Smart glass facade subjected to wind loadings · design for the back-up structural system. An adequate glass suspension system must be able to cope with the weight of the glass elements

Proceedings of the Institution of Civil Engineers

http://dx.doi.org/10.1680/stbu.13.00011

Paper 1300011

Received 11/02/2013 Accepted 04/04/2014

Keywords: buildings, structures & design/dynamics/wind loading &

aerodynamics

ICE Publishing: All rights reserved

Structures and Buildings

Smart glass facade subjected to windloadingsSantos, Goncalves, Cismasiu andGamboa-Marrufo

Smart glass facade subjectedto wind loadingsFilipe Amarante dos Santos PhDProfessor of Civil Engineering, Centro de Investigacao em Estruturas eConstrucao – UNIC, Faculdade de Ciencias e Tecnologia, UniversidadeNova de Lisboa, Quinta da Torre, Caparica, Portugal

Pedro F. Goncalves MScGraduate Student, Centro de Investigacao em Estruturas e Construcao –UNIC, Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa,Quinta da Torre, Caparica, Portugal

Corneliu Cismasiu PhDProfessor of Civil Engineering, Centro de Investigacao em Estruturas eConstrucao – UNIC, Faculdade de Ciencias e Tecnologia, UniversidadeNova de Lisboa, Quinta da Torre, Caparica, Portugal

Mauricio Gamboa-Marrufo DPhilProfessor of Civil Engineering, Facultad de Ingenierıa UniversidadAutonoma de Yucatan, Yucatan, Mexico

The design of a modern glass facade translates an architectural aspiration for transparency. Innovative technological

solutions have made it possible to materialise a transparent planar surface, exploring the load-bearing capabilities of

the glass itself. Facades also need to have back-up structures, which are designed to withstand seismic and wind

actions. This paper analyses the behaviour of a ‘smart’ glass facade, based on a bow-string truss solution, which is

able to continuously adapt its shape in order to compensate for the wind dynamic displacements, affecting the

structural appearance. The wave superposition method is used to generate samples of the wind distributions, using

sinusoidal functions. A proportional–integral–derivative control strategy enables a significant reduction of the

displacements shown by the facade during wind events. This design approach yields an optimised structural solution

in terms of weight, allowing the materialisation of a very light facade.

NotationA, B, C, D coefficients

B(s) feedback stress signal

b dimension in across-wind direction

C amplitude of the harmonic function

C(s) cable stress output signal

c damping coefficient (Ns/m)

cp,e pressure coefficient for the external surface

d dimension in along-wind direction

E(s) actuating error signal

Fw force in the able system due to detonator (N)

f frequency (Hz)

fL dimensionless frequency

Gc(s) controller transfer function controlled process

Gcp(s) transfer function

H(s) feedback-path transfer function

h height of facade

Kd derivative gain

Ki integral gain

Kn generalised nodal stiffnesses (N/m)

Kp proportional gain

Ku ultimate gain

k stiffness (N/m)

L turbulence scale

m mass (kg)

n natural frequency (Hz)

Pu ultimate period (s)

p load excitation (N)

qp wind dynamic pressure (Pa)

R(s) reference cable stress input

SL spectral density function

s complex variable

T control force (kN)

Td derivative time

Ti integral time

Tw force in the cable system due to wind (N)

t time

U(s) output signal of controller

u displacement (m)

v instantaneous wind speed (m/s)~vv turbulent fluctuations of wind speed (m/s)

vm mean wind speed (m/s)

we wind pressure on the external surface (Pa)

z height (m)

� damping ratio

r air density (kg/m3)

� time variable (s)

�k phase angle (rad)

øD damped frequency (rad/s)

øn natural frequency (rad/s)

1. IntroductionModern glass suspension techniques, exploiting the load-bearing

capabilities of glass, enable the elimination of structural elements

from the glass pane. The materialisation of a transparent planar

surface can only be truly achieved if the back-up structures, which

are designed to support the seismic and wind forces, are reduced

to their minimum expression. These structures can vary from

glass mullion systems, using glass fins, to steel trusses and cable-

stayed systems (tension structures). In either of these systems, a

1

close integration of glass and steel is of utmost importance in

order for the complete facade to meet high performance require-

ments (Dutton and Rice, 1996; Schittich et al., 1999).

