Wind Effects in Tensile

Membrane Structures

Pedro Gil Marques de Queirós Ferreira

Elsa de Sá 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 + Qz2 X t l

Cs Xf Xini qs F Xend t l S σ = 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

Configuração 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

Configuração 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

𝑓 =1

𝑁∆𝑡 𝑐𝑐𝑟𝑖𝑡 = 4𝜋𝑚𝑓

𝑈𝑘 =1

2 𝑀𝑈

𝑥 𝑇𝑈

𝑥 + 𝑀𝑈 𝑦

𝑇𝑈

𝑦 + 𝑀𝑈 𝑧

𝑇𝑈

𝑧

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

ξ = 0

ξ < 1

ξ = 1

ξ > 1

Equilibrium position:

→ Máx. kinetic energy 𝑢 𝑚á𝑥

𝑢 = 0

Instable position: 𝑢 = 0 𝑢 𝑚á𝑥

Vibration

F

𝜉 =𝑐

𝑐𝑐𝜉

= 0 𝑢𝑛𝑑𝑎𝑚𝑝𝑒𝑑 𝑣𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛< 1 𝑢𝑛𝑑𝑒𝑟𝑑𝑎𝑚𝑝𝑒𝑑 𝑣𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛

= 1 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙𝑙𝑦 𝑑𝑎𝑚𝑝𝑒𝑑 𝑣𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛> 1 𝑜𝑣𝑒𝑟𝑑𝑎𝑚𝑝𝑒𝑑 𝑣𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛

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

ên

cia

(H

z)

Fa

tor

de

pa

rtic

ipa

ção

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

ação

(F

H)

Am

plitu

de

Frequência (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-estático

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