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12. Connections for lattice structures and bracing 12.1 Introduction This chapter deals with the connections we encounter in trusses, lattice girders, lattice towers, gantries, and the various types of bracing roof, floor, vertical, etc. The common denominator of these connections is that the smaller members connected to them are typically regarded as carrying only axial force (i.e. they are designed with pin connections). The bracing can be attached to a beam, column or chord that carries large moments, in particular to the compression flanges of such members Because only tensile and compressive forces act on these connections, they are commonly regarded as easy and left to somebody with limited training to do. But they demand the same respect as any other connection: they can be designed incorrectly and they can fail. Moreover, some aspects of the design of these simple joints may not be familiar to all engineers engaged in steel design. Note that here we only mention (in 12.2 below) heavy all-welded trusses, vierendeel girders, etc., that occur for example in trusses welded up from H-sections. The joints in such structures are best handled in the same way as rigid beam-to-column connections (see Chapter 8). 12.2 Typical connections and practical details. Figure 12.1 shows a typical light truss, all bolted. Typical connections encountered in such trusses and similar lattice girders are shown in Figure 12.2.

Figure 12.1 Light bolted truss

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Figure 12.2 Typical bolted connections in light trusses The following remarks are apposite:

The splice plate shown in Figure 12.2 (b) serves to enhance the stability of this connection which involves a change in the direction of the force. Nevertheless, the joint still requires bracing against deflection out of the plate of the truss which may, for a small enough truss, be provided by placing the two top purlins close to the apex.

The gusset plates in the sketches are shown neatly trimmed. But if the aesthetics of the structure is of little importance, rectangular gussets may be more economic.

In Figure 12.2 (d) the gusset plate serves both as a gusset and as a splice plate. There is nothing wrong with this arrangement, but the design must be handled with due care.

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In (g) the intersection of the chords falls on the centreline of the column, but in (h) the vertical and diagonal forces cross on the column face. This eccentricity will cause bending moment in the column.

Figure 12.3 Bolted connections in heavier trusses Figure 12.3 shows bolted connections where the chords of the truss, and possibly even the diagonals, consist of heavy sections. In some of the examples shown the gussets are welded to the chord, but they can also be bolted, or vice versa.

Figure 12.4 Light welded truss

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Figure 12.5 Welded connections in light to medium trusses. Figure 12.4 shows a typical welded truss for a roof, whilst typical joint details for such trusses appear in Figure 12.5. In Figure 12.5 (d) the diagonals are welded on two sides of the vertical leg of the chord. This may be attractive from an engineering point of view (although some doubts have been expressed about the torsional effect on the chord) but it requires the whole truss to be turned over during fabrication, which is highly inadvisable from the point of view of minimizing labour. Figure 12.5 (b) requires welding for which quality can hardly be guaranteed. The detail in (f) is easier to make, but the eccentricity e must be taken into account in designing the members. Several of the details shown make it difficult to provide an adequate length of weld (see the discussion in 12.4 below). It may be necessary to provide gusset plates. In such a case it may be tempting to provide toe plates, as shown in Figure 12.6(a), but the temptation should be resisted: it is difficult and expensive to weld a toe plate properly and to ensure quality. A proper gusset is shown in Figure 12.6 (b).

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(a) Toe plate (b) Gusset plate Figure 12.6 Toe and gusset plate Figure 12.7 contains sketches of heavy welded connections. Such connections can make real demands on the capacity of the engineer to innovate, especially as they permit the opportunity to create steel structures that are aesthetically truly pleasing. Note the connection in (f) applicable to large box columns, beams and bracing. The flanges of the bracing element are brought together to allow bolting of the shoe serving the function of gussets. This box is bolted to the column and beam.

Figure 12.7 Welded connections in heavy trusses and girders

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Figure 12.8 shows various kinds of vertical (wall) bracing. Note that in Figure 12.8(c) the slanted bracing element is itself braced by lattice members connecting it to a similar element parallel to it.

