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71
solely based on geometric proportions: you attempt to
find reproducible magnitudes, to give a form, a sort of
id
card, independent of its size and its component mate-
rials. These are geometric laws, according to a purely
analytic and non-numerical approach’.
15
DISPLACEMENT INDICATOR
Displacement indicator Δ is a non-dimensional
number that characterises the deformation of an ele-
ment (a rotation indicator can be defined by analogy).
If rigidity is sought (limited deformation), the goal is to
find elements with minimum Δ. This is defined by the
following expression:
Δ =
e
δ
/
σ
l
where
e
is the material’s modulus of elasticity, assumed
to be homogenous or equivalent (
n
/m²);
δ
is the ele-
ment’s maximum displacement (m);
σ
is the allowable
stress to which the element is assumed to be exposed
(
n
/m²);
l
is the length of the element along its load axis
(m). The displacement indicator thus corresponds to the
displacement (
δ
) of a unitary structure (
l
= 1 m), and a
material with a unitary modulus of elasticity (
e
= 1 Pa),
whose elements are sized such that they are subjected
to a unitary allowable stress (
σ
= 1 Pa). It also allows
the user easily to calculate the first natural frequency
n
1
(the lowest) of vibration of the structure, and thus its
sensitivity to dynamic effects, from the stage of the first
structural sketches.
16
If there are no live loads to take into
consideration,
17
the first own frequency (in Hz) is deter-
mined by the expression n
1
= (g
e
/ (Δ
l
σ
))
1/2
/ 2π where g
is the acceleration of gravity (9.81 m/s²). In his doctoral
thesis,
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for which he benefited from the exceptional
calculation skill and close cooperation of Pierre Lateur,
Samyn demonstrated that these two indicators depend
only on the element’s
l
/
h
slenderness ratio, with
h
being the element’s transversal dimension
(figure 22)
.
The determination of the quantity of material for these
structures, on the basis of
w
, is exact and reliable, on
the condition that the quantity of material of assemblies
in tension is negligible, and that phenomena of elastic
instability under compression may be excluded. To do
this, Philippe Samyn carefully studies the indicator
w
of
the compressed element and the means of assembly
under tension, in order to take it into consideration from
the first drawings. Traditionally, the goal of a structural
engineer is to not exceed allowable stress and the
minimum slenderness ratio for buckling, instead of
searching for the minimum weight that will satisfy these
two conditions. In addition, the engineer’s faith in the
benefits of tension will often lead him or her to forget
the far from negligible weight of assembled structures.
To a certain extent, geometric indicators are ‘genomes’
of a shape that operates within allowable stress under
given loading and boundary conditions, and that
depends solely on the geometry and on its proportions.
Understanding them means that one can build as light
as possible; this becomes an obligation when you know
that the increase of knowledge and the world’s growing
population of people living below the poverty line leads
to more and more consumption of products and that,
in the prices of these products, the percentage of the
cost of grey matter diminishes in inverse proportion
to the cost of physical material. In addition, lightness
combined with symmetry creates a virtuous circle that
should be respected in order to obtain the best resist-
ance to earthquakes; since the effect of an earthquake
is in proportion to the acceleration of a structure’s
mass, the less mass there is, the lower the effect.
Philippe Samyn calls himself a Hegelian, in the sense
that, according to the thought of G.W.F. Hegel, he
considers that in the area of hyper-light structures, there
is an absolute (which is the outcome of the Hegelian
system) towards which every previous moment in
the evolution of the system points. Nevertheless, he
acknowledges that everyone is free to choose other
foundations for their systems of thought, i.e. other
philosophical choices. He concludes that engineering is
an art because there is freedom of choice.
Figure 22 : Slenderness ratio
l
/
h
of an element
22