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1 INTRODUCTION
Quite often the design of a structure is based on a shape imposed by the designer. It is clear that
optimizing structural shapes is a field in itself, but the question in the early design phase is to
estimate the impact of different structural topologies and boundary conditions on the overall
behaviour of the structure. Considering the computing power at hand, it is not that exceptional to
model a three-dimensional complex geometry, conduct a finite element analysis with all load
cases and run the code checks to dimension and verify the structure, with optional optimization
process. At the end of the process, the calculation will have a clear output: the weight of the
structure. When wanting to compare five topological alternatives, this approach becomes very
time consuming, and only allows comparing the final weight of the structure.
Whilst an interesting approach, it does not provide the structural designer in a clear and
obvious way with information how the variants differ in structural behaviour. An experienced
structural designer will start to point compare structures: maximal normal forces, maximal
bending moments, maximal deformations, etc. However, this gives punctual information about
peak performance, while neglecting the view on the overall performance and behaviour.
This paper proposes a novel approach, using intricate three-dimensional models, but
lightweight calculations followed by a dashboard of graphs representing and comparing the
overall behaviour and performance of structural design alternatives. The approach will be
illustrated on the basis of a case study of a grid shell. The tool is aimed to offer the experienced
engineer a synthetic view of the whole, whilst not reducing the complex behaviour of free form
shell structures to a single number.
Figure 1. Various design proposals for a grid shell need to be assessed quickly in early design phase
(c) Ney + Partners.
How to re-open the black box in the structural design of complex
geometries
K. Verbeeck
Partner Ney & Partners, Brussels, Belgium
L. Loos & L. De Laet
Vrije Universiteit Brussel, Belgium
L. Muller
Université Libre de Bruxelles, Belgium
Structures and Architecture – Cruz (Ed)
© 2016 Taylor & Francis Group, London, ISBN 978-1-138-02651-3
316
2 INTEGRATED METHODS FOR STRUCTURAL DESIGN CONSIDERATIONS
2.1 Traditional sequential approach
Traditionally, structures are being designed in a sequential approach. The overall geometry
(shape, topology) is first conceived (often by an architect). During this phase architectural and
functional criteria such as aesthetics and boundary conditions are taken into account. The
structural behaviour and efficiency is only considered in a second phase, in which the geometry
is subjected to finite element calculations and in which the results are analysed (figure 2). If the
results are not satisfying, the design is changed iteratively. If design modifications are made in
the geometric modelling tools, those changes need to be remodelled as well in the engineering
tools, an approach which is time consuming and can lead to errors.
According to Clune et al. (Clune 2012), the reason for this sequential approach is the
specificity of the software applied by the architects and engineers. Architects use geometrical
modelling tools that stimulate the exploration of the design space and creativity, mostly without
considering structural efficiency, whereas engineers conduct finite element calculations on a
predefined shape. In addition, the results generated with a finite element analysis software can in
general only be checked case per case, making it hard for the structural designer to compare design
alternatives. Also, only maximum values are often taken into account with this approach, leaving
into the shadow the global structural behaviour. To a large extent this sequential process is also a
result of the fact that architect and engineer are two different persons. In this paper, we assume
that the engineer also takes a more prominent role as a designer of an architectural structure (i.e.
a structural designer).
Figure 2. Diagram of a 'traditional' sequential design process.
2.2 Structural design tools and their focus
It is clear that structural considerations should preferably be introduced in the first stages of the
design process as the structure's efficiency is mainly determined by its geometrical properties,
such as shape and topology. Computational structural design tools tend to enable a better
integration of structural performances during the early conceptual design phase. Various
structural design tools exist, all with their specific focus, complexity, user interactivity and
required technical background. Each of the existing structural design tools has its own goal and
is very suited for a specific use.
However, we are looking for an approach whereby various three-dimensional complex
designed proposals can be calculated quickly in a familiar FEA software, after which the load
bearing behaviour of all cases can be compared with each other rapidly and easily in one general
overview, without the need for custom made software. Most importantly, the comparison of
structures should be possible without the need to calculate the total weight of the structure. First
comes understanding the structure, afterwards dimensioning that structure.
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Before elaborating on the developed approach, we first present the case study that will serve
to illustrate the approach.
3 CASE STUDY: ONE GRID SHELL, NINE VARIANTS
The considered grid shell is a covering of one of the two courtyards of the Osterrieth Huis, situated
in Antwerp (Belgium), which was built in 1746 in full Rococo-style. A steel grid shell covered
with glass was chosen as transparent covering for the courtyard, since its intrinsic efficiency
allows covering a reasonable large span with a low self-weight (figure 3).
Figure 3. Two grid shells as covering for the atria of the Osterrieth Huis (c) Ney + Partners.
3.1 Geometry, topology and boundary conditions
In this case study, the influence of the topology of the grid shell and its boundary conditions are
analysed. Nine cases are considered: three different topologies, each with three different boundary
conditions. The global shape of the grid shell is kept constant for all cases to allow comparison.
