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).

**Connection
Behavior**

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):

(1)

where Φ = 0.9, the subscript *i*
= 1 or 2 (pertains to the two members in Figure 1(b)), *M _{ip}* is the applied in-plane bending moment, and

*Z*= plastic section modulus of member

_{i}*i*about the appropriate bending axis. The thickness of the stiffening plate (Figure 1(b)) is required to be

*t*≥ 1.5

_{p}*t*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):

(2)

where, for θ = 90^{o}:

(3)

and the orientation of the HSS, to give *H* and *B*, is shown in Figure 1(a). The HSS nominal yield stress, *F _{y}*, is in units of ksi. For connection angles ≠ 90

^{o},

for 90^{o} < θ ≤ 180^{o}:

(4)

which confirms that for obtuse angle connections (θ > 90^{o})
one can take advantage of a strength enhancement. Eqs. (2), (3) and (4) are
valid within the ranges: 90^{o} ≤ θ ≤ 180^{o}, 0.5 ≤ *B/H* ≤ 2.0, 10 ≤ *B/t ≤ *compact, and also subject to the limits on *P _{i} *and

*V*(see Figure 1) given by Eqs. (5) and (6):

_{i}(5)

(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 *t _{p}* ≥ 1.5

*t*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 90^{o} ≤ θ ≤ 135^{o}:

(7)

with *F _{y}* in ksi. Eqs.
(2) and (7) are valid within the ranges: 90

^{o}≤ θ ≤ 135

^{o}, 8 ≤

*D/t ≤*compact, and also subject to the limits on

*P*and

_{i}*V*(see Figure 1) given by Eqs. (5) and (8):

_{i}(8)

**References**

AISC. 2016. “Specification for Structural Steel Buildings”, ANSI/AISC 360-16, and Commentary, American Institute of Steel Construction, Chicago, IL.

Hancock, G.J., Wilkinson, T. and Zhao, X.-L. 2005. “Cold-Formed Tubular Members and Connections: Structural Behaviour and Design”, Elsevier, Amsterdam, The Netherlands.

Karcher, D. 2001. “Tragverhalten von Rahmen-ecken aus Rundhohlprofilen”, PhD thesis, University of Karlsruhe, Germany.

Karcher, D. and Puthli, R.S. 2001. “The Static Design of Stiffened and Unstiffened CHS L-Joints”, Proceedings of the 9th. International Symposium on Tubular Structures, Düsseldorf, Germany, pp. 221-228.

Mang. F., Herion, S. and Karcher, D. 1997. “L-Joints made of Circular Hollow Sections”, Final Revised CIDECT Report 5BE-10-96, rev. 1997, University of Karlsruhe, Germany.

Mang, F., Steidl, G. and Bucak, Ö. 1980. “Design of Welded Lattice Joints and Moment Resisting Knee made of Rectangular Hollow Sections”, IIW Doc. XV-436-80, University of Karlsruhe, Germany.

Mang, F., Puthli, R. and Karcher, D. 1998. “Investigations on Stiffened and Unstiffened L-Joints made of Circular Hollow Sections”, Proceedings of the 8th. International Symposium on Tubular Structures, Singapore, pp. 197-202.

Packer, J.A. and Henderson, J.E. 1997. “Hollow Structural Section Connections and Trusses – A Design Guide”, 2nd. edition, Canadian Institute of Steel Construction, Toronto, ON.

Packer, J.A., Wardenier, J., Zhao, X.-L., van der Vegte, G.J. and Kurobane, Y. 2009. “Design Guide for Rectangular Hollow Section (RHS) Joints under Predominantly Static Loading”, CIDECT Design Guide No. 3, 2nd. edition, CIDECT, Geneva, Switzerland.

Puthli, R., Mang, F. and Karcher, D. 1997. “The Static Strength of Stiffened and Unstiffened L-Joints made of Circular Hollow Sections”, Proceedings of the 7th. International Offshore and Polar Engineering Conference, Honolulu, Hawaii, USA.

Wardenier, J., Kurobane, Y., Packer, J.A., van der Vegte, G.J. and Zhao, X.-L. 2008. “Design Guide for Circular Hollow Section (CHS) Joints under Predominantly Static Loading”, CIDECT Design Guide No. 1, 2nd. edition, CIDECT, Geneva, Switzerland.

Wilkinson, T. and Hancock, G.J. 1998a. “Tests of Stiffened and Unstiffened Welded Knee Connections in Cold-Formed RHS”, Proceedings of the 8th. International Symposium on Tubular Structures, Singapore, pp. 177-186.

Wilkinson, T. and Hancock, G.J. 1998b. “Tests of Portal Frames in Cold-Formed RHS”, Proceedings of the 8th. International Symposium on Tubular Structures, Singapore, pp. 521-529.

Wilkinson, T. 1999. “The Plastic Behaviour of Cold-Formed Rectangular Hollow Sections”, Ph.D. thesis, University of Sydney, Australia.

June 2019