16
Co-ordination of Dimensions
16.1 Introduction As used in this chapter, the term co-ordination of dimensions in buildings means the determination at the planning stage of the main and secondary dimensions of a building on a methodical basis that will result in a simple, orderly and therefore more economical layout of the structure. It implies that no dimension should be decided upon without thought being given to its inter-relationship with other dimensions. It embraces the choice of the main overall dimensions, the division of these into suitable sub-multiples, as well as the choice of the dimensions of the components in the building. The latter would include such pre-fabricated items as windows, doors, cladding panels, pre-cast floor slabs, etc. As these items are usually available in standard sizes it may in fact be their dimensions that will have a bearing on the choice of the main dimensions of the structure rather than the other way around. Some of the advantages of pre-determining dimensions on a methodical basis instead of in a haphazard manner are: a)
Simplification and convenience in the planning stage.
b)
A better relationship between the various parts of the structure.
c)
A greater opportunity for the incorporation of standard components.
d)
The simplification of setting out on site.
e)
Economy of construction resulting from the achievement of maximum similarity, compatibility and repetition of the structural elements and their dimensions.
16.2 Modular co-ordination Modular co-ordination is the principle whereby a standard module is used as the basis of measurement for dimensional co-ordination. A module is therefore a linear dimension that, when used in whole-number multiples, gives the dimensions used in a planning grid. Modular co-ordination as referred to here, and dimensional co-ordination as outlined above, both form part of the overall physical planning of the building. In South Africa a basic module of 100 mm has been adopted, as in most Western countries where modular co-ordination is being applied. This is in line with Recommendation R 1006 of the International Standards Organisation, which states that the international standard value of the Basic Module is 100 mm. For convenience, the symbol M is used to denote the basic module.
16.1
Derived modules are multiples or sub-multiples of the basic module. According to SABS 993-1972 the preferred multi-modules for horizontal dimensions of large components and structural work are 3M (300 mm), 6M (600 mm) and 12M (1 200 mm). Therefore, in choosing values for the main setting-out dimensions of buildings, multiples of the above multi-modules should preferably be used. An important advantage of modular co-ordination is that, when applied to standard building components, it yields a range of products that, though widely diversified in shape, size and material, are all inter-related dimensionally in a way that will enable them to be used together in a building without modification. It is clear that if the building framework on the one hand and the components that go into it on the other are both designed on the same modular principles, their combination in the final structure will be made so much easier. So far, full advantage has not been taken of metrication in South Africa in the implementation of the modular dimensioning of components, but it is to be hoped that the manufacture of prefabricated components on a modular basis will become more widespread as time goes on.
16.3 Application to steel framed buildings In the context of the structural framework for steel buildings, the co-ordination of dimensions has to do with the orderly selection of controlling dimensions for the main planning grid (e.g. column centres), which in turn is a measure of the span sizes and bay lengths, and then the division of these dimensions into suitable sub-multiples such as truss and intermediate column spacings, truss and girder panel sizes, etc, to achieve maximum simplicity, convenience and repetition. The best way to illustrate the idea is by reference to a typical building structure, and the following paragraphs deal with particular aspects of building framing, viz. main dimensions, bay lengths, spans, truss spacings, lattice girder framing, crane girders, handrailing, etc. The principles outlined can of course be applied to almost any part of the structure.
16.4 Main dimensions in plan Fig 16.1 shows the arrangement of a typical steel-framed crane gantry building with one main bay and a lean-to. It will be used as an example of how the main or controlling dimensions are divided up in accordance with the concept stated above. It is assumed that the building length, width and height have been dictated by functional requirements, but that the bay lengths (along the building) are left to the designer. In this case it is suggested that a bay length of 12,0 m be chosen, for the following reasons:
16.2
Fig 16.1: General arrangement of typical steel-framed building
16.3
•
This dimension is a multiple of 3,0 m (= 30 M) and is therefore a preferred multiple of the basic module.
•
It is divisible by 2, 3, 4, 5, 6 and 8 without yielding awkward numbers, thus facilitating the sub-divisions described in 16.5 and 16.6 below.
•
It approaches the longest length (13,0 m) of steel sections normally available from mills, and all longitudinal members in the building (e.g. purlins, girts, crane girders, lattice girder chords, etc) can thus be made in one length without splices.
•
It is an economical dimension for a building of this size.
Other suitable bay lengths might have been, 9,0 m, 15,0 m and 18,0 m, depending on whether the building spans and heights were smaller or greater.
16.5 Bay-length sub-division Having determined the bay length, the next most important decision is how to divide this to suit intermediate truss spacings, post spacings, lattice girder panel sizes, crane girder stiffener spacing, etc so as to yield maximum economy. The figure shows in detail how this is done and in Fig 16.2 the exercise is taken further to include all items on the gantry girders, viz. lateral plate splices and stiffeners, auxiliary girder panels, rail clips and handrailing. An examination of the spacing of these items will show how each dimension is co-ordinated into the whole system, yet at the same time represents an optimum spacing of the item in question. The following comments can be made with regard to these spacings: •
Trusses (Item 4): For trusses of this span the spacing of 6,0 m is economical and yields a good balance between truss and purlin content in the roof. The 6,0 m span of the purlins and girts is efficient and enables a light section to be used. These members may be designed in either the two-span or the fully-continuous configuration. The purlins and girts require only one sag bar per span.
