Wind Effects in Tensile
Membrane Structures
Pedro Gil Marques de Queirs Ferreira
Elsa de S Caetano
2016
PhD 2016 | 2
2016 CONSTRUCT PhD Workshop
Wind Effects in Tensile Membrane Structures
Motivation
Growing use of tensile membranes in special
structures has brought increased demand in the
assessment of their structural behavior
Membrane structures are characterized by: high
flexibility, leading to strong geometric nonlinear
behavior; complex shapes; slight prestress;
orthotropic materials; and construction methods
Recent damages due to aerodynamic and
ponding effects of these lightweight structures
and lack of standards motivated this work
PhD 2016 | 3
2016 CONSTRUCT PhD Workshop
Wind Effects in Tensile Membrane Structures
Objectives & Tasks
The work focused two main aspects
Form-finding
Characterization of the wind effects in membranes
Two types of examples
Roof of a multisport arena
Role of prestress & orthotropy on structural behavior
Wind effects considering generation of stochastic wind
loads and numerical evaluation of membrane response
through a simplified model, characterizing the
aerodynamic mass, stiffness and damping
470 Sailboat
Develop and validate a methodology of form-finding of
a boat sail in real-time based on strain measurements
Case studies
Roof
Sailboat
PhD 2016 | 4
2016 CONSTRUCT PhD Workshop
Wind Effects in Tensile Membrane Structures
Structural form-finding and optimization methods
Force Density Method (FDM): 1lFDM and 2nlFDM
Independent of the material properties and linearize the
Equilibrium equations using a force density coefficient q
= t/l for the truss elements
Surface Stress Density Method
Analogous to FDM setting a surface stress density
coefficient qs for the constant strain triangle elements
Dynamic Relaxation Method: Viscous & Kinetic model
Explicit direct time-integration of the dynamic
Equilibrium equations using central finite differences.
[Cs Xf q F]1,2 + Qz
2 X t l
Cs Xf Xini qs F Xend t l S = 4qsS
Cs Xf Xini F (E A ti )truss el. Xend t l
kN/m
0 2 4 6 8 100
1
2
3
4
5
6
7
8
9
10
1 2
3
4 5
6
7 8
9
Geometria Inicial - MDFl
x
y
0 2 4 6 8 100
1
2
3
4
5
6
7
8
9
10
1
2
3
4 5
6
7 8
9
Geometria Inicial - MDFl
x
y
0 2 4 6 8 100
1
2
3
4
5
6
7
8
9
10
1
2
3
4 5
6
7 8
9
Geometria Inicial - MDFl
x
y
0 2 4 6 8 100
1
2
3
4
5
6
7
8
9
10
1 2
3
4 5
6
7 8
9
Geometria Inicial - MDFl
x
y
PhD 2016 | 5
2016 CONSTRUCT PhD Workshop
Wind Effects in Tensile Membrane Structures Linear Force Density Method (lFDM)
Example of a cooling tower
Solution is obtained iteratively: rinf 9
m, rsup 7 m, Hc 21 m e Hm 25 m
Configurao a) b) c)
qs (N/m) 400 400 400
qcomp (N/m) -2800 -3000 -3000
qc,v (N/m) 100 100 1000
qc,h (N/m) 100 100 100
Configurao a) b) c)
qs (N/m) 400 400 400
qcomp (N/m) -2800 -3000 -3000
qc,v (N/m) 100 100 1000
qc,h (N/m) 100 100 100
Suspension cables
Upper compression ring
Lateral cable net (horizontal
or circumferential and vertical
cables)
Mast
Lower compression ring
PhD 2016 | 6
2016 CONSTRUCT PhD Workshop 2016 CONSTRUCT PhD Workshop
Wind Effects in Tensile Membrane Structures Viscous Dynamic Relaxation Method
1 Evaluation of the critical damping:
2 Evaluation of the static equilibrium response
Kinetic Dynamic Relaxation Method
=1
= 4
=1
2
+
+
0
1
2
3
4
5
0 50 100 150 200
Kin
eti
c e
nerg
y (
J)
Iterations
0.01
0.03
0.05
0.07
0.09
0 500 1000 1500 2000
u (
m)
Iterations
= 0
< 1
= 1
> 1
Equilibrium position:
Mx. kinetic energy = 0
Instable position: = 0
Vibration
F
=
= 0 < 1
= 1 > 1
PhD 2016 | 7
2016 CONSTRUCT PhD Workshop
Wind Effects in Tensile Membrane Structures
Roof of a multisport arena
Tensile membrane roof structure located in Cartuja Island, Seville
Doubly symmetric tubular metallic structure in plan, nearly rectangular in
plan 24 x 46 m2, including suspended cables and calibrated rods
Tensile membrane made of PES/PVC, comprised by 4-top (hip. parab.)
