EN 1993-1-8 Hollow Section Joint Design — Chord Face, K/N Joints & CIDECT
Complete reference for EN 1993-1-8:2005 hollow section (HSS/RHS/CHS) joint design. Covers chord face plastification (Clause 7.4), gap and overlap K-joints (Clause 7.2), chord shear and punching shear checks (Clause 7.5), the chord stress function k_n, validity ranges from Table 7.1, and CIDECT design guide methodology. Includes fully worked examples for a CHS truss K-joint and an RHS T-joint, plus practical fabrication guidance.
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Hollow Section Joints — Why They Are Different
Hollow structural sections (circular CHS, square SHS, rectangular RHS) produce elegant, efficient trusses and frames — but their joint design differs fundamentally from open-section connections. The continuous chord wall is the connection medium; force transfer from bracing to chord occurs through the chord face, not through discrete bolts or welds.
EN 1993-1-8 Clause 7 provides a unified joint resistance method based on yield line theory developed through CIDECT research. The approach covers T, Y, X, K, and N joints in both CHS and RHS.
The governing failure mode depends on the brace-to-chord width ratio β. At low β (< 0.7), chord face plastification governs. At β approaching 1.0, chord side wall failure controls. These transitions drive truss geometry selection.
Joint Types and Notation
| Joint Type | Configuration | Typical Application |
|---|---|---|
| T | One brace perpendicular to chord | Pinned brace, simple truss vertical |
| Y | One brace at angle θ to chord | Diagonal bracing end connections |
| X | Two braces, opposite sides, aligned | Cross-bracing, continuous column |
| K | Two braces, same side, gap or overlap, forces opposite | Warren truss, Pratt truss |
| N | K-joint with unequal brace angles or sections | Asymmetric truss panels |
Chord = member 0 (continuous through joint). Brace = member 1 (compression in K-joint), member 2 (tension).
Validity Ranges — Table 7.1
Before applying any joint resistance formula, verify the joint geometry satisfies EN 1993-1-8 Table 7.1. Joints outside these limits are outside the scope of the code — they require advanced analysis (FE) or physical testing per EN 1990 Annex D.
| Parameter | CHS | RHS | Notes |
|---|---|---|---|
| β = d_1/d_0 or b_1/b_0 | ≥ 0.2 | ≥ 0.35 | Low β: chord face too flexible |
| d_0/t_0 (chord) | ≤ 50 (Class 2) | ≤ 40 | Higher slenderness = chord buckling |
| d_i/t_i (brace) | ≤ 50 | ≤ 35 | Brace must develop full yield |
| θ_i (brace angle) | ≥ 30° | ≥ 30° | Acute angles: weld access issues |
| g (gap, K-joint) | ≥ t_1 + t_2 | ≥ t_1 + t_2 | Minimum gap for weld access |
| λ_ov (overlap) | ≥ 25% | ≥ 25% | Overlap < 25% treated as gap joint |
A common design mistake: SHS 100×100×3 (b_0/t_0 = 33.3) with SHS 40×40×5 braces (b_1/t_1 = 8). This violates the b_0/t_0 validity — the yield mechanism assumed in the formula does not develop.
Chord Face Plastification — The Governing Mode
For gap K-joints where β is moderate (0.4-0.8), chord face plastification governs.
CHS K-Gap Joint Resistance
N_i,Rd = (f_y0 × t_0² / sin θ_i) × k_g × k_p × k_n / γ_M5
Where:
- f_y0, t_0 = chord yield strength and wall thickness
- k_g = gap factor = γ^0.2 × (1 + 0.024γ^1.2/(e^{0.5g/t_0 - 1.33} + 1))
- k_n = chord stress function
- γ_M5 = 1.00 (joint resistance partial factor)
The gap factor k_g is significant: a tightly spaced joint (small g) has much higher capacity than a widely spaced joint because the yield line mechanisms from the two brace footprints merge.
RHS K-Gap Joint Resistance
N_i,Rd = (k_n × f_y0 × t_0²) / ((1 - β) × sin θ_i) × (2β/sin θ_i + 4√(1 - β)) / γ_M5
Chord Stress Function k_n
Truss chords carry significant axial force in addition to local joint forces:
For RHS chords with n = N_0,Ed/N_pl0,Rd + M_0,Ed/M_pl0,Rd:
- Compression chord (n < 0): k_n = 1.3 + 0.4n/β, limited to k_n ≤ 1.0
- Tension chord (n ≥ 0): k_n = 1.0
For a compressed chord at 70% utilisation (n = -0.70), β = 0.6: k_n = 1.3 - 0.467 = 0.833. Joint capacity reduced by 17%. At 90% utilisation (n = -0.90): k_n = 1.3 - 0.60 = 0.70 — 30% reduction. This interaction drives chord sizing in trusses.
Worked Example — CHS Warren Truss K-Joint
Geometry: Roof truss, 24 m span, 2.0 m panel spacing. Top chord: CHS 168.3×6.3 (S355). Bottom chord: CHS 168.3×5.0 (S355). Braces: CHS 88.9×4.0 (S355). Brace angle: θ = 45°. Gap: g = 30 mm.
Brace design forces (ULS): N_1,Ed = -95 kN (compression), N_2,Ed = +125 kN (tension). Chord axial at joint: N_0,Ed = -210 kN (compression, top chord).
