Seismic Behavior of RC Coupled Shear Walls With Strengthened

8/13/2019 Seismic Behavior of RC Coupled Shear Walls With Strengthened

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KSCE Journal of Civil Engineering (2013) 17(2):403-414

DOI 10.1007/s12205-013-1286-9

403

www.springer.com/12205

Structural Engineering

Seismic Behavior of RC Coupled Shear Walls with Strengthened

Coupling Beams by Bonded Thin Composite Plates

S. A. Meftah*, F. Mohri**, and E. M. Daya***

Received July 30, 2010/Accepted April 19, 2012

Abstract

The present study investigates the dynamic analysis of Reinforced Concrete (RC) coupled shear walls strengthened by bondedCarbon Fibre Reinforced Polymer (CFRP) composite plates applied on both sides of the coupling beams. For this purpose, new finiteelement models are developed for both the walls and strengthened coupling beams. In the validation process of the proposed model,static and free vibration analyses of coupled shear walls were firstly studied. Comparisons with ABAQUS code using shell elementswere made and good agreement was observed. After this stage, dynamic analysis was carried out under El Centro and Northridgeearthquake records. In these conceptual studies, the maximum top lateral deflection responses of strengthened and unstrengthened

RC coupled shear walls are computed. The obtained results showed that mitigation of seismic behaviour of RC coupled shear wallsby using CFRP bonded composite plates depends on the geometrical characteristics of shear wall structure and dominant rangefrequencies of the input earthquake records.

Keywords: composite plate, earthquake, finite element, sandwich beam, strengthened structure, vibration

1. Introduction

Many reinforced concrete buildings have coupled shear walls

to resist lateral loads due to earthquakes. The system is designed

with the shear walls coupled with beams (coupling beams) that

are the weak ductile links to dissipate energy from earthquake.

Coupling beams are important structural elements in seismicdesign due to their ability to reduce bending moments at the base

of coupled shear walls (Hindi and Hassan, 2004; Mancini and

Savassi, 1999).

Numerous analytical as well as experimental studies have been

devoted to establish technical seismic design recommendations

of coupled shear walls (Canadian standard association (1994);

National Building Code of Canada). These studies found that the

seismic behavior of coupled shear walls is directly linked to the

Degrees of Coupling (DC), namely the ratio of stiffness of the

coupling beam relative to the walls.

In the analysis of coupled shear wall structures, commercial

codes such as SAP2000 and ABAQUS are customized. In meshprocess a combination of plane stress and beam elements are

used to model shear walls and coupling beams respectively.

Indeed, it is necessary to use a refined finite element model for

an accurate analysis of shear wall with openings. But it would be

inefficient to subdivide the entire shear wall building into a finer

mesh with a large number of elements because of the tremendous

analysis time and computer memory costs.

Continuum approaches have been frequently used for the

dynamic analysis of coupled shear wall structures, where the

discrete system of connecting beams is replaced by a homogen-eous medium of equivalent properties (Kuang and Chau, 1999;

Li and Choo, 1996). Mukherjee and coull (1972) and Coull and

Mikherjee (1973) used the Galerkins method by representing

the lateral deflection in terms of trigonometric series. An approxi-

mate formula for the natural frequencies has been obtained making

use of Dunkerleys formula by considering the lateral deflection of

coupling beam as a result of pure flexural and shear-flexural

deflection terms (Retenberg, 1975). In all of these studies the

Euler-Bernoulli beam model was adopted for the solid wall.

In order to investigate the influence of shear deformation on

the lateral deflection of coupled shear walls structures, the finite

strip method was used (Cheung et al., 1998). However, the finiteelement method becomes more powerful for analysis of coupled

shear wall structures due to their efficiency and accuracy by em-

ploying the shear wall element with drilling degree of freedom

*Associate Professor, Laboratoire des Structures et Matriaux, Universit de Sidi Bel Abbes, BP 89 Cit Ben Mhidi. 22000 Sidi Bel Abbes, Algeria (Cor-

responding Author, E-mail: [email protected])

**Associate Professor, Universit de Lorraine, Laboratoire dEtude des Microstructures et de Mcanique des Matriaux (LEM3), UMR CNRS 7239, Ile du

Saulcy F-57045, Metz Cedex01, France (E-mail: [email protected])

