Free Steel Truss Design Calculator -- AISC 360

Q: What is the most efficient truss configuration for long-span roofs?

The Warren truss (alternating diagonals, no verticals) is most efficient for spans up to 100 feet. For longer spans (100-200+ feet), the Pratt truss with diagonals sloping toward center is preferred since longer Warren compression diagonals become inefficient.

Q: What slenderness limits apply to truss members?

AISC 360 limits tension members to L/r less than 300 under stress reversal, and compression members to L/r less than 200. Effective length (KL) for in-plane buckling is typically 0.5 to 1.0 times member length depending on end conditions.

Q: How are truss connections designed at panel points?

Truss connections use gusset plates at panel points. The gusset plate is checked for Whitmore section yielding, block shear, and buckling. Welded connections are typical for shop fabrication; bolted connections for field splices.

Q: What is the difference between top chord and bottom chord design?

The top chord is typically in compression, governed by buckling. The bottom chord is in tension, governed by net section rupture at bolt holes. Panel point eccentricity must be considered for both chords.

Design steel trusses for roof and floor framing -- Pratt, Warren, Howe, Fink, and custom configurations. The calculator determines member axial forces using method of joints, checks tension and compression members against all applicable limit states, verifies slenderness limits, and designs welded or bolted connections at panel points per AISC 360-22 Chapters D, E, and J, AS 4100 Section 8, EN 1993-1-1 Section 6.2-6.3 and EN 1993-1-8, and CSA S16 Sections 13 and 14.

Steel trusses are triangulated structural frameworks in which all members are assumed to carry only axial force (tension or compression), with moments from joint rigidity treated as secondary effects. The triangulation ensures geometric stability; a quadrilateral panel would form a mechanism. Trusses provide an efficient use of material for long spans, since the axial load path uses the full cross-section uniformly compared to flexural members where only the extreme fibers reach yield.

Truss configurations supported:

Pratt truss: Diagonals slope downward toward the center, carrying tension in the outer panels (longer diagonals) and compression in the inner panels. Verticals carry compression. Most efficient under gravity loading since the longer members near midspan are in tension, avoiding buckling.
Warren truss: Alternating diagonals form equilateral triangles with no verticals. Under gravity load, diagonals alternate between tension and compression. Most efficient member count, but longer compression diagonals at midspan may be governed by buckling.
Howe truss: Diagonals slope downward away from the center, carrying compression in the outer panels. Verticals carry tension. Preferred when compression members are not a concern (e.g., short spans or heavy timber construction historically).
Fink truss: A fan configuration with sub-diagonals for very long spans (100-200+ ft), dividing the panel points into smaller intervals.
Custom: Arbitrary joint coordinates define member connectivity for irregular roof profiles, transfer trusses, crane girders, or Vierendeel panels.

What this calculator does not cover: truss camber and fabrication tolerances (per AISC Code of Standard Practice), truss erection stability (temporary bracing), connection flexibility effects on member forces (secondary moments), and fire-rating requirements for exposed trusses.

How to Use This Calculator

Step 1 -- Select truss configuration. Choose from Pratt, Warren, Howe, Fink, or custom geometry. For standard configurations, enter the span, depth, and number of panels. The span-to-depth ratio typically ranges from 8 to 15 for roof trusses and 10 to 18 for floor trusses. Deeper trusses reduce chord forces but increase web member lengths and are more susceptible to lateral-torsional buckling of the compression chord between panel points.

Step 2 -- Enter loads at panel points. For roof trusses, loads are typically applied at top chord panel points from purlins at 4-6 ft spacing. Input dead load (roofing, purlins, truss self-weight), live load or snow load per ASCE 7-22, wind uplift (net suction per Components and Cladding, typically 15-40 psf upward), and seismic lateral loads if the truss is part of the lateral system. Load combinations per ASCE 7-22 Section 2.4 (ASD) or 2.3 (LRFD) are automatically generated.

Step 3 -- Analyze member forces. The calculator performs a method of joints analysis solving equilibrium at each joint. For statically indeterminate trusses (redundant members or Vierendeel panels), a stiffness matrix method is used. The output shows each member's axial force (tension positive, compression negative) for each load combination.