Figure 12.8 Vertical bracing Several of the connection details relating to trusses can also be used for vertical bracing, especially the heavy connections, but Figure 12.9 shows more. In most countries it is common practice always to design such details so that the centre lines of the braces, column and horizontal element all cross at a single point, as shown in (a) and (e). However, in South Africa the centreline of the brace is frequently made to hit the column face at the level of the top or the bottom of the beam (as shown in (c), (d) and (h)) or at the level of the centreline of the horizontal member ((b), (e) and (g)). This makes eminent sense if the bracing element is relatively small compared to the beam and/or the column, as it yields small gussets and little if any change in the size of the column and/or beam. The eccentricity resulting from this practice must, of course, be taken into account during design (see12.5 below).

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Figure 12.9 Typical connections for vertical bracing Another common form of bracing is floor bracing, which will, in the case of concrete or composite floors, only be of value during the construction process to ensure that the floor is square and stable until the concrete has hardened. For buildings with steel plate or grating floors the floor bracing will retain their function during the life of the building. Figure 12.10 shows typical details for floor brace connections. In all of the sketches the bracing is placed below the floor so as not to interfere with the flooring, and with sufficient space to install the bolts. A distance of 110 mm from the top of the beams to the gusset, as shown in (g), is normally sufficient. It would be ideal to attach the bracing to the top flanges of the beams, but the bolt heads would then interfere with the flooring. Countersunk bolts can be used to obviate this problem, but that will be expensive.

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Figure 12.10 Typical connections for floor bracing The last form of bracing we will single out (there can be many other situations in which some form of bracing can be used) is roof bracing. Such bracing is commonly installed just below the purlins of a roof and serves the purpose of stabilizing the roof trusses or rafters during erection and to assist in squaring up the building. They are also often called on to resist wind forces acting on the gables of a building during its lifetime. It is in any case comforting to know that the roof bracing is there during the life of the building in case the big steel membrane that is the roof sheeting turns out not to be as stiff or as stable as we assume. Typical roof bracing connections are shown in Figure 12.11. With small buildings it is commonly assumed that certain purlins will form part of the bracing system, as implied by (a) and (b) in Figure 12.11. It is important that these purlins are actually designed to resist the bracing forces.

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Figure 12.11 Typical roof bracing connections 12.3 Attachment of members and its effect on their strength 12.3.1 Bolted connections When a member in tension is attached with bolts, holes have to be drilled or punched through the member, which means that it is weakened. As discussed in 6.3 above, this is taken into account by deducting the cross-sectional area of the holes from the cross-sectional area of the element, giving an effective net area neA for that element. See 6.3 above for how to calculate the net area of a plate or section.

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Here we deal with angles, which are commonly used in lattice structures or bracing, but also with channels and other profiles. In some cases the diagonals or verticals in a truss or bracing members may have all of their constitutive parts fully connected at their ends, such as in Figure 12.7 (d) and (e), but as can be seen in all the other examples in Figure 12.1 to 12.9 (Figure 12.9 (g) is another exception), only some of the parts are typically connected. In the case of an angle, for example, only one of the legs is usually attached. In such a case shear lag will occur. Figure 12.13 demonstrates this phenomenon where, in an angle, the connecting bolts apply force only to one leg. The stress spreads to the other leg, but not abruptly. By the time you get to the last bolt, quite a bit of the stress has found its way into the other leg, but the stress in the connected leg is still higher than the average stress in the whole angle. Only at some distance after the last bolt do we reach a situation where the stress is reasonably uniform in the angle. To ensure that the localised overstress of the connected leg will not cause failure, Clause 12.3.3.2 of SANS 10162-1 requires that we work with an adjusted effective net area 1neA : If there at least 4 bolts in line (i.e. in the direction the force is applied): nene AA 8,0

1 = (12.1) For 3 or less bolts in line: nene AA 6,0

1 = (12.2) where =neA the net area of the angle, calculated as discussed in above.

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Figure 12.13 Shear lag in angle connected by one leg For an H-section connected only by the flanges with at least 3 fasteners in a line Clause 12.3.3.2 (a) defines: nene AA 9,0

1 = (12.3) For all other sections Clause 12.3.3.2 (c) states that: If there are at least 3 fasteners in line parallel to the direction of force: nene AA 85,0

1 = (12.4) For 2 fasteners in line: nene AA 75,0

1 = (12.5) Then, according to Clause 13.2(a), the resistance, rTof the connection is the lesser of: =rT Ag yf (12.6) uner fAT '85,0 = (12.7) where gA = gross area of the section. 12.3.2 Welded connections In the case of a welded joint the elements are not weakened by holes, but shear lag will still occur if the welds are only placed at the edges of elements. Figure 12.14 (a) shows that there is negligible shear lag in a plate element with an end weld, but if there are only welds along the sides as in (b) there will be significant shear lag.