***Professor, Universit de Lorraine, Laboratoire dEtude des Microstructures et de Mcanique des Matriaux (LEM3), UMR CNRS 7239, Ile du Saulcy F-

57045, Metz Cedex01, France (E-mail: [email protected])


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S. A. Meftah, F. Mohri, and E. M. Daya

404 KSCE Journal of Civil Engineering

such as the Kwans elements (Kwan, 1993) with rotational

degrees of freedom defined as vertical fibre rotation to ensure the

compatibility with the connecting lintel beam. More recently,

Kim (2003), proposed an efficient method for dynamic analysis

of coupled shear wall structures. This method is based on the use

of fictitious beams to enforce the compatibility at the boundary

of super element shear wall units.

In order to control lateral deflection and inter-storey drift,

adequate stiffness is required in RC buildings. In fact, different

techniques were used in order to achieve satisfactory earthquake

behaviour of RC coupled shear wall structures, such as isolation,

energy absorption at plastic hinges and mechanical devices

providing structural control (Julio et al., 2004; Jingning et al.,

1999; Abhijit, 1999). It is well known that these techniques can

lead to a change in seismic behaviour of the initial building.

However, in recent years a promising technique adopting

composite materials to retrofit deficient RC structures becoming

more common. In the literature, the most research works under-

going in this field were concerned beam and plate structures

separately (Tounsi, 2006; Shen et al., 2003; Chen and Teng,

2003; Teng et al.,2000; Benyoucef et al.,2006). Few studies are

dedicated to strengthened coupled shear walls (Meftah et al.,

2006, 2007a,b; Balsamo etal.,2005).

The objective of this study is to develop a numerical model for

seismic analysis of RC coupled shear walls with coupling beams

strengthened by CFRP bonded composite thin-plates in the two

sides of the element. For this aim, a three-layered finite element

sandwich beam including shear deformation was developed for

coupling beams strengthened by bonded composite plates. For

wall segments, another finite element was formulated where the

number of DOF is reduced by condensation technique from 12 to

eight. The assembly procedure, the compatibility between the wall

unit and strengthened coupling beam is checked in the assembly

process. The accuracy of the proposed elements is studied by

comparison to ABAQUS simulations.

2. Finite Element Approach for Three-LayeredSandwich Beam

In this section, a three-layered sandwich finite element is pre-

sented for RC coupled shear walls with coupling beams strength-

ened with bonded thin composite plates

2.1 Kinematic

The coupling beam element is formulated as three-layered

sandwich beam with distinct layers 1, 2 and 3 as shown in Fig. 1.

Each layer has its own geometric and material properties with a

superscript (i) denoting the layer number i (1i3).

The following assumptions common to many works (Cupial

and Niziol, 1995; Rao, 1978 ; Hu et al.,2005) are adopted:

- All points on a normal to the beam have the same transverse

displacement.

- The top and bottom layers (i=1, 3) are assumed to have no

shear stiffness, therefore the Euler Bernoulli beam theory (Rao,

1978) is adopted in these layers and E(i), h(i), A(i), I(i) denote

respectively Youngs modulus, thickness, cross section area and

moment of inertia of area of the layer i.In Layer 2, the shear

stiffness is considered and the shear modulus is denoted by G.

- The displacement is continuous along the interfaces between

the core and faces.

Thus, the axial displacements at the interface between layers 1

& 2 and 2 & 3 are respectively given by:

(1a)

(1b)

In matrix formulation, these expressions can be rewritten as:

(2)

The layer 2 of the sandwich beam is considered as Timoshenko

beam element with shear deformation taken into account by

assuming uniform shear distribution along the height of the cross

section of the beam. The Timoshenko beam element is formulated

with two nodes, where each node has 4 DOF (Two rotations and

two displacements) as depicted in Fig. 2. The beam element has

eight DOF arranged as:

(3)

The rotation (x) is defined in terms ofxderivative of vertical

displacement v(x) as:

(4)

The axial displacement of each point withen the layer 2 is done

as:

(5)

u 2( ) x( ) x( )h 2( )

2

-------+ u1( )

x( )h 1( )

2

-------x( )=

u 2( ) x( ) x( )h 2( )

2------- u

3( )x( )

h 3( )

2-------x( )+=

u1( )

x( )

u 2( ) x( ) 1

h 2( )

2-------

h 1( )

