9
Trusses and Lattice Girders
9.1 Introduction Latticed trusses and girders are extremely efficient in material usage for spanning long distances, provided a suitable configuration and depth-to-span ratio is chosen. However, because of their more complex construction, their fabrication requires a high labour input and the cost per ton for such trusses and girders is thus very much higher than that of plain I-beams or welded plate girders. It is therefore important to design trusses and lattice girders efficiently. Not only must the material content be kept to a minimum, but, above all, their construction must be kept simple and straightforward.
9.2 Configuration Various truss and lattice girder layouts were discussed in Chapter 5 in the context of their application to different building types. The more common layouts were shown in Figs 5.1, 5.4 and 5.5. In this chapter the advantages of particular configurations and construction details will be considered in greater detail. Most of the comments will apply equally to parallel-chord girders and to trusses with low-pitched rafters. The most commonly used shapes are illustrated in Fig 9.1. The triangular trusses shown in details (a) and (b) have been used for many years and because of their steep pitch, were especially suited to roof sheeting having end laps within the slope length. With the advent of deeper profile sheeting, supplied in single lengths from eaves to ridge, much flatter slopes are possible and the low-pitch trusses shown in details (c) and (d) have become popular as a result. As explained in Section 5.2, the low-pitch truss is structurally more efficient than the triangular one because of its shape (see Fig 5.2), but it does require a greater height of column. The Warren truss or girder in details (d) and (f) has a more attractive appearance than the Pratt or N-braced truss in details (c) and (e) because of the uniform, rhythmic flow of the diagonals. It also has a slightly lesser total length of web members. However, where the maximum gravity loading (dead plus live loads) exceeds the net uplift loading (dead plus wind loads), as is usual in roofs of buildings, the web compression members under gravity loading attract higher forces because of their slope. The combination of
9.1
t
Camber (a) Fink truss - small
(b) Fink truss - large
(c) Pratt truss
(d) Warren truss
(e) Pratt girder
( f ) Warren girder
(g) Sub-divided Pratt girder
(h) Sub-divided Warren
( j ) Pratt truss - alternative layout
Fig 9.1: Truss and girder configurations his higher compressive force with greater buckling length generally requires the trusses or girders to be of larger section than the vertical compression members of a Pratt truss or girder. On the other hand, under reversal (net uplift) loading the diagonals in the N-braced configuration are in compression and the larger member sizes required to meet this condition would make this layout less efficient. It is often necessary to do a quick preliminary analysis to determine which is the better configuration for any particular case. In general it will be found that for smaller spans, or where there is net uplift loading, a Warren truss will be lighter than a Pratt truss.
9.2
It should also be noted that the diagonals at the centre of the Warren truss in detail (d) are in tension under gravity loading, whereas they are in compression in the Pratt truss in detail (c) (as shown in solid lines). The combination of tensile force and short length in the Warren truss would be much more favourable than the compressive force and long length in the Pratt truss. In the alternative Pratt truss web member layout shown dotted the centre diagonals are in tension and are thus more efficient. Where the lower chord of a truss is stabilised by kneebraces from the purlins the alternative Pratt layout shown in detail (j) can be used. Here the 'verticals' have been placed at 90º to the rafters and are thus in the same plane as the kneebraces, making the connection of the latter more simple. For all roof trusses the panel lengths of the rafter should be equal to the purlin spacing, i.e. the purlins should be located on the panel points. In this way local bending of the rafter, which would be caused by random location of the purlins, is avoided and the rafter is designed for axial force only.
9.3 Bolted or welded construction The decision on whether to use bolted or welded construction for a truss or girder will be governed mainly by the preference of the client or the fabricator. Welding produces a simpler truss of attractive appearance, slightly lower in mass than a bolted truss and easier to paint. A fabricator may, however, prefer to use bolting if his workshop is suitably equipped with automatic punching or drilling equipment. Bolted trusses are much easier and quicker to assemble because they are self-jigging and do not require the assembly beds that are needed for welded trusses. They also do not have to be turned over for access to far side welds. A disadvantage of a tensile member with bolted end connections is that the effective sectional area is reduced by the extent of the bolt holes.
