Steel Truss Design

What Is a Steel Truss?

A truss is a structural assembly of straight members connected at their endpoints (joints). Under ideal conditions — pinned joints, loads applied only at joints, members that are straight and prismatic — each member carries only axial force: either tension or compression. The absence of bending is the truss's fundamental efficiency advantage over solid beams.

In practice, joints are welded or bolted with some rotational stiffness, and self-weight is distributed rather than point-loaded. Secondary bending moments arise but are typically small relative to axial forces and are often neglected in preliminary design. For long-span or heavy-loaded trusses, a frame (finite-element) analysis captures both effects.

Common Truss Configurations

Method of Joints

The classical Method of Joints analyses each joint as a free body in equilibrium under its applied load and the member forces meeting at that joint. Starting from a joint with at most two unknown forces (a support or a free end), the equations ΣF_x = 0 and ΣF_y = 0 give two equations per joint. For a statically determinate truss with m members and j joints:

For larger trusses, matrix stiffness (direct-stiffness) methods and finite-element software solve the full system simultaneously. This calculator uses the stiffness method to determine member forces from the applied loads and geometry.

Sign Convention and Member Forces

• Tension (+): member elongates; force pulls the joint toward the member. Section design uses AISC Chapter D.
• Compression (−): member shortens; force pushes the joint away. Section design uses AISC Chapter E (buckling governs).
• Zero-force members: some members carry no load under a specific loading condition. They are retained for stability against out-of-plane loads and to reduce the unbraced length of adjacent compression members.

Load Path — Flat Pratt Truss under Gravity

Under uniformly distributed gravity load applied at the top chord panel points:

• Top chord: compression — maximum at mid-span (for simply-supported truss)
• Bottom chord: tension — maximum at mid-span
• Diagonals: tension (Pratt configuration) — maximum near the supports where shear is highest
• Verticals: compression (Pratt) — maximum near mid-span where the diagonal force change is largest

This pattern reverses for uplift loading, which is critical for roof trusses: previously tensile diagonals become compressive, and a compression-designed diagonal may be inadequate for the reversed load case.

Unbraced Length and Out-of-Plane Stability

Compression members in a truss are prone to flexural or flexural-torsional buckling out of the plane of the truss. The unbraced length L_b in the out-of-plane direction is determined by the location of lateral bracing (roof purlins, cross-bracing, or girts). In practice:

• Top chord: braced at each purlin point — effective length = purlin spacing
• Bottom chord: braced at each bridging or diagonal connection — effective length = panel length or bridging spacing
• Verticals and diagonals: effective length = member length (K = 1.0, pinned–pinned) unless continuous connections indicate otherwise

AISC 360-22 Chapter D Tension Members

The design tensile strength φ_tT_n is the lesser of:

AISC 360-22 Chapter E Compression Members

All truss compression members are designed per Chapter E using the column buckling equations. The governing slenderness ratio KL/r determines whether buckling is inelastic (F_cr from inelastic formula) or elastic (Euler buckling).

AISC 360-22 §B4 Section Classification

Before computing strength, confirm the section is not slender for compression:

Slender sections require reduced effective area Q × A_g per §E7 — most standard hot-rolled sections are non-slender for common grades.

ASCE 7-22 §2.3 LRFD Load Combinations for Roof Trusses

Combination 5 (uplift) frequently governs the design of roof truss diagonals and bottom chord. A member sized for tension under gravity may need to be resized to resist compression under uplift.

AISC 360-22 Chapter H Combined Axial + Bending (Secondary Effects)

In trusses with rigid or semi-rigid joints, or where members have intermediate loads (self-weight), secondary bending exists. If the moment is significant, apply the beam-column interaction equations of §H1-1. For joints assumed fully pinned and loads applied only at panel points, P/(φP_c) alone is checked.

Example — AISC 360-22 LRFD Flat Pratt Truss (8-Panel)

Given: Flat Pratt roof truss, span L = 20 m, 8 equal panels (panel width = 2.5 m), truss depth h = 2.0 m. Gravity loads at top chord panel points: dead P_D = 18 kN/panel, live P_L = 22 kN/panel. Steel Grade A992: F_y = 345 MPa, F_u = 450 MPa, E = 200,000 MPa. φ_c = 0.90, φ_t = 0.90 (gross section).