2-------

1h 2( )

2-------

h 3( )

2-------

u 2( ) x( )

x( )

x( )

=

T u12( )v111u2

2( )v222{ }=

x( ) v x( )x

-------------=

u x y,( ) u 2( ) x( ) yx( )+=

Fig. 1. Kinematic and Properties of a Three-layered Sandwich Beam

Fig. 2. Timoshenkos Beam Element with Two Rotational DOF at

Each Node


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Seismic Behavior of RC Coupled Shear Walls with Strengthened Coupling Beams by Bonded Thin Composite Plates

Vol. 17, No. 2 / March 2013 405

Taking derivative of this equation with respect to y, one then

obtains:

(6)

2.2 Strain Field

The axial strains in the middle lines of layers 1, 2 and 3 are

given respectively by:

(7a)

(7b)

(7c)

Additionally, the shear strain in the layer 2 is defined as:

(8)

2.3 Derivation of Stiffness Matrix of Three-layered Sand-wich Beam Element

The strain energy is due to axial deformation of the three layers

and shear strain contribution in layer 2. Strain energy in each

layer is defined as:

(9a)

(9b)

(9c)

kis the shear coefficient or section shape factor (k= 2/12 for

rectangular section shape). The total strain energy of the three

layered sandwich beam is then:

U = U (1) + U (2) + U (3) (10)

Linear shape function are assumed for axial displacement u(2)

(x) and shear strain xy(x), cubic function for the vertical dis-

placement v(x) is used in natural coordinate.

Applying virtual variation to strain deformation , The element

stiffness matrix is derived in terms of {b}T={u1

(2)v1, 2, 1u2(2)

v2 2, 2} vector. In order to reduce the DOF of the beam

element the static condensation technique is applied to the model

(Kim and Lee, 2003). As the horizontal fibre rotation 1and 2has no direct relation with the corresponding values at the wall

side of the beam-wall joint, it is reasonable to treat rotations of

the vertical fibres 1and 2at section ends as external rotations.

3. Shear Wall Finite Element

3.1 Basic Formulation

The proposed 2D shear wall element with dimensions (b, h) is

depicted in Fig. 3. Three lateral displacements u1, u2and u3and

three rotations of the vertical fibres 1, 2 and 3 are

respectively assigned to the bottom, top and the middle levels of

the wall element. Again, for each level, one defines vertical

displacements v1and v2 in the bottom level, v3and v4 in the top

level and v5 and v6 in the middle level. According to wall

behaviour under lateral loads, the following variations of the

strain within the wall element are considered:

(11)

(12)

(13)

After integrating of relationships (15-17) we arrive to the

displacements within the wall element given by:

(14)

(15)

Solving the 12aicoefficients by equating the nodal translation

and rotations DOF of the element and substituting their back into

Eqs. (18), (19), the displacement functions in terms of nodal

DOF of the element are obtained. Again, the strain energy of the

wall element is obtained from bending and shear contributionUBand USas:

U= UB + US (16)

Bending and shear strain energies, written in terms of strains,

are the followings:

(17)

(18)

The strain energy of the wall can be formulated as a quadratic

function of wall DOF vector as follow:

(19)

{} denotes wall displacement vector and [Kw] is the wall

stiffness matrix. {} components are:

x( ) u x y,( )

y------------------=

1( )x u 1( ) x( )

x------------------=

2( )x u 2( ) x( )

x------------------=

3( )x u 3( ) x( )

x------------------=

xy x( ) x( ) x( )+=

U1( ) 1

2---E

1( )A

1( ) 1( ) x( )( )2

0

l

dx1

2---E

1( )I

1( ) x( )x

-------------

2

0

l

dx+=

U2( ) 1

2---E

2( )A

2( ) 2( ) x( )( )2

0

l

dx1

2---E

2( )I

2( ) x( )x

--------------

2

0

l

dx+=

1

2---kA

2( )G xy x( )( )20

l

dx+

U3( ) 12---E3( )A 3( ) 3( ) x( )( )20

l

dx 12---E3( )I3( ) x( )x

-------------

2

0

l

dx+=

x x( ) 0=y x y,( ) a1 a2y a3 a4y a5y

2a6y

3+ + +( )x+ +=

xy y( ) a7 a8y a9y2

+ +=

v x y,( ) a10 a1ya22----y

2a11 a3y

a42----y

2 a52----y

2 a64----y

4+ + + +

x+ + +=

u y( ) a12 a7 a11( )ya8 a3

2

--------------y2 a9

3

----a4

6

----

y3a5

12

------y4 a6

20

------y5

+ + +=

UB 12--- E

vol y x( )( )2dvol=

US1

2--- G

vol xy x( )( )2dvol=

U1

2--- { }TKW[ ] { }=

Fig. 3. Proposed of Basic Wall Element


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(20)

