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