OTHER TYPES OF JOINTS OR OTHER LOAD CONDITIONS

9.7.1 Related types of joints

As for circular hollow section joints, various joint configurations exist for which the resistance can be directly related to the basic types presented in Tables 9.1 and 9.2.

Table 9.3 gives the design resistance for some special types of RHS uniplanar joints with braces directly welded to the chord; notice the similarity with Table 8.2 for circular hollow section joints.

9.7.2 Joints between circular braces and a rectangular chord

As far as chord face plastification is concerned, the strength of a joint with a circular hollow section brace with diameter di is about π/4 times that of a joint with a square hollow section brace with a width bi = di, see Fig. 9.14 (Wardenier, 1982; Packer et al., 2007). As a consequence, the same formulae can be used as for square hollow section joints, but the resistances have

to be multiplied by π/4. This also means that the joints have the same efficiency, i.e. the joint strength divided by the squash load of the brace.

9.7.3 Joints between plates or I sections and RHS chords

Joints between plates or I sections and RHS chords are approached in a similar manner as the rectangular hollow section joints and in principle the same modes of failure have to be considered. Within the scope of this book, these joints are not further discussed, but reference is made to Lu (1997), Packer et al. (2009a) and Chapter 12. The design resistances are given in Table 9.4.

Tee joints to the ends of RHS members

When an axial force is applied to an RHS member, via a welded Tee joint as shown in Fig. 9.15, the capacity is determined by local failure of the RHS walls or the Tee web.

For a commonly used distribution slope of 2.5:1 from each face of the Tee web (Kitipornchai & Traves, 1989), the dispersed load width is (5tp + tw). A conservative assumption is to use this effective width at two sides of the RHS member. Thus, the resistance of the RHS can be computed by summing the contributions of the parts of the RHS cross sectional area into which the load is distributed:

1

A similar load dispersion can be assumed for the capacity of the Tee web. If the Tee web has the same width as the width of the cap plate, i.e. (h1 + 2s), the capacity of the Tee web is:

) the Tee web has been conservatively ignored.

Gusset plate-to-slotted RHS joints

Single gusset plates, slotted into the ends of hollow section members and concentrically aligned with the axis of the member, as shown in Fig. 9.16, are commonly found in diagonal brace members of steel framed buildings.

As a consequence of only part of the RHS cross section being connected, an uneven stress distribution

around the RHS perimeter occurs during load transfer at the connection. This phenomenon, known as shear lag, is illustrated in Fig. 9.16.

The possible failure modes for the gusset plate-to-slotted RHS joints loaded in tension are circumferential failure of the RHS and tear out or

"block shear" failure of the RHS. Shear lag is principally influenced by the weld length, Lw in relation to the dimension w which is the distance between the welds measured from plate face-to-plate face, around the perimeter of the RHS.

For long weld lengths, shear lag effects become negligible, while for short weld lengths, tear out governs over circumferential fracture of the RHS.

However, if Lw = 1,65b for square braces and 1,3d for circular braces, it can be assumed that the capacity is equal to that of the connected hollow section or plate.

Detailed design rules are given by Packer et al.

(2009a).

9.7.4 Multiplanar joints

Compared to uniplanar joints, multiplanar joints have a geometric effect and a loading effect to be considered.

It is plausible that a multiplanar joint has a geometric influence only if the β value is large, because then the chord side wall is stiffened, see e.g. Fig. 9.17 for an XX joint.

For multiplanar joints of rectangular hollow sections, the tendency of the loading effect is similar but less pronounced compared to that of joints of circular hollow sections, see Fig. 9.18.

Extensive analytical and numerical research by Liu &

Wardenier (2001, 2003) showed that the differences in capacity between uniplanar K gap and multiplanar KK gap joints are caused by the larger chord force acting in multiplanar joints. Based on this work, the following design recommendations are given for multiplanar KK joints (see Table 9.5).

