Steel Truss Calculator

Joint capacity and member axial design for Warren, Pratt, and Howe truss configurations. Educational use only.

This page documents the scope, inputs, outputs, and computational approach of the Steel Truss Calculator on steelcalculator.app. The interactive calculator is designed to run in your browser for speed, but this documentation is written so the page remains useful (and indexable) even if JavaScript is not executed.

What this tool is for

• Fast screening and iteration while you are exploring truss geometries and member sizes.
• Creating a repeatable calculation workflow that a reviewer can audit.
• Learning the terminology and the "shape" of a typical check for steel truss joints and axially loaded members.

What this tool is not for

• It is not a complete design package and does not replace the governing standard, project specification, or an engineer's judgment.
• It is not a substitute for system-level checks (global stability, constructability, fatigue/seismic detailing, secondary bending from joint fixity).
• It does not guarantee compliance with any specific standard, because compliance depends on configuration, edition, and jurisdictional requirements.

Key concepts this page covers

• Truss geometry and member force analysis (method of joints, method of sections)
• Axial tension and compression member design per multiple codes
• Welded and bolted gusset plate joint design
• Slenderness limits and effective length factors for truss members
• Connection eccentricity and its effect on member design

Inputs and naming conventions (high-level)

The calculator UI may present different groupings depending on the selected standard or mode, but inputs generally fall into these categories:

1) Actions / demands Values that represent the loading on the truss (point loads at panel points, uniform loads on top chord, wind uplift/suction). Ensure you understand whether the workflow expects factored actions (strength) or service actions (serviceability), and keep that consistent across your verification.

2) Geometry and detailing parameters Truss type (Warren, Pratt, Howe, modified Warren), span, depth, number of panels, top chord slope (if applicable), and joint eccentricity. Many "unexpected" results come from geometry assumptions that are implicitly different from the real detail — particularly the effective length of compression chords and web members at joints.

3) Material properties Strength values (yield/ultimate), stiffness values (E), and any standard-specific parameters that affect resistance models. For hollow section joints, the chord face deformation capacity depends on the yield strength ratio between chord and brace members.

4) Standard / method selection The same physical truss can be checked using different methods, with different reduction factors and definitions. A tool can only be unambiguous when you lock down the standard and edition you are matching.

The most common inputs for this tool include: span, depth, panel count, truss type, chord sections, web sections, joint type (welded gusset, direct hollow section), load cases.

Outputs you should expect

A well-behaved calculator output should be both summary-friendly and auditable:

• A small set of headline results (pass/fail indicators, utilization ratios for each member, controlling joint).
• Member forces (axial tension/compression) for each chord and web element.
• Intermediate values that let you reproduce at least one limit state independently (effective lengths, slenderness ratios, compressive resistance, joint capacity components).
• Clear units on every numeric value and a statement of the method used.

If the output is not auditable, treat it as a black box and do not rely on it for anything beyond quick intuition.

Computation approach (what happens under the hood)

This calculator is intended to implement a deterministic sequence of steps:

1. Normalize inputs into a consistent internal unit system (for example, all lengths in meters, all forces in newtons), then convert back for display.
2. Derive truss geometry — joint coordinates, member lengths, and inclination angles from span, depth, panel count, and truss type.
3. Solve member forces using the method of joints or direct stiffness method for statically determinate trusses. For indeterminate trusses, a linear-elastic stiffness analysis is performed.
4. Evaluate candidate limit states for each member: tension yielding, tension rupture (net section at connections), compression buckling (flexural buckling about both axes, torsional/flexural-torsional buckling for single-angle webs).
5. Evaluate joint capacity: for welded gusset plate connections — weld strength, gusset plate block shear, gusset plate buckling (Whitmore section). For direct hollow section joints — chord face plastification, chord sidewall buckling, chord shear, brace effective width, punching shear per CIDECT / code-specific provisions.
6. Compute utilization as a dimensionless ratio (demand divided by resistance, or resistance divided by demand depending on convention). The controlling utilization is the maximum across the evaluated checks.
7. Render the report with intermediate values and the controlling failure mode, so a user can trace "why" the governing mode controls.

The implementation should also apply predictable rounding rules: keep higher precision internally, and only round for display. This is essential for stable regression tests.

Verification workflow (recommended QA steps)

This section is not a design instruction; it is a quality-assurance pattern for checking any engineering calculator.

1. Unit sanity check: confirm that each input has the unit you think it has. A common failure mode is mixing MPa and Pa, or mm and m.
2. Independent replication: pick one member (top chord, bottom chord, or a critical web) and replicate its axial design with an independent method (hand check, spreadsheet, or trusted reference). You are validating the method, not chasing an exact rounded match.
3. Sensitivity test: change one input in a direction that should clearly increase or decrease the capacity (for example, increase chord section depth) and confirm the output changes logically.
4. Boundary test: test extreme-but-possible values — zero-length members, very shallow trusses (depth/span < 1/20), very steep trusses — to make sure the UI doesn't silently overflow, divide by zero, or return NaN/Infinity.
5. Documentation: record the standard/mode, inputs, and the controlling output in a calculation note format so the result can be reviewed later.