9.4 Chords and web members The choice of sections for the chords and web members will depend on the force to be transmitted and whether construction is by bolting or welding. Typical sections used are shown in Fig 9.2, where they are arranged approximately in ascending order of cost. All these sections may be used as both chord and web members, except (b), which is normally used only as a chord. Chord members (a), (b), (k), (l) and (m) would normally be used for welded construction and (a) and (c) to (j) for bolted construction. The sections in (e) to (j) require double gussets and are used for larger girders. The double-angle section (c), when used as a web member in a heavily loaded bolted girder, has the advantage of requiring only about half the usual number of bolts since the bolts at the member ends are in double shear. It is a very efficient member, especially in compression, but is not suitable in corrosive environments because of the difficulty in painting the surfaces between the angles.
9.3
(a)
(b)
(e)
(c)
(f)
(h)
(k)
(d)
(g)
(j)
(l)
(m)
Fig 9.2: Member sections
Welded girders with single rather than double angle chords and web members are much easier to assemble since they do not require turning over for welding. The combination of T-chords and single-angle web members is particularly efficient, especially when gussets are not required. Where double members require battens, these are indicated by dotted lines. The (j) section requires battens to both flanges and is thus expensive to fabricate. It is only used in heavily loaded girders with long member lengths. The use of battened starred angles (not shown in Fig 9.2) is uneconomical. Although the section might appear efficient on a resistance unit mass rating, it is subject to the rather onerous requirements of clauses 19.1.4 and 19.1.5 of SABS 0162-1, which state that an increased equivalent effective length must be used unless the battens are welded or friction-grip bolted. Furthermore, because the end connection bolts are in single shear only and because of the width of the section, larger gussets are required.
9.4
Bolted and welded concentric
(a)
(b)
Bolted and welded eccentric
(c)
(d)
Welded gussets
(f)
(e)
Bolted gussets
(g)
(h)
Fig 9.3: Connections at nodes
9.5
9.5 Connections at nodes The selection of the type of connection used at nodes or panel points has a significant bearing on the economy of a girder. On smaller girders where eccentricity of member axes at a panel point is acceptable, the omission of gussets is especially cost-effective. This requires lapping of the web member and welding or bolting it directly onto the chord, as shown in details (c) and (d) of Fig 9.3. Where eccentricity is to be avoided the details shown in (a) and (b) can be applied, but these require alternate web members to be on the far side of the chord. The single bolt, as shown in detail (a), is obviously an economical connection. Gussets are required for larger members and forces. In welded construction the node layout may be as indicated in details (e) or (f) of the figure, with eccentricity avoided in (e) but present in (f). In bolted construction the detail shown in (g) or (h) could be applied, where (g) avoids eccentricity but requires a larger gusset than (h), and in this example, requires one extra bolt in the chord member. In all cases where eccentricities in connections are involved they should be according to the designer's specifications or, if incorporated by the detailer, should be with the designer's approval. In simple node connections where single-angle diagonal web members are directly welded to the chords, the details shown in Fig 9.4 may be applied with good effect. In (a) the web angle is turned toe-up to get a better balance of welding on the heel and toe and takes account of the greater depth of the compression chord as compared with the tension chord. Alternatively, the web angle toe can be sniped at the tension chord, as shown in detail (b). This permits longer welds than are possible in the connection shown in detail a), at very little increase in cost. Compression chord
Tension chord (a)
(b)
Fig 9.4: Welded angle web members
If it is decided to use the (a) connection detail, a set-out should be done to ensure that there is in fact sufficient overlap of the diagonal onto the chords to accommodate the heel weld at the compression chord and the toe weld at the tension chord.
9.6
The transfer of shear from a diagonal web member to an adjacent vertical member must be properly catered for. This is especially important at the end of a girder where the shear is high. In Fig 9.5 the vertical shear at position X should be checked, since without gussets the vertical element(s) of the chord may be overstressed. Gussets, as shown dotted, may have to be added to increase the shear resistance.