Figure 12.14 Shear lag in welded plate

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The requirements of Clause 12.3.3.3 can be explained with reference to Figure 12.15.

Figure 12.15 Welds in various positions If the connected leg has a transverse weld (either at the end, as shown in (b) or on a transverse line away from the end) it can be regarded as fully effective, i.e. for the connected leg: wtAne =1 (12.8) If the connected leg only has welds along its sides, as shown in (c): If wtAwL ne = 1:2 (12.9) If LtwtAwLw ne 25,05,0:2 1 +=> (12.10) If LtAwL ne 75,0: 1 =< (12.11) The other leg is connected only along its one edge, as shown in Figure 12.15 (d). Let the length of this weld be 1L . Then, according to Clause 12.3.3.3 (c):

If twLxAwL ne 21

221 1:

= (12.12)

If tLAwL ne 1221 5,0: =< (12.13) x is, as shown in (d), the distance from the weld to the centroid of the unconnected leg. The effective net area of the whole section is: 21 nenene AAA += (12.14) A channel would be treated the same way, except that the definitions of connected both sides and connected on one side change, while some elements may have to be disregarded see Figure 12.16.

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Figure 12.16 Effective net area of a channel If the flange of a Tsection is properly connected, the stem may be regarded as connected on one side. Designers may be concerned about placing the welds for an angle in such a way as to balance the load. However, researchers have found that it does not make much of a difference to the strength of a connection where the welds are placed. Clause 21.7 of SANS 10162 -1 states expressly that it is not necessary to balance the welds about the neutral axis of an angle, except in fatigue situations. Thus the effective net area of the connected leg will be the same for the angles in Figure 12.17 (a) and (b), provided that the value of L is the same.

Figure 12.17 Distribution of welds The effective net area of the other leg will, however, depend on the length 1L . There comes a point, however, where the weld on one side of a connected leg may be so short as to be ineffective. For that reason it would be wise to specify: 1L and wL 5,02 , and 40 mm. As for bolted connections, the tensile resistance rT will be the lesser of:

ygr fAT = (12.15) uner fAT 85,0= (12.16)

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Tables 12.1, 12.2 and 12.3 at the end of this chapter show the resistance of equal and unequal angles when all these considerations are taken into account. For members in compression the effective area is taken as the full area, except where local buckling can play a role, i.e. in slender members. In other words, shear lag is negated in compression members. 12.4 Nodes in trusses When designing connections such as shown in Figure 12.18 an effort should be made to let the gravity axes of the members meet at a single point, as shown in (a) and (b). Space considerations may not allow this, however, in which case there will be an eccentricity e, as shown in (c).

Figure 12.18 Truss modes with an without eccentricity If there is eccentricity in a node, the vertical and diagonal members can still be designed as pinned at the ends, but the resulting moment must be taken into account in the design of the truss, at least if ,5/we > where w is the depth of the chord member. The best way of doing this during analysis of the structure is to assume that the chord is a continuous member with the diagonals and verticals (all pinned) attached at the actual positions. Each sketch in Figure 12.18 shows a line A-A. The shear capacity of the chord on this line must be able to resist the shear force at this position. In (a) and (b) minimum spacings between the members are indicated to ensure that proper welds can be deposited in these areas. When designing welded connections, it is logical to work with the actual gravity axes of all the members. When detailing a bolted truss or bolted bracing, however, it is acceptable to use the line of bolts closest to the heel of an angle as the setting out line, as shown in Figure 12.19. This is, in fact, explicitly allowed by Clause 21.7 of SANS 10162-1.

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Figure 12.19 Setting out lines for bolted angles 12.5 Design of gusseted connections The first question to be answered is whether the gusset can resist the tensile and compressive forces applied to it.

Figure 12.20 Gussets with tension and compression members attached Consider Figure 12.20 and let us assume that the elements connected to each gusset as well as the connecting elements bolts or welds - are strong enough and that the bearing of the bolts on the gusset has been checked. For a tensile force uT in the connected element the next step should be to check for tension and shear block failure, but as described in 6.5 above, it is safe to only do a check on the Whitmore width as shown in Figure 12.20 (a) :

wypu LftT (12.17) This simple check confirms that the gusset plate is strong enough against all tensile effects, including tension and block shear failure.

