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.

Typical span ranges for steel trusses

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.
• Fink truss -- a modified Pratt with subdivided panels for longer spans. Common in industrial buildings.
• Bowstring truss -- parabolic top chord with a straight bottom chord. The parabolic shape minimizes web member forces under uniform load.

Truss type comparison

Chord force calculation

The primary chord forces in a parallel-chord truss are determined from the global bending moment:

Top chord compression = M / d
Bottom chord tension  = M / d

Where M = global bending moment at the panel point, d = truss depth (centroid to centroid of chords).

Chord forces for uniform load on simply supported truss

Web member forces (Pratt truss, 6 panels)

Where V = shear force at the panel, theta = angle of diagonal from horizontal.

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. phiPn = 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. phiPn = 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. 2L65x65x6 (Ag = 14.8 cm^2 = 1,480 mm^2) provides ample capacity.

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.

Gusset plate connections

Gusset plates connect truss members at joints. AISC Manual Part 13 provides the design methodology. Key checks:

1. Gusset plate shear and tension at the Whitmore section (effective width through the bolt group)
2. Gusset plate buckling in the compression zone (effective column width)
3. Bolt bearing and tearout on the gusset plate
4. Weld capacity connecting the member to the gusset
5. Block shear at bolt groups

Gusset plate sizing guidelines

Uniform Force Method (AISC Manual Part 13)

For bracing connections to columns/beam, the Uniform Force Method distributes the brace force among the gusset-to-beam, gusset-to-column, and gusset-to-beam web interfaces. The method ensures equilibrium without designing for more than the actual force.

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.

Secondary bending from inter-nodal loading

When a purlin load P is applied between panel points on the top chord, the chord bends locally:

M_secondary = P * a * b / L_panel

Where a and b are the distances from the load to each adjacent panel point. For a centered load (a = b): M = P * L_panel / 4. This must be combined with the chord axial force using AISC interaction equations (Chapter H).

Deflection of trusses

Truss deflection is estimated using the virtual work method or simplified formulas:

delta = sum(F_i * f_i * L_i) / (A_i * E)

Where F_i = member force from real loads, f_i = member force from unit virtual load, L_i = member length, A_i = member area.

Typical deflection limits for trusses

Camber

Trusses are typically cambered to offset dead load deflection. Camber = dead load deflection (plus a small percentage for connection slip, typically 1/16" per connection). Fabricators achieve camber by cutting members slightly short or long.

Multi-code comparison

Truss design approach by code

Truss Types Comparison

Selecting the appropriate truss type depends on span, loading pattern, architectural constraints, and fabrication cost. The following table summarizes the most common configurations for building structures:

Per AISC 360-22, truss members are designed as axial members per Chapters D (tension) and E (compression), with chords also checked for combined axial and bending per Chapter H when panel loads create flexure between nodes.

Span-to-Depth Ratios for Preliminary Sizing

The depth of a steel truss is the single most important parameter for initial sizing. Deeper trusses have smaller chord forces, lighter members, and less deflection, but consume more vertical space:

For floor trusses supporting composite deck, the minimum depth-to-span ratio of L/16 is typical to meet L/360 live load deflection limits without excessive camber.

Typical Member Sizes for Building Trusses

Preliminary member sizes for common building truss configurations. Actual sizes must be verified by detailed analysis per AISC 360-22:

Members with high compression-to-tension ratios (diagonals and verticals in Pratt trusses) are often HSS sections because of their superior buckling resistance per AISC Chapter E (higher rx/ry ratio means less tendency for weak-axis buckling).

Node Design and Connection Types

Truss node design is critical because member forces converge at single points. Per AISC Steel Construction Manual Part 13:

Key AISC 360-22 provisions for node design:

• Gusset plate yield lines: Per AISC Manual Part 13, the Whitmore section (30-degree dispersion from the first and last bolt in the connection) must be checked for yield and rupture.
• Block shear: Per AISC Chapter J4.3, check block shear rupture at all bolted gusset connections.
• Eccentricity: Where member centroids do not converge at a common working point, the resulting moment must be distributed to the gusset plate and connecting elements using the Uniform Force Method (AISC Manual Part 13).
• HSS connections: Per AISC Chapter K, check chord plastification, punching shear, and local yielding at all HSS-to-HSS nodal connections.

Bracing Requirements

Trusses require bracing to prevent lateral-torsional buckling of compression chords and to maintain truss stability during erection:

Per AISC 360-22 Appendix 6, the required bracing strength and stiffness for compression members are:

Required bracing strength:  Prb = 0.008 * Pr (nodal bracing)
Required bracing stiffness: betabr = 2 * Pr / (Lb) (nodal bracing)

Where Pr is the required compressive strength of the braced member and Lb is the distance between brace points. These requirements ensure the bracing is strong and stiff enough to prevent lateral buckling of the compression chord.

Common mistakes

1. 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.

2. 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.

3. Designing all web members for the maximum diagonal force. Web member forces decrease from the support toward mid-span. Size each member individually or group into zones.

4. 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.

5. Forgetting to check gusset plate buckling. Compression diagonal gusset plates must be checked for plate buckling in the compression zone. This is a separate check from bolt and weld capacity.

6. Not providing out-of-plane bracing at bottom chord. The bottom chord is in tension under gravity but compression under wind uplift. Without bottom chord bracing, the entire bottom chord could buckle laterally under uplift.

7. Oversimplifying connection design. The gusset plate is often the most complex part of a truss design. A well-designed member can fail at its connection if the gusset is undersized or the bolt layout is inadequate.

Frequently asked questions

When should I use a truss instead of a beam? For spans over 40 ft, trusses become more economical than deep rolled sections. Beyond 60 ft, trusses are almost always the better choice.

What is the most efficient truss type? For uniform gravity loads, the Pratt truss is most efficient because diagonals are in tension. For equal tension/compression capability (e.g., RHS sections), the Warren truss is preferred for its simpler fabrication.

How much do trusses weigh compared to beams? For the same span and loading, a truss typically weighs 40-60% less than a rolled beam. The savings increase with span length.

Do I need to check all members individually? Yes, each member has unique forces, unbraced lengths, and slenderness ratios. However, grouping members into zones (e.g., end third, middle third) with the heaviest member in each zone is common practice.

What about truss deflection? Trusses are more flexible than beams of equivalent depth. Check deflection early in design and provide camber to offset dead load deflection. For floor trusses, also check vibration.

Can trusses be designed for moment connections? Yes, for special applications (moment frames, Vierendeel trusses). The connections become much heavier and more complex. Standard trusses use pinned connections.

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Related references

• Gusset Plate Design
• Tension Member Design
• Column Buckling Equations
• Truss Analysis
• Structural Systems
• Braced Frame Design
• Connection Types
• Steel Grades
• How to Verify Calculations

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.