Various forms of cable-stayed back-up system designs can be

used to support a glass facade. They can take the form of simple

steel trusses, with a secondary rigging system, yielding the most

rigid structural solutions, or bow-string trusses and cable tension

structures, with increased transparency (Nijsse, 2003; Vyzantia-

dou and Avdelas, 2004; Wurm, 2007). Cable trusses have the

disadvantage of generating high tensile loads in the boundary

structure, which needs to be stiffer. In all instances, the capabil-

ities and loading of the glass must be used as the basis of the

design for the back-up structural system.

An adequate glass suspension system must be able to cope with

the weight of the glass elements as it braces the facade against

wind and seismic loads (Dutton and Rice, 1996). The glass

facade itself, while responding dynamically to the wind excita-

tion, must have sufficient strength to resist wind-induced forces

and adequate stiffness to satisfy serviceability criteria.

The purpose of this paper is to present a numerical study of a

‘smart’ glass facade based on a bow-string truss solution, as

shown in Figure 1, which is able to continuously adapt its shape

in order to compensate for the dynamic displacements induced by

the turbulent fluctuations of the wind. This is achieved by the

implementation of a proportional–integral–derivative (PID)

closed-loop control system, which allows the force in the cables

of the truss to be controlled. The response is studied for a

constant transversal wind load, perpendicular to the plane of the

glass, which is added to a random time-varying excitation

representative of the gust component.

2. Glass facade

2.1 Design of the glass facade

The glass facade is 8 m tall by 16 m wide and is integrated in a

building with an implantation area of 16 3 16 m2: The glass

panes, with dimensions 2000 3 2000 3 16 mm3, are suspended

from a main frame, which is not analysed in this study. Each

vertical alignment of suspended glass comprises four sheets,

connected to each other by point fixing systems (Bernard and

Daudeville, 2009). In the case of suspended facades, toughened

or tempered glass is most commonly used (Vyzantiadou and

Avdelas, 2004). These thermo-mechanical methods raise the

resistance threshold at which cracking of the glass occurs, by

creating a self-balanced stress condition within its cross-section

(Wurm, 2007). The resistance of the suspended glass facade to

wind is guaranteed by four bow-string trusses. These trusses are

built up of a vertical element and three horizontal brackets, which

act as deviators (circular hollow section with 76.1 3 3.0 mm),

and two pre-stressed stainless-steel cables with d ¼ 8.1 mm. One

of the main advantages of pre-stressing the cables is that, instead

of having one single cable resisting the wind load, there are two

cables in tension relative to each other. The bow-string trusses are

stabilised by three horizontal cable trusses, composed of pre-

stressed stainless-steel cables with a cross-section of d ¼ 8.1 mm.

The general configuration and the main dimensions of both the

glass facade and its supporting bow-string trusses are shown in

Figures 1 and 2.

The cables (2) of the two central trusses are active elements,

which are able to apply forces to the structure in a prescribed

manner (Housner et al., 1997). The control system is an active

control system with feedback, in which the applied forces are a

function of the tension in the cables, which are continuously

monitored. The control strategy for the facade is illustrated in

Figures 3 and 4. Figures 3(a) and 4(a) represent the initial state

of the facade, in which both cables have the same force,

T1 ¼ T2 ¼ Ti associated with the prescribed pre-stress. Figures

3(b) and 4(b) represent the facade subjected to the corresponding

wind loadings, which do not directly interact with the trusses. As

the trusses are within the building, the wind forces act on the

glass panes and are transmitted to the trusses through the point

fixings. According to Parts 1–4 of Eurocode 1, as the height of

the structure is low and the h/b , 1, where b is the dimension in

the across-wind direction and h is height of the facade, the wind

pressure profile is considered to be constant (BS EN 1991-1-4

(BSI, 2005a)). In Figure 3(b) the force in cable 1 decreases by

Tw, as the facade deforms due to the wind pressure loading. In

cable 2, the force increases by the same amount originating a

total force of T2 ¼ Ti + Tw: In the case of a wind suction loading,

the final forces in the cables are T1 ¼ Ti + Tw and T2 ¼ Ti � Tw, as

shown in Figure 4(b). In order to compensate for the wind-

induced deformations, the control system introduces an additional

load, Fw, in cable 1. In the case of a wind pressure load, this force

is positive and translates into an additional stress in cables 1 and

2, as seen in Figure (3(c). In the case of a wind suction load, Fw

is negative and translates into stress release in cables 1 and 2, as

seen in Figure 4(c). In either situation, one can observe that the

final force in cable 1, in order to compensate for the total wind-

induced displacements, amounts to Ti: For this reason, the control

variable of the control system is T1, and the correspondingFigure 1. General view of the proposed glass facade

2

Structures and Buildings Smart glass facade subjected to windloadingsSantos, Goncalves, Cismasiu andGamboa-Marrufo

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

set-point is Ti: One can also see that the maximum force

fluctuation in the cables equals 2Tw and hence the initial force in

the cables, Ti, has to be larger than this value, in order for the

cables to remain tensioned.