by employing the condensation technique matrix the 12 DOF of

wall element can be reduced to 8 DOF by eliminating the

displacements and rotation of the middle level (i.e., u3, v5, v6, 3).

Lets the system stiffness matrix equation of the structure be

given in partitioned form as:

(21)

where subscript aand iare assigned to the DOF for the active

and inactive zones respectively. Taking {Fi} as zero and

eliminating {i}, the matrix equation is reduced to:

(22)

where the equivalent stiffness matrix [K*W] is given by:

(23)

and the active vector {a} is defined by:

(24)

4. Numerical Approach

The present model is performed with development of a Fortran

program for static and dynamic of coupled shear walls structures.

Before proceeding to dynamic analysis, the applicability of the

structural model is first checked under static loads with numeri-

cal finite elements results obtained from ABAQUS Software.

After the validation process, the shear walls with openings are

analysed under seismic loads.

4.1 Static Analysis of Three-layered Sandwich Beam Struc-

ture

In this introduction example, two cantilever three-layered sand-

wich beams called TSB1 and TSB2 are studied. The geometrical

characteristics of the beams are depicted in Fig. 4. The materials

properties used for the upper and lower layers are of steelE(1)=

210 GPa. The middle layer of the beams is a reinforced concrete

material with E(2) = 30 GPa and Poissons ratio = 0.2. Static

analysis of these beams under concentrated loads applied at the

free end is performed to check the efficiency and accuracy of the

proposed analysis method.

The beam deflections at the free ends of the two sandwich

beams are summarized in Tables 1 and 2 respectively. The lateral

displacements computed by the present method employing one

three-layered sandwich beam element are compared with those

obtained by the classical laminate theory (Emam and Nayfeh,

2009) that neglects the shear deformation in the core layer and

standard finite element analysis package ABAQUS, where shell

elements (S8R5) are adopted. The composite sheets are divided

in some elements along the beam. For the middle layer, many

elements are needed through beam depth and along the beam

span. The beam mesh and deflection are viewed in Fig. 5. Good

agreement of the present model and ABAQUS code is remarked.

The difference between the two models is within the range of 1%.

4.2 Free Vibration of Cantilever Shear Wall Structures with

Different Aspect Ratio

In this paragraph one presents results of fundamental frequen-

cies of a number of RC shear walls with dimensions (H, b, e). In

the analysis, the wall width band thickness eare constant, different

T u11v1v2u22v3v4u33v5v6{ }=

Kii Kia

KaiKaai

i

a Fi

Fa

=

KW*[ ] a{ } Fa{ }=

KW*[ ] Kaa[ ] Kai[ ] Kii[ ] 1 Kia[ ]=

a{ } T u11v1v2u22v4v5{ }=

Fig. 4. Geometric Characteristics of Cantilever Three-layered Sand-

wich Beam: (a) TSB1, (b) TSB2

Table 1. Lateral Deflection of Unstrengthened and Three-layered

Sandwich Beam TSB1

Without upper and lowerlayers (unstrengthened)

(mm)

Sandwich beamstructure

(mm)

ABAQUS 9.7708 5.566

Present model 9.792 5.620

classical laminate theory 9.342 5.213

Table 2. Lateral Deflection of Unstrengthened and Three-layered

Sandwich Beam TSB2

Without upper and lowerlayers (unstrengthened)

(mm)

Sandwich beamstructure

(mm)

ABAQUS 2.960 1.740

Present model 2.972 1.730

classical laminate theory 2.839 1.616

Fig. 5. Deflection of Cantilever Sandwich Beam Modelled with

Abaqus Shell Elements


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Vol. 17, No. 2 / March 2013 407

wall heightsHwere considered in the study. The wall geometry is

shown in Fig. 6(a). ABAQUS mesh model follows in Fig. 6(b).