Step 4 -- Select member sections. For each member, select the section type: double-angle (most common, good for bolted gusset plate connections), HSS round or square (efficient for compression, higher cost), WT section (single-sided connection, good for tension), or wide-flange (heavy trusses). Enter grade: A36 (Fy=36 ksi), A572 Gr 50 (Fy=50 ksi), or A992 (Fy=50 ksi for W-shapes). The calculator retrieves section properties from the built-in AISC database.

Step 5 -- Check all limit states. Tension members: yielding on gross area (phi=0.90), rupture on net effective area (phi=0.75), block shear (phi=0.75). Compression members: flexural buckling about both axes (phi=0.90), torsional buckling for cruciform or single-angle sections, and local buckling of elements. Slenderness limit: L/r ≤ 300 for tension members subject to stress reversal, L/r ≤ 200 recommended for compression members.

Step 6 -- Design connections at panel points. The calculator designs gusset plates using the Whitmore section method for yielding, the Thornton method for buckling, and block shear checks. Weld sizes for shop-welded connections and bolt counts for field-bolted connections are determined per AISC 360 Chapter J. Eccentricity moments from single-angle or WT connections are accounted for via AISC 360 Section D3 shear lag factors (U factor).

Engineering Theory -- Truss Design

Method of Joints and Force Distribution

The method of joints applies equilibrium at each joint, assuming all members are two-force members (axial force only) and joints are pinned. At each joint, sum Fx = 0 and sum Fy = 0. Starting from a reaction point where only two unknown member forces meet, solve sequentially through the truss. For a Pratt truss under uniform gravity load, the chord force at any panel point is approximately M/h where M is the bending moment at that section if the truss were a solid beam and h is the truss depth. This analogy illustrates why chord forces are largest at midspan and decrease toward the supports.

Web member forces follow the shear diagram. For a uniformly loaded simply supported Pratt truss, the end diagonals carry the largest forces (equal to the support reaction divided by sin(theta) where theta is the diagonal angle), while midspan verticals carry near-zero load under symmetric loading.

Compression Member Buckling

Compression chord design requires careful attention to the unbraced length for buckling. For truss compression chords, the critical unbraced length depends on whether the chord is restrained in both directions at each panel point:

In-plane buckling: The unbraced length is the panel point spacing. Gusset plates are typically considered to provide rotational restraint equivalent to K = 0.5 to 1.0, though the conservative K = 1.0 is used unless a rational analysis justifies a lower value.
Out-of-plane buckling: The unbraced length is the distance between points of lateral bracing (purlins or fly braces). For roof trusses, purlins at 4-6 ft o.c. typically brace the top chord out-of-plane. The bottom chord may require lateral bracing or a sway frame to prevent lateral buckling under wind uplift conditions that put the bottom chord in compression.

The compression capacity follows AISC 360 Section E3:

Fe = pi^2 * E / (KL/r)^2
Fcr = [0.658^(Fy/Fe)] * Fy   when KL/r ≤ 4.71 * sqrt(E/Fy)  (inelastic buckling)
Fcr = 0.877 * Fe              when KL/r > 4.71 * sqrt(E/Fy)  (elastic buckling)
phi_Pn = 0.90 * Fcr * Ag

Gusset Plate Design -- Whitmore Section

The Whitmore section defines the effective width of gusset plate resisting the member axial force. Per AISC 360 Section J4 and the AISC Steel Construction Manual Part 9, the Whitmore width is measured as 30-degree lines spreading from the first row of bolts (or the weld start) to the last row of bolts, projected to the end of the gusset plate connection. The gusset plate is checked for:

Whitmore section yielding: phi_Rn = 0.90 x Fy_plate x tw x Lw where Lw is the Whitmore width
Gusset plate buckling: The unbraced length is the average of three distances from the Whitmore section centroid to the adjacent truss member lines. The plate is treated as a column with width Lw and thickness tw, checked using AISC 360 Section E3 with K = 0.65 (partial fixity).
Block shear: per AISC 360 J4.3, combining the shear yield/rupture path with the tension rupture path through the bolt group.

Tension Member Design -- Shear Lag

Tension members connected by only some elements of the cross-section (e.g., single angles bolted through one leg, WT sections bolted through the flange) are subject to shear lag. The effective net area is Ae = An x U, where U is the shear lag factor per AISC 360 Table D3.1. For bolted connections, U = 1 - x_bar/L where x_bar is the distance from the connected face to the centroid and L is the connection length. For a 4-inch angle with x_bar = 1.08 in and a connection length L = 8 in (four bolts at 2-1/2 in spacing): U = 1 - 1.08/8 = 0.865. The 13.5% reduction in effective area reflects the non-uniform stress distribution at the connection.

