Table K4.2 · AISC 360-22

Available Strengths of Rectangular HSS-to-HSS Moment Connections

Connection Type	Connection Available Flexural Strength
Branch(es) under out-of-plane bending T- and cross-connections t_b H_b M H B	Limit state: chord sidewall local yielding M_n-op = F′_yt (B - t) (H_b + 5t) (K4-6) φ = 1.00 (LRFD) Ω = 1.50 (ASD)
	Limit state: chord distortional failure, for T-connections and unbalanced cross-connections M_n-op = 2F′_yt [ H_bt + √BHt(B+H) ] (K4-7) φ = 0.95 (LRFD) Ω = 1.58 (ASD)
Branch(es) under in-plane bending T- and cross-connections H_b t_b B_b M θ t H B Not present for T-connection	Limit state: sidewall local yielding When β ≥ 0.85 M_n-ip = 0.5F′_yt (H_b + 5t)² (K4-8) φ = 1.00 (LRFD) Ω = 1.50 (ASD)
For T- and cross-connections, with branch(es) under combined axial load, in-plane bending, and out-of-plane bending, or any combination of these load effects P_r/P_c + M_r-ip/M_c-ip + M_r-op/M_c-op ≤ 1.0 (K4-9) P_r = required axial strength in branch using LRFD or ASD load combinations, kips (N) M_r-ip = required in-plane flexural strength in branch using LRFD or ASD load combinations, kip-in. (N-mm) M_r-op = required out-of-plane flexural strength in branch using LRFD or ASD load combina-tions, kip-in. (N-mm) P_c = available axial strength, kips (N) M_c-ip = available strength for in-plane bending, kip-in. (N-mm) M_c-op = available strength for out-of-plane bending, kip-in. (N-mm) = φM_n-op (LRFD); = M_n-op/Ω (ASD)
Functions
F′_y = F_y for T-connections and 0.8F_y for cross-connections P_ro = P_u for LRFD, and P_a for ASD; M_ro = M_u for LRFD, and M_a for ASD

Figure description:

TABLE K4.2A: Limits of Applicability of Table K4.2

Parameter	Limit
Branch angle	$\theta \cong 90^\circ$
Chord wall slenderness	$B/t$ and $H/t \leq 35$
Branch wall slenderness	$B_b/t_b$ and $H_b/t_b \leq 35$ and $\leq 1.25\sqrt{E/F_{yb}}$
Width ratio	$B_b/B \geq 0.25$
Aspect ratio	$0.5 \leq H_b/B_b \leq 2.0$ and $0.5 \leq H/B \leq 2.0$
Material strength	$F_y$ and $F_{yb} \leq 52$ ksi (360 MPa)
Ductility	$F_y/F_u$ and $F_{yb}/F_{ub} \leq 0.8$ (Note: ASTM A500/A500M Grade C is acceptable)

where

$F_{n w}=$ nominal stress of weld metal in accordance with Chapter J, ksi (MPa)

$S_{i p}=$ effective elastic section modulus of welds for in-plane bending (Table K5.1), in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$
$S_{o p}=$ effective elastic section modulus of welds for out-of-plane bending (Table K5.1), in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$
$\begin{aligned} l_{e} & =\text { total effective weld length of groove and fillet welds to HSS for weld } \\ & \text { strength calculations, in. (mm) }\end{aligned}$
$\begin{aligned} t_{w} & =\text { smallest effective weld throat thickness around the perimeter of branch or } \\ & \text { plate, in. (mm) }\end{aligned}$

User Note: Where flexure results in tension in any load case in the weld the directional strength increase factor cannot exceed 1.0 in fillet welds to the end of rectangular HSS.

When a rectangular overlapped K-connection has been designed in accordance with Table K3.2, and the branch member component forces normal to the chord are 80% balanced (in other words, the branch member forces normal to the chord face differ by no more than 20%), the hidden weld under an overlapping branch may be omitted if the remaining welds to the overlapped branch everywhere develop the full capacity of the overlapped branch member walls.

The weld checks in Tables K5.1 and K5.2 are not required if the welds are capable of developing the full strength of the branch member wall along its entire perimeter (or a plate along its entire length).

User Note: The approach used here to allow downsizing of welds assumes a constant weld size around the full perimeter of the HSS branch. Special attention is required for equal width (or near-equal width) connections to rectangular HSS, which combine partial-joint-penetration groove welds along the matched edges of the connection, with fillet welds generally across the chord member face.

TABLE K5.1 Effective Weld Properties for Connections to Rectangular HSS
Connection Type	Weld Properties
Transverse plate T- and cross-connections under plate axial load [Diagram with labels: R, t_p, H, t, B_b, B]	Effective weld properties l_e = 2B_e (K5-4) where l_e = total effective weld length for welds on both sides of the transverse plate, in. (mm)
T-, Y-, and cross-connections under branch axial load or bending [Diagram with labels: M or P, t_b, H_b, B_b, A, θ, H, t, B, Note: Not present for T- or Y-connection] [Section A-A Diagram with labels: H_b/sinθ, B_e/2] Section A-A: Effective weld	Effective weld properties l_e = 2H_b / sinθ + 2B_e (K5-5) S_ip = (t_w / 3)(H_b / sinθ)² + t_wB_e(H_b / sinθ) (K5-6) S_op = t_w(H_b / sinθ)B_b + (t_w / 3)(B_e)² - ((t_w / 3)(B_b-B_e)³) / B_b (K5-7) When β > 0.85 or θ > 50°, B_e/2 shall not exceed B_b/4.
Gapped K-connections under branch axial load [Diagram with labels: H_b, t_b, A, θ, P, g, +e, H, t, B] [Section A-A Diagram with labels: H_b - 1.2t_b / sinθ, B_b - 1.2t_b] 4th side effective when θ ≤ 50° Section A-A: Effective weld for ≥ 60°	Effective weld properties When θ ≤ 50° l_e = 2(H_b - 1.2t_b) / sinθ + 2(B_b - 1.2t_b) (K5-8) When θ ≥ 60° l_e = 2(H_b - 1.2t_b) / sinθ + B_b - 1.2t_b (K5-9) When 50° < θ < 60°, linear interpolation shall be used to determine l_e.