The material characteristics areE=30 GPa, = 0.2, r = 2400 kg/m3.

Figure 7 depicts the variation of the eigenfrequencies of the

shear wall structures according to their aspect ratio (H/b) varying

from 1.0 to 4.0. The results given by the proposed element and

Kwans element (Kwan, 1993) using one element are compared

to ABAQUS shell elements. The proposed element is in good

agreement with ABAQUS for all the aspect ratio. Kwan element

overestimates the fundamental eigenfrequencies in the case of

small aspect ratio.

4.3 Static and Free Vibration Analyses of Strengthened

Coupled Shear Wall Structure

Static and free vibration analyses of coupled shear wall struc-

tures shown in Fig. 8(a) are studied here. The material properties

of the structure are listed in Table 3. The structure was analysed

twice. Firstly, without the strengthened plates and in the second

way by employing sheets in coupling beams. The analyses were

performed using the proposed finite elements and ABAQUS

programme, where the adopted mesh is pictured in Fig. 8(b).

Table 4 shows the top displacements under a concentrated static

load of 500 kN applied at the top end. The first fundamental

eigenfrequency of the wall is enclosed. It is observed that results

from the present model agree very well with those obtained by

ABAQUS in static and vibration for unstrengthened as well as

for the strengthened structures.

5. Parametric Investigations

5.1 Time-history Analysis

In this section, the coupled shear wall structures are subjected

to time-history analysis using two different earthquake records.

For consistant analysis, all earthquake records are scaled to the

peak acceleration of 1.0g(g= 9.81 m/s2). Duration of strong motion

and range of dominant frequencies have been kept unchanged

Fig. 6. Cantilever Shear Wall Structure: (a) Geometrical Proper-

ties, (b) Finite Element Modelling (ABAQUS)

Fig. 7. Convergence Study of Cantilever Shear Wall Structure in

Free Vibration Analysis Fig. 8. Coupled Shear Wall Structure: (a) Geometrical Characteris-

tics, (b) Finite Element Modeling ABAQUS

Table 3. Material Properties of Coupled Shear Wall Structure

Couplingbeams

Youngs modulusPoissons

ratioMaterialdensity

Upper layer E(1)

= 140 GPa

Middle layer E(2) = 30 GPa 0.2 2500 kg/m3

Lower layer E(3)

= 140 GPa

Shear wall E = 30 GPa 0.2 2500 kg/m3

Table 4. Comparison Results of Static and Free Vibration Analysis

of Coupled Shear Wall Structure

Unstrengthened coupledshear wall

Strengthened coupledshear wall

Topdisplacement

(mm)

1st

frequency(Hz)

Topdisplacement

(mm)

1st

frequency(Hz)

ABAQUS 3.445 32.901 3.062 33.199

Present 3.066 33.075 2.937 33.435

Classical laminatetheory 2.701 34.110 2.661 34.229


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and are evaluated by Welchs method (Welch, 1967) using fast

Fourier transform techniques. The earthquake records considered

for the investigation of the dynamic response of strengthened

coupled shear wall structures are:

El Centro with duration of strong motion in the range of 1.5-5.5

s and dominant frequencies in the range 0.39-6.39 Hz. The

earthquake acceleration is shown in Fig. 9(a). The power density

spectrum follows in Fig. 9(b).

Northridge with duration of strong motion in the range of 3.5 to

8 s and dominant frequencies in the range 0.14 to 1.07 Hz. The

earthquake acceleration record is shown in Fig. 10(a). The

power density spectrum follows in Fig. 10(b).

The time history analyses is conducted by considering the damp-

ing matrix of the structural model to be proportional to the stiffness

and mass matrices by Rayleighs proportionality factors (Clough

and Penzien, 1993). In the present analysis devoted to concrete

material, the 1st and 2nd vibration modes are selected, and the

viscous damping is fixed to 5% of critical damping. The Newmark-

step by-step time integration method (Newmark, 1959) was em-

ployed to obtain the solution of the dynamic equation, expressed as:

(25)

in which, [C] and [K] are the global damping and stiffness

matrices of the structures, respectively, , , and are

the relative displacement, velocity and acceleration vectors of the

structure with respect to base; lis a location vector which defines

the location of effective seismic loads and is the horizontal

ground acceleration.

