Formulas: welds of plates and branches to HSS

Formula 1

| Chord wall slenderness | $B/t$ and $H/t \leq 35$ |

H/t \leq 35

Formula 2

| Branch wall slenderness | $B_b/t_b$ and $H_b/t_b \leq 35$ and $\leq 1.25\sqrt{E/F_{yb}}$ |

H_b/t_b \leq 35

Formula 3

| Width ratio | $B_b/B \geq 0.25$ |

B_b/B \geq 0.25

Formula 4

| Aspect ratio | $0.5 \leq H_b/B_b \leq 2.0$ and $0.5 \leq H/B \leq 2.0$ |

0.5 \leq H_b/B_b \leq 2.0

Formula 5

0.5 \leq H/B \leq 2.0

Formula 6

| Material strength | $F_y$ and $F_{yb} \leq 52$ ksi (360 MPa) |

F_{yb} \leq 52

Formula 7

| Ductility | $F_y/F_u$ and $F_{yb}/F_{ub} \leq 0.8$ (Note: ASTM A500/A500M Grade C is acceptable) |

F_{yb}/F_{ub} \leq 0.8

Formula 8

Section A-A: Effective weld layout for conditions where $B_{bj} \le 0.85$ and $\theta_j \le 50^\circ$ .

B_{bj} \le 0.85

Formula 9

\theta_j \le 50^\circ

Formula 10

when $\frac{B_{b j}}{B} \leq 0.85$ and $\theta_{j} \leq 50^{\circ}$

\frac{B_{b j}}{B} \leq 0.85

Formula 11

\theta_{j} \leq 50^{\circ}

Formula 12

$\frac{B_{bj}}{B} > 0.85$ OR

\frac{B_{bj}}{B} > 0.85

Formula 13

\theta_j > 50^\circ

Formula 14

When $25 \% \leq O_{\mathrm{v}}<50 \%$

25 \% \leq O_{\mathrm{v}}<50 \%

Equation K5-10

\begin{aligned} l_{e, i} & =\frac{20 O_{v}}{50}\left[\left(1-\frac{O_{v}}{100}\right)\left(\frac{H_{b i}}{\sin \theta_{i}}\right)+\frac{O_{v}}{100}\left(\frac{H_{b i}}{\sin \left(\theta_{i}+\theta_{j}\right)}\right)\right] \\ & +B_{e o i}+B_{e o v} \end{aligned}

Equation K5-11

\begin{aligned} l_{e, i} & =2\left\{\left(1-\frac{O_{v}}{100}\right)\left(\frac{H_{b i}}{\sin \theta_{i}}\right)+\frac{O_{v}}{100}\left[\frac{H_{b i}}{\sin \left(\theta_{i}+\theta_{j}\right)}\right]\right\} \\ & +B_{e o i}+B_{e o v} \end{aligned}

Formula 17

When $80 \% \leq O_{y}<100 \%$

80 \% \leq O_{y}<100 \%

Equation K5-12

\begin{aligned} l_{e, i} & =2\left\{\left(1-\frac{O_{v}}{100}\right)\left(\frac{H_{b i}}{\sin \theta_{i}}\right)+\frac{O_{v}}{100}\left(\frac{H_{b i}}{\sin \left(\theta_{i}+\theta_{j}\right)}\right)\right\} \\ & +B_{b i}+B_{e o v} \end{aligned}

Equation K3-13

B_{e o i}=\frac{10}{B / t}\left(\frac{F_{y} t}{F_{y b i} t_{b i}}\right) B_{b i} \leq B_{b i}

Formula 20

B_{\mathrm{eov}}=\frac{10}{B_{b j} / t_{b j}}\left(\frac{F_{y b j} t_{b j}}{F_{y b i} t_{b i}}\right) B_{b i} \leq B_{b i}

Formula 21

When $B_{b i} / B>0.85$ or $\theta_{i}>50^{\circ}, B_{e o i} / 2$ shall not exceed $B_{b i} / 4$ and when $B_{b i} / B_{b j}>0.85$ or $\left(180-\theta_{i}-\theta_{j}\right)>50^{\circ}, B_{e o v} / 2$ shall not exceed $B_{b i} / 4$ .

B_{b i} / B>0.85

Formula 22

\theta_{i}>50^{\circ}, B_{e o i} / 2

Formula 23

B_{b i} / B_{b j}>0.85

Formula 24

\left(180-\theta_{i}-\theta_{j}\right)>50^{\circ}, B_{e o v} / 2

Equation K5-13

l_{e, j}=\frac{2 H_{b j}}{\sin \theta_{j}}+2 B_{e j}

Equation K5-14

B_{e j}=\frac{10}{B / t}\left(\frac{F_{y} t}{F_{y b j} t_{b j}}\right) B_{b j} \leq B_{b j}

Formula 27

When $B_{b j} / B>0.85$ or $\theta_{i}>50^{\circ}$

B_{b j} / B>0.85

Formula 28

\theta_{i}>50^{\circ}

Formula 29

l_{e, j}=2\left(H_{b j}-1.2 t_{b j}\right) / \sin \theta_{j} \quad \text { (K5-15) }

Formula 30

l_e = \frac{4}{\sqrt{2\beta(D/t}} l_w \le l_w

Equation K5-17

l_w = \pi D_b \frac{1 + 1/\sin\theta}{2}

Found in

WELDS OF PLATES AND BRANCHES TO HSS