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The Whitmore section test is also applicable where in the case of a gusset that is properly attached to strong members it goes outside the plate proper, as shown in (b). However, where the 30 lines go outside the free edges of the gusset, as shown in (c), wL should be limited to the actual width of the plate at the end of the connected element. This sketch also demonstrates that the Whitmore section applies to welded joints just as it does to bolted joints. It is important that gussets should not buckle in compression; in fact, the design of the diagonals and verticals in trusses and lattice girders assumes that the gussets will give a degree of moment support to the ends of these members. The acceptable approach is to design the end part of the gusset as a column of width wL , thickness pt and effective length 0,6 times the longest of 1 , 2 and 3 shown in (a).

A problem arises in a situation as shown in (d), where the Whitmore sections of the various elements connected to the gusset overlap. The best approach to this situation is to combine the forces in the elements and to work with a combined Whitmore section. It is obviously always desirable to make the gusset as small as possible and bring the elements in as close as possible. Note how this was achieved in (e). It is customary in American practice to check the moment resistance of gusset plates against the forces acting on various sections through the plate. However, if the Whitmore section approach is used, the gusset is made as small as possible, and it is welded to a sturdy member such a check will not be needed. It is still necessary to check the shear resistance in certain situations, such as on the line A-A in Figure 12.21.

Figure 12.21 - Line for shear checks Another issue to deal with regarding gussets is their attachment to the supporting elements, be that by welding or bolts.

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Figure 12.22 - Attachments of gussets Whatever the forces acting on the gusset (provided they all act in the plane of the gusset), they can be resolved into a tensile (or compressive) force uF , a shear force

uV and a moment uM , as shown in Figure 12.22(a). Note that even where the centrelines of the members meet at a single point, as shown in (b), the forces could still cause moment about the point X. Only if the centrelines of all the members attached to the gusset intersect at X will there be no moment on the joint. If the gusset is bolted to the supporting member the joint should be designed as described in , while welded joints can be designed as described in ---. Much attention has been given in American literature to connections for major bracing members, such as one would find in braced multi-storey buildings (see Figure 12.24). The bracing is attached to a gusset, which is, in turn, attached to both the column and the beam by welds or bolts. The beam, being primarily part of the bracing system, is considered to have little bending moment at its end, but it could carry a significant axial force. If there is a beam on the far side of the column, with axial force in it, it will influence how much horizontal force the connection can transfer to the column. Without a beam on the far side the bending stiffness of the column may cause it to resist some horizontal force, but this will typically be small.

Figure 12.24 Gusset connection for brace

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It is, of course, possible to do a detailed analysis of the joint, including the possibly using finite elements, and to design each part of the connection properly, including the connection of the gusset to the beam and to the column, and the beam to the column. It would then be possible to handle any shear and bending moment in the beam too, and to look at the attachment of the gusset and the beam to the column as one connection. However, this is hardly practicable in a real design office situation. Also, in most braced frames the moment and shear forces in the beam are small. Several approximate methods have been advanced and used over the years for the analysis and design of these connections, and any one that satisfies the Lower Bound Theorem (see 1.5 above) can be used. We will here discuss a Generalised Uniform Force (GUF) Method based on earlier work by Larry Muir and William Thornton, which approximates what happens in actual connections better than most other approaches and thus yields economical connections.

Figure 12.24 Sketches for GUF method Figure 12.24 (a) shows a typical brace connection. Note that we leave it to the engineer to specify the details of the connection: where the line of force in the brace crosses the centreline of the column, and the lengths (and positions) of the connections of the gusset to the column and beam. Figure 12.24 (b) shows the assumptions we make with respect to how the connection works:

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The line of force in the brace crosses the centreline of the column at A, a distance zabove the point O on the mid-height of the beam (zis negative if A lies below O).

O is the centroid of the connection of the gusset to the column. Because we assume that there will be no bending moment in this connection (and equilibrium does not require it to) we can replace the whole connection with a hinge at C.

Similarly, theres a hinge at B, the centroid of the connection of the gusset to the beam.

