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Volume and displacement indicators as conceptual tools for engineers
Dr. Eng. Philippe Samyn
FABI-CSTC: Symposium “From Bright Idea To Implementation“ 28 November 2007,
Royal Military School, Brussels.
Background
Volume and displacement indicators, which I have been studying since August
1997, allow the conceptual engineer to evaluate his approach, starting already with
the preliminary sketches, in the quest for saving material.
Two biennials of Industrial Research of the Brussels Capital Region have allowed
us to greatly develop the theory between 2000 and 2004. The effort is now being
taken forward by my colleagues at the Free University Brussels (VUB-ULB), among
others.
My book “Studies in the morphology of structures with the help of volume and
displacement indicators“, published in 2004 by Classe des Sciences of the Royal
Academy Belgium, presents the results up to the end of the first biennial.
The body of work is already significantly complemented by the PhD dissertations
submitted to the ULB by Pierre Latteur, Jan Van Steirteghem and Ben Verbeeck
(approaching completion).
Definitions and objectives
The volume indicator W represents the volume of material of a plane structure, on
a given support system, of unitary length (L=1m) and of a height H where all parts
are equally subjected to a unitary stress (σ =1Pa), when it is acted upon in its plane
by a resultant of the unitary force (F=1N).
Any structural shape, irrespective of the material, under given support conditions
and with a given force resultant, irrespective of its magnitude, is characterised by
a single value W (in a way its gene), which is solely a function of the ratio H/L, as
far as none of its constituents is in a state of elastic instability and the material of
the components are taken into consideration.
The volume of material V (m³) of the same structure of length L (m) (and of height H
(m)), in which all parts are equally subjected to a stress σ (Pa) when it is acted upon
in a plane by a resultant of the force F (N), will be V = (FL/σ ). W (function of H/L).
Knowledge of the values of W for different structural morphologies, with their
respective support systems and loads, is important not only for the purpose of
guiding the designer already during the preliminary sketches, but also to allow him
to evaluate the efficiency of his proposal as compared to others.
It also facilitates the very precise evaluation of the quantity of material needed and
the cost of a structure during the very early stages of the project.
The displacement indicator Δ represents the (maximum) displacement of the
same unitary structure in which the elasticity module is unitary (E=1Pa); it is also
determined solely by the H/L ratio.
The displacement of the same structure of length L(m), in which all components are
affected by the same stress σ, in a material of elasticity module E (Pa), when acted upon