conceptual design of coupled shear wall

8/10/2019 Conceptual Design of Coupled Shear Wall

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A CONCEPTUAL DESIGN APPROACH OF COUPLED SHEAR

WALLS

Dipendu Bhunia1, Vipul Prakash

2and Ashok D. Pandey

3

1Asssistant Professor, Civil Engineering Group, BITS Pilani,[email protected]

2Associate Professor, Department of Civil Engineering, IIT Roorkee3Assistant Professor, Department of Earthquake Engineering, IIT Roorkee

ABSTRACT

A recent earthquake in India on 26 th January, 2001 caused considerable damage to a

large number of RCC high-rise buildings (number of storey varies from 4 to 15) andtremendous loss of life. The reasons were: (a) most of the buildings had soft and weakground storey that provided open space for parking; (b) poor quality of concrete in

columns and (c) poor detailing of the structural design. Therefore, this particularincident has shown that designers and structural engineers should ensure to offeradequate earthquake resistant provisions with regard to planning, design and detailing in

high-rise buildings to withstand the effect of an earthquake and minimize disaster.As anearthquake resistant system, the use of coupled shear walls is one of the potential

options in comparison with moment resistant frame (MRF) and shear wall framecombination systems in RCC high-rise buildings. Further, it is reasonably wellestablished that it is uneconomical to design a structure considering its linear behavior

during earthquake. Hence an alternative design philosophy needs to be evolved in theIndian context to consider the post- yield behavior wherein the damage state is evaluated

through deformation considerations. In the present context, therefore, performance-based seismic design (PBSD) has been considered to offer significantly improvedsolutions as compared to the conventional design based on linear response spectrum

analysis.

Since coupling beam mainly governs the behavior of coupled shear walls, this paperinvestigates the behavior of coupling beam through an analytical model. The next step is

to develop a design technique to obtain an adequate ductility of coupled shear wallsconsidering its ideal seismic behavior (stable hysteresis with high earthquake energydissipation). Parametric study is carried out to find the limitations along with remedial

action of this technique. Finally, nonlinear static analysis is considered to assess theproposed design technique. It has been recemmended that proposed des ign technique

can be considered to design the coupled shear walls under earthquake motion.

KEYWORD: Performance-based seismic design, coupled shear walls, coupling beam,RCC, design technique

INTRODUCTION

The growth of population density and shortage of land in urban areas are two majorproblems for all developing countries including India. In order to mitigate these two


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problems the designers resort to high-rise buildings, which are rapidly increasing innumber, with various architectural configurations and ingenious use of structural

materials. However, earthquakes are the most critical loading condition for all landbased structures located in the seismically active regions. The Indian subcontinent is

divided into different seismic zones as indicated by IS 1893 (Part 1) (2002), facilitating

the designer to provide adequate protection against earthquake. A recent earthquake inIndia on 26th January, 2001 caused considerable damage to a large number of RCC

high-rise buildings (number of storey varies from 4 to 15) and tremendous loss of life.The reasons were: (a) most of the buildings had soft and weak ground storey that

provided open space for parking; (b) poor quality of concrete in columns and (c) poordetailing of the structural design (http://www.nicee.org/eqe-iitk/uploads/EQR_Bhuj.pdf). Therefore, this particular incident has shown that

designers and structural engineers should ensure to offer adequate earthquake resistantprovisions with regard to planning, design and detailing in high-rise buildings to

withstand the effect of an earthquake to minimize disaster.

As an earthquake resistant system, the use of coupled shear walls is one of the potentialoptions in comparison with moment resistant frame (MRF) and shear wall framecombination systems in RCC high-rise buildings. MRF system and shear wall frame

combination system are controlled by both shear behavior and flexural behavior;whereas, the behavior of coupled shear walls system is governed by flexural behavior.However, the behavior of the conventional beam both in MRF and shear wall frame

combination systems is governed by flexural capacity and the behavior of the couplingbeam in coupled shear walls is governed by shear capacity. During earthquake, infilled

brick masonry cracks in a brittle manner although earthquake energy dissipates throughboth inelastic yielding in beams and columns for MRF and shear wall framecombination systems; whereas, in coupled shear walls earthquake energy dissipates

through inelastic yielding in the coupling beams and at the base of the shear walls.Hence, amount of dissipation of earthquake energy and ductility obtained from both

MRF and shear wall frame combination systems are less than coupled shear wallssystem in the high-rise buildings [Jain (1999), Englekirk (2003), Park and Paulay(1975), Penelis and Kappos (1997), Smith and Coull (1991), Naeim (2001), Fortney and

Shahrooz (2009), Harries and McNeice (2006), El-Tawil et al. (2010) & Paulay andPriestley (1992)]. However, the Indian codes of practice governing the earthquake

resistant design, such as IS 1893 (Part 1) (2002) and IS 4326 (1993) do not providespecific guidelines with regard to earthquake resistant design of coupled shear walls. Onthe other hand, IS 13920 (1993) gives credence to the coupled shear walls as an

earthquake resistant option but it has incorporated very limited design guidelines of

coupling beams that are inadequate for practical applications. It requires furtherinvestigations and elaborations before practical use.