2.2 Dynamic characterisation of the glass facade

To evaluate the structural behaviour of the glass facade, a three-

dimensional finite-element (FE) model is implemented, in a

SAP2000 framework, including the glass elements of the facade

16·0

Front view

2·02·0

Side view

(1) (2)

1·15

8·0 8·01·4

2·8

Figure 2. Geometry and dimensions (in m) of the glass facade

and one bow-string truss

Ti Ti

W

T Ti w� T Ti w�

Tw

Ti

Tw

T Ti w2�

Fw

(a) (b) (c) (d)

Figure 3. Control strategy for a wind pressure load

Ti Ti

W( )�

T Ti w� T Ti w�

�Tw

Ti

�Tw

T Ti w2�

Fw

(a) (b) (c) (d)

Figure 4. Control strategy for a wind suction load

3



and corresponding back-up structure. The FE model of the glass

facade enables the characterisation of the modal configurations

and frequencies. Figure 5 shows some of the first modal shapes of

the glass facade, as well as the corresponding vibration frequen-

cies. The first eight modes correspond to global modes of the

glass facade, with frequencies ranging from 4.53 Hz to 8.16 Hz.

Mode 9 is the first local mode, mainly involving the glass panes.

3. Wind modelWind is a dynamic and random phenomenon in both time and

space. Assuming that the wind speed only depends on the height

above the ground, the instantaneous wind speed v(z, t ), may be

described as a mean value v(z), at a given height, upon which

turbulent fluctuations are superimposed ~vv(z, t) (Holmes, 2007)

v(z, t) ¼ vm(z)þ ~vv(z, t)1:

Regarding the variable gust ~vv(z, t), it is usually assumed to be a

stationary Gaussian random process, having zero mean and a

specified spectral density, SL(z, n) (Pasca et al., 1998). According

to Parts 1–4 of Eurocode 1, the spectral density function may be

calculated as

SL(z, n) ¼ 6.8 f L(z, n)

[1þ 10.2 f L(z, n)]5=32:

where fL(z, n) is a dimensionless frequency, given by

f L(z, n) ¼ nL(z)

vm(z)3:

where L(z) is the turbulence scale and n is the natural frequency.

A sample of the wind speed can be generated using the wave

superposition method with sinusoidal functions. This method

assumes that the turbulent gust is caused by a superposition of

eddies simulated by harmonic summation. Once a power spectral

density function is given, the weighted amplitude wave super-

position method (WAWS) allows evaluation of the amplitude of

these harmonics (Kareem, 2008). The single process ~vv(z, t) can be

written as

~vv(z, t) ¼XN

K¼1

C(z, nk) cos (2�nkt þ �k)4:

with

C(z, nk) ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2Sw(z, nk)˜n

p5:

where nk (k ¼ 1, 2, . . .) are the central frequencies of the

intervals n into which the frequency range of the power spectral

density function Sw of the process has been divided, and the

random phase angles �k have a uniform distribution between 0

and 2�.

Given the random nature of the generated samples of wind

turbulence, the glass facade is subjected to 20 different wind

series. Figure 6 shows the obtained power spectral density

function and one of the generated time histories of the wind

turbulence, superimposed over the calculated mean value of the

velocity. The mean value of the velocity is determined according

to Parts 1–4 of Eurocode 1, considering a basic value for the

reference mean wind of 30 m/s, a terrain roughness of 0.005 m

and a reference height of 10 m, yielding a value of 35.6 m/s. This

is approximately the characteristic wind velocity corresponding

to the 95% fractile of the statistical distribution of maximum

wind velocities in periods of 50 years (1000 years return period).