The height difference between the highest point of the shell and the edge is two meters. Note that
the plan is not a perfect square, which is typical for courtyards of historical buildings. The three
considered topologies, consisting of triangles or quadrilaterals, are presented in figure 5. The total
length of the steel elements for each case is also mentioned in the figure.
Topology A
(563,56m of grid elements)
Topology B
(892,13m of grid elements)
Topology C
(386,01m of grid elements)
Figure 5. The three considered topologies for the grid shell.
Figure 6 shows the three different boundary conditions. The edge beam takes the horizontal thrust
forces to make the shell a self-standing structure and thus to prevent horizontal forces on the
masonry of the historical buildings.
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Figure 6. The three types of support conditions.
3.2 Traditional approach: Full finite element calculations according to the Eurocode
As often done in a traditional engineering approach, in order to compare the nine design cases,
each element in each case was dimensioned to satisfy Eurocode requirements. This allows
comparing the solutions based on a single number: their total weight. All nine design cases have
been fully calculated in the finite element software Scia Engineer (Nemetschek), considering
wind, snow and maintenance loads as prescribed in the Eurocodes (EN 1991-1-4:2005 and
Eurocode EN 1991-1-3), taking into account calculated buckling lengths. By means of the
integrated AutoDesign feature, the sizes of the solid steel cross sections of the various design
cases were optimized to use their material in the most efficient way, as well in ULS as SLS. The
results show that the topology and boundary conditions have a large influence on the required
amount of steel, with differences going up to a factor of three. The weight of the cases is generated
through nine different full finite element calculations, including the optimization of sections,
which is clearly a time inefficient approach during the conceptual design stage. In addition, these
numbers give no additional information or feedback about the global structural behaviour.
If the experienced structural designer would like to compare the cases, he/she will start to point
compare structures (regardless of the design software used): maximal normal forces, maximal
bending moments, maximal deformations, etc. However, this gives punctual information about
peak performance, while neglecting the view on the overall performance. Also, to do this
comparison, he/she will have to switch between models, screens, scales of legends, etc. As each
piece of information is in a different window, this represents a time-consuming approach prone
to errors.
4 DASHBOARD APPROACH
4.1 General process
To reduce time wasted jumping between windows, a low-tech yet fast approach was developed
to eliminate the need to switch between windows. Hereby a comprehensive and global overview
of the structural behaviour of all nine cases is represented in one single place. This overview, the
dashboard, gives the structural engineer all the necessary information to compare the structural
behaviour of the various proposals, and facilitates the choice of a proposal that both satisfies the
architectural and structural criteria imposed by the structural designer.
The dashboard is a table of graphs, representing the normal forces, bending moments and
displacements of all members of the structure, under one single reference load case. Figure 7
illustrates the approach to compare the design alternatives according to the traditional approach
(left) and with the dashboard (right). The dashboard represents 10 aspects (N, My, Mz, uy, and uz
for both the edge beams and grid members) for 9 variants. In order to obtain the same information
in a classical FEM software this would imply cycling through 90 different result screens. Recently
a remarkable paper (Joyce, 2015) called for more intuitive, informed and interactive decision-
making tools, based on data visualization, in order to make informed structural decisions already
in the first design phases.
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Figure 7. The approach to compare the design alternatives according to the traditional approach with its
many windows (left) and with the dashboard (right).
To allow quick comparison of various design alternatives, it is also important to reduce the
complexity of the calculations. Instead of considering various load cases and load combinations
according to the eurocode, one reference load of 85 kg/m2 is applied on all cases. This reference
load is a fixed assumptive self-weight for all cases, based on experience in previous grid shell
projects and representing the weight of the steel and the glass. All grid members of the nine cases
are modelled as 3D beam models and have an identical cross section. The numerical model is thus
basic and approximate, which makes it very fast to model and analyse, making it tempting to the
structural designer to check more alternatives. All results from these quick calculations are then
compiled with a script to generate the graphs in the dashboard (figure 8). Section 4.2 will explain
the dashboard more in detail by explaining one case.
Figure 8. Dashboard, representing the structural behaviour of nine different structural designs.
Because the information given by the dashboard stays quite abstract, we advise to combine it with
additional tools that make use of the generated structural data. To further analyse the nine
alternatives, we also made visual plots of all forces, moments and displacements. Figure 9
illustrates the normal force occurring in all nine cases under the same distributed load, helping to
interpret the graphs from the dashboard. In addition, the data from the quick calculations can also
be analysed statistically to get a more informed view on the distribution of the internal forces of
all structural elements.
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Figure 9. The normal force of the nine cases under the same distributed load, helping to interpret the graphs
from the dashboard.
