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in its plans by a resultant of the forces F(N), will be δ = (σ L/E) Δ (function of H/L).
Knowing the value of Δ allows for the evaluation of both the stiffness and the
sensitivity to vibrations of the structure.
Progress and results
The following list reviews the archetypal morphologies we have studied until
now; it has to be integrated with those studied since 2005, particularly at the Free
University Brussels.
- The compressed element subjected to elastic instability,
- The element tightened with its anchorage system and the light balloon,
- Horizontal impact under vertical load (uniformly distributed or mobile point
load):
- The straight continuous beam,
- The trellis,
- The arches and cables,
- The guyed structures,
- The beams on continuous support,
- The suspended beams,
- The masts,
- The porticoes,
- The revolving cupolas in a membrane under vertical load (uniformly
distributed or mobile point load).
For example, figures 1 and 2 show the values of W and Δ (both functions of H/L) for
some morphologies of the horizontal isostatic range under vertical and uniform
load.
Figure 3 provides the linearised values of W for the horizontal range under vertical
and uniform load. This approximation is very useful to calculate the value of W for
complex structures made up of elements with different morphologies.
Figure 4 shows the study of the optimum slenderness of a trellis beam, taking
into consideration the cost of the glass façade that covers it: the hyperbolic curve
of the façade cost (Ev) is added at the right of the structure cost (i.e.: W deriving
from figure 3 and transformed in k). When the façade is taken into consideration,
the optimum slenderness of the entire structure is greater than that of the trellis
alone.
This was the method by which we determined the proportion of beam to trellis of
the bridge of Nivelles-Orival. (fig. 5)
The indicators of several hybrid structures have also been computed for
commissioned projects, in order to improve them. To mention a few:
- The trellis bridge of the motorway ramp of Nivelles-Orival (1998-2000; fig. 5)
- The guyed masts of wind turbines considered by Fabricom (1999-2001; fig. 6)
- The roofing of the Leuven train station (1999-2007; fig. 7)
- The roofing project of the highway ramp of Thieu (2001; fig. 8)
- The project for a footbridge over the Po in Turin (2001; fig. 9)
- The project of extra-light roofing of the courtyard of the Alden Biesen castle
(2001; fig. 10)
- The first project of a footbridge in the Leuven train station (2002; fig. 11) and,