An important part of engineering design is that it should be expressive of the forces in play. In the example of the bridge pier given above, all other things being equal, it is better for the greater moment at the base to be resisted by increasing the size of the pier, and thus acknowledging the greater strength required, rather than by keeping the size constant and increasing the reinforcement that is hidden within the concrete envelope.
Some types of structure are more expressive than others. A beam of constant depth is singularly inexpressive of the fact that the greatest bending moment is at mid-span. Various designers, including Morandi, have adopted 'fish belly' beams, which do express the fact that they need greater strength at mid-span, and allow the removal of redundant web material near the ends, Figure 1.6, despite the fact that they most probably cost slightly more than a beam of constant depth; the additional complication of the formwork and the reinforcement is likely to outweigh any savings in the volume of concrete. The designer was justified in attempting to make the structure more expressive, and hence more interesting, although the final judgement must be whether it works aesthetically, as well as expressing engineering values.
An engineer may be justified in choosing a type of bridge that is not the most economical, but that is more expressive. Clearly, this needs the approbation of the client and cannot be done as part of a competitive tender where no credit is given for appearance. For instance, it may be established that the most economical bridge for a site is a girder bridge on vertical supports. However, the site may be just right for an arch, Figure 1.7, with the strong foundations required, although the arch would be more expensive. Such an arch bridge design can only achieve distinction if it is a rational choice and if the designer then strives for and achieves economy in the design as described above. It could not be considered a good design if the designer had imposed an arch on the site, despite its unsuitability; for instance, if the arch required massive and expensive foundations to resist the thrust, even if these foundations could not be seen by the public.
This demonstrates that good engineering design has an esoteric component only to be appreciated by professionals. A good example is the series of valley piers of the Byker Viaduct in Newcastle, which were flared to resist the wind and centrifugal forces of the twin-track railway it carried. The central part of each pier was cut away at ground level to save materials and to reduce the impact on walkers in the park. The size of these cut-outs was made just large enough to allow the precast units of the bridge deck to fit through, in an economical and innovative construction method, Figure 1.8. This fact is only known to those who remember the bridge being built, but forms part of the intellectual justification for the shape and size of the cut-out. The final judgement on a design must rest with the combined response of public and profession.
The choice of a solution that is expressive of the flow of forces applies to the design of members and details of a bridge as well as to the structure as a whole.
The detailed shape of the towers for the two-level Ah Kai Sha cable-stayed bridge designed by Benaim to cross the Pearl River close to Guangzhou, further illustrates the relationship between technical and aesthetic decisions, Figure 1.9. The bridge has
Figure 1.7 Beam or arch?
a main span of 360 m, and is exceptionally wide, at 42 m. The bridge is described in more detail in Chapter 18.
The towers rise 100 m above the ground, some 70 m above the deck. Their functions are to provide the height necessary to attach the cable stays that support the deck, to carry the loads down to the foundations and to give stability to the deck under the effects of typhoon winds and earthquake.
The tapering shape of the towers has been determined by the progressive increase in weight applied to them by the stay cables and due to their own considerable self weight, by the longitudinal forces imposed by earthquakes, wind and the expansion and contraction of the deck, and by the lateral forces due to earthquakes and wind. As the towers cantilever from the foundations, all these forces increase their effect towards their base, particularly below the level of the deck. Consequently, the rate of taper increases below deck level. This tapered shape of the towers expresses the forces acting on them as well as providing the necessary strength.
Most cable-stayed bridge towers have at least two cross-beams, one of which supports the deck, which make the towers into portals. These cross-beams are always heavily reinforced and slow down the construction of the towers, particularly when it is intended to build the towers by slip-forming, as in this case. Furthermore, the great width of the deck would have required the beams to be very substantial. As a consequence it was decided to omit the cross-beams, and to provide the necessary stability by designing the towers as vertical cantilevers, built into the pile caps.
Support for the deck, in the absence of cross-beams, is provided by powerful concrete brackets which are attached by prestress after slip-forming the columns.
All bridges expand and contract with changing temperature and either the deck has to be separated from the piers by movable bearings, or the piers have to be made flexible enough to permit this movement. Here, the deck is fixed to the piers, which have been made flexible by splitting them into two leaves, Figure 18.18.
Each leaf of the tower has a dumbbell shape, which represents the most efficient use of material. The dumbbells become solid at the junction with the deck to resist the concentration of forces that occur in that zone, Figure 18.19.
The towers are situated outside the deck and, as a result, the stay cables all pull slightly inwards. The combined effect of these pulls is very significant, and the towers would require larger, more expensive columns if they were not propped apart at the top. The prop is designed to be made on the deck and winched up into place, and so has to be as light as possible. For this reason it is made in an 'I' section. It must be stiff enough to resist buckling under compression and bending under its own weight as it spans between the columns, but the connections of the prop with the towers must be sufficiently small so that they do not attract bending moments under the effect of lateral loads. The prop is designed with the depth increasing towards mid-span, its shape expressing these constraints and actions.
Every significant dimension of these towers had a technical, rational justification, and none were chosen for appearance alone. However, the appearance of the towers was present in the mind of the designer at all times, and was chosen to express the forces and actions acting on them.
The splendid Alex Fraser Bridge in Canada, designed by Buckland and Taylor, Figure 1.10, solved some of the same problems differently. The bridge is narrower
than Ah Kai Sha and only has one level of traffic. The transverse stability of the towers is provided by the portal action of two cross-beams, and consequently, the legs of the towers do not need to increase in size substantially below the deck. The deck is carried by bearings on the lower cross-beam. Although the columns are outside the deck as at Ah Kai Sha, the designers have cranked them inwards above the deck, so that the stay cables pull concentrically, and a top strut is not necessary. The horizontal forces created by the crank are carried by the two cross-beams.
This comparison is not intended to imply that one solution is better than the other but to emphasise how the engineering and aesthetic decisions interact to produce two quite different solutions to a problem that has similar components.
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The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.