K4HSS-to-HSS moment connections

AISC 360-22, Specification for Structural Steel Buildings

Last Updated 29 Oct 2026

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HSS-to-HSS moment connections are defined as connections that consist of one or two branch members that are directly welded to a continuous chord that passes through the connection, with the branch or branches loaded by bending moments.

A connection shall be classified as

(a) A T-connection when there is one branch and it is perpendicular to the chord and as a Y-connection when there is one branch, but not perpendicular to the chord
(b) A cross-connection when there is a branch on each (opposite) side of the chord

K4.1 Definitions of Parameters

$Z_{b}=$ plastic section modulus of branch about the axis of bending, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$

K4.2 Round HSS

The available strength of round HSS-to-HSS moment connections within the limits of Table K4.1A shall be taken as the lowest value of the applicable limit states shown in Table K4.1.

TABLE K3.2

Available Strengths of Rectangular HSS-to-HSS Truss Connections

Connection Type Connection Available Axial Strength

Gapped K-Connections

Technical diagram of a Gapped K-Connection involving rectangular hollow structural sections

Figure description:

Technical diagram of a Gapped K-Connection involving rectangular hollow structural sections (HSS:

Main Member (Chord: Specified by height ( $H$ , width ( $B$ , and wall thickness ( $t$ .
Branch Members: Two diagonal members with height ( $H_b$ , width ( $B_b$ , and wall thickness ( $t_b$ , applied axial load ( $P$ , and connection angle ( $\theta$ .
Connection Geometry:
- $g$ : Gap distance between the two branch members on the chord face.
- $e$ : Eccentricity, indicating the vertical offset between the branch axes intersection and the chord centerline.

Overlapped K-Connections

Key Information: Overlapped K-Connection Connection Type: Overlapped K-connection joining two

Figure description:

Key Information: Overlapped K-Connection

Connection Type: Overlapped K-connection joining two diagonal branch members (labeled i and j to a main horizontal chord.
Chord Dimensions:
- $B$ : Chord width
- $H$ : Chord height
- $t$ : Chord wall thickness
Branch Dimensions (Members i & j:
- $B_b$ : Branch width
- $H_b$ : Branch height/depth
- $t_b$ : Branch wall thickness
Geometric & Structural Parameters:
- $\theta$ : Angle between the branch and the chord.
- $e$ (Eccentricity: Vertical distance between the chord's longitudinal axis and the intersection point of the branches' axes.
- $P$ : Axial force applied to branch members.
Configuration Detail: Branch i overlaps branch j at the junction on the chord surface.

Note that the force arrows shown for overlapped K-connections may be reversed; i and j control member identification.

Limit state: chord wall plastification, for all $\beta$ $P_{n}\sin \theta =F_{y}t^{2}\left( 9.8\beta _{eff}\gamma ^{0.5}\right) Q_{f}$ (K3-7) $\phi =0.90$ (LRFD) $\Omega =1.67$ (ASD) Limit state: shear yielding (punching), when $B_{b}<B-2t$ This limit state need not be checked for square branches. $P_{n}\sin \theta =0.6F_{y}tB\left( 2\eta +\beta +\beta _{eop}\right)$ (K3-8) $\phi =0.95$ (LRFD) $\Omega =1.58$ (ASD) Limit state: shear of chord side walls in the gap region Determine $P_{n}\sin \theta$ in accordance with Section G4. This limit state need not be checked for square chords. Limit state: local yielding of branch/branches due to uneven load distribution This limit state need not be checked for square branches or where $B/t\geq 15$ . $P_{n}=F_{yb}t_{b}\left( 2H_{b}+B_{b}+B_{e}-4t_{b}\right)$ (K3-9) $\phi =0.95$ (LRFD) $\Omega =1.58$ (ASD)

