# D12.B.7 Tubular Joint Resistance

## D12.B.7.1 Basic Joint Resistances

The characteristic joint resistance between a chord and a brace is given by:

${N}_{Rd}=\frac{{f}_{y}{T}^{2}}{{\gamma}_{M}\mathrm{sin}\theta}{Q}_{u}{Q}_{f}$ |

${M}_{Rd}=\frac{{f}_{y}{T}^{2}d}{{\gamma}_{M}\mathrm{sin}\theta}{Q}_{u}{Q}_{f}$ |

Where:

- N
_{Rd}is the joint design axial resistance - M
_{Rd}is the joint design bending moment resistance. - f
_{y}is the yield strength - γ
_{m}= Default material resistance =1.15 - θ is the angle between the chord and the brace (max θ = 90 degrees)
- Q
_{u}= Strength factor which varies with the joint type and the action type in the brace. Refer to Table 6-3 and Clause 6.4.3.3 of N-004 for these equations. - Q
_{f}= 1.0 – λA^{2}

${A}^{2}={C}_{1}{\left(\frac{{\sigma}_{a,Sd}}{{f}_{y}}\right)}^{2}+{C}_{2}\left(\frac{{\sigma}_{my,Sd}^{2}+{\sigma}_{mz,Sd}^{2}}{1.62{f}_{y}^{2}}\right)$

- σ
_{p,Sd}is the design axial stress in the chord - σ
_{my,Sd}is the design in-plane bending stress in the chord - σ
_{mz,Sd}is the design out-of-plane bending stress in the chord - C1 is the coefficient used for the axial stress term in calculating the joint resistance. C2 is the coefficient used for the bending stress term in calculating the joint resistance. The default values of C1 and C2 are as given in Table 6-4 of N-004. The actual values used are dependent on the values of K, X, and Y specified for the joint in the external geometry file.
- See also Figures 6-3 to 6-6 of N-004 for definition of the various terms for various joint classes.

## D12.B.7.2 Strength Check for Joints

Each brace to chord joint to be checked will have to satisfy the following condition:

$\frac{{N}_{Sd}}{{N}_{Rd}}+{\left(\frac{{M}_{z,Sd}}{{M}_{z,Rd}}\right)}^{2}+\frac{{M}_{y,Sd}}{{M}_{y,Rd}}\le 1$

Where:

- N
_{Sd}is the design axial force in the brace, - N
_{Rd}is the joint design axial resistance - M
_{z,Sd}is the in plane bending moment in the brace - M
_{y,Sd}is the out of plane bending moment in the brace - M
_{z,Rd}is the in plane bending moment resistance - M
_{y,Rd}is the out of plane bending moment resistance