Multiplanar KK gap joints (Fig. 9.19)

- For chord face plastification (small or medium β), the strength of the joint can be based on the joint resistance formulae for uniplanar joints given in Tables 9.1 and 9.2, and no further multiplanar correction is necessary, provided that the actual, total chord force is used for the chord stress function Qf.

- For large  ratios or rectangular chord sections, the strength of a KK gap joint is governed by chord shear and chord axial force interaction, presented in Table 9.5. The KK gap joint (with  = 90) is subjected to a shear force of 0,5 2V_gap,0,Ed in each plane, where Vgap,0,Ed is the total "vertical" shear force. The shear force in each plane is resisted by the two walls of the RHS chord.

Multiplanar overlap KK joints

- For multiplanar overlap KK joints, the strength of the joint is similar to that for uniplanar overlap joints given in Chapter 11. Thus, compared to the previous IIW (1989) recommendations, a brace shear criterion and a local chord yielding criterion have been added.

9.7.5 Joints loaded by brace bending moments

The design resistances for joints loaded by brace bending moments are derived in a similar way to that for axially loaded joints. To simplify the design, limitations are also given here for the range of validity to reduce the criteria to be checked.

For Vierendeel girders it is recommended to choose joints with  = 1,0 to provide sufficient stiffness and strength.

The design resistance formulae are based on the analyses of Wardenier (1982), Mang et al. (1983), Yu (1997) and Packer et al. (2009a), and are given in Table 9.6.

9.7.6 Interaction between axial loads and bending moments

For joints with brace members subjected to combined loading, the effect of axial load on the joint moment capacity depends on the critical failure mode, and hence a complex set of interactions exists.

Consequently, it is conservatively proposed to use a linear interaction relationship:

0

9.8 DESIGN CHARTS

In Figs. 9.20 to 9.23, the joint resistances are

expressed in terms of the efficiency of the connected braces in a similar way to that for circular hollow section joints, i.e. the joint resistance is given as a fraction of the yield capacity Ai fyi of the connected brace. This results in the following efficiency formula:

i multiplied by

i brace considered.

For a detailed explanation, see Section 8.8.

Using the chart of Fig. 9.23 shows that e.g. a K gap joint with 2  20 and b₁ = b2 gives an efficiency parameter CK  0,37. Thus, for an angle θi = 45, a 100% efficiency can be obtained if:

9

If the chord load effect Qf is included, this ratio should be slightly larger. Figs. 9.24 and 9.25 show the chord load effect Qf as a function of the parameter n, defined as the ratio between the maximum stress in the connecting chord face and the chord yield stress.

9.9 CONCLUDING REMARKS

For more detailed information about joints loaded by bending moments as well as special types of joints, reference is made to the appropriate literature, see Dutta (2002), Korol et al. (1977), Packer & Henderson (1997), Packer et al. (2009a), Ono et al. (1991), Syam

& Chapman (1996), Wardenier (1982) and Wardenier

& Giddings (1986).

Table 9.1 Design axial resistances of welded joints between RHS or CHS braces and RHS chord

Type of joint Design limit state

T, Y and X joints Chord face plastification (for β  0,85)

Local brace failure (general check)

) See chord shear equations for K gap joints, but with V_0,Ed instead of V_gap,0,Ed

Chord side wall failure (for  = 1,0) ⁽¹⁾

K gap joints Chord face plastification (general check)

f

Local brace failure (general check)

)

Chord shear (general check)

RHS braces:

)

Chord compression stress (n < 0) Chord tension stress (n  0) T, Y and X joints C1 = 0,6 – 0,5β f_k where  = reduction factor for column buckling according to e.g. Eurocode 3 (EN 1993-1-1, 2005) using

the relevant buckling curve and a slenderness

1

(1) For 0,85 <  < 1,0 use linear interpolation between the resistance for chord face plastification at  = 0,85 and the resistance for chord side wall failure at  = 1,0.

Table 9.1 Design axial resistances of welded joints between RHS or CHS braces and RHS chord (continued)

T, Y, X and K gap joints with CHS