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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
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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
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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+=
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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
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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.
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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:
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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.
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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
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