Once the wind instantaneous speed is determined, it is possible to

compute the wind dynamic pressure accordingly

qp(z, t) ¼ 1

2rv2(z, t)6:

where r is the air density, which is usually taken as 1.25 kg/m3: The

wind pressure on the outside surface of the glass facade we(z, t ) is

obtained in the following way

we(z, t) ¼ qp(z, t)cp,e7:

where cp,e is the pressure coefficient for external surfaces, which

is a function of the building geometry, including aspect ratios

such as h/b and d/b, where d is the dimension in the along-wind

direction, roof pitch and wind direction. The pressure coefficients

presented in Parts 1–4 of Eurocode 1 generally produce con-

servative design load distributions, representing approximate

worst-case pressure distributions. For this study, it appears

sufficient to define simultaneous pressure coefficient distributions,

as an approximation, for calculating the extreme displacements in

the main trusses (Kasperski, 1996). The pressure coefficients for

external surfaces are identified in Figure 7, for the considered

wind directions. A positive wind load stands for pressure,

whereas a negative wind load indicates suction on the surface.

4. Dynamic response of the glass facade towind excitation

In order to investigate the efficiency of active control in reducing

the glass facade displacements induced by a random gust, gener-

ated according to the weighted amplitude wave superposition

(WAWS) method and Eurocode prescriptions, a numerical time-

stepping method for the integration of the equation of motion is

used. The stiffness of the system is determined using 11 degrees

4



(a) (b)

(c) (d)

(e) (f)

Figure 5. Modal shapes and frequencies of the complete facade:

(a) mode 1 ( f ¼ 4.53 Hz); (b) mode 2 ( f ¼ 6.05 Hz); (c) mode 3

( f ¼ 6.22 Hz); (d) mode 4 ( f ¼ 7.15 Hz); (e) mode 6

( f ¼ 7.64 Hz); (f) mode 9 ( f ¼ 8.35 Hz)

5



of freedom (DOF), represented in Figure 8, which are associated

with the horizontal displacements in the centre of the glass panes

and in the nodes of the truss. In this way, the additional

aerodynamic self-induced loads due to the vibration of the glass

panes are also accounted for in the simulations. As the system is

linear, an exact solution for the equation of motion is obtained,

interpolating the excitation over each time interval (Chopra,

2001). The excitation function, p(t ), results from the combined

action of the wind load, W(t ), and the tension in the cables, T(t ),

for each degree of freedom. The wind load acts on the DOF

associated with the glass panes, which are DOF 4 through 8 and

the tension load acts on the DOF associated with the nodes of the

truss, which are DOF 1 through 3. The calculation of the

excitation function is illustrated in Figure 8.

For the time interval ti < t < tiþ1, the excitation function is

given by

p(�) ¼ W (�)þT (�)¼ pi þ˜pi

˜ti

�8:

where

˜pi ¼ piþ1 � pi9:

For the general case of a damped system, the equation of motion

is given by

m€uþ c _uþ ku ¼ pi þ˜pi

˜ti

�10:

The structural response in terms of displacements, u, is given by

u(�)¼ uie��øn�

�ffiffiffiffiffiffiffiffiffiffiffiffi1��2

p sinøD�þcosøD

!

þ _uie��øn� 1

øD

sinøD�

� �

þ pi

Kn

1�e��øn� cosøD�þ�ffiffiffiffiffiffiffiffiffiffiffiffi

1��2p sinøt

D

!" #

þ ˜pi

Kn

�

˜ti

� 2�

øn˜ti

þe��øn� 2�2�1

øD˜ti

sinøD�

"

þ 2�

øn˜ti

cosøD�

��11:

0

0·05

0·10

0·15

0·20

0·25

0·001 0·01 0·1 1 10 100 1000

Sf

LL

()

fL

(a)

34·0

34·5

35·0

35·5

36·0

36·5

37·0

37·5

38·0

0 100 200 300 400 500 600

v: m

/s

t: s(b)

Figure 6. Characterisation of the wind action: (a) power spectral

density function; (b) wind velocity–time history

�0·8(a)

�0·4(b) (c) (d)

�0·8 �1·2

W W W W

�1·2 �0·8

Figure 7. Characterisation of cp,e for different wind directions

6



The corresponding velocities yield

_u(�) ¼� uie��øn� ønffiffiffiffiffiffiffiffiffiffiffiffiffi

1� �2p sinøD��

þ _uie��øn� cosøD��

�ffiffiffiffiffiffiffiffiffiffiffiffiffi1� �2

p sinøD�

!