Limit state: local yielding of branch/branches due to uneven load distribution $\phi=0.95(\text{LRFD})$ $\Omega=1.58(\text{ASD})$ When $25\%\le O_v<50\%$ $P_{n,i}=F_{ybi}t_{bi}\left[\frac{O_v}{50}(2H_{bi}-4t_{bi})+B_{eoi}+B_{eov}\right]$ (K3-10) When $50\%\le O_v<80\%$ $P_{n,i}=F_{ybi}t_{bi}\left(2H_{bi}-4t_{bi}+B_{eoi}+B_{eov}\right)$ (K3-11) When $80\%\le O_v\le100\%$ $P_{n,i}=F_{ybi}t_{bi}\left(2H_{bi}-4t_{bi}+B_{bi}+B_{eov}\right)$ (K3-12) $B_{eoi}=\frac{10}{B/t}\left(\frac{F_y t}{F_{ybi}t_{bi}}\right)B_{bi}\le B_{bi}$ (K3-13) $B_{eov}=\frac{10}{B_{bj}/t_{bj}}\left(\frac{F_{ybj}t_{bj}}{F_{ybi}t_{bi}}\right)B_{bi}\le B_{bi}$ (K3-14) Subscript $i$ refers to the overlapping branch. Subscript $j$ refers to the overlapped branch. $P_{n,j}=P_{n,i}\left(\frac{F_{ybj}A_{bj}}{F_{ybi}A_{bi}}\right)$ (K3-15)

Functions

$\beta_{eff}=\left[\left(B_{b}+H_{b}\right)_{compression\ branch}+\left(B_{b}+H_{b}\right)_{tension\ branch}\right]/4B$ (K3-16) $\beta_{eop}=\frac{B_{ep}}{B}$ (K3-17)

TABLE K3.2ALimits of Applicability of Table K3.2

Connection eccentricity:	-0.55 ≤ e/H ≤ 0.25 for K-connections
Chord wall slenderness:	B/t and H/t ≤ 35 for gapped K-connections and T-, Y-, and cross-connections
	B/t ≤ 30 for overlapped K-connections
	H/t ≤ 35 for overlapped K-connections
Branch wall slenderness:	B_b/t_b and H_b/t_b ≤ 35 for tension branch
	≤ 1.25 √E/F_yb for compression branch of gapped K-, T-, Y-, and cross-connections
	≤ 35 for compression branch of gapped K-, T-, Y-, and cross-connections
	≤ 1.1 √E/F_yb for compression branch of overlapped K-connections
Width ratio:	B_b/B and H_b/B ≥ 0.25 for T-, Y-, cross-, and overlapped K-connections
Aspect ratio:	0.5 ≤ H_b/B_b ≤ 2.0 and 0.5 ≤ H/B ≤ 2.0
Overlap:	25% ≤ O_v ≤ 100% for overlapped K-connections
Branch width ratio:	B_bi/B_bj ≥ 0.75 for overlapped K-connections, where subscript i refers to the overlapping branch and subscript j refers to the overlapped branch
Branch thickness ratio:	t_bi/t_bj ≤ 1.0 for overlapped K-connections, where subscript i refers to the overlapping branch and subscript j refers to the overlapped branch
Material strength:	F_y and F_yb ≤ 52 ksi (360 MPa)
Ductility:	F_y/F_u and F_yb/F_ub ≤ 0.8 Note: ASTM A500/A500M Grade C is acceptable.

Additional Limits for Gapped K-Connections

Width ratio:	B_b / B and H_b / B ≥ 0.1 + γ / 50
	β_eff ≥ 0.35
Gap ratio:	ξ = g/B ≥ 0.5(1-β_eff)
Gap:	g ≥ t_b compression branch + t_b tension branch
Branch size:	smaller B_b ≥ 0.63(larger B_b), if both branches are square

TABLE K4.1Available Strengths of Round HSS-to-HSS Moment Connections

Connection Type	Connection Available Flexural Strength
Branch(es) under in-plane bending T-, Y-, and cross-connections [Diagram of in-plane bending connection: Shows a round HSS chord with a branch HSS welded to it at an angle, illustrating dimensions M, D_b, t_b, θ, t, D]	Limit state: chord plastification M_n-ip = 5.39F_yt²0.5β (D_b/sinθ) Q_f (K4-1) φ = 0.90 (LRFD) Ω = 1.67 (ASD)
	Limit state: shear yielding (punching), when D_b < (D-2t) M_n-ip = 0.6F_ytD_b² ((1+3sinθ)/(4sin²θ)) (K4-2) φ = 0.95 (LRFD) Ω = 1.58 (ASD)
Branch(es) under out-of-plane bending T-, Y-, and cross-connections [Diagram of out-of-plane bending connection: Shows a round HSS chord with a branch HSS welded perpendicular to it, illustrating dimensions M, D_b, t_b, t, D]	Limit state: chord plastification M_n-op = (F_yt²D_b/sinθ) ((3.0)/(1-0.81β)) Q_f (K4-3) φ = 0.90 (LRFD) Ω = 1.67 (ASD)
	Limit state: shear yielding (punching), when D_b < (D-2t) M_n-op = 0.6F_ytD² ((3+sinθ)/(4sin²θ)) (K4-4) φ = 0.95 (LRFD) Ω = 1.58 (ASD)
For T-, Y-, and cross-connections, with branch(es) under combined axial load, in-plane bend-ing, and out-of-plane bending, or any combination of these load effects P_r/P_c + (M_r-ip/M_c-ip)² + M_r-op/M_c-op ≤ 1.0 (K4-5) 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 combinations, kip-in. (N-mm) P_c = available axial strength obtained from Table K3.1, 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)