Worked Example -- Pratt Roof Truss

Problem: Design a Pratt roof truss spanning 80 ft with depth of 8 ft (span/depth = 10). 8 panels at 10 ft each. Roof dead load = 20 psf (roofing + purlins + self-weight), roof live load = 20 psf (ASCE 7 reduced, slope ≤ 4:12). Truss spacing = 20 ft o.c. Panel point load P = (20 + 20) x 10 x 20 = 8,000 lb = 8.0 kips per panel (service). Factored load per panel = 1.2 x 4.0 + 1.6 x 4.0 = 11.2 kips. Total factored load = 11.2 x 7 intermediate panels = 78.4 kips. Reactions = 78.4/2 = 39.2 kips.

Step 1 -- Determine member forces (factored). Top chord maximum compression (midspan panels): C ≈ Mmax/h, Mmax = wL^2/8 equiv = 11.2 x 7 x 80/8 = 784 kip-ft (equivalent uniform). C = 784/8 = 98.0 kips compression at midspan.

Bottom chord maximum tension: T = 98.0 kips tension at midspan.

End diagonal (first panel from support): Reaction = 39.2 kips. Diagonal angle = arctan(8/10) = 38.7 degrees. Diagonal force = 39.2/sin(38.7) = 62.7 kips tension.

First vertical (at support): near zero under symmetric load.

Midspan vertical: small compression under pattern live load, approximately 11.2 kips compression.

Step 2 -- Design top chord (compression, Cmax = 98 kips). Try double angle 2L5x5x1/2 (A36). Properties (per angle): A = 4.75 in^2, rx = 1.53 in, ry = 1.54 in (individual), rz = 0.98 in. For double angles connected by stitch bolts at 4 ft o.c.:

In-plane (x-axis): KL/rx = 1.0 x 10 x 12 / 1.53 = 78.4. Fe = pi^2 x 29,000/78.4^2 = 46.5 ksi. Fcr = 0.658^(36/46.5) x 36 = 0.704 x 36 = 25.3 ksi.
Out-of-plane (y-axis): Purlins brace the chord at 5 ft. KL/ry = 1.0 x 5 x 12 / 2.45 (composite ry for double angle pair) = 24.5. Fe = pi^2 x 29,000/24.5^2 = 476 ksi. Fcr = 0.658^(36/476) x 36 = 0.967 x 36 = 34.8 ksi.
For 2L: Ag = 2 x 4.75 = 9.50 in^2. phi_Pn = 0.90 x 25.3 x 9.50 = 216 kips (governs by in-plane). DCR = 98/216 = 0.45. Passes.

Step 3 -- Design bottom chord (tension, Tmax = 98 kips). Try 2L4x4x3/8 (A36). Ag = 2 x 2.86 = 5.72 in^2. Tension yielding: phi_Pn = 0.90 x 36 x 5.72 = 185 kips. OK. For net section: assume two lines of 3/4-inch bolts per splice at midspan. An = 5.72 - 2 x (3/4 + 1/8) x 0.375 = 5.72 - 0.656 = 5.06 in^2. Shear lag: U = 1 - x_bar/L = 1 - 1.15/10.5 = 0.89. Ae = 0.89 x 5.06 = 4.51 in^2. Tension rupture: phi_Pn = 0.75 x 58 x 4.51 = 196 kips. DCR = 98/185 = 0.53 for yielding. Passes.

Step 4 -- Design end diagonal (tension, T = 62.7 kips). Try 2L4x4x5/16 (A36). Ag = 2 x 2.40 = 4.80 in^2. Tension yielding: phi_Pn = 0.90 x 36 x 4.80 = 156 kips. DCR = 62.7/156 = 0.40. With two bolts per leg: An = 4.80 - 2 x 0.875 x 0.313 = 4.25 in^2. Ae = 0.89 x 4.25 = 3.78 in^2 (same U = 0.89). Rupture: phi_Pn = 0.75 x 58 x 3.78 = 164 kips. DCR = 0.38. Passes.

