The effect of scale

The span of an architectural structure, which is determined by the required sizes of the spaces which are enclosed by it, has a very significant effect on both the generic type of structure which should be used and on the selection of the types of structural element of which it should be composed. The underlying principle which governs the relationship between span and structure type is that the ratio of self- weight to load carried should be satisfactory.

For a given type of structure the strength-to- weight ratio tends to become less favourable as the span increases.15 More efficient types of

structure must therefore be specified as spans are increased to maintain the ratio at an acceptable level.

Table 2.1 shows the ranges of span for which basic types of structure are most suitable and therefore normally specified. The figures must be regarded as approximate but serve to give an indication of the applications for which each is most appropriate. Separate figures are provided for floor and roof structures to allow for the variations which are caused by the significantly different levels of gravitational load to which they are subjected.

Table 2.1 Normal span ranges for commonly used structural systems

A Timber structures

Structural system Normal span range (m) Span/depth ratio

softwood planks floor 0.6-0.8 25-35 roof 2-6 45-60 plywood board floor 0.3-0.9 30-40 roof 0.3-1.2 50-70 softwood timber joist floor 3.5-6 12-20 roof 2-6 20-25 stressed skin timber panel floor 3-6 20-30 roof 3-9 30-35 laminated timber beam floor 5-12 14-18 roof 4-30 15-20 plyweb beam floor 5-18 8-10 roof 6-20 10-15 trussed rafter roof 5-11 4-6 parallel chord truss roof 12-25 8-10 gluelam portal frame roof 12-35 30-50 gluelam arch roof 15-100 30-50 lattice dome roof 15-200 40-50

B Steel structures

Structural system Normal span range (m) Span/depth ratio

profiled decking floor 2-3 35-40 roof 2-6 40-70 profiled decking with composite concrete topping floor 2-6 25-30 beam (hot-rolled section) floor 6-25 15-20 roof 6-60 18-26 cold-formed open-web joist roof 4-30 15-25 hot-rolled triangulated parallel-chord truss floor 12-45 4-12 roof 12-75 10-18 pitched, triangulated truss roof 25-65 5-10 space deck roof 10-150 15-30 braced barrel vault roof 20-100 55-60 portal framework roof 9-60 35-40 cable-stayed roof roof 60-150 5-10 hanging cable roof roof 50-180 8-15

C Reinforced concrete structures

Structural system Normal span range (m) Span/depth ratio

one-way span solid slab reinforced 2-7 22-32 prestressed 5-9 38-45 two-way span solid slab reinforced 4.5-6 30-35 one-way span ribbed slab reinforced 4-11 18-26 prestressed 10-18 30-38 two-way span coffered slab reinforced 6-15 18-25 prestressed 10-22 25-32 beam/column frame with beam/slab floor slab 3.5-6 30-36 beam 6-12 15-20 portal framework 12-24 22-30 arch 15-60 28-40 36

All structure types have a potential maximum span and the less efficient the structure, the lower is this practical

maximum span. An indication of this is given in Table 2.1 in which it will be observed that the maximum span given for each type of structure is related to its potential efficiency. Thus, elements with simple, solid rectangular cross-sections, such as sawn timber joists or rectangular cross-section reinforced concrete slabs, have relatively low maximum spans. Simple elements with 'improvements', such as l-section steel beams or triangulated trusses of timber or steel, have higher maximum spans. The highest spans are achieved by highly efficient vaulted shells or cable networks.

The effect of the variation in the maximum span potential of different types of element is that the choice of element types which is avail- able to the structural designer diminishes as the span increases. If the span to be achieved is small (say 5 m) virtually all structure types are available. At this scale the designer could therefore choose to use any type of structure from simple, solid beams or slabs to sophisti- cated forms such as the arch or the vault. In the context of contemporary architecture, it would probably be regarded as technically inappropriate to use a complex form for a short span, unless some special requirement for high efficiency existed, because much simpler post-and-beam forms would perform adequately. It would nevertheless be a choice which the architect could make. As the span increases the number of different types of structure which would be viable decreases until, at the very long span (say 200 m), only the most efficient form-active types, such as steel cable networks or thin concrete shells, are feasible. In summary, from the point of view of the designer, the choice of structure type is large if the span is small and becomes progressively more limited as the span increases.

The most basic post-and-beam types of structure (loadbearing-wall arrangements in masonry or timber with simple horizontal elements such as timber beams or reinforced

concrete slabs) are suitable for short-span structures in the 5 m to 10 m range. The span range can be extended by the use of more efficient types of horizontal structure such as triangulated trusses in either timber or steel. The use of walls with 'improved' cross-sections (fin wall or diaphragm wall) allows the very basic structural system to be used for larger enclosures with high external walls, such as sports halls, where spans of up to 30 m have been achieved.

The post-and-beam frame (in either

reinforced concrete or steel) is a more sophis- ticated and therefore more flexible system than the loadbearing wall. In the multi-storey version the span range is slightly more exten- sive than that for loadbearing-wall structures (5 m to 20 m). The most basic types of element are used at the low end of the range (solid reinforced concrete slabs, rolled-steel sections) and at the upper end more efficient types such as coffered, reinforced concrete slabs and hollow-web steel beams. Spans greater than 20 m are unusual in multi-storey buildings but where these occur, efficient types of structural elements must be specified (e.g. triangulated girders used to achieve a span of around 25 m at the Centre Pompidou in Paris).

In single-storey structures the change from the most basic forms to more efficient struc- ture types (e.g. space frame horizontal struc- tures or semi-form-active structures) normally occurs when the span is in the range 20 m to 30 m, with spans greater than 30 m usually requiring the use of a semi-form-active struc- ture such as a portal framework. As with short- span structures, the type of element which is used can vary and the tendency is always for the level of efficiency (and therefore of complexity) to increase as the span increases. Thus, short-span portal frameworks (20 m) would normally be accomplished with rolled- steel sections such as the universal beam while a triangulated-truss longitudinal profile might be specified for a longer-span version (say 50 m).

The transition from the semi-form-active to the highly efficient fully form-active structure

2.3.3 The effect of cost example by columns. There have, of course,