Further, it is reasonably well established that it is uneconomical to design a structure

considering its linear behavior during earthquake as is recognized by the Bureau ofIndian Standards [IS 4326 (1993), IS 13920 (1993) and IS 1893 (Part 1) (2002)]currently in use. Hence an alternative design philosophy needs to be evolved in the

Indian context to consider the post- yield behavior wherein the damage state is evaluatedthrough deformation considerations.

In the present context therefore, performance-based seismic design (PBSD) can be

considered to offer significantly improved solutions as compared to the conventionaldesign based on linear response spectrum analysis. Performance-based seismic design


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(PBSD) implies design, evaluation, and construction of engineered facilities whoseperformance under common and extreme loads responds to the diverse needs and

objectives of owners, tenants and societies at large. The objective of PBSD is to producestructures with predictable seismic performance. In PBSD multiple levels of earthquake

and corresponding expected performance criteria are specified [ATC 40 (1996)]. This

aspect emphasizes nonlinear analyses for seismic design verification of any structure.This procedure gives some guidelines for estimating the possible local and global

damages of structures. A retrofitted structure can be evaluated with the help of PBSD.Similarly, economics in the form of life-cycle cost along with construction cost of the

structure is inherently included in PBSD [Prakash (2004)].

On the basis of the aforesaid discussion, an effort has been made in this paper to

develop a comprehensive procedure for the design of coupled shear walls.

INVESTIGATION OF COUPLING BEAM

Coupled shear walls consist of two shear walls connected intermittently by beams alongthe height. The behavior of coupled shear walls is mainly governed by the coupling

beams. The coupling beams are designed for ductile inelastic behavior in order todissipate energy. The base of the shear walls may be designed for elastic or ductile

inelastic behavior. The amount of energy dissipation depends on the yield momentcapacity and plastic rotation capacity of the coupling beams. If the yield momentcapacity is too high, then the coupling beams will undergo only limited rotations and

dissipate little energy. On the other hand, if the yield moment capacity is too low, thenthe coupling beams may undergo rotations much larger than their plastic rotationcapacities. Therefore, the coupling beams should be provided with an optimum level of

yield moment capacities. These moment capacities depend on the plastic rotation

capacity available in beams. The geometry, rotations and moment capacities of couplingbeams have been reviewed based o n previous experimental and analytical studies in thispaper. An analytical model of coupling beam has also been developed to calculate therotations of coupling beam with diagonal reinforcement and truss reinforcement.

Geometry of Coupling Beam

The behavior of the reinforced concrete coupling beam may be dominated by (1) shearor by (2) flexure as per ATC 40 (1996), FEMA 273 (1997) and FEMA 356 (2000).

Shear is dominant in coupling beams when 2 [Penelis and Kappos (1997)]

or 4

bb dL .There are various types of reinforcements in RCC coupling beams described as follows:

i. Conventional reinforcement

Conventional reinforcement consists of longitudinal flexural reinforcement andtransverse reinforcement for shear. Longitudinal reinforcement consists of top and

bottom steel parallel to the longitudinal axis of the beam. Transverse reinforcement

consists of closed stirrups or ties. If the strength of these ties 431 sV required shear

strength of the beam and the spacing these ties 3d over the entire length of the beam,

then stable hysteresis occurs, and such transverse reinforcement is said to be

conforming to the type now mandatory for new construction. If the transversereinforcement is deficient either in strength or spacing then it leads to pinched


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hysteresis, and such reinforcement is said to be non-conforming [ATC 40 (1996),FEMA 273 (1997) and FEMA 356 (2000)].

According to IS 13920 (1993), the spacing of transverse reinforcement over a length of

d2 at either end o f a beam shall not exceed (a) 4d , and (b) 8 t imes the diameter of the

smallest longitudinal bar; however, it need not be less than 100 mm. Elsewhere, the

beam shall have transverse re inforce ment at a spacing not exceeding 2d . Whereas, the

shear force to be resisted by the transverse reinforcement shall be the maximum of:

(1) calculated factored shear force as per analysis, and (2) shear force due to formationof plastic hinges at both ends of the beam plus the factored gravity load on the span.

ii.

Diagonal reinforcement

Diagonal reinforcement consists of minimum four bars per diagonal. It gives a betterplastic rotation capacity compared to conventional coupling beam during an earthquake

when 5.1

b

b

d

L as per Penelis and Kappos (1997). The provisions for diagonal

reinforcement according to different codes have already been shown in

Table 1.1. If the diagonal reinforcement is subjected to compressive loading it maybuckle, in which case it cannot be relied on to continue resisting compressive loading.