Step 1: Check Validity Ranges
| Parameter | Value | Limit | OK? |
|---|---|---|---|
| β = d_1/d_0 | 88.9/168.3 = 0.528 | ≥ 0.2 | OK |
| d_0/t_0 | 168.3/6.3 = 26.7 | ≤ 50 | OK |
| d_1/t_1 | 88.9/4.0 = 22.2 | ≤ 50 | OK |
| θ | 45° | ≥ 30° | OK |
| g | 30 mm | ≥ t_1+t_2 = 8 mm | OK |
Step 2: Chord Stress Function
N_pl0,Rd = A_0 × f_y0 / γ_M0 = 3206 × 355 / 1.00 = 1,138 kN. n = -210/1138 = -0.185. For CHS: k_n = 1.3 + 0.4(-0.185)/0.528 = 1.16 → capped at 1.0. k_n = 1.00.
Step 3: Chord Face Plastification Resistance
γ = d_0/(2t_0) = 168.3/(2×6.3) = 13.36. k_g = γ^0.2 × [1 + 0.024γ^1.2/(exp(0.5g/t_0 - 1.33) + 1)] = 1.68 × [1 + 0.139] = 1.91.
N_i,Rd = (f_y0 × t_0² / sin θ_i) × (1.8 + 10.2d_1/d_0) × k_g × k_n / γ_M5 = (355 × 39.69 / 0.707) × (1.8 + 10.2×0.528) × 1.91 × 1.00 / 1.00 = 19,933 × 7.19 × 1.91 = 274 kN
Step 4: Capacity Check
Brace 1 (compression): N_1,Ed = 95 kN < N_1,Rd = 274 kN → UC = 0.35 ✓ Brace 2 (tension): N_2,Ed = 125 kN < N_2,Rd = 274 kN → UC = 0.46 ✓
Overlap K-Joints
When braces overlap (λ_ov ≥ 25%), the joint behaves differently. The overlapping brace force transfers partially through the overlapped brace face.
Classification per Clause 7.1.2:
- Type 1 (25% ≤ λ_ov < 50%): Reduced joint capacity
- Type 2 (50% ≤ λ_ov < 80%): Intermediate — some composite action
- Type 3 (λ_ov ≥ 80%): Overlapping brace transfers force directly
100% overlap joints are essentially direct brace-to-brace connections — the chord becomes a bearing plate. The hidden weld (between overlapping brace and overlapped brace) is critical for Types 1 and 2.
CIDECT Design Guides — Practical Supplement
CIDECT design guides are the research foundation of EN 1993-1-8 Clause 7:
| CIDECT Guide | Title | Coverage Beyond EN 1993-1-8 |
|---|---|---|
| DG 1 | Design Guide for CHS Joints | All CHS joint configs, design charts |
| DG 3 | Design Guide for RHS Joints | RHS yield line analysis, weld design |
| DG 4 | Bolted Connections to HSS | Blind bolts, flowdrill, through-bolts |
| DG 7 | Fabrication and Welding of HSS | Weld details, tolerances, inspection |
| DG 8 | RHS Joints Under Fatigue | FAT curves for HSS joints |
CIDECT DG 3 is the most consulted reference in design offices. It provides design resistance tables for every combination of chord size, wall thickness, and brace geometry — saving the designer from computing the full formula for every joint in a large truss.
Fabrication and Welding
Weld Design for HSS Joints
Hollow section joints are almost exclusively fillet-welded. The weld throat a_w must develop full brace capacity per Clause 7.6: a_w ≥ (β_w × f_y1 × t_1) / (2 × f_u/(√3 × β_w × γ_M2)). For S355 braces with E42 electrodes: a_w_min ≈ 0.92 × t_1.
Note: the weld is placed around the full brace perimeter, including the heel and toe. The acute-angle toe is difficult to access; gap joints must have sufficient clearance (g ≥ t_1 + t_2) for the welder.
Corrosion Protection
HSS joints have internal cavities vulnerable to corrosion. Good practice:
- Seal all joint gaps with continuous fillet weld
- Provide drain holes (minimum Ø10 mm) at lowest points of CHS chords
- Hot-dip galvanise completed truss (SHS/RHS must be vented)
- For painted systems, fill or seal-weld gaps between braces
Summary of EN 1993-1-8 HSS Joint Design Procedure
- Select sections based on member forces (truss analysis)
- Check validity ranges (Table 7.1) — reject sections outside limits
- Classify joint type (T, Y, X, K, N) and subtype (gap or overlap)
- Compute chord utilisation n and chord stress function k_n
- Compute joint resistance for each failure mode
- Check all braces — lowest N_i,Rd/N_i,Ed ratio governs
- Size welds per Clause 7.6 to develop brace capacity
- Detail for fabrication — minimum gap, weld access, drainage, galvanising vents
Joint efficiency (N_joint,Rd/N_brace,pl,Rd) typically ranges from 0.4 (low β, thin chord) to 1.0 (high β, stout chord). Aiming for 0.7-0.8 joint efficiency balances steel weight and fabrication complexity.
RHS T-Joint Quick Example
Column: SHS 200×200×10 (S355). Beam: SHS 120×120×8 (S355). θ = 90°. Tension: N_1,Ed = +180 kN.
β = 120/200 = 0.60. For RHS T-joints: N_1,Rd = (k_n × f_y0 × t_0²)/((1 - β)) × (2β + 4√(1 - β))/γ_M5 = (1.0 × 355 × 100)/(0.40) × (1.20 + 2.528) = 88,750 × 3.728 = 331 kN. UC = 180/331 = 0.54 ✓
Educational reference only. Verify all values against the current EN 1993-1-8 and applicable National Annex. HSS joint design is sensitive to geometric parameters — small changes in gap or β can significantly alter resistance. CIDECT design tables should be cross-referenced for production designs. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification by a qualified structural engineer.