design

Hollow structural sections (HSS) are the preferred chord sections for modern steel trusses. Their advantages include:

• High radius of gyration for a given weight, maximising compression capacity
• Closed shape with high torsional stiffness, eliminating lateral-torsional buckling concerns
• Flat faces that simplify welded joint detailing
• Excellent architectural appearance for exposed trusses

Compression Chord Design: The top chord of a roof truss is typically an HSS member in compression with intermediate lateral bracing provided by purlins. The design must consider:

1. Cross-sectional strength: P_n = F_y × A_g (yielding) or F_cr × A_g (buckling). For compact HSS sections per AISC Table B4.1a, the full yield strength is available.
2. Flexural buckling: The effective length factor K for in-plane buckling of the chord between panel points is typically 1.0 (pin-ended). Out-of-plane, K depends on the purlin bracing; for continuous top chords with lateral bracing at every purlin (1.5–2.0 m spacing), K_y = 1.0.
3. HSS wall slenderness: Per AISC 360 Table B4.1a, HSS round sections with D/t ≤ 0.11E/F_y and HSS rectangular sections with b/t ≤ 1.12√(E/F_y) (flanges) and h/t ≤ 2.42√(E/F_y) (webs) are classified as compact.

For a typical top chord carrying 675 kN compression over a 2-meter panel length:

• HSS 127 × 127 × 6.4 (HSS 5 × 5 × 1/4): A_g = 2970 mm², r_x = 48.8 mm, KL/r = 1.0 × 2000 / 48.8 = 41.0
• F_e = π²E / (KL/r)² = π² × 200000 / 41.0² = 1174 MPa
• F_cr = 0.658^(F_y/F_e) × F_y = 0.658^(345/1174) × 345 = 316 MPa
• φP_n = 0.9 × 2970 × 316 × 10⁻³ = 845 kN > 675 kN. OK.

Tension Chord Design: The bottom chord is in tension for gravity loads and compression for wind uplift. It must be checked for:

1. Tensile yielding: φP_n = 0.9 × F_y × A_g
2. Tensile rupture: φP_n = 0.75 × F_u × A_e at the net section at connections
3. Compression under uplift: The uplift case often governs bottom chord design in light roof structures

Joint Eccentricity and Connection Design

Truss joints are a point of significant design attention. The ideal truss joint has all member centroidal axes intersecting at a single working point. In practice, this is achieved through gusset plates (for angle members) or direct welded connections (for HSS members).

Eccentricity Limits: Per AISC 360 Section J1.5, joints with eccentricities less than the larger of (a) the chord depth / 10, or (b) 25 mm do not need to be explicitly considered in the member force analysis, provided the members and connections are designed for the resulting moments. For HSS trusses, keeping all member centre lines within the chord wall thickness of the working point eliminates practical eccentricity.

Gap vs Overlap Joints: In welded HSS trusses, the branch members can be connected with a gap (branch-to-branch gap ≥ t_1 + t_2) or with overlap. Gap joints are easier to fabricate and inspect but require the chord face to be checked for plastification, punching shear, and local yielding. Overlap joints are stiffer and stronger but require the overlapping branch to be welded to both the chord and the through branch, increasing fabrication complexity.

Gusset Plate Connections: For angle-member trusses, gusset plates provide the connection medium. The gusset plate must be designed for block shear at the connection to the chord, for buckling under compression member loads (using the Whitmore section or Thornton method), and for the weld capacity to each connected member.

Slenderness and Buckling Checks

Truss members, particularly slender diagonals in compression, are governed by buckling.

Slenderness Ratio Limits: AISC 360 does not impose a strict slenderness limit on compression members, but a KL/r exceeding 200 is discouraged by Section E2. For tension members, the recommended maximum KL/r is 300. Eurocode 3 limits λ_bar (non-dimensional slenderness) to 3.0 (approximately KL/r = 260 for S355 steel).

Effective Length Factors for Truss Members: The effective length factor K depends on the end restraint provided by the joints:

• For in-plane buckling of web members, K is typically taken as 0.9 (partially restrained ends in welded HSS joints or bolted gusset plate connections)
• For out-of-plane buckling, K = 1.0 unless the member is laterally restrained at both ends
• For chord members between panel points, K = 1.0 in-plane and K = 1.0 out-of-plane (unless continuous chord action is considered, which can reduce K to 0.85)

Buckling of Web Members in RHS/Vierendeel Trusses: For RHS web members welded to RHS chords, the joint flexibility reduces the rotational restraint and K should be taken as 0.9 (not 0.65 as sometimes assumed). CIDECT Design Guide 3 provides comprehensive guidance on effective lengths for welded RHS truss connections.