The damping matrix of the model is assumed to be propor-

tional to the stiffness and mass matrices by the Rayleighs propor-

tionality factors (Clough and Penzien, 1993). 1,2as follows:

(26)

The proportionality factors 1,2can be obtained from:

, (27)

Where j and pare two chosen natural frequencies of the

coupled shear wall structures, which are determined by solving

the undamped eigenvalue equation:

(28)

5.2 Parametric Study

The finite element model proposed is applied to 4 examplescoupled shear walls having 3, 6, 10 and 20 stories to investigate

the effects of the geometrical characteristics of the coupling

beams on enhancing as far as possible the Degree of Coupling

(DC) and therefore reducing the peak top displacement of struc-

tures subjected to El Centro and Northridge earthquake records.

The geometric parameters of coupled shear walls are presented in

Fig. 11. The heightHbof the coupling beams has been varied from

0.2 to 1 m. The length l of the coupling beam has been changed

from 0.5 to 3 m. The material properties of the reinforced concrete

and the composite plates adopted in this study are respectively:

- ConcreteE(2)= 20 GPa, = 0.2, r = 2400 Kg/m3

- CFRP Composite sheets:E(1)

=E(3)

= 140 GPaAs mentioned in the Canadian Concrete Standard (CSA), the

DC is defined as the portion of the base overturning moment

carried by the axial tension and compression forces resulting

from shears in the coupling beams.

In the major modern codes such as CSA , DC is directly linked

to the seismic force modification (reduction) factor,R, as follow:

More recent study in this field carried out by Chaallal et al.

M[ ]D t( ) C[ ]D t( ) D[ ]D t( )+ + M[ ]lDg t( )=

D t( ) D t( ) D t( )

D

g t( )

C[ ] 1 M[ ] 2 K[ ]+=

1 2jpj p+--------------= 2

2

j p+--------------=

K[ ] 2 M[ ] 0=

DC 0.66 R 4=DC 0.66< R 3.5=

Fig. 9. El Centro Earthquake: (a) Earthquake Acceleration Record,

(b) Power Density Spectrum

Fig. 10. Northridge Earthquake: (a) Earthquake Acceleration Re-

cord, (b) Power Density Spectrum


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Vol. 17, No. 2 / March 2013 409

(1996) shows that there exists no unique limit value of DC that

can be reasonably assumed for coupled shear walls. The limiting

values of DC are as follow:

for 6 stories buildings



display good performances of the CFRP plates to enhance the

DC of coupled shear walls

Typical plots of DC versusHband l are presented in Figs. 12-15

for different numbers of stories likewise. As can be seen, figures

display good performances of the CFRP plates to enhance the

0.101 DC 0.316 0.211 DC 0.561 0.304 DC 0.420

Fig. 11. Geometric Characteristics of Coupled Shear Walls Consid-

ered in Parametric Study

Fig. 12. Variation of DC of 03 Stories Coupled Shear Wall Struc-

ture: (a) Typical Plot of DC versus H, (b) Typical Plot of DC

versus l



versus l



versus l


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DC of coupled shear walls within or beyond the limiting values.

For instance, in the case of thin and slender coupling beams,

bonded CFRP plates proved an efficient way to upgrading the

seismic demand of coupled shear walls by modifying their seismic

force factorRfrom 3.4 to 4 as recommended by the seismic cods.

Figures 16-19 show time history responses obtained by the

present model of coupled shear wall structures respectively of 3,

6, 10 and 20 stories at the top level before and after strengthening

under El Centro earthquake. The time deflection response of the

four types of strengthened coupled shear wall structures demon-

strates that incorporation of CFRP composite plates can reduce

the peak deflection of the structures under seismic loads.

Figures 20-23 illustrate the variation of the peak values of the

top deflections according to beams height(Hb) expected by the

structures strengthened by CFRP bonded composite sheets, com-

pared with results of unstrengthened structures. These curves

concern El Centro and Northridge earthquakes. One can remark,

that for 3 and 6 stories (Figs. 20-21), the beam height Hbhas no

significant influence on coupled shear wall stiffness.

No significant reduction of top deflection was noted for 10 and

20 stories shear walls subjected to El Centro earthquake (Figs.

22a, 23a). The effect of the CFRP composite bonded plates on

reducing lateral displacement is remarked for 10 and 20 stories

coupled shear walls under Northridge earthquake (Figs. 22b, 23b).