þ pi

Kn

e��øn�ønffiffiffiffiffiffiffiffiffiffiffiffiffi1� �2

p sinøD��

þ ˜pi

Kn˜ti

3 1� e��øn� �ffiffiffiffiffiffiffiffiffiffiffiffiffi1� �2

p sinøD�þ cosøD�

!" #12:

These equations can be rewritten as recurrence formulas, after

substituting Equation 9

uiþ1 ¼ Aui þ B _ui þ Cpi þ Dpiþ113:

_uiþ1 ¼ A9ui þ B9 _ui þ C9pi þ D9piþ114:

The resulting coefficients A, B, . . ., D9, depend on the system

parameters øn, k and �, and on the time interval ˜t � ti (Chopra,

2001). Given that the recurrence formulas are derived from the

exact solution of the equation of motion, the only restriction in

terms of ˜t is that it enables a close approximation of the

excitation function. The total response of the dynamic system is

obtained by the superposition of the modal responses.

4.1 Implementation of the PID controller

The control strategy for the active glass facade is based on a PID

controller, combining the proportional, integral and derivative

control actions. The controller transfer function Gc(s) compre-

hends three terms, each one associated with the corresponding

control action, yielding

Gc(s) ¼ Kp 1þ 1

T isþ T ds

� �15:

where Kp is the proportional gain, Ti ¼ Kp/Ki is the integral time

and Td ¼ Kd/Kp is the derivative time. Being a closed-loop control

system, the cable stress output signal C(s) is fed back to the

summing point, where it is compared with the reference cable

stress input R(s), yielding the actuating error signal E(s). The

output signal of the controller is U(s), and the feedback-path

transfer function, H(s), corresponds to a force sensor, which

measures the output variable in order to make it comparable with

the reference input signal, resulting in the feedback stress signal,

B(s). Figure 9 shows the block diagram of the stress control

system of the cables. The controlled process is defined by the

transfer function Gcp(s). The transfer function Gcp(s) evaluates

the dynamic response of the system for the current excitation

load, which comprises the wind load effects as well as the tension

input in the cables. As in many control systems, the input

4 8

59

2

6

103

7

11

W4 W8

W5W9

W10

W6

W7

W11

T

T1

T2

T3

T

1

Figure 8. Characterisation of the excitation load

7



excitation is of unpredictable nature and cannot be expressed

deterministically by a mathematical expression (Ogata, 1997).

This constitutes a practical difficulty during the design and testing

of a control system, since it is not feasible to implement a system

that performs adequately for every input signal. In order to

achieve an acceptable performance, the constants Kp, Ti and Td, in

Equation 15 have to be adequately adjusted. To improve the

performance of the controller, a tuning algorithm based on the

Ziegler–Nichols stability boundary rule is implemented. In this

tuning method, the Ki and Kd gains are first set to zero and the Kp

gain is increased until it reaches the ultimate gain, Ku, at which

the output of the loop starts to oscillate. The corresponding

period of oscillation, Pu is called the ultimate period. The

ultimate gain Ku and the corresponding oscillation period Pu are

used to set the gains as Kp ¼ 0.6Ku, Ti ¼ 0.5Pu and Td ¼ 0.12Pu,

in order to obtain a quarter decay ratio, yielding a good

compromise between quick response and adequate stability

margins (Franklin et al., 1994).

For the proposed prototype the ultimate gain yields an approx-

imate value of Ku ¼ 4.00 and the ultimate period Pu ¼ 0.05 s.

Hence, the gains of the PID controller are finally set to Kp ¼ 2.4,

Ti ¼ 0.025 and Td ¼ 0.006.

5. Results of the numerical simulationThe evaluation of the performance of the system is done using

the 78%-fractile value of the extreme displacement (u2) asso-

ciated with the 20 time series (ISO 4354 (ISO, 2007)), as well as

the corresponding control force in the active cable. For the

positive wind pressure case, the displacement yields 39.88 mm,

for the uncontrolled system, and 2.7 mm, for the controlled

system. In the case of negative pressures, the displacement yields

60.0 mm, for the uncontrolled system, and 3.88 mm, for the

controlled system. This represents a reduction of the displace-

ments of about 94%. The control force yields 17 kN and 26 kN,

for the positive and negative wind pressures, respectively. The

histograms of the structural response, in terms of horizontal

displacements and cable forces, associated with one of the

artificially generated wind series, can be seen in Figures 10 and

11, respectively.