For a structured approach, see: How to verify calculator results.

How the Steel Truss Calculator Works

The calculator analyzes planar steel trusses under static joint loads. The truss is modeled as a pin-jointed (determinate or indeterminate) framework where members carry only axial forces. The user defines truss type (Warren, Pratt, Howe, or custom), span, depth, number of panels, top chord slope, and member section assignments. Joint loads are applied at panel points. The tool solves for member forces, then designs each member and joint per the selected design code.

Member force determination uses the method of joints for statically determinate trusses. Starting from a support joint with at most two unknown member forces, the tool marches joint by joint through the truss, solving force equilibrium at each node. For indeterminate trusses (those with redundant members or continuous chords), a stiffness matrix approach is used. The stiffness of each truss element is AE/L (axial rigidity), and the global stiffness matrix is assembled and solved for joint displacements, from which member forces are back-calculated.

Compression member design accounts for flexural buckling about both principal axes, with effective length factors K = 1.0 for in-plane buckling (assuming pinned joints) and K = 1.0 for out-of-plane buckling (unless lateral bracing is specified by the user). For single-angle web members, the equivalent slenderness ratio per code provisions is used to account for eccentricity at the connection. Torsional and flexural-torsional buckling modes are checked for doubly-symmetric and singly-symmetric sections respectively.

Tension member design checks gross section yielding and net section rupture at bolt holes. For welded connections, the effective net area accounts for shear lag per code provisions (AISC Table D3.1, AS 4100 Cl 7.3, EN 1993-1-8 Cl 6.2.2, CSA S16 Cl 12.3).

Joint design for gusset plate connections follows the Uniform Force Method (AISC DG29) or the Whitmore section approach. For welded hollow section joints, CIDECT Design Guide 3 methodology is used, with chord face plastification (K-joint capacity), chord sidewall buckling, chord shear, and brace effective width criteria evaluated.

Key Equations

Member force in a Warren truss top chord under uniform panel loading (symmetric, simply supported):

F_chord = M / d

Where M = bending moment at the equivalent beam section at that panel point, d = truss depth (center-to-center of chords). The top chord force is compressive; the bottom chord force is tensile.

Elastic flexural buckling resistance (AISC 360-22 E3):

P_n = F_cr * A_g
F_cr = (0.658^(F_y/F_e)) * F_y    when F_e >= 0.44*F_y
F_cr = 0.877 * F_e                 when F_e < 0.44*F_y
F_e = pi^2 * E / (K*L/r)^2

Web member force in a Pratt truss under uniform panel point load P:

F_diagonal = P / sin(theta)
F_vertical = P  (compression, posts)

Where theta = angle of diagonal from horizontal. Diagonals carry tension (or compression depending on orientation), verticals carry compression.

Gusset plate buckling — Whitmore effective width (AISC DG29):

b_e = 2 * L_w * tan(30 deg) + b_w

Where L_w = weld length along the member, b_w = member width. The effective width defines the column strip checked for buckling at the gusset plate edge. Effective length factor K = 0.65 (fixed-free edge condition) or 1.2 (pinned edge).

Direct hollow section K-joint capacity — chord face plastification (CIDECT DG3 / EN 1993-1-8 Table 7.10):

N_1,Rd = (k_n * f_y0 * t_0^2 / sin(theta_1)) * (1.8 + 10.2*d_1/d_0) * f(gamma, beta, theta) / gamma_M5

Where d_0, t_0 = chord diameter and wall thickness, d_1 = brace diameter, theta_1 = brace angle, gamma = d_0/(2*t_0), beta = d_1/d_0.

Design Code Requirements

Key difference: EN 1993-1-8 has the most comprehensive hollow section joint provisions (Tables 7.10, 7.11, 7.12 covering CHS, RHS, and multiplanar joints). AISC 360 K2 provides separate equations for T/Y, K, and cross connections in CHS and RHS but is more limited in scope. CIDECT design guides fill the gap where codes are silent.

Step-by-Step Example

Problem: Design a simply-supported Warren truss spanning 60 ft with depth 6 ft, 6 panels (each 10 ft). Top chord slope: flat (parallel chords). Uniform factored panel point loads P = 20 kips at each bottom chord joint (5 loaded joints). Top chord: HSS 6x6x3/8 (A500 Gr. B, F_y = 46 ksi, A_g = 8.08 in^2, r = 2.28 in). Bottom chord: HSS 6x6x3/8 (same). Web members: HSS 4x4x1/4 (A500 Gr. B, F_y = 46 ksi, A_g = 3.59 in^2, r = 1.52 in). Design code: AISC 360-22 LRFD.

