-------------- | ----------------------------------- | --------------------------------------------------- | | X-joint | Brace to brace crossing | Chord face plastification, punching shear | | T-joint | Brace perpendicular to chord | Chord face plastification, chord side wall buckling | | Y-joint | Brace at angle to chord | Chord face plastification, brace effective width | | K-joint (gap) | Two braces, same chord, gap | Chord face/brace/chord shear interaction | | K-joint (overlap) | Two braces, overlapping | Local yielding, brace wall buckling | | N-joint | K configuration, one vertical brace | Same as K-joint |

Chord Face Plastification — CHS Joints (EN 1993-1-8 Table 7.2)

For CHS joints, the joint resistance is based on chord face plastification:

[ N*{i,\text{Rd}} = \frac{f*{y0} t0^2}{\sin \theta_i} (2.8 + 14.2 \beta^2) \frac{k_g k_p}{\gamma{M5}} ]

Where β = d₁/d₀, γ = d₀/(2t₀), k_g = gap factor, and k_p = chord stress factor.

Chord Face Plastification — RHS Joints (EN 1993-1-8 Table 7.11)

For RHS T, Y, and X joints:

[ N*{1,\text{Rd}} = \frac{f*{y0} t0^2}{\sin \theta_1} \left( \frac{2 \eta}{\sqrt{1 - \beta}} + 4 \sqrt{1 - \beta} \right) \frac{1}{\gamma{M5}} ]

Where η = h₁/b₀ and β = b₁/b₀.

Validity Limits (EN 1993-1-8 Table 7.1)

CHS joints:

RHS joints:

Joint Resistance Table — CHS K-Joints, S355J2

Punching Shear Check (EN 1993-1-8 Clause 7.2.3.2)

[ N*{i,\text{Rd}} = \frac{f*{y0} t0}{\sqrt{3} \sin \theta_i} \cdot \frac{\pi d_1 (1 + \sin \theta_i)}{4 \sin \theta_i} \cdot \frac{1}{\gamma{M5}} ]

Worked Example — CHS K-Joint with Gap

Given: Chord CHS 219.1×10 S355J2, brace CHS 139.7×6.3 S355J2, angle 45°, gap 30 mm.

β = 0.64, γ = 10.95. Validity: β OK (0.2-1.0), γ OK (7-50), gap 30 > 12.6 (OK).

k_g = γ^{0.2} (1 + 0.024 γ^{1.2}) = 1.61 × 1.49 = 2.40 k_p = 1.0 (chord at 50% utilisation)

Compression: N_i,Rd = 355 × 100 / sin(45°) × (2.8 + 14.2 × 0.64²) / 1.0 × 2.40 × 10⁻³ = 425 kN

Tension: N_i,Rd = 340 kN (punching shear governs)

Design Resources

• UK HSS Section Properties — CHS/RHS/SHS tables
• UK Connection Design — General design
• UK Weld Capacity — Fillet weld design
• UK Brace Connection — Bracing joints
• All UK References

Frequently Asked Questions

How are HSS joint capacities calculated per EN 1993-1-8?

Per EN 1993-1-8 Clause 7 using specific formulas for each joint type. The primary failure modes are chord face plastification (most common), punching shear, chord side wall buckling, and brace effective width failure. The governing mode depends on geometry parameters β (diametre/width ratio) and γ (chord slenderness).

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

The formulas are valid only within specific parameter ranges. For CHS: 0.2 ≤ β ≤ 1.0, 7 ≤ γ ≤ 50. For RHS: 0.25 ≤ β ≤ 1.0, 7 ≤ γ ≤ 35. Outside these limits, finite element analysis or testing is required per EN 1993-1-8 Clause 7.

What is the difference between gap and overlap K-joints in UK practice?

In gap K-joints, the two braces are separated by a gap. Failure involves chord face plastification between the braces. In overlap K-joints, one brace overlaps the other, changing the load transfer path. UK practice generally prefers gap joints for fabrication simplicity.

What γ_M5 factor applies per UK NA for HSS joints?

EN 1993-1-8 specifies γ_M5 = 1.00. The UK NA adopts this recommended value without modification. For member design, γ_M0 = 1.00 and γ_M1 = 1.00 per UK NA to EN 1993-1-1.

Connection Design Methods

Eccentric Load on Bolt Groups

When a bolt group is subject to combined shear and moment, the instantaneous centre of rotation (ICR) method provides the most accurate analysis. The critical bolt has the maximum resultant force from:

1. Direct shear component: P/n (equal distribution assumed for serviceability)
2. Moment component: M × r / Σr² (elastic vector method for preliminary design)

For ultimate design, the ICR method accounts for nonlinear bolt deformation using: Rn = Rult(1 - e⁻¹⁰Δ)⁰·⁵⁵ (per AISC Manual)

Block Shear

Block shear is a limit state combining tension rupture on one plane and shear rupture or yielding on a perpendicular plane. The controlling resistance is:

AISC: Rn = min(0.60FuAnv + UbsFuAnt, 0.60FyAgv + UbsFuAnt)

Where Ant = net tension area, Anv = net shear area, Agv = gross shear area, and Ubs = 1.0 for uniform tension stress.

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Frequently Asked Questions

What is the recommended design procedure for this structural element?

The standard design procedure follows: (1) establish design criteria including applicable code, material grade, and loading; (2) determine loads and applicable load combinations; (3) analyse the structure for internal forces; (4) check member strength for all applicable limit states; (5) verify serviceability requirements; and (6) detail connections. Computer analysis is recommended for complex structures, but hand calculations should be used for verification of critical elements.

How do different design codes compare for this calculation?

AISC 360 (US), EN 1993 (Eurocode), AS 4100 (Australia), and CSA S16 (Canada) follow similar limit states design philosophy but differ in specific resistance factors, slenderness limits, and partial safety factors. Generally, EN 1993 uses partial factors on both load and resistance sides (γM0 = 1.0, γM1 = 1.0, γM2 = 1.25), while AISC 360 uses a single resistance factor (φ). Engineers should verify which code is adopted in their jurisdiction.

Reference only. Verify all values against the current edition of EN 1993-1-1:2005, UK National Annex, and BS EN 1090-2. This information does not constitute professional engineering advice.