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Figure 21: The grey energy required to build a
structure (in KWh) or the cost (in €), including the
facade(s), may be calculated based on
w
.
The optimal slenderness ratio of the structure
increases when the facade is taken into account.
Philippe Samyn’s persistent interest in geometry
stems from his awareness of the importance of the
layout; as we have seen, the origin of the use of
symmetry comes from technical cost-saving con-
cerns for projects, particularly the search for the
greatest possible structural lightness.
‘The building is motionless; it does not drive, sail or fly.
In principle, its problems should be simpler than those
of moving machines, for which research into lightness
is aimed at reducing the quantity of energy required for
movement. For buildings, lightness is aimed at reduc-
ing the energy necessary to construct them.’
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His
reflections on the morphology of structures, and the
search for conceptual tools for facilitating the technical
and economic optimisation of projects, gradually led
Philippe Samyn to the concept of geometric indicators,
which came to him when on vacation in 1997. With the
goal of characterising a shape subjected to a load under
given boundary conditions, he defined two indicators:
volume indicators
(figures 23 and 24)
and displacement
indicators.
GEOMETRIC INDICATORS
VOLUME INDICATOR
Volume indicator
w
is a non-dimensional number that
characterises the quantity of material in a shape-resist-
ant element. If one is seeking to use as little material as
possible, the goal is to find elements with a minimum of
w
. It is defined by the expression:
14
w
=
σ
v
/
fl
where
σ
is the allowable stress to which the element
is assumed to be exposed (
n
/m²);
v
is the volume of
material of the element, assumed to be homogenous
or equivalent (m³);
f
is the resulting force to which
the element is subjected under loading and boundary
conditions (
n
);
l
is the length of the element along its
load axis (m). No matter what materials make up a
structure, the engineer’s art consists in getting all parts
of the structure to work to their maximum stress. If we
work this shape under loading and boundary conditions,
under these circumstances we will have to seek the
lightest structure. If we give this object a unitary dimen-
sion (
l
= 1 m), and subject it to a unitary force (
f
= 1
n
)
and we consider that this structure is made of a mate-
rial that performs at a unitary level of resistance (
σ
= 1
Pa), the volume of the material
v
is the volume indica-
tor. This is a purely morphological concept. I analyse an
abstract object that has a unitary dimension, subjected
to the resultant of unitary forces and in a material that
has a unitary resistance: it is a shape, a drawing. But
this allows me to proportion the material in such a way
that the structure is at its optimum at every point. The
volume of the material will depend solely on geometry,
for a given load and given boundary conditions, and all
of this at the unit level: we free ourselves from the size
of the object, from the intensity of the resultant and the
resistance of the material. If you begin to compare the
world of structures of every size, load intensity and type
of material, you are faced with an infinite number of
structures. You must therefore find a reference system
to make comparison possible. The volume indicator is
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