Worked Example: 30 m Span Pratt Roof Truss

Problem Statement: Design a Pratt roof truss for a warehouse with a 30 m span, 7.5 m truss spacing, and 10° roof pitch. Top chord supported by purlins at 2.0 m centres. The truss depth at centre is 2.5 m (span/12). Dead load: 0.4 kPa (cladding + purlins + self-weight). Live load: 0.25 kPa (roof). Wind uplift: -0.6 kPa. Steel: A572 Gr 50 (F_y = 345 MPa). HSS members throughout.

Step 1 — Load determination:

Tributary load per unit plan length (7.5 m spacing):

• Dead load: w_D = 0.4 × 7.5 = 3.0 kN/m
• Live load: w_L = 0.25 × 7.5 = 1.875 kN/m
• Wind uplift: w_W = -0.6 × 7.5 = -4.5 kN/m (upward)

LRFD load combinations:

• LC1: 1.4D = 4.2 kN/m (down)
• LC2: 1.2D + 1.6L = 6.6 kN/m (down)
• LC3: 0.9D + 1.0W = 2.7 - 4.5 = -1.8 kN/m (upward)

Governing: LC2 = 6.6 kN/m (downward, member design) and LC3 = -1.8 kN/m (uplift, tension-only diagonals).

Step 2 — Truss geometry:

Span = 30 m, depth at centre = 2.5 m, panel length = 2.0 m, 15 panels. Number of joints = 16 (top chord) + 16 (bottom chord) = 32 nodes.

Top chord nodes: y-coordinates increase linearly from 0 at eave to 2.5 m at ridge (10° pitch gives 30/2 × tan(10°) = 2.64 m — adjust for 2.5 m design depth).

Step 3 — Determine member forces by method of sections:

Maximum top chord force (at ridge panel): The chord force is maximum at the centre where the truss moment is maximum.

M_max = w_u × L² / 8 = 6.6 × 30² / 8 = 742.5 kNm. C_max = M_max / d_centre = 742.5 / 2.5 = 297 kN. T_max = 297 kN (bottom chord at centre).

End diagonal force (panel 1): The shear at the support is V = w_u × L / 2 = 6.6 × 30 / 2 = 99 kN. The end diagonal carries this shear: F_diag = V / sin(θ), where θ is the angle between the diagonal and horizontal.

At the first panel, the truss depth at the first interior bottom chord node is approximately 1.67 m (linear interpolation from 0 at support to 2.5 m at centre over 7 panels). The diagonal angle: tan(θ) = 1.67 / 2.0, θ = 39.8°. F_diag = 99 / sin(39.8°) = 154.5 kN (tension in Pratt, gravity).

Step 4 — Design top chord:

Maximum compression = 297 kN. Try HSS 102 × 102 × 6.4 (HSS 4 × 4 × 1/4).

• A_g = 2340 mm², r_min = 38.4 mm
• KL/r = 1.0 × 2000 / 38.4 = 52.1
• F_e = π² × 200000 / 52.1² = 727 MPa
• F_cr = 0.658^(345/727) × 345 = 275 MPa
• φP_n = 0.9 × 2340 × 275 × 10⁻³ = 579 kN > 297 kN. Ratio = 0.51. OK.

Check the top chord under uplift (LC3: w = -1.8 kN/m, M = 202.5 kNm): C_max_uplift = 202.5 / 2.5 = 81 kN. The member is in compression under uplift — still within capacity. The bottom chord, however, is now in compression and must be checked.

Step 5 — Design bottom chord:

Under gravity (LC2): T_max = 297 kN (tension).

• Tensile yielding: φP_n = 0.9 × 345 × 2340 × 10⁻³ = 726 kN > 297 kN.
• Check net section at connection: Assume a gusset plate connection with two bolt holes in the cross-section. A_n = 2340 - 2 × (22 + 2) × 6.4 = 2340 - 307 = 2033 mm². φP_n = 0.75 × 450 × 2033 × 10⁻³ = 686 kN > 297 kN. OK.

Under uplift (LC3): T_max_uplift = 81 kN (compression in bottom chord). The bottom chord must now be checked for compression:

• KL/r = 2000 / 38.4 = 52.1, φP_n = 579 kN > 81 kN. OK.

Step 6 — Design diagonal members:

Panel 1 diagonal (LC2): F_t = 154.5 kN (tension). Use HSS 51 × 51 × 4.8 (HSS 2 × 2 × 3/16).