Step 5 -- Design compression vertical (midspan, C = 11.2 kips). Try 2L3x3x1/4 (A36). Ag = 2 x 1.44 = 2.88 in^2. rx = 0.93 in. KL/rx = 1.0 x 8 x 12 / 0.93 = 103. Fe = pi^2 x 29,000/103^2 = 27.0 ksi. Fcr = 0.658^(36/27.0) x 36 = 0.576 x 36 = 20.7 ksi. phi_Pn = 0.90 x 20.7 x 2.88 = 53.7 kips. DCR = 11.2/53.7 = 0.21. Passes. Note the vertical is substantially oversized for strength; the minimum size is often governed by connection geometry and fabrication minimums.

Step 6 -- Gusset plate at typical panel point. At an interior top chord panel point, the Whitmore width for the diagonal member connection: 4 bolts at 2.5 in o.c. gives L = 7.5 in connection length. Whitmore width at end of gusset ≈ 7.5 + 2 x 7.5 x tan(30) = 7.5 + 8.7 = 16.2 in. For 3/8 in gusset plate: phi_Rn_yield = 0.90 x 36 x 0.375 x 16.2 = 197 kips. Diagonal force = 62.7 kips. DCR = 0.32. Passes.

Result: Pratt truss, 80 ft span, 8 ft depth. Top chord: 2L5x5x1/2 (A36), bottom chord: 2L4x4x3/8 (A36), end diagonals: 2L4x4x5/16 (A36), interior diagonals: 2L3-1/2x3-1/2x5/16 (A36), verticals: 2L3x3x1/4 (A36). Gusset plates: 3/8 in A36 at all panel points. Total truss weight approximately 18 plf.

Frequently Asked Questions

What is the most efficient truss configuration for long-span roofs?

The Warren truss (alternating diagonals with no verticals) is typically the most efficient for spans up to 100 feet because it minimizes member count while maintaining adequate load distribution. The Pratt truss (diagonals sloping toward center) is preferred for longer spans (100-200+ feet) because the longer compression diagonals in the Warren configuration become governed by buckling. The Fink truss with sub-diagonals is economical for spans over 150 ft, reducing the unbraced length of compression chord members.

What slenderness limits apply to truss members?

AISC 360-22 Section D1 limits tension member slenderness to L/r ≤ 300 for members subjected to stress reversal (wind uplift on roof trusses, seismic). For static tension only (bottom chord under gravity load), there is no code-mandated slenderness limit, though practical considerations (sag, vibration, handling damage during erection) typically keep L/r under 400. For compression members, AISC E2 recommends L/r ≤ 200 for main members, with L/r ≤ 120 preferred for members designed to yield in compression (seismic).

How are truss connections designed at panel points?

Truss connections use gusset plates at panel points to connect converging web and chord members. The gusset plate is checked for Whitmore section yielding (30-degree spread from first to last fastener), buckling using the Thornton method (plate treated as a column with average unbraced length), and block shear. Welded connections are common in shop-fabricated trusses for erection speed; bolted connections are used for field splices and chord continuity. Eccentricity moments should be minimized by aligning working points at member centroid intersections, though small eccentricities (under 3 inches) can typically be neglected if the gusset plate is adequately proportioned.

What is the difference between top chord and bottom chord design for trusses?

The top chord is typically in compression under gravity load and is governed by flexural buckling about the weak axis unless laterally braced by purlins or deck at close spacing. Under wind uplift, the bottom chord goes into compression and may govern the bottom chord size. The bottom chord in tension is governed by net section rupture at splice connections. For long-span trusses, chord splices at panel points need careful detailing to transfer full chord force through the gusset plate. Panel point eccentricity -- the distance between the working point (member centerline intersection) and the actual bolt group centroid -- introduces moments that must be considered per AISC 360 Section J1.7.

When should HSS sections be used for truss members instead of double angles?

HSS sections (round or square) are preferred when compression controls, since HSS provides equal radius of gyration about all axes, eliminating the weak-axis buckling concern. HSS members are also torsionally stiff, reducing erection stability concerns. However, HSS connections at panel points are more expensive (slotted gusset plates or end plates with bolts outside the section), and HSS chords require more complex connection detailing at joints where both web members and purlins attach. Double angles remain the most common choice for roof trusses due to lower connection fabrication cost and easier field bolting.

Disclaimer (Educational Use Only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice. All structural designs must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) registered in the project jurisdiction. The site operator disclaims all liability for any loss or damage arising from the use of this page or the associated calculator tool. Results are preliminary -- not for construction.