The topology of the form diagram is first sketched and labelled, although the precise geometry of the lower chord is as yet unknown. Figure 2 shows the first approximation to the reciprocal form and force diagrams for the central section of the roof. As explained in Refs, a graphic analysis of the roof under uniform symmetric loads leads naturally to the characteristic funicular shape of the lower chord tension members at Chiasso. However, Maillart did not envisage the roof as such a structure, and took a completely different perspective on its structural action. There were thus limited tools available for analysing a rigid quad frame. Vierendeel had proposed simplified methods for analysing his structures from the early 1900s, but Hardy Cross did not publish his method of moment distribution until 1930. Maillart designed the Chiasso roof around 1925.
12 They remain hugely influential, the Infante Dom Henrique Bridge in Porto being a recent example 13 that acknowledges Maillart’s innovations. A famous early exponent of structural reinforced concrete, his bridge designs at Salginatobel (1929) and Schwandbach (1933) in Switzerland are exemplars of efficient design and aesthetic form. Robert Maillart (1872–1940) stands amongst the greatest of all structural engineers. The more substantial aim is to demonstrate how the new methods can provide more general understandings of structural stability, such that these may be of use in future designs. The first is minor: it seeks to improve the understanding of Maillart’s classic design. This paper illustrates the procedures, with two aims. Stability is required, and now stability can be studied graphically. The modern resurgence of graphic statics has been greatly bolstered by computer implementations, and its use as a design tool can lead to a rich set of economical shapes that necessarily satisfy equilibrium for the load cases considered. The approach is essentially a distillation and then a graphical interpretation of Guest’s matrix description 11 of the prestress stiffness of trusses. to assess the structural stability within the same graphical ansatz is an interesting development. Given that graphic statics can lead to forms that are potentially unstable, the extension in Ref. However, optimising a triangulated morphology for a unique reference loading case leads to funicular chords and to diagonal bracing being discarded, creating the appearance of Vierendeel-like structures that nevertheless behave according to a totally different structural principle. It is often stated that the funicular forms that arise via graphic statics gain their efficiency by the avoidance of bending, but even standard triangulated structures such as Pratt or Warren trusses carry the applied loads via predominantly axial actions.
The diagonals or other forms of bracing are required for other loading cases and for stability. 10 Such a geometrical optimum without bracing can be reached only for one reference loading case, a scenario that never occurs in actual structures. When applied to the design of trusses, however, the method can have a tendency to minimise or even eliminate diagonal bracing members, particularly if the form is optimised. Although most modern structural analyses now employ computerised matrix methods, there has been renewed interest in graphic statics, and particularly in the way that it can be used to arrive at efficient structural forms. Maillart learned the techniques from Wilhelm Ritter whilst a student at ETH in Zurich in the 1890s, Ritter having been the main assistant and successor of Culmann. Considerable advances were made in the late nineteenth century by Maxwell, 6, 7 Cremona, 8 Culmann 9 and others. Typically, these are two-dimensional pin-jointed trusses, although there are methods that deal with arches and beams, and there have even been attempts to analyse 3D structures. With origins that date back to Stevin 4 in 1586 and Varignon 5 in 1687, graphic statics is a way of determining the equilibrium forces in structures by purely graphical means.
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