1. Factored panel point load (governing ASCE 7-22 Combo 2)
   P_u = 1.2×18 + 1.6×22 = 21.6 + 35.2 = 56.8 kN/panel
   Total factored load = 8×56.8 = 454.4 kN · Support reaction R = 454.4/2 = 227.2 kN
2. Maximum chord forces (mid-span, panel 4–5)
   Mid-span moment: M = R×L/2 − P_u×(2.5+5.0+7.5+10.0) = 227.2×10 − 56.8×25
   = 2,272 − 1,420 = 852 kN·m
   Top chord (compression): F_TC = −M/h = −852/2.0 = −426 kN
   Bottom chord (tension): F_BC = +M/h = +852/2.0 = +426 kN
3. Maximum diagonal force (first panel, near support)
   Shear at left support: V₁ = R − 0 = 227.2 kN (half-panel loads not shown for brevity)
   Diagonal angle: θ = arctan(h/d) = arctan(2.0/2.5) = 38.66°
   F_diag,1 = V₁/sin θ = 227.2/sin(38.66°) = 227.2/0.625 = +364 kN (tension)
4. Design top chord — compression — W8×31 trial
   W8×31: A_g=5,870mm², r_x=89.4mm, r_y=40.6mm. Unbraced length both axes L_b=2,500mm (purlins at each panel point).
   KL/r_y = 1.0×2,500/40.6 = 61.6 (governs)
   F_e = π²×200,000/61.6² = 521 MPa
   4.71√(200,000/345) = 113.4 > 61.6 → inelastic: F_cr = 0.658^345/521×345 = 0.658^0.662×345 = 0.789×345 = 272 MPa
   φ_cP_n = 0.90×272×5,870/1,000 = 1,437 kN > 426 kN ✓ (DCR = 0.30)
   Note: Top chord DCR is low because compression is not maximum at mid-span for panel-point loads; it builds up to the full value over the central panels. In practice self-weight also adds to the chord force. Try W8×18 for optimisation.
5. Design bottom chord — tension — 2L3½×3½×¼ (double angle)
   2L3½×3½×¼: A_g = 2×1,680 = 3,360 mm²
   φ_tT_n = 0.90×345×3,360/1,000 = 1,043 kN > 426 kN ✓ (DCR = 0.41)
   Select 2L3½×3½×¼ (or equivalent W or HSS section for fabrication preference)
6. Design diagonal (tension) — 2L3×3×¼
   F_diag = 364 kN. 2L3×3×¼: A_g = 2×1,420 = 2,840 mm²
   φ_tT_n = 0.90×345×2,840/1,000 = 881 kN > 364 kN ✓ (DCR = 0.41)

References

• [1]
  AISC 360-22 — Specification for Structural Steel Buildings. American Institute of Steel Construction, 2022. Chapter D (Tension members), Chapter E (Compression members / buckling), Chapter H (Combined loading).
• [2]
  ASCE 7-22 — Minimum Design Loads and Associated Criteria for Buildings and Other Structures. ASCE, 2022. §2.3 (LRFD load combinations), Chapter 7 (Snow loads), Chapter 26–30 (Wind loads).
• [3]
  AISC Steel Construction Manual, 16th Ed. — American Institute of Steel Construction, 2022. Part 2 (Section properties), Part 4 (Design of compression members), Part 5 (Design of tension members).
• [4]
  Leet, K., Uang, C-M. & Gilbert, A. — Fundamentals of Structural Analysis, 5th Ed. McGraw-Hill, 2018. Chapter 11 (Truss analysis — method of joints and sections).
• [5]
  Salmon, C.G., Johnson, J.E. & Malhas, F.A. — Steel Structures: Design and Behavior, 5th Ed. Pearson, 2009. Chapter 3 (Tension members), Chapter 6 (Compression members), Chapter 16 (Trusses).
• [6]
  Segui, W.T. — Steel Design, 6th Ed. Cengage Learning, 2018. Chapter 4 (Compression) Chapter 3 (Tension).