and 4-lateral modules (flat)
Tubular section F 323x8 (mmxmm)
Tubular section F 200x6 (mmxmm)
Tubular section F 150x5 (mmxmm)
Cable F 36 mm
Calibrated rod F 25 mm
U warp
T fill
PhD 2016 | 8
2016 CONSTRUCT PhD Workshop
Wind Effects in Tensile Membrane Structures
Roof of a multisport arena
Form-finding of the membrane with prestress of 2 kN/m
through all implemented methods and specialized
software, and comparing the same premises of
orthotropic orientations, showed slightly different results
Numerical simulation studies of the influence of the
prestress, orientation of orthotropic directions, and
Poisson coefficient evidenced significant differences on
the static and dynamic responses of the membrane
Nonlinear dynamic analysis in time domain considering
geometric nonlinearity and large displacements showed
dynamic amplification coefficients Rdyn of about 0,8
Identification of wrinkles on the corners of the lateral
modules due to non-economic shapes
0
1
2
3
4
5
6
7
0
20
40
60
80
100
120
140
160
0 10 20 30 40
Fre
qu
n
cia
(H
z)
Fa
tor
de
pa
rtic
ipa
o
Modo
X
Y
Z
Freq.
3.79
5.97
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.E-12
1.E-08
1.E-04
1.E+00
0 5 10 15 20 Fato
r d
e h
ibri
diz
ao
(F
H)
Am
plitu
de
Frequncia (Hz)
Dir. x
FH
Pa
rtic
ipa
tio
n f
ac
tor
Mode
Fre
qu
en
cy (
Hz)
Dis
p.
(m)
Am
plitu
de
Hy
bri
diz
ati
on
facto
r
Frequency (Hz) Time (s)
-0.002
-0.001
0.000
0.001
0.002
0.003
100 150 200 250 300
Deslo
cam
en
to (
m)
Tempo (s)
Rdin = 1.08
Ux, quasi-esttico
Ux, din
quasi-static
0
5
10
15
20
25
30
35
40
45
50
0 100 200 300 400 500 600 700 800
Ve
loc
ida
de
(m
/s)
Tempo (s)
1
534
Velo
cit
y (
m/s
)
Time (s)
PhD 2016 | 9
2016 CONSTRUCT PhD Workshop
Wind Effects in Tensile Membrane Structures
Form-finding of a boat sail in real-time
This work describes a monitoring system based
on fiber optic strain gauge sensors used to
reconstruct in real time the form of a sail
The installation of FBG sensors on a beam allows
to obtain curvatures in specific cross-sections,
and evaluate, by interpolation, the coordinates of
the deformed beam and consequently the most
significant parameters of the sail shape
Uncertainties related to optical technology,
require the calibration and validation of the results
through an alternative system.
Since large amplitudes of deformations are
measured, the fiber optic monitoring system was
validated based on a imaging based system
Draft position
Chord
Cam
ber
(cm
)
(%)(cm)
Conclusions
Implementation of form-finding routines
Application to a tensile membrane roof
Identification of more relevant aspects of
the behavior through parametric analysis
Wind action and effects assessment
Sail case: development, implementation
and validation of an algorithm already
patented for real-time assessment of sail
shape. This methodology can be used for
SHM of other engineering applications
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