• A_g = 796 mm²
• Tensile yielding: φP_n = 0.9 × 345 × 796 × 10⁻³ = 247 kN > 154.5 kN. OK.
• KL/r = 0.9 × 2600 / 18.6 = 126 (connect length ≈ √(2.0² + 1.67²) = 2.60 m)

The same diagonal under uplift (LC3) will be in compression (Pratt diagonals reverse under uplift). Check compression:

• KL/r = 126, F_e = π² × 200000 / 126² = 124.5 MPa
• F_cr = 0.658^(345/124.5) × 345 = 90.2 MPa
• φP_n = 0.9 × 796 × 90.2 × 10⁻³ = 64.6 kN

The uplift force in this diagonal: The end shear under LC3 is V_uplift = -1.8 × 30 / 2 = -27 kN. The end diagonal must carry F_uplift = 27 / sin(39.8°) = 42.2 kN (compression). φP_n = 64.6 kN > 42.2 kN. OK.

Step 7 — Deflection check:

Service load: w_service = 3.0 + 1.875 = 4.875 kN/m. The truss deflection can be approximated as: Δ_max ≈ 5 × w × L⁴ / (384 × E × I_equivalent)

Where I_equivalent for a parallel-chord truss is approximately A_chord × (d/2)² × 2 = 2340 × (2500/2)² × 2 = 7.31 × 10⁹ mm⁴.

Δ ≈ 5 × 4.875 × 30000⁴ / (384 × 200000 × 7.31 × 10⁹) = 35.4 mm.

Deflection limit for roof with no brittle finishes: L/240 = 30000/240 = 125 mm. OK.

Design Summary: HSS 102 × 102 × 6.4 for top and bottom chords, HSS 51 × 51 × 4.8 for diagonals. The Pratt configuration is efficient for gravity loads; uplift governs the end diagonal design (compression) but HSS 2 × 2 × 3/16 is adequate. All members satisfy AISC 360 requirements.

Engineering Best Practices

• Camber the bottom chord upward by an amount equal to the dead load deflection plus 50% of the live load deflection to achieve a level appearance under service conditions.
• For HSS trusses, specify the working point at the intersection of member centrelines. Maintain a minimum gap of (t_1 + t_2) between branch members at the joint to allow weld access.
• Provide lateral bracing to the top chord at every purlin line. If purlins are at 2.0 m centres, the unbraced length of the top chord is 2.0 m. For bottom chords in uplift, lateral bracing or fly braces must be provided.
• For angle-member trusses, stagger the gusset plates on opposite sides of the chord to avoid double-eccentricity that induces weak-axis bending.
• Always check the truss under the erection condition (self-weight only, before purlins and cladding) to ensure the bottom chord compression during lifting does not cause buckling.
• For trusses spanning more than 40 m, break the truss into transportable segments (typically 12–15 m) with bolted site splices at panel points. Design the splice for full member capacity.

FAQ

Q: Which truss configuration is best for a given span? A: For spans under 25 m with uniform roof loading, a Warren truss is the most economical (fewer members and joints). For spans 25–60 m, a Pratt truss is preferred — the tension diagonals allow slender sections, and the short compression verticals minimise weight. For spans over 60 m, consider a modified Warren with verticals, a K-truss, or a double-pitched Pratt with subdivided panels.

Q: How do I handle wind uplift in truss design? A: Wind uplift reverses the force pattern in the truss — tension members go into compression and vice versa. The uplift combination (0.9D + 1.0W) is always checked. Pratt truss diagonals that are in tension under gravity become compression members under uplift and may require larger sections than the gravity case. Tension-only diagonal systems (single rods with turnbuckles) should be avoided in high-wind regions unless counter-diagonals are provided.

Q: What is the optimal truss depth? A: The optimal structural depth for a parallel-chord roof truss is span/10 to span/15. Deeper trusses produce lower chord forces but increase diagonal lengths and cladding area. The economic optimum balances steel weight against increased building envelope cost and is typically span/12 for utilitarian structures and span/15 for architecturally driven projects. For pitched roof trusses, the average depth is approximately 0.7 × the ridge depth for force estimation purposes.

Q: Can I use bolted connections instead of welding for HSS trusses? A: Bolted HSS connections are possible but less common than welded joints due to the difficulty of accessing the inside of the tube for nut installation. Solutions include through-bolts with backing plates, blind bolts (Lindapter, Hollo-Bolt), or shop-welded end plates that are bolted in the field. Flattened HSS ends with a single pin connection (fork-end detail) are common in architectural trusses and allow all-bolted site assembly.

References

• AISC 360-22 — Specification for Structural Steel Buildings, Chapter E (Compression) and D (Tension)
• AISC Steel Construction Manual, 16th Edition — Part 9 (Truss Connections)
• CIDECT Design Guide 3 — Design of Welded RHS Joints Under Predominantly Static Loading
• Steel Construction Institute P374 — Design of Steel Trusses
• ASCE/SEI 7-22 — Minimum Design Loads for Buildings
• AS 4100:2020 — Steel Structures, Section 6 (Members in Tension) and Section 7 (Members in Compression)

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