TABLE K4.1ALimits of Applicability of Table K4.1

Chord wall slenderness:	D/t ≤ 50 for T- and Y-connections D/t ≤ 40 for cross-connections
Branch wall slenderness:	Db/tb ≤ 50 0.05E/Fyb ≤ Db/tb
Width ratio:	0.2 < Db/D ≤ 1.0
Material strength:	Fy and Fyb ≤ 52 ksi (360 MPa)
Ductility:	Fy/Fu and Fyb/Fub ≤ 0.8 Note: ASTM A500/A500M Grade C is acceptable.

K4.3 Rectangular HSS

The available strength, $\phi P_{n}$ and $P_{n} / \Omega$ , of rectangular HSS-to-HSS moment connections within the limits in Table K4.2A shall be taken as the lowest value obtained according to limit states shown in Table K4.2 and Chapter J.

User Note: Outside the limits in Table K4.2A, the limit states of Chapter J are still applicable and the applicable limit states of Chapter K are not defined.

K4HSS-to-HSS moment connections

AISC 360-22, Specification for Structural Steel Buildings

Last Updated 29 Oct 2026

Hover any section to copy its link or text, ask Copilot about it, or bookmark it.

A connection shall be classified as

(a) A T-connection when there is one branch and it is perpendicular to the chord and as a Y-connection when there is one branch, but not perpendicular to the chord
(b) A cross-connection when there is a branch on each (opposite) side of the chord

K4.1 Definitions of Parameters

$Z_{b}=$ plastic section modulus of branch about the axis of bending, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$

K4.2 Round HSS

The available strength of round HSS-to-HSS moment connections within the limits of Table K4.1A shall be taken as the lowest value of the applicable limit states shown in Table K4.1.

TABLE K3.2

Available Strengths of Rectangular HSS-to-HSS Truss Connections

Connection Type Connection Available Axial Strength

Gapped K-Connections

Technical diagram of a Gapped K-Connection involving rectangular hollow structural sections

Figure description:

Technical diagram of a Gapped K-Connection involving rectangular hollow structural sections (HSS:

Main Member (Chord: Specified by height ( $H$ , width ( $B$ , and wall thickness ( $t$ .
Branch Members: Two diagonal members with height ( $H_b$ , width ( $B_b$ , and wall thickness ( $t_b$ , applied axial load ( $P$ , and connection angle ( $\theta$ .
Connection Geometry:
- $g$ : Gap distance between the two branch members on the chord face.
- $e$ : Eccentricity, indicating the vertical offset between the branch axes intersection and the chord centerline.

Overlapped K-Connections

Key Information: Overlapped K-Connection Connection Type: Overlapped K-connection joining two

Figure description:

Key Information: Overlapped K-Connection

Connection Type: Overlapped K-connection joining two diagonal branch members (labeled i and j to a main horizontal chord.
Chord Dimensions:
- $B$ : Chord width
- $H$ : Chord height
- $t$ : Chord wall thickness
Branch Dimensions (Members i & j:
- $B_b$ : Branch width
- $H_b$ : Branch height/depth
- $t_b$ : Branch wall thickness
Geometric & Structural Parameters:
- $\theta$ : Angle between the branch and the chord.
- $e$ (Eccentricity: Vertical distance between the chord's longitudinal axis and the intersection point of the branches' axes.
- $P$ : Axial force applied to branch members.
Configuration Detail: Branch i overlaps branch j at the junction on the chord surface.

Note that the force arrows shown for overlapped K-connections may be reversed; i and j control member identification.

