by Jeffrey A. Packer
Bahen/Tanenbaum Professor of Civil Engineering, University of Toronto, Ontario, Canada
Single-story frames can be fabricated by welding round or square/rectangular HSS together, typically with a pitched roof, forming so-called Knee connections as illustrated in Figure 1. Such frames are used in light construction, such as with greenhouses, and as portal frames (Hancock et al., 2005).
These planar frame connections are loaded principally in bending, with the moments causing opening or closing of the connection angle. They have a rotational stiffness that generally characterizes them as semi-rigid, or partially restrained (PR), unless the members are stocky and the connection is stiffened. As noted in the AISC 360-16 Specification Section B3.4b(b), the load-deformation response characteristics need to be included in the analysis of the structure. Moreover, PR connections need to have sufficient strength, stiffness and deformation capacity at the strength limit states. In order to investigate these characteristics, research has been performed on this type of moment connection, both stiffened and unstiffened (see Figure 1), particularly in Germany where they are known as “L-joints”. Initially, experimentation was done on rectangular HSS Knee connections (Mang et al., 1980), and later experimental and numerical studies were performed on round HSS Knee connections, both under static and fatigue loading (Mang et al., 1997, 1998; Puthli et al., 1997; Karcher 2001; Karcher and Puthli, 2001). Summaries of the static behavior of Knee connections are given in CIDECT Design Guides 1 (Wardenier et al., 2008) and 3 (Packer et al., 2009), and in Packer and Henderson (1997). Knee connections using German hot-formed square and rectangular HSS, when unstiffened, tended to fail by excessive deformation of the lateral HSS cross-wall in compression. On the other hand, for connections with a stiffening plate excessive deformations only appeared for very thin-walled members; with thicker-walled HSS complete plastification was reached. Subsequent research on cold-formed rectangular HSS Knee connections in Australia (Wilkinson and Hancock, 1998a, 1998b; Wilkinson, 1999) has shown that both unstiffened and plate-stiffened welded Knee connections, meeting the design criteria presented below, do not always have sufficient moment-rotation properties for use in plastically designed frames, particularly under opening moments. Hence, such Knee connections are appropriate only in elastically designed frames. For all the design criteria below, the use of HSS with compact cross sections is required.
Design of Rectangular HSS Knee Connections
Matched-width HSS can be mitered and welded together as illustrated in Figure 2. For the unstiffened case, weld quality and HSS edge preparations are critical. The opportunity to fillet weld to a plate clearly simplifies fabrication for the stiffened connection case, as well as producing a stiffer and stronger connection. Mang et al. (1980) showed that the design of Knee connections could be performed based on a check of the utilization of the HSS capacity under axial load and bending.
For the reinforced case (Figure 1(b)), the connection needs to satisfy, for LRFD (Mang et al., 1980):
where Φ = 0.9, the subscript i = 1 or 2 (pertains to the two members in Figure 1(b)), Mip is the applied in-plane bending moment, and Zi = plastic section modulus of member i about the appropriate bending axis. The thickness of the stiffening plate (Figure 1(b)) is required to be tp ≥ 1.5t and ≥ 3/8 in. Eq. (1) applies to all connection angles, θ. With the stiffened connection, which is preferable, there is the opportunity to have two slightly different rectangular HSS sizes.
For the unreinforced case (Figure 1(a)), the connection degree of utilization is reduced to a factor α ≤ 1.0, according to Eq. (2), for LRFD (Mang et al., 1980):
where, for θ = 90o:
and the orientation of the HSS, to give H and B, is shown in Figure 1(a). The HSS nominal yield stress, Fy, is in units of ksi. For connection angles ≠ 90o,
for 90o < θ ≤ 180o:
which confirms that for obtuse angle connections (θ > 90o) one can take advantage of a strength enhancement. Eqs. (2), (3) and (4) are valid within the ranges: 90o ≤ θ ≤ 180o, 0.5 ≤ B/H ≤ 2.0, 10 ≤ B/t ≤ compact, and also subject to the limits on Pi and Vi (see Figure 1) given by Eqs. (5) and (6):
Design of Round HSS Knee Connections
For the reinforced case (Figure 1(d)), the connection needs to satisfy Eq. (1) for LRFD (Karcher, 2001; Karcher and Puthli, 2001), in the same manner as for rectangular HSS Knee connections. The thickness of the stiffening plate (Figure 1(d)) is required to be tp ≥ 1.5t and ≥ 3/8 in. Eq. (1) again applies to all connection angles, θ. With the stiffened connection, which is preferable, there is the opportunity to have two slightly different round HSS sizes.
For the unreinforced case (Figure 1(c)), the connection degree of utilization is reduced to a factor α ≤ 1.0, according to Eq. (2), for LRFD (Karcher, 2001; Karcher and Puthli, 2001). In Eq. (2),
for 90o ≤ θ ≤ 135o:
with Fy in ksi. Eqs. (2) and (7) are valid within the ranges: 90o ≤ θ ≤ 135o, 8 ≤ D/t ≤ compact, and also subject to the limits on Pi and Vi (see Figure 1) given by Eqs. (5) and (8):
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