4.2 Interpretation - example
We will explain the dashboard and illustrate its ease of use with the next example, considering
the three topologies for boundary condition 2 (for reasons of clarity). Figure 10 illustrates a
selection of the dashboard graphs. The y-axis represents in the graph respectively the normal
force, the bending moments around the local y- and z-axis, and the vertical displacement (global
z-axis). The x-axis represents the various elements of each grid shell topology, sorted by value
(and normalized to their length). Because the topologies A, B and C are constituted of a different
amount of steel length, the curves of the three topologies stop at a different x-value.
Figure 10. Selection of the dashboard graphs, showing the normal force, bending moments, and the vertical
displacement of the three topologies for boundary condition 2.
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Figure 11. Internal forces (N, My) of the grid members of the three topologies for boundary condition 2,
plotted in a M-N-chart.
Interval Median Mean Value
min max
Normal force [kN] Case A2 neg -122 -0,2 -15,6 -34,15
pos 0,1 63,1 5,4 7,94
Case B2 neg -215,3 -0,1 -14,9 -25,46
pos 0,1 57 9,3 15,32
Case C2 neg -271,9 -0,2 -12,75 -60,59
pos 0,3 36,6 8,7 12,53
Bending moment around y [kNm] Case A2 neg -12,3 -0,1 -2,4 -3,63
pos 0,1 9,5 4,3 4,36
Case B2 neg -3,7 -0,1 -0,5 -0,52
pos 0,1 6,2 0,4 0,76
Case C2 neg -19,1 -0,4 -4,3 -6,99
pos 1,5 12,7 5,8 6,29
Table 1. Numerical values (peak, median and mean) add numerical information to the graphical dashboard.
From the dashboard selection (figure 10) can be seen that all three topologies have a different
structural behaviour under the reference load case for boundary condition two. Figure 11 shows
that the internal force distribution of the grid members of the different cases is very different for
each case. This will clearly have an influence on the choice of cross sections while calculating
the structure. On the other hand it becomes immediately clear whether the structure is mainly
acting in bending or compression. For a more comprehensive insight in the charts and their
interpretation the reader is referred to the paper presented at the IASS conference in 2015
(Verbeeck, Muller, De Laet, 2015) discussing this case study more elaborately.
From this dashboard, the structural designer can then start to categorize or order the structures
according to their efficiency. Table 2 shows the classification according to the quick 'dashboard
strategy' and puts it next to the results of the time consuming traditional engineering strategy. The
efficiency order of the first column is based on the total weight of the structure. The table shows
that conclusions of both approaches are very similar. This approach manages to give clear
direction to the structural design process, both based on quantitative results (internal forces), and
in terms of understanding of particular shell behaviour.
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Table 2. Conclusions of both approaches are very similar, resulting in a similar order of efficiency.
Traditional strategy Dashboard strategy
B1 A1 – B1
A1
B2 B2
B3 B3
A2 A2 – A3
A3
C1 C1
C2 C2
5 CONCLUSIONS
In an early structural design stage, it is important to quickly and easily assess the structural
behaviour of various design alternatives. In the case of a grid shell for example, various topologies
and boundary conditions can be envisaged by a (structural) designer and should thus be analysed
before proposing as a viable design solution. In a classical calculation approach, both the ultimate
limit state and service limit state should be calculated, taking load cases prescribed by the
Eurocode into account. This process is time consuming and complex, whereby the user needs to
make comparisons based on a lot of various screens and extreme values. To avoid this, we
proposed a quick and easy approach whereby the comparison of the structural behaviour of a large
amount of design proposals is facilitated.
The various design proposals are calculated under one reference load case after which the
generated data is read by a script and automatically plotted in a dashboard of graphs. This
dashboard allows to roughly compare at a glance the structural behaviour of the various proposals.
By combining the dashboard with an automated graphical plot of all the occurring forces and with
a table containing key numerical values, the structural designer has all the tools at hand to quickly
assess design alternatives.
Despite the many approximations made in the dashboard approach (such as applying one
single load case and a single uniform cross section of the members), comparison with the
'traditional' approach shows that both methods lead to similar conclusions with regard to the
'categorization' based on the structural efficiency.
With this approach, the structural designer can assess more quickly the different design proposals
based on a more complete understanding of the structure. The goal is to replace a 'computed
therefore it is' approach for a knowledgeable approach in the structural design thinking.
REFERENCES
Clune R., Connor J.J., Ochsendorf J.A., Kelliher D., An object-oriented architecture for extensible
structural design software. Computers & Structures, 2012; 100-101; 1-17.
Joyce S. C., Web Based Data Visualisation Applied to Creative Decision Making in Parametric Structural
Design. Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium
"Future Visions" Amsterdam, 2015.
Verbeeck K., Muller L., De Laet L., Structural Design by a Dashboard Approach. Proceedings of the
International Association for Shell and Spatial Structures (IASS) Symposium "Future Visions"
Amsterdam, 2015.
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