Functions

$\beta_{eff}=\left[\left(B_{b}+H_{b}\right)_{compression\ branch}+\left(B_{b}+H_{b}\right)_{tension\ branch}\right]/4B$ (K3-16) $\beta_{eop}=\frac{B_{ep}}{B}$ (K3-17)

TABLE K3.2ALimits of Applicability of Table K3.2

Connection eccentricity:	-0.55 ≤ e/H ≤ 0.25 for K-connections
Chord wall slenderness:	B/t and H/t ≤ 35 for gapped K-connections and T-, Y-, and cross-connections
	B/t ≤ 30 for overlapped K-connections
	H/t ≤ 35 for overlapped K-connections
Branch wall slenderness:	B_b/t_b and H_b/t_b ≤ 35 for tension branch
	≤ 1.25 √E/F_yb for compression branch of gapped K-, T-, Y-, and cross-connections
	≤ 35 for compression branch of gapped K-, T-, Y-, and cross-connections
	≤ 1.1 √E/F_yb for compression branch of overlapped K-connections
Width ratio:	B_b/B and H_b/B ≥ 0.25 for T-, Y-, cross-, and overlapped K-connections
Aspect ratio:	0.5 ≤ H_b/B_b ≤ 2.0 and 0.5 ≤ H/B ≤ 2.0
Overlap:	25% ≤ O_v ≤ 100% for overlapped K-connections
Branch width ratio:	B_bi/B_bj ≥ 0.75 for overlapped K-connections, where subscript i refers to the overlapping branch and subscript j refers to the overlapped branch
Branch thickness ratio:	t_bi/t_bj ≤ 1.0 for overlapped K-connections, where subscript i refers to the overlapping branch and subscript j refers to the overlapped branch
Material strength:	F_y and F_yb ≤ 52 ksi (360 MPa)
Ductility:	F_y/F_u and F_yb/F_ub ≤ 0.8 Note: ASTM A500/A500M Grade C is acceptable.

Additional Limits for Gapped K-Connections

Width ratio:	B_b / B and H_b / B ≥ 0.1 + γ / 50
	β_eff ≥ 0.35
Gap ratio:	ξ = g/B ≥ 0.5(1-β_eff)
Gap:	g ≥ t_b compression branch + t_b tension branch
Branch size:	smaller B_b ≥ 0.63(larger B_b), if both branches are square

TABLE K4.1Available Strengths of Round HSS-to-HSS Moment Connections

Connection Type	Connection Available Flexural Strength
Branch(es) under in-plane bending T-, Y-, and cross-connections [Diagram of in-plane bending connection: Shows a round HSS chord with a branch HSS welded to it at an angle, illustrating dimensions M, D_b, t_b, θ, t, D]	Limit state: chord plastification M_n-ip = 5.39F_yt²0.5β (D_b/sinθ) Q_f (K4-1) φ = 0.90 (LRFD) Ω = 1.67 (ASD)
	Limit state: shear yielding (punching), when D_b < (D-2t) M_n-ip = 0.6F_ytD_b² ((1+3sinθ)/(4sin²θ)) (K4-2) φ = 0.95 (LRFD) Ω = 1.58 (ASD)
Branch(es) under out-of-plane bending T-, Y-, and cross-connections [Diagram of out-of-plane bending connection: Shows a round HSS chord with a branch HSS welded perpendicular to it, illustrating dimensions M, D_b, t_b, t, D]	Limit state: chord plastification M_n-op = (F_yt²D_b/sinθ) ((3.0)/(1-0.81β)) Q_f (K4-3) φ = 0.90 (LRFD) Ω = 1.67 (ASD)
	Limit state: shear yielding (punching), when D_b < (D-2t) M_n-op = 0.6F_ytD² ((3+sinθ)/(4sin²θ)) (K4-4) φ = 0.95 (LRFD) Ω = 1.58 (ASD)
For T-, Y-, and cross-connections, with branch(es) under combined axial load, in-plane bend-ing, and out-of-plane bending, or any combination of these load effects P_r/P_c + (M_r-ip/M_c-ip)² + M_r-op/M_c-op ≤ 1.0 (K4-5) 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 combinations, kip-in. (N-mm) P_c = available axial strength obtained from Table K3.1, 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)

TABLE K4.1ALimits of Applicability of Table K4.1

Chord wall slenderness:	D/t ≤ 50 for T- and Y-connections D/t ≤ 40 for cross-connections
Branch wall slenderness:	Db/tb ≤ 50 0.05E/Fyb ≤ Db/tb
Width ratio:	0.2 < Db/D ≤ 1.0
Material strength:	Fy and Fyb ≤ 52 ksi (360 MPa)
Ductility:	Fy/Fu and Fyb/Fub ≤ 0.8 Note: ASTM A500/A500M Grade C is acceptable.

K4.3 Rectangular HSS

User Note: Outside the limits in Table K4.2A, the limit states of Chapter J are still applicable and the applicable limit states of Chapter K are not defined.