Step 1 — Reactions and member forces: Total load = 5 _ 20 = 100 kips. Reactions = 50 kips each end. Panel moment (at midspan) = 50 _ 30 - 20 * (20 + 10) = 1500 - 600 = 900 kip-ft. Max top chord compression = M/d = 900/6 = 150 kips. Max bottom chord tension = 900/6 = 150 kips.

Web member force (first panel diagonal, angle from horizontal = arctan(6/10) = 31.0 deg): Shear at first panel = 50 kips. F_diagonal = 50 / sin(31.0 deg) = 50 / 0.515 = 97.1 kips (tension for typical Warren layout).

Step 2 — Top chord compression check (HSS 6x6x3/8): Member length L = 10 ft = 120 in. KL/r = 1.0 _ 120 / 2.28 = 52.6. F_e = pi^2 _ 29000 / (52.6)^2 = 103.5 ksi. Fy = 46 ksi. 0.44 * Fy = 20.24 ksi. F_e > 20.24, so inelastic buckling. F_cr = 0.658^(46/103.5) * 46 = 0.658^0.444 _ 46 = 0.821 _ 46 = 37.8 ksi. phi*P_n = 0.90 * 37.8 * 8.08 = 274.7 kips. Utilization = 150 / 274.7 = 0.546 PASS.

Step 3 — Bottom chord tension check (HSS 6x6x3/8): Tension yielding: phi*P_n = 0.90 * 46 * 8.08 = 334.5 kips. Utilization = 150 / 334.5 = 0.448 PASS.

Step 4 — Web diagonal compression check (HSS 4x4x1/4): Member length L = sqrt(10^2 + 6^2) = 11.66 ft = 140 in. KL/r = 1.0 _ 140 / 1.52 = 92.1. F_e = pi^2 _ 29000 / (92.1)^2 = 33.8 ksi. 0.44 _ F_y = 20.24 ksi. F_e > 20.24, inelastic buckling. F_cr = 0.658^(46/33.8) _ 46 = 0.658^1.361 _ 46 = 0.572 _ 46 = 26.3 ksi. phi*P_n = 0.90 * 26.3 * 3.59 = 85.0 kips. Assuming the diagonal carries compression in the alternate load case: utilization = 97.1 / 85.0 = 1.14 FAIL — increase web size to HSS 4x4x5/16 or reduce panel load.

Step 5 — Joint check (bottom chord panel point, K-joint with gap): Chord: HSS 6x6x3/8, web: HSS 4x4x1/4. Angle theta = 31 deg. Per AISC 360 K2.3, check chord face plastification: gamma = B/(2t) = 6/(20.349) = 8.6. beta = 4/6 = 0.667. Rn sin(theta) = F_y * t^2 _ [9.8 * beta * sqrt(gamma)] / sin(theta) _ Qf = 46 * 0.349^2 _ [9.8 _ 0.667 _ sqrt(8.6)] / sin(31) _ 1.0 = 46 _ 0.122 _ [9.8 * 0.667 * 2.933] / 0.515 = 5.61 * 19.17 / 0.515 = 208.8 kips. phi = 0.90. phi*R_n = 187.9 kips. Demand = 97.1 kips. Utilization = 0.517 PASS.

Result: Top chord and bottom chord OK. Web diagonal needs upgrade for compression case. Joint capacity adequate for K-joint at panel points. Total truss weight (approximate): top + bottom chords: 2 _ 60 ft _ 27.5 lb/ft = 3,300 lb; webs: ~70 ft * 12.2 lb/ft = 854 lb; total ~4,154 lb.

Common Design Mistakes

• Assuming all web members carry only tension: In a Warren truss under gravity load, diagonal web members alternate between tension and compression. Under asymmetric loading (partial span load, wind uplift), the force reversal can put a tension-designed member into compression. Always check both signs.
• Neglecting effective length for compression chord buckling: The top chord is continuous across panel points in most trusses. The effective length factor K for in-plane buckling is typically 0.9 (not 1.0) for continuous chords. However, K = 1.0 is conservative. For out-of-plane buckling, the chord is laterally braced only at purlin/girt locations, which may be at larger spacing.
• Using the gross section for net section checks at bolted connections: Web members connected with one leg of an angle (or one face of an HSS) experience shear lag. The net effective area A_e = U * A_n, where U is the shear lag factor (AISC Table D3.1). For angles connected by one leg, U can be as low as 0.60, dramatically reducing tension capacity.
• Overlooking gusset plate buckling: A gusset plate loaded in compression by a web member can buckle out of plane if the free edge length behind the Whitmore section is excessive. The effective column length is the average of the Whitmore width distances to the connected edges, and if the free edge exceeds ~2x the plate thickness, buckling controls.
• Welding HSS branches to HSS chords without checking chord plastification: Hollow section joints fail by chord face deformation before the brace itself yields. The CIDECT/AISC K-connection equations are geometry-sensitive — small changes in chord wall thickness dramatically change capacity because capacity varies with t^2.
• Not accounting for secondary bending moments from joint eccentricity: When the working lines of truss members do not intersect at a single point at the joint, an eccentricity moment is introduced. For gusset plate connections, limiting the eccentricity to the Whitmore section width is common practice. For HSS joints, a gap (positive eccentricity) or overlap (negative) in K-joints shifts the moment into the chord, which should be included in the chord interaction check.