•
Roof girders (Item 5): Here again the span of 12,0 m is suitable. Each girder carries a truss reaction at mid-span. An economical depth of these girders would be about 1 8 span = 1,5 m. The division of the span into eight panels gives an efficient slope of 45º for the web diagonals. Note that an alternating web compression-tension (Warren girder) configuration is used for economy. If a double unequal angle with long legs outstanding is used for the top chord it will not need to be stabilised laterally on the 6,0 m length. The centre vertical member in each girder forms part of the intermediate side post (Item 2) and is extended downwards to support a leanto intermediate rafter. The intermediate roof trusses are connected to the centre verticals.
•
Crane girders (Item 6): The sub-division of the span into eight panels gives a 1,5 m spacing of web stiffeners. The likely web thickness for this girder would be 10 mm and the 1,5 m panel size would be suitable for this thickness. The rail clips, at two per panel length, would be at 750 mm centres, which is about the recommended spacing for a Class 2 crane.
16.4
•
Lateral plates (Item 1, Fig 16.2): The stiffener spacing matches the crane girder panel length and the plate is made up of two 6,0 m lengths, spliced at mid-span, this being a suitable length for ordering. The central or mid-span stiffeners act as bearing stiffeners to pick up the horizontal wind loading from the intermediate side posts.
•
Auxiliary girders (Item 7): The configuration follows that of the roof girders (Item 5) and the 1,5 m panel lengths tie in with the crane girder panel sizes. The girder depth is about 1,2 m, so the slope of the diagonals is slightly flatter than the preferred slope of 45º, but this is not serious because of the very light loading on these girders.
•
Handrailing (Item 7, Fig 16.2): The spacing of the posts at 1,5 m is commonly used and is the maximum recommended for the usual handrail size of 34 mm diameter. The handrail posts are located at auxiliary girder node points, with stronger base support as a consequence.
•
Eaves bracing: The nodes coincide with roof girder nodes, thus simplifying their connection.
•
Girt sag bars: The suspension of the sag bars at the top is facilitated as the location again coincides with the roof girder nodes.
16.6 Span sub-division In the transverse or truss span direction of the building there is also scope for a systematic subdivision of the main dimensions. The following should be noted: •
Truss panels: The panel points or nodes coincide with the purlin positions, thus eliminating local bending in the rafters, which usually needs to be overcome by specifying a larger rafter size.
•
Truss bracing system: The web bracing configuration used for the trusses is of the same general type (subdivided Warren) as in the roof girders, thus producing a more harmonious effect than incompatible systems.
•
Gable rafter bracing: The nodes of the bracing system coincide with the purlin positions, which makes for simpler detailing and improved appearance. They also coincide (in plan) with the tops of the gable posts, so that the horizontal wind reactions from the posts are transmitted directly into the bracing without inducing lateral bending in the truss rafters.
•
Gable posts: These are placed at equal sub-divisions of the truss span in order to have them coincide with the rafter bracing and purlin positions (see above) and also to ensure equal gable girt spans. If desired, a horizontal wind girder could be placed at about mid-height of the gable posts, as shown dotted in Fig 16.1, to reduce the size of the posts. This is discussed in detail in Section 5.5 of Chapter 5.
16.5
2
1
3
4
Plan on Lateral Plate
8 x 1 500 = 12 000
5
Elevation on Crane Girder
7
Elevation on Auxiliary Girder
1. 2. 3. 4. 5. 6. 7. 8.
7 1 2
6
1 240
8
Lateral plate Lateral plate stiffeners Lateral plate splice Rail clips Crane girder stiffeners Bottom bracing (if required) Handrailing Auxiliary girder
Section through Girder
Fig 16.2: Details of crane girder 16.6
Longitudinal ties to truss bottom chords: These are not shown in the figures. They run longitudinally down the length of the building from truss to truss to provide lateral restraint to the bottom chords when in compression under uplift forces. There are three ties, located at the quarter-points of the truss span, to coincide with the gable post positions. They are thus connected directly to the posts, which provide the necessary restraint in the lengthwise direction of the ties, thereby obviating the need for horizontal bracing at the level of the truss chord.
16.7 Vertical dimensions All that has been stated above refers to the plan dimensions of a building, i.e. in the longitudinal or the transverse direction. In the vertical direction there is less scope, but also less need, for dimensional coordination. The vertical dimensions are mainly governed by required overhead clearances, which in turn are dictated by the functional requirements of the building. Thus in multi-storey industrial buildings the floor-to-floor levels usually vary, depending on the operations or activities occurring on the different floors. Likewise in multi-bay buildings the heights of the different bays will often be different. While it would obviously be an advantage from the point of view of simplicity to have equal storey and bay heights, the lack of uniformity would be less serious, economically, than in the plan directions. In other multi-storey buildings such as offices, warehouses, garages, etc the storey heights would usually be uniform and here economy would be gained from the equal column lengths from floor to floor.
16.8 Conclusion It is clear that a detailed consideration of all the aspects discussed above at the planning or design stage will result in the achievement of considerable simplification and hence economies in the subsequent activities of detailing, fabrication and erection. This may appear self-evident, yet it is remarkable how frequently the spacing of components is determined haphazardly and without reference to other components. The building shown in Fig 16.1 is of course a hypothetical one, used for the purpose of illustrating the principles of dimensional co-ordination. It was therefore possible to choose main dimensions that were amenable to suitable sub-division. In reality, however, the main dimensions of structures are usually governed by functional requirements or are determined by a client without considering co-ordination. It is then more difficult for the structural designer or the steelwork detailer to apply the principles to all details, but there is nevertheless always scope for the application of the method, even within these constraints, with beneficial results.
16.7
