1. Civil@UL
Form Finding
Non-linear Behaviour
Hypothesis
“The relationship between load-deflection and pre-stress-
deflection is non-linear within pre-stressed cable structures (e.g.
cable nets) and increases in pre-stress will result in lesser deflec-
tions. This behaviour is governed by geometric non-linearity.“
Computational numerical model
Recommendations
Geometric NOT Material
Linear-Elastic
Physical experimental model
“In the presence of pre-stress, geometric non-linearity’s are of the same
order of magnitude as linear-elastic effects in structures”
In the past—purely empirical
Simply supported cable
1x1 cable net
2x2 cable net
Equation of vertical equilibrium (expanded)
Deflection can be shown to be
Simply supported cable
Equation of vertical equilibrium (compact)
As members added,
method impractical, a more
generic form was required
KG KE
Architect—like a conductor,
leads an orchestra
Structural Engineer—can be part
of the orchestra, but also a solo-
Form follows Function
Form follows Force Force follows Form
Engineers, in form finding, must:
Conceive a new form
Visualise the final appearance
Refine it by calculations
Develop a means to construct it
Feasible structural form and set
of internal forces for equilibrium
Intrinsically linked!
Objectives
1) All load cases and boundary condi-
tions are considered
2) Material properties are taken into
account
3) Stresses and displacements are lim-
ited to design values
4) A uniform membrane stress state
5) Undesirable conditions are avoided
6) Guarantee of a reasonable design life
7) Manufacturing costs are justified
8) The design is aesthetically pleasing
Numerical & Analytical techniques
Stiffness matrix methods
Dynamic equilibrium methods
Geometric stiffness methods
Force Density Method (FDM)
Computer generated image of numerical/analytical solution
A cable net is highly flexible due to a very small elastic rigidity, therefore it must undergo deformations in order to
satisfy equilibrium, in comparison to a beam which undergoes small deformations in order to satisfy equilibrium.
Converting to a
Linear system
of equations
Various solutions
Point based iterative method
Must solve the following
equation using finite element
displacement methods:
Unbalanced load vector
Tangent stiffness matrix
Displacement vector
Assumptions
1) Loaded @ Nodes
only
2) Linear-elasticity
3) Homogenous,
Isotropic material
4) Constant cross-
sectional area
5) Fixed boundary
nodes
Internal forces and displacements are calculated through an iterative process,
by breaking the system into sub-systems as shown fpr a 2x2 cable net
(interdependent calculations)
Discussion
Incorrect assumptions in computer model
Increasing pre-stress reduces slippage
Physical model always ‘softer’ than computer model
Increasing pre-stress correlates with closer agree-
ment between models
Non-linear and linear relationships both present
Increasing load correlates with more disagreement
between models
Script errors evident as some behaviour not physically
representative in certain instances (2x2 cable net)
Conclusions
Tensile structures = modern development, becoming increasingly popular
Form finding is integral to the design of tensile structures, further research required
All aspects (theoretical, computational and experimental) are complex, with many differ-
ent variables and parameters requiring attention
Simply supported and 1x1 cable net successively compared, 2x2
was not as the computational model was not giving physically
representative outputs
General behaviour successfully displayed:
- Pre-stress reduces deflection
- Deflection decreases with increasing load
Theory
Comparative analysis of pre-stressed cable net roof structures:
via computational and experimental methods
Conor Meaney
11138874—4th
year Civil Engineering
Dissertation/FYP
Viva Voce
16/04/2015
Professor Tom Cosgrove
Introduction to MATLAB
Iterative calculation/
procedure
Extracts of script—Iterations
Why!!!
Essential to
Modelling!
Input of experimental data
Fundamentals used to build progressively
more ‘complex’ models
Are the two computational model in agreement?
PBIM CFMS
A graphic of what the iterations are actually doing/calculating—Equilibrium!
Basic components/skeleton
tested here in order to build
larger models
Possibly not safe for human health!
Issues with scripting..
Application of pre-stresses in one
cable causes changes in others!
Form finding was conducted to find the nodal
(vertical) locations after pre-stressing
Measurements be-
came tedious and
diligent care was
needed for accuracy
Tensile structures are gaining traction!
Beware of assumptions used as reality may prove different..
Variety of load cases introduced (3x3 shown)
A example of improvements to the physical model
GUI’s and form finding soft-
ware would help massively in
this project!
Long strings of code are to be avoided!
Compress/compact code
as much as possible
A lower Young’s modu-
lus material will high-
light geometric non-
linearities
Scale model of velodrome used for
boundary nodes co-ords
Loading of each model
Changes made since previous dissertations..
Testing conducted for de-
sign parameters
Iteration and interdependent calculations
1x1 cable net—CFMS
A guiding principle