What failure modes govern hollow section joint design under EN 1993-1-8?

EN 1993-1-8 Clause 7 identifies six failure modes: chord face plastification (Mode A — most common for K/N joints), chord side wall buckling (Mode B — β ≈ 1.0), chord shear (Mode C — K-gap joints), punching shear (Mode D — thin chord face), brace failure (Mode E — brace yield or buckling), and local brace buckling (Mode F — high d/t brace). The lowest resistance across all applicable modes governs. For typical truss K-joints with β = 0.6-0.8, chord face plastification governs.

How does the CIDECT design guide relate to EN 1993-1-8 HSS joint design?

CIDECT design guides 1-9 are the research foundation for EN 1993-1-8 Clause 7. The EN 1993-1-8 tables are directly derived from CIDECT Design Guide 3 (RHS joints) and Design Guide 1 (CHS joints). CIDECT guides provide additional joint configurations (multi-planar, plate-to-RHS, bolted flange plate) not fully covered in EN 1993-1-8, plus extensive design charts. EN 1993-1-8 is normative; CIDECT guides are complementary non-contradictory references.

What are the validity ranges for EN 1993-1-8 HSS joint design formulas?

EN 1993-1-8 Clause 7 imposes strict validity ranges: β = b_1/b_0 ≥ 0.35 for RHS (≥ 0.2 for CHS), b_0/t_0 ≤ 35 for RHS (≤ 50 for CHS), b_i/t_i ≤ 35 for RHS braces, brace angle θ ≥ 30°, gap g ≥ t_1 + t_2 for K-joints, and overlap λ_ov ≥ 25% for overlapped joints. Joints outside these limits require FE analysis or physical testing per EN 1990 Annex D.

How is the chord stress function k_n applied in HSS joint design?

The chord stress function k_n reduces joint capacity when the chord carries significant axial stress. For RHS chords: k_n = 1.3 - 0.4|n|/β with 1.0 ≥ k_n ≥ 0.4 (compression) or k_n = 1.0 (tension). n is the chord utilisation ratio. A chord in heavy compression (n > 0.7) can reduce joint capacity by up to 60%, meaning chord members should be sized for the joint check, not just the member axial check.

What is the difference between gap, overlap, and butt K-joints?

Gap K-joints have a physical gap g ≥ t_1 + t_2 between braces on the chord face. Chord face plastification is the typical governing mode. Overlap K-joints (λ_ov ≥ 25%) have braces overlapping on the chord face, with load transferring partially through the overlapping brace. 100% overlap joints are essentially direct brace-to-brace connections. Overlap joints are more efficient but more complex to fabricate. The hidden weld of the overlapped brace toe is critical for Types 1 and 2 overlap.

How are K-joint chord face plastification resistances calculated per EN 1993-1-8?

For RHS K-gap joints: N_i,Rd = (k_n × f_y0 × t_0²)/((1 - β) × sin θ_i) × (2β/sin θ_i + 4√(1 - β)) / γ_M5. The term (2β/sin θ_i + 4√(1 - β)) represents the effective width of the chord face yield line mechanism. γ_M5 = 1.00 (recommended value). For CHS joints, the gap factor k_g = γ^0.2 × [1 + 0.024γ^1.2/(exp(0.5g/t_0 - 1.33) + 1)] accounts for the merging of yield line patterns at small gaps.

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.

Quick access: Bolted Connections Calculator | EN 1993 Connection Design | EN 1993 Beam Design | Beam Capacity Calculator

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.