6. DiscussionWith reference to part 1-1 of Eurocode 3 (BSI, 2005b), the

horizontal deflections affecting the appearance of a structure are

limited to h/300, in which h is the storey height. The mean

maximum horizontal displacement in the system without control

amounts to h/133. This value does not comply with the design

prescriptions regarding maximum admissible deflections in build-

ings. The control system is able to reduce this displacement to

h/2105, guaranteeing the fulfilment of this serviceability limit

state. Observing Figures 10 and 11 it can be seen that the

displacements shown by the facade, when subjected to a wind

loading, can be expressed as the superposition of a mean

displacement, associated with the mean value of the wind

loading, and the additional oscillations due to turbulence. The

mean displacement is positive, in the case of wind pressure

loadings, or negative, in the case of wind suction loadings. The

effect of the proposed control system in the overall behaviour of

the facade is two-fold; that is, it greatly reduces the displacement

amplitude of the facade due to wind turbulence as it shifts the

system back to its original position, by eliminating the mean

displacement component of the response. This is achieved by a

control force of 26 kN, corresponding to a maximum travel of

0.020 m at the end of the active cable. This type of performance

can be easily achieved by a small electromechanical linear

actuator, yielding a rated speed of 1.0 m/s, which is the maxi-

mum speed needed to comply with the proposed control solution.

R s( )

(Ref.stress)

B s( ) (Stressfeedback)

E s( )

(Error)��

(Stress PID controller)

K K s K sp i d/� � Gcp( )s

H s( )

(Force-sensor)

C s( )U( )s

Figure 9. Block diagram of the stress control system

�0·05

�0·04

�0·03

�0·02

�0·01

0

0·01

0 100 200 300 400 500 600

μ 2: m

t: s(a)

ControlledFree

�0·005

0

0·005

0·010

0·015

0·020

0·025

0·030

0·035

0·040

0 100 200 300 400 500 600

μ 2: m

t: s(b)

ControlledFree

Figure 10. Time history of the horizontal displacements, during

wind events (u2): (a) negative wind pressures; (b) positive wind

pressures

8



The proposed active glass facade enables a significant reduction

of the mean maximum displacement of about 94%, for both

positive and negative wind pressures. This is a very clear

indicator of the good performance shown by the system. It has to

be stressed that the proposed cable control system is designed

mainly to satisfy serviceability criteria regarding deflections. This

means that the structural resistance and overall stability of the

facade is not impaired by the deactivation of the control system.

All the design prescriptions of Part 1-1 of Eurocode 3 (BS EN

1993-1-1 (BSI, 2005b)) are verified, regardless of the control

system status.

The approval of innovative systems in structural engineering

results from a combination of performance enhancement set

against construction costs and long-term effects (Soong and

Spencer, 2002). In order to obtain the same level of displace-

ments shown by the active glass facade, the steel structure would

require ten times more material.

7. ConclusionThe essence of a suspended glass facade is transparency. The

inventive capacity of engineers has enabled the development of

sophisticated technological solutions, which are able to fulfil this

architectural aspiration. With the wider implementation of active

control in civil engineering applications, the integration of these

systems in suspended glass facades opens new possibilities both

in terms of lightness and structural performances.

This paper presents a new proposal for an active facade, aiming

to provide a realistic evaluation of its dynamic performance

during wind events. It is shown that the active system is

extremely effective in reducing the horizontal wind displace-

ments of the facade, allowing structural solutions to be obtained

that are more slender, while also complying with the mandatory

design prescriptions regarding ultimate and serviceability limit

states.

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�14·0

�13·5

�13·0

�12·5

�12·0

�11·5

�11·0

�10·5

�10·0

0 100 200 300 400 500 600

T: k

N

t: s(a)

6·0

6·5

7·0

7·5

8·0

8·5

9·0

9·5

10·0

0 100 200 300 400 500 600

T: k

N

t: s(b)

Figure 11. Time history of control force in the active cable, during

wind events (u2): (a) negative wind pressures; (b) positive wind

pressures

9



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Smart glass facade subjected to wind loadings · design for the back-up structural system. An adequate glass suspension system must be able to cope with the weight of the glass elements