The beam is connected to the column with a hinge at E. The horizontal component of uF is resisted by an axial force in the beam. There

are no other horizontal forces acting on the beam. The column resists the vertical component uF and the moment because of any

eccentricity ( )SinFz u , the latter by moments Mand 2M , proportional to the stiffness of the column above and below the connection.

There is no moment in the beam. (If the beam is loaded we design it as simply supported and assume that it will not cause moment in the connection.)

Here it is assumed that the line of force of the brace is always above point E. Figure 12.24 (c) shows free body diagrams for the column, beam and gusset. From (b) we can say: uFSinzMM =+ 21 (12.21) From the free body diagram for the column: ( ) ( ) ccECbc eVVyeHMM ++=+ 21 (12.22) Vertical equilibrium of the column gives us: cosuCE FVV =+ (12.23) Thus we can combine (12.21), (12.22) and (12.23) to say:

( )Cb

cuC ye

CoseSinzFH++= (12.24)

Horizontal equilibrium of the gusset yields: CuB HSinFH = (12.25) Moment equilibrium for the beam about E (equilibrium considerations do not require us to have a bending moment in the beam) gives an expression for BV :

B

bBB x

eHV = (12.26)

And from vertical equilibrium of the gusset:

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BuC VCosFV = (12.27) Horizontal equilibrium of the column gives us: CE HH = (12.28) And vertical equilibrium of the beam gives us: BE VV = (12.29) We have all the information to design the connection. However, in practice there can also be a horizontal force coming from a beam and/or brace on the other side of the column (see also the discussion on transfer force under 12.6 below) and a shear force in the beam because of loads applied along the span of the beam, as shown in Figure 12.25. In the case depicted in Figure 12.25(a) the connection of the beam to the column at E has to be designed for a larger force: uCE FHH = (12.30) In the case of (b): SinFHH uCE = (12.31) Furthermore, there can be a shear force in the beam, as also shown in Figure 5.25, in which case: uBE VVV = (12.32)

Figure 12.25 Forces on opposing side

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Consider now the case where the beam and gusset are connected to the web of a column, as depicted in Figure 12.26 (a). We can follow exactly the same approach as before, with the points O and E coinciding. Equations (12.16) to (12.24) can be used to determine the forces to be designed for, taking 0=ce . Again, there will be no moment in the beam.

Figure 12.26 Setting out point at end of beam The situation is quite similar if the setting out point is placed at mid-height of the beam but on the column face, as shown in Figure 12.26 (b). The difference is that now the column has to be designed for a couple equal to ( ) cubc eVV , where ubV is the shear force in the beam not resulting from the connection. Another option is to place the setting out point at the place where the top of the beam meets the face of the column, as shown in Figure 12.27.

Figure 12.27 Setting out point in corner Now 0=BV and 0=cH . This will give a solution where we only have shear forces

( )uhB FH = and ( )uvc FV = along the two interfaces. The column has to be designed

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for a locally-applied bending moment equal to cubc eVV , while the couple acting on the beam at X equals Bb He . The last situation to be considered is where the gusset is only connected to the beam and not to the column, as shown in Figure 12.28 (a). This may be economical where the force in the brace is relatively modest compared to the beam size.

Figure 12.28 Brace attached to beam only Figure 12.28 (a) shows the setting out point on the face of the column, a logical place, but it could be anywhere else. Considering the free body diagram of the gusset in (b), we can say from considerations of equilibrium that: uvB FV = (12.33) uhB FH = (12.34) ( )xxFM BuvB = (12.35) This implies that the gusset-to-beam joint must be designed to resist the vertical and horizontal forces and the moment. The beam (see free body diagram in (c)) must be designed for a vertical force BVand a horizontal force BH acting at X, as well as a couple equal to bbB eHM + , and the loads on the beam itself, including ubV and ubF . The connection of the beam to the column must be able to resist a shear force ubB VV and a horizontal force

ubB FH . The column must be designed to resist the locally-applied moment ( ) cubB eVV .