X
X
Fig 9.5: End nodes in welded girders Where the web members do not overlap the chords but connect to their horizontal faces, as shown in Fig 9.6, it is preferable to separate the web members, as in examples (b) and (d), rather than to maintain common intersection points as in details (a) and (c) where much more work is obviously required to cut and fit the members. It is essential, however, to check the vertical element(s) of the chord sections to ensure adequate shear resistance. The design of node connections for girders made of welded structural hollow sections is given in Chapter 5 and Appendix 2 of the Structural Hollow Sections Handbook (Ref. 8).
(a)
(b) CHS members
(c)
(d) H - Section members
Fig 9.6: Node connections for girders with SHS and H-section members
9.7
9.6 Gussets Economy in gusset fabrication can be obtained by following a few simple rules as illustrated in Fig 9.7 and set out below, viz.:
(a)
(b)
(e)
(c)
(f)
(d)
(g)
Fig 9.7: Gusset shapes
•
Opposite edges should be parallel where possible.
•
Adjacent edges should be at right angles where possible.
•
Corners should not be sniped unless the included angle is less than 90º.
•
The number of edges should be kept to a minimum.
In Fig 9.7 gussets (a) to (d) are arranged in descending order of simplicity. They can all be cut economically, either by shearing or by machine-gas cutting, from a large plate because the shapes can be 'nested' when being marked off. In following the above rules it is sometimes necessary to depart from the standard bolt pitch, as for example in gusset (c) where the bolt pitch in the vertical line has been increased for the sake of having parallel edges to the plate. Using a uniform pitch would result in a shape as in gusset (e). In gusset shape (f) standard bolt pitches are employed for all members, but this is an expensive gusset to make. In detail (g) the large number of bolts along the left edge implies a heavy load in the vertical member and consequently the gusset should be widened as shown dotted to spread the load over a greater width of plate.
9.7 Girders with double-plane webs In the case of girders with wide top chords, as in details (e) to (j) of Fig 9.2, it is also necessary for the web diagonals to be wide, or else to be in two planes, as shown by details (a) and (b) respectively of Fig 9.8. The battening of double compression members,
9.8
where the battens have to be welded or FG bolted, is very expensive and the use of a single member should be considered in this instance, provided the extra mass is not excessive.
(a)
(b)
Fig 9.8: Single and double web members
On the other hand, where the force is not high, the battens could possibly be dispensed with and the two elements of the member be designed as separate struts. For double tension members the battens could in any case be omitted provided the slenderness ratio of the individual members is not excessive.
9.8 Summary •
An efficient layout of truss or girder should be selected, taking account of the overall size and the presence of uplift loading. The lengths of compression members should be limited. In general, the Warren configuration represents an economical shape for many applications.
•
In roof trusses the node points should correspond with the purlin locations.
•
Welded trusses are lighter, easier to paint and more attractive in appearance than bolted ones, but the latter might be preferred by fabricators suitably equipped to handle bolted assembly.
•
Where possible, welded girders should be designed for welding from one side only.
•
The shape of chord members is dependent mainly on the magnitude of the load, but is also influenced by whether bolted or welded construction is used. The section
9.9
should be kept simple and be suitable for the easy connection of the web members, either directly or with gussets. •
Double-section web members require smaller gussets and less bolting or welding because of the reduced load per section.
•
Web members comprising two separated sections connected by battens are expensive. The battens should be kept compact (but be checked for shear loading), or the sections may be designed to act separately without battens.
•
Starred-angle members need non-slip connectors in the battens unless an increased effective length is used and require extra gusset width at the end connections. Their use should thus be avoided.
•
At web member to chord connections in smaller trusses and girders, gussets may be dispensed with, provided the chord is checked for the eccentric application of force and also for the shear effect in the vertical element(s) of the chord.
•
In larger welded girders the web members may overlap the chord member, with a small gusset added to cater for the higher loads or to eliminate eccentricity.
•
Economy in gusset fabrication can be achieved by following the simple rules given.
9.10
