Formulas: HSS-to-HSS truss connections

Formula 1

$R_{n}\text{sin}\theta=F_{y}t^{2}\left[\frac{5.5}{1-0.81\left(\frac{B_{b}}{D}\right)}\right]Q_{f}$ (K2-1a):

R_{n}\text{sin}\theta=F_{y}t^{2}\left[\frac{5.5}{1-0.81\left(\frac{B_{b}}{D}\right)}\right]Q_{f}

$M_{n}=0.5B_{b}R_{n}$ (K2-1b):

M_{n}=0.5B_{b}R_{n}

Plate axial load: $R_{n}\sin\theta=5.5F_{y}t^{2}\left[1+0.25\left(\frac{l_{b}}{D}\right)\right]Q_{f}$

R_{n}\sin\theta=5.5F_{y}t^{2}\left[1+0.25\left(\frac{l_{b}}{D}\right)\right]Q_{f}

In-plane: $M_{n}=0.8l_{b}R_{n}$

M_{n}=0.8l_{b}R_{n}

HSS wall slenderness: $D/t \leq 50$ for T-connections under branch plate axial load or bending

D/t \leq 50

$D/t \leq 40$ for cross-connections under branch plate axial load or bending

D/t \leq 40

Width ratio: $0.2 < B_{b}/D \leq 1.0$ for transverse branch plate connections

0.2 < B_{b}/D \leq 1.0

Material strength: $F_{y} \leq 52$ ksi (360 MPa)

F_{y} \leq 52

Ductility: $F_{y}/F_{u} \leq 0.8$ Note: ASTM A500/A500M Grade C is acceptable.

F_{y}/F_{u} \leq 0.8