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12.5 Underfloor bracing Bracing under a floor is often attached to the webs of the beams and girders, as shown in several of the sketches in Figure 12.10. If bracing is attached to the centre of a web as shown in Figure 12.10 (f) there should not be any lateral forces acting on the web. However, it is possible that in some instances there may be a lateral force uF as shown in Figure 12.28, and this case can be handled as follows:

Figure 12.28 Gusset attached to web of beam At issue here is the resistance of the web to a horizontal force uF . Assuming, conservatively, that the gusset is at mid-height of the web, that the web acts as a simply-supported beam between the flanges and that the force act over a width equal to

wg tL 12+ , the moment per unit width of web equals.

( )( )wgwu

U tLthFM

1242

1 += (12.36)

Which should be less than

4

2

1yw

r

ftM

= (12.37)

This implies:

f

wbywu th

tLftF212

.2+ (12.38)

The only case from Figure 12.10 that requires further discussion is that of the boomerang gusset as shown in (e) and also in Figure 12.29 (a) below. A variation on the theme is shown in (b). It can be shown that the force in the bracing is resisted primarily in shear where the gusset is connected to the beam webs, with only a minimal lateral force exerted on each web. This means that it is correct to assume, as shown in the figure, that the components uxF and uyF of the force uF are applied as shear forces and that any other forces acting on the webs can be neglected.

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Figure 12.29 Boomerang gusset The stress conditions in the boomerang gusset are quite complex and the dimensions can be substantial, involving shear, bending and compressive stresses, which can cause buckling. No problems should be experienced with buckling if the thickness of the plate is made to be more than 04,0 times its biggest (diagonal) dimension.

12.6 Transfer forces

Consider the connection in Figure 12.30 (a). The two diagonals and the vertical member are in equilibrium and no force is transferred to the chord. The two bolts shown connecting the gusset to the chord carry no loads. In contrast, three bolts are required to connect the gusset to the chord in (b), because there is an unbalanced horizontal force of 240 kN that has to be transferred to the chord.

In cases like that shown in Figure 12.30 one cannot complete the connection design from the maximum member forces alone. A load case which does not reflect the maximum member forces may result in the maximum force to be transferred to the chord. The load case with the smallest member forces may actually be the one requiring the most bolts for connecting the gusset to the chord. This example illustrates that there are situations where it is not possible to design a connection safely and economically if only the maximum forces in all the members are available.

We can call the controlling force from the gusset to the chord in Figure 12.30 (b) a transfer force. In general a transfer force is any controlling force that is transmitted

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across a joint and needs to be communicated to the connection designer because it is not evidently calculable from maximum member forces.

(a) No transfer force to chord (b) Transfer force to chord

Figure 12.30 Illustration of transfer force

A discussion of transfer forces is only relevant where the steelwork structural engineer designing the structure as a whole is not the connection designer as well. This is frequently the case in South Africa but it is important to note that the steelwork structural engineer remains responsible for the adequacy of the design of the connections even where the actual work is delegated to another entity. This means the engineer must provide the connection designer with sufficient information to design connections that are safe and economical.

In order for such delegated work to be successful the engineer must accurately anticipate what connection types and geometries are likely to be used by the connection designer. This will allow the engineer to provide relevant information without unduly including extraneous and confusing data. The engineer can provide the requisite information to the connection designer in one of two forms:

All the member forces for each load combination that can realistically act on the structure can be provided.

The maximum forces in each member (tensile and compressive where applicable) can be provided in addition to the controlling force(s) that must be transferred through a joint.

The second option is typically more manageable for large or complex structures where multiple load combinations may control the design of various members. In the case of Figure 12.30 (b) for instance the only requirement besides the maximum forces in the diagonals would be to say that a force of 240kN has to be transferred to the chord.

One can find relatively more information on the concept of transfer forces in American literature as compared to others. The concept can at times be complicated to understand or difficult and tedious to apply in practice. However, it is one of the most efficient and accurate ways of communicating forces to the

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connection designer. Therefore it is not uncommon for large and complex projects to use commercial software or in-house spreadsheets that calculate transfer forces for common connection configurations.

Two more examples can be used to illustrate the concept of transfer forces.

The shear force uV in the panel zone of Figure 12.31 is equal to ( ) hMMu /2 . However its value is not evident from maximum member forces alone. uV depends not only on the maximum values of 1M and 2M but also on their direction in each load case and on their relative values.

