K1General provisions and parameters for HSS connections

For the purposes of this chapter, the centerlines of branch members and chord members shall lie in a common plane. Rectangular HSS connections are further limited to having all members oriented with walls parallel to the plane.

The tables in this chapter are often accompanied by limits of applicability. Connections complying with the limits of applicability listed can be designed considering the limit states provided for each joint configuration. Connections not complying with the limits of applicability listed are not prohibited and must be designed by rational analysis.

User Note: The connection strengths calculated in Chapter K, including the applicable sections of Chapter J, are based on strength limit states only. See the Commentary if excessive connection deformations may cause serviceability or stability concerns.

User Note: Connection strength is often governed by the size of HSS members, especially the wall thickness of truss chords, and this must be considered in the initial design. To ensure economical and dependable connections can be designed, the connections should be considered in the design of the members. Angles between the chord and the branch(es) of less than 30° can make welding and inspection difficult and should be avoided. The limits of applicability provided reflect limitations on tests conducted to date, measures to eliminate undesirable limit states, and other considerations discussed in the Commentary. See Section J3.11b for through-bolt provisions.

This section provides parameters to be used in the design of plate-to-HSS and HSS-to-HSS connections.

The design strength, $\phi R_{n}, \phi M_{n}$, and $\phi P_{n}$, and the allowable strength, $R_{n} / \Omega, M_{n} / \Omega$, and $P_{n} / \Omega$, of connections shall be determined in accordance with the provisions of this chapter and the provisions of Chapter B.

K1.1 Definitions of Parameters

• $A_{g}=$ gross cross-sectional area of member, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$
• $B$ = overall width of rectangular HSS chord member measured $90^{\circ}$ to the plane of the connection, in. (mm)
• $B_{b}=$ overall width of rectangular HSS branch member or plate measured $90^{\circ}$ to the plane of the connection, in. (mm)
• $B_{e}=$ effective width of rectangular HSS branch member or plate for local yielding of the transverse element, in. (mm)
• $\begin{aligned} B_{e p} & =\text { effective width of rectangular HSS branch member or plate for punching shear, } \\ & \text { in. (mm) }\end{aligned}$
• $D \quad$ = outside diameter of round HSS chord member, in. (mm)
• $D_{b}=$ outside diameter of round HSS branch member, in. (mm)
• $\begin{aligned} F_{c} & =\text { available stress in chord member, ksi (MPa) } \\ & =F_{y} \text { for LRFD; } 0.60 F_{y} \text { for ASD }\end{aligned}$
• $F_{u}=$ specified minimum tensile strength of HSS chord member material, ksi (MPa)
• $F_{u b}=$ specified minimum tensile strength of HSS branch member material, ksi (MPa)
• $F_{y}=$ specified minimum yield stress of HSS chord member material, ksi (MPa)
• $\begin{aligned} F_{y b} & =\text { specified minimum yield stress of HSS branch member or plate material, ksi } \\ & \text { (MPa) }\end{aligned}$
• $\begin{aligned} H & =\text { overall height of rectangular HSS chord member measured in the plane of the } \\ & \text { connection, in. (mm) }\end{aligned}$
• $H_{b}=$ overall height of rectangular HSS branch member measured in the plane of the connection, in. (mm)
• $Q_{f}=$ chord-stress interaction parameter
• $\begin{aligned} l_{\text {end }} & =\text { distance from the near side of the connecting branch or plate to end of chord, } \\ & \text { in. (mm) }\end{aligned}$
• $t \quad$ = design wall thickness of HSS chord member, in. (mm)
• $t_{b} \quad=$ design wall thickness of HSS branch member or thickness of plate, in. (mm)
• $\beta$ = width ratio; the ratio of branch diameter to chord diameter $=D_{b} / D$ for round HSS; the ratio of overall branch width to chord width $=B_{b} / B$ for rectangular HSS
• $\beta_{e f f}=$ effective width ratio; the sum of the perimeters of the two branch members in a K-connection divided by eight times the chord width
• $\begin{aligned} \gamma & =\text { chord slenderness ratio; the ratio of one-half the diameter to the wall thickness } \\ & =D / 2 t \text { for round HSS, or the ratio of one-half the width to wall thickness } \\ & =B / 2 t \text { for rectangular HSS }\end{aligned}$
• $\begin{aligned} \eta & =\text { load length parameter, applicable only to rectangular HSS; the ratio of the } \\ & \text { length of contact of the branch with the chord in the plane of the connection to } \\ & \text { the chord width }=l_{b} / B\end{aligned}$
• $\theta \quad=$ acute angle between the branch and chord, degrees

K1.2 Rectangular HSS

K1.2a Effective Width for Connections to Rectangular HSS

For local yielding of transverse elements, the effective width of elements (plates or rectangular HSS branches) perpendicular to the longitudinal axis of a rectangular HSS member that deliver a force component transverse to the face of the member shall be taken as

For shear yielding (punching), the effective width of the face of a rectangular HSS member, adjacent to the transverse element (plates or rectangular HSS branches) shall be taken as

User Note: Section J4 addresses the strength of affected elements in tension, compression, flexure, and shear. The effective widths defined in this section are used to establish the effective areas to be used when checking these limit states. The Commentary provides further guidance.

K1.3 Chord-Stress Interaction Parameter

Where required, the chord-stress interaction parameter, $Q_{f}$, shall be taken as the fol- lowing:

(a) For HSS chord member connecting surface in tension, $Q_{f}=1$

• (b) For round HSS chord member connecting surface in compression

• (c) For rectangular HSS chord member connecting surface in compression
• (1) For T-, Y-, cross-, and transverse plate connections

• (2) For gapped K-connections

(K1-5)

• (3) For longitudinal plate connections

where

(K1-6)

where $P_{r o}$ and $M_{r o}$ are determined in the HSS chord member on the side of the joint that has lower compression stress for round HSS and higher compression stress for rectangular HSS. $P_{r o}$ and $M_{r o}$ refer to required strengths in the HSS chord: $P_{r o}=P_{u}$ for LRFD, and $P_{a}$ for ASD; $M_{r o}=M_{u}$ for LRFD, and $M_{a}$ for ASD.

Limits of applicability:

$D / t \leq 50$ for round HSS T-, Y-, and K-connections

$D / t \leq 40$ for round HSS cross-connections

$B / t$ and $H / t \leq 35$ for rectangular HSS gapped K-connections and T-, Y-, and cross-connections

$F_{y} \leq 52 \mathrm{ksi}(360 \mathrm{MPa})$

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

K1.4 End Distance

The available strength of the connection in Chapters J and K assume a chord member with a minimum end distance, $l_{\text {end }}$, on both sides of a connection.

(a) For rectangular sections

(b) For round sections

When the connection occurs at a distance less than $l_{\text {end }}$ from an unreinforced end of the chord, the available strength of the connection shall be reduced by 50%.