Frequently Asked Questions

What is the difference between a Warren truss and a Pratt truss for steel design? A Warren truss uses a series of equilateral or near-equilateral triangles, with diagonal web members alternating in tension and compression. It is materially efficient for symmetric loading because chord forces are nearly uniform along the length. A Pratt truss has vertical posts in compression and diagonal tension members, which works well under gravity loading where diagonals are always in tension (if oriented correctly). Warren trusses use fewer members and joints but require compression design of every diagonal; Pratt trusses have more members and joints but diagonals are designed for tension only, reducing buckling concerns for those elements. For long-span steel trusses (over 80 ft), Pratt trusses with counter-diagonals are often preferred because the tension-only diagonal scheme is lighter.

How do I determine effective length factors for truss compression members? For in-plane buckling of web members, K = 1.0 is standard for pin-connected trusses. For welded trusses with gusset plates, the end restraint provided by the gusset plate and chord can reduce the effective length — K = 0.9 is commonly used for welded web members in the plane of the truss. For out-of-plane buckling, K = 1.0 typically governs unless later bracing is provided at mid-length. For continuous chord members (compression), in-plane K = 0.9 (continuous through joints), out-of-plane K = 1.0 (laterally braced at panel points). Always check the actual restraint condition at each end — a single-bolt connection provides near-zero rotational restraint.

When should I use gusset plate connections versus direct welded hollow section joints? Gusset plate connections are preferred when: (a) member sections are open profiles (angles, channels, W-sections), (b) multiple members frame into a single joint at different angles, (c) site bolting is preferred over site welding, or (d) the truss depth is large enough that gusset plates do not proportionally dominate. Direct welded HSS connections are preferred when: (a) all members are hollow sections (architecturally exposed trusses), (b) shop fabrication and galvanizing are feasible, (c) the truss depth is moderate and chord wall thickness is sufficient to resist face plastification. HSS joints are generally stiffer and cleaner-looking but are more demanding on fabrication tolerance and quality control.

What slenderness limits apply to truss web members in tension? AISC 360 specifies a preferred slenderness limit of L/r <= 300 for tension members, though this is a serviceability recommendation (not a strength limit) to prevent sagging and vibration. For wind bracing and secondary members, L/r up to 300 is acceptable. For primary truss tension members, L/r <= 240 is commonly targeted. AS 4100 recommends L/r <= 300 for rods and 250 for other tension members. EN 1993-1-1 does not specify an explicit slenderness limit for tension members. In practice, slender tension members (L/r > 300) are prone to wind-induced vibration and accidental damage during erection.

Why does the truss joint capacity often control over member capacity? Truss joints concentrate forces from multiple members into a confined region of the chord or gusset plate. For HSS trusses, the chord face is loaded out-of-plane by the brace members, and the chord wall thickness (not the brace section) typically controls joint capacity — this is why strengthening a HSS truss joint often requires increasing the chord wall thickness rather than the brace section. For gusset plate connections, block shear along the bolt lines and buckling of the free gusset edge (Whitmore section) frequently control. The joint is the nexus of all member forces, and the complex triaxial stress state at the joint panel zone means simple member-level checks do not capture the governing mode.

How do I handle a truss with top chord slope (pitched roof truss)? A pitched truss (non-parallel chords) introduces a vertical component to the chord forces at each joint. The method of joints still applies, but the force resolution is more complex because chord members are not horizontal. The key additional checks are: (a) at the ridge joint, the top chord compression force has both horizontal and vertical components that must be resisted by the ridge connection detail, and (b) at the eaves (bearing), the inclined top chord reaction has a horizontal thrust component that must be resisted by the support (tie beam, buttress, or moment-resisting column). For steeply pitched trusses (slope > 30 deg), the horizontal thrust can be significant and must be included in the bearing and foundation design.

Related pages

• Portal frame calculator
• Steel brace frame design
• Steel diagonal bracing calculator
• Beam calculator
• Column capacity calculator
• Bolted connections calculator
• Welded connections calculator
• Gusset plate calculator
• Section properties database
• Unit converter
• Tools directory
• How to verify calculator results
• Disclaimer (educational use only)

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

The site operator provides the content "as is" and "as available" without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.