Figure 12.31 Shear in panel zone

Figure 12.32 shows an elevation and a plan of a node in a multi-story braced frame. The horizontal (tensile) force transferred to the column by the beam, vertical and horizontal bracing on the left hand side of the column is:

uxlublublut FFFF ++= (12.39)

This must clearly be the same as the forces on the right hand side:

uxruhrubrut FFFF ++= (12.40)

We must design the connections on both the right and left of the column to resist utF in addition to the other forces. The problem is of course that the maximum values of all the forces don't necessarily occur in the same load case. But if we are given the maximum forces in the members and the maximum value of the transfer force we can design a safe and economical connection.

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Figure 12.32 Node in a multi-story braced frame

12.7 Examples Example 12.1 What tensile force can we put on the angle below?

M20 Class 8.8 bolts 22 mm holes, punched

935=sA mm2 355=yf MPa

Shear resistance of bolts:

3506,8744 === xVV ru kN

Bearing resistance of bolts:

End distance = 35 mm < 602033 == xd mm

Thus equation 3.8:

ubrr antfB =

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265479643567,0 == xxxxBr kN

Block failure:

Equation 6.4:

ygvuntu fAfAT 6,0+

( ) 6463556)35703(9,06,06)222(5,09359,0 =+++ xxxTu kN

Equation 6.5:

unvuntu fAfAT 6,0+

( ) 6104706))222(5,335703(9,06,04706)222(5,09359,0 =++++ xxxxTu kN

Effect of shear lag, with 4 bolts in line:

Equation 12.1:

nene AA 8,0' =

7916)222(935' =+=neA mm2

Equation 12.6:

ygr fAT =

2993559359,0 == xxTr kN

Equation 12.7:

uner fAT'85,0 =

2844707919,085,0 == xxxTr kN

Thus 265=rT kN

Conclusion

The bearing resistance of the bolts controls. If the end distance was made more than 35 mm (in fact, if it was made 37,5 mm) the shear lag resistance would control.

Example 12.2

Design the following welded connection:

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Diagonals: 100x100x8 L

Horizontal chord: 150x150x10L

All 6 mm fillet welds.

Resistance of welds (taking resistance of fillet weld from Table ):

36229,1100914,0)75180( =++= xFrw kN > 300 kN OK

Resistance of angle:

Connected leg fully effective.

Other leg:

100751

30

Example 12.3

Check whether the connection below can carry the force of 35 kN in the brace.

Angles attaching boomerang gusset to beam web 70x70x6L with M20 bolts. A force of 27 kN will be transferred in shear to the beam running in the vertical direction of the paper, and 22,4 kN to the horizontal beam. These are small forces and the cleats, bolts and beam webs will obviously be strong enough to carry them

Check resistance of gusset to buckling in compression:

Estimate 375=L mm; 75,0=K ; 281=KL mm

250010250 == xA mm2

89,21012

103 ===xA

Ir mm

3,97=rKL

From Table 4.3 in the Red Book: 155=ACr

MPa

Thus 34915525009,0 == xxCr kN > 27 kN OK

Check bending in the gusset:

Consider the horizontal leg of the gusset, at the inner corner:

67,521,027 == xMu kN.m

31

yer fZM =

104167625010

6

22

=== xtbZe mm3

3,333551041679,0 == xxM r kN.m > 5,67 kN.m OK

Example 12.3

Design the gusset in the connection below.

Check bolt bearing:

The member with the 1200 kN tensile load clearly governs.

Equation 3.11:

226747010201267,033 === xxxxxtdnfB ubrr kN > 1200 kN OK

Equation 3.12:

151247012104067,0 === xxxxantfB ubrr kN >1200 kN OK

We need only check the Whitmore width, but will also do block failure.

Check tension and shear block failure:

Equation 6.4:

ygvuntr fAfAT 6,0+=

32

169535012)40704(29,06,047012)2270(9,0 =++= xxxxxTr kN > 1200 kN OK

unvuntr fAfAT 6,0+=

159047012)225,440704(29,06,047012)2270(9,0 =++= xxxxxxTr kN OK

Check the Whitmore width:

Equation 6.13:

39270)15(15,170)12()1(15,1)1( =+=+= sngmLw mm

Equation 6.13:

1481350123929,0 == xxxtfLT ywr kN > 1200 kN OK

Check buckling of the gusset with the 1200 kN compressive force acting on it.