Under this seismic loading, the highest reduction was achieved

by 10-story coupled shear walls with beam heightsHb = 0.2 m

with a reduction of 34%, this followed by 20 stories buildings



versus l

Fig. 16. Top Deflection Response of 03 Stories Coupled Shear Wall

Structure


Structure


Structure


Structure


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Vol. 17, No. 2 / March 2013 411

with beam heightHb = 0.2 m with 20%.

The effect of the coupling beams length (l) on coupled shear

wall stiffness is pictured in Figs. 24-27 under the same earth-

quake forces and for the same coupled shear wall stories. In the

Fig. 20. Variation of Peak Top Displacement of 03 Stories Structure

versus Hb: (a) El Centro Earthquake, (b) Northridge Earth-

quake



quake



quake



quake


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case of 3 stories structures (Figs. 24a, 24b), no significant effect

has been reported. For 6 stories structures, the effect of lon top

deflection is more noticeable compared to the 3-story structures.

Reduction of 20% is reached under El Centro earthquake. In the

case of 10 stories level under El Centro earthquake (Fig. 26a),

the effect of lon top deflection is mitigated. A softening effect is

observed for 1.25l2.25 m, but significant reduction was

obtained for lvalues higher than 2.5. For l= 3 m, the reduction

of top deflection is of order 40%. In the case of 20 stories

building under El Centro earthquake (Fig. 27a), the results

demonstrate that no hardening effect has been achieved on

structure behaviour but the deflection increases with l. The struc-

tures become more vulnerable to seismic loads after strengthen-

ing with bonded composite sheets. Under the Northridge earth-

quake (Fig. 27b), the strengthening of the structure by composite

sheets is more efficient for higher values of l.

A summary of results for all models in terms of percentage

reductions in peak values of top displacement is presented in Fig.

28. Results display very good performance in peak reduction of

the structures (higher than 20%) for frequencies varying between

2.5477 Hz to 4.458 Hz under Northridge earthquake.

This study has demonstrated the feasibility of using CFRP com-

posite sheets to reduce the seismic response of coupled shear

walls. It has been proved that the effect of CFRP composite

sheets to reduce the top deflection is strongly dominated by the

dominant frequency range of the earthquake records as source

of resonance effects. It was probably due to this reason that

there were no particular trends in the response under the earth-

quake loads.Fig. 24. Variation of Peak Top Displacement of 03 Stories Structure

versus l: (a) El Centro Earthquake, (b) Northridge Earth-

quake



quake



quake


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Vol. 17, No. 2 / March 2013 413

6. Conclusions

This study investigated the use of composite material located

in the top and bottom of coupling beam in order to reduce as far

as possible the lateral displacements of RC coupled shear wall

structures. Finite element formulation has been established for

both three layered sandwich coupling beam and wall elements. It

has demonstrated that the proposed structural elements agree

very well in static and free vibration analyses problems in com-

parison with the very rigorous finite element models. The influence

of geometric characteristics of different scale of RC coupled

shear wall structure to enhance the seismic performances of

strengthened couples shear walls has been studied.

The results show that a substantial improving of seismic per-

formances of strengthened couples shear walls by enhancing

their DC and therefore the seismic-force modification factorR.

Dynamic time history Seismic analysis results under El Centro

and Northridge confirmed that substantial reduction in deflection

of the RC coupled shear walls could be achieved by the bonded

CFRP composite plates. Reduction of up to 40% in the peak values

of the top deflection. In terms of reduction in the top deflection,

the best performance was observed for lvalues higher than 2.5 m

in the case of 10 and 20 stories level buildings.

The comparison example show that, this method had some, but

limited potential for mitigation the seismic response of 03 and 06

story buildings by varying the beam heightHb. Again, it has also

indicated that, in the case of 10 and 20 story buildings a more

significant structural improving can be obtained under Northridge

earthquake rather then El Centro earthquake

However, these performances have not been achieved in

certain structural configuration, with a substantial amplification

in lateral top displacement. This is due probably to resonance

effect. This suggests determining the dominant frequencies range

of the seismic record before any strengthening of RC coupled

shear walls by employing the CFRP sheets.

The outcome of this study will find applications in retrofitting

high-rise buildings braced by coupled shear wall systems accord-

ing to seismic codes.

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