Stress on Whitmore width:

29812392

1400000 ==x

MPa

280* =L mm

5,312

3

===t

tAIr mm

485,32806,0* == x

rKL

According to Table 4.3 in the Red Book:

288=ACr

MPa

Thus 871288122809,0 == xxxCr kN

This is less than 1200 kN, so we have to increase the thickness of the gusset . A check will show that 16 mm is adequate.

Design the welding connecting the gusset to the column.

Resolve the forces in vertical and horizontal components and apply them where they intersect the weld line, as shown in the sketch. The welds are subjected to the following forces:

700=uT kN; 16968482 == xVu kN; 2540008481502 == xxMu kN.mm

33

1670006

10002 ==weldZ mm2

Thus maximum vertical force per mm, noting that there is a weld each side:

848,010002

1696 ==x

fv kN/mm

Maximum horizontal force par mm:

76,01670002

254000 ==x

fh kN/mm

896,0848,076,01 == Tan , thus o42=

Resultant force per mm:

14,176,0848,0 22 =+=ruf kN/mm

According to Table 5. A 6 mm weld will be just strong enough.

Check shear in gusset:

226016100067,03559,066,067,066,0 === xxxxxbtfV yr kN > 1200 kN OK

Conclusion

Reflection on this example proves that, if such a connection is subjected to various load cases, it would be impossible to design the connection properly if all the forces were not given for each load case. However, if the maximum member forces are given as well as the transfer forces uT , uV and uM the connection can be designed.

Example 12.4

Determine the forces in the members, the cleated connections of the gusset to the column and the beam to the column, and the welded connection of the gusset to the beam in the following connection. Note that C is the centroid of the gusset-to-column cleat, and B the centroid of the gusset-to-beam weld, neither of which has necessarily been shown to scale.

34

Using the symbols in Figure 12.24 we can say:

127=ce mm 203=be mm

300=Cy mm 300=Bx mm

50=z mm

Couple acting on column because of connection:

Equation 12.21, plus eccentricity of shear force of 150 kN in beam:

3,361271506003505,021 =+=+=+ xSinVeFSinzMMo

ucu kN.m

Horizontal forces:

On connection of gusset to column from Equation 12.24:

903,0203,0

)35127,03505,0(600( =++=

++=

oo

Cb

cuC

CosSinye

CosezSinFH kN

On connection of gusset to beam from Equation 6.25:

2549035600 === oCuB SinHSinFH kN

Vertical forces:

On connection of gusset to beam from Equation 6.26:

35

1723,0203,0254 ===

B

bBB x

eHV kN

On connection of gusset to column from Equation 12.27:

32017235600 === oBuC CosVCosfV kN

Forces on connection of beam to column:

Vertical force, from Equation 12.32:

22150172 === uBE VVV kN

Horizontal force, from Equation 12.30:

1010090 === uCE FHH kN

12.8 Resistance tables

The only tables contained in this chapter relate to the tensile resistances of angles connected by welding or bolts. These tables cover essentially the same subject matter as Tables 3.2, 3.3 and 3.4 in the Red Book.

Figure 12.30 shows the dimensions and assumptions relating to the tables for bolted angles Tables 112.1 to 12.3. Figure 12.31 contains the same information for Tables 12.4 to 12.6, for welded angles. The tables in the Red Book are presented as resistance tables for angle ties; here we see the situation from the point of view of the connections.

36

Bolt holes 2 mm larger than bolt diameter; assumed for calculations to be 4 mm larger. Dimensions and bolt classes:

M16 M20 M24 a 25 35 45 s 50 70 90

Class 4.8 8.8 8.8 Steel: Equal angles up to 60x60 assumed

200=yf MPa, 365=uf MPa All other angles: 355=yf MPa, uf = 470 MPa

Figure 12.30 Dimensions, details and symbols for bolted connections for angles.

221 LLL +=

For calculating contribution of unconnected ('other') leg, assumed LL 5,01 = .

All welding E70xx

Steel:

Equal angles up to 60x60: 200=yf MPa, 365=uf MPa

Other angles: 355=yfMPa, 470=uf MPa

Figure 12.31 Dimensions, details and symbols for welded connections for angles.

Single line of bolts Two lines of bolts

Without transverse weld With transverse weld

37

38

39

40

41

42