Under the action of reversing loads, reinforcement that buckles in compression withloading in one direction may be stressed in tension with loading in the oppositedirection. This action may lead to low-cycle fatigue failure, so that the reinforcement

cannot continue to resist tensile forces. For this reason, it is necessary to ensure that thisreinforcement does not buckle. To prevent buckling due to compressive lo ading the

spacing between two adjacent diagonal bars should be greater than

12

dL [based on

buckling condition of a column]. It has also been noticed from Englekirk (2003) thatdiagonal reinforcement should not be attempted in walls that are less than 16 in.(406.4 mm) thick. Unless strength is an overriding consideration, diagonally reinforced

coupling beams should not be used.

iii. Truss reinforcement

Truss reinforcement represents a significant and promising departure from traditional

coupling beam reinforcements. The primary load transfer mechanism of the system isrepresented by the truss taken to its yield capacity. A secondary load path is created by

the global strut and tie. The load transfer limit state will coincide with yielding of a ll ofthe tension diagonals, provided the so-produced compression loads do not exceed thecapacity of the concrete compression strut. The yield strength of the primary truss is

governed by the tensile strength of its diagonal; whereas, the primary truss transfermechanism must include the shear travelling along the compression diagonal.

According to Penelis and Kappos (1997) & Galano and Vignoli (2000), when 1.5

b

b

d

L 4, truss reinforcement offers best seismic performance in comparison with

conventional and diagonal reinforcements. This type of reinforcement has not been used

till now. Detailing and placement problems must be carefully studied if its use iscontemplated. Clearly additional experimentation is required because the system

appears to have merit, especially in thin walls [Englekirk (2003)].


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When the post yield rotational level is much higher compared to rotational level fortruss reinforcement then steel beam can be provided as a coupling beam. There are two

types of steel beams which are provided as coupling beams based on the followingfactors as per Englekirk (2003), AISC (1997), AISC (2000) and AISC (2005).

a.

Shear dominant

In this beam, the shear capacity spV is attained and the corresponding bending moment

is equal to2

eVsp which must be less than 0.8 pM . The post yield deformation is

accommodated by shear and it is presumedsp

p

V

Me

6.1 ; where e = clear span of the

coupling beam+2 concrete cover of shear wall, pM = moment capacity of coupling

beam and spV = shear capacity of coupling beam.

b.

Flexure dominant

In this beam, the bending moment capacity p

M is attained and the corresponding shear

force is equal toe

Mp2which must be less than 0.8 spV . The post yield deformation is

accommodated by flexure and it is presumedsp

p

V

Me

6.2 .

Moment Capacity of Coupling Beam

The bending moment capacity of coupling beam depends on the geometry and material

property of coupling beam. Bending moment capacity and shear force capacity of thecoupling beam are related with each other. Englekirk (2003), Park and Paulay (1975),Paulay (1986), Harries et al. (1993), AISC (1997), AISC (2000) and AISC (2005)

describe these capacities as follows:

i. Reinforced concrete coupling beam

Shear capacity of coupling beam with conventional reinforcement can be calculated as:

b

ys

b

psp

L

ddfA

L

MV

'2

2

(1)

Whereas, shear capacity of coupling beam with diagonal reinforcement can becalculated as:


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d

b

ys

b

ys

b

p

dfsp

L

d

d

fA

L

ddfA

TL

M

VVV

'24'2

sin22

''

1

1

(2)

and shear capacity of coupling beam with truss reinforcement is as:

2

"

1

"

2

''

1

'

21

'2'2

22

2

d

yss

d

ys

dd

d

sp

L

ddfAA

L

ddfA

L

ddT

L

ddT

VVV

(3)

Where, 2'2

12

ddL

L bd

and 2'22 ddLL bd . All three shear

capacities must be less than equal

to

0

''

0

''

0

'' 08.025.035.035.0

ddbfor

L

ddLbfor

L

ddwbf bc

d

dbc

d

bc which is

based on the statement, i.e. capacity of a concrete strut in cylindrical elements will

dimnish to a level of 30 to 35% of 'cf as cracking increases, where, 0 is member over

strength factor of 1.25.

ii.

Shear dominant steel coupling beam

For I-section type of steel coupling beam, shear capacity (permissible shear resisted by

web only) for shear dominant steel coupling beam is denoted as fwysp tDtFV 26.0

and moment capacity isp

M = ypFZ ; where, yF is yield stress of structural steel, wt is

web thickness, D is the overall depth of the section,ft is flange thickness and pZ is

plastic section modulus.

iii.

Flexure dominant steel coupling beam

The transferable shear force ( nfV ) for flexure dominant steel coupling beam is the lesser

ofe

Mp2and spV ; where, pM is the moment capacity which is ypFZ .

Rotational Capacity of Coupling Beam

The rotation capacity in coupling beams depends upon the type of coupling beam. Whenthe rotational demand is greater than rotational capacity ofRCC coupling beam with conventional flexural and shear reinforcement then diagonal

or truss reinforcement type of coupling beam could be provided depending on the


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b

b

d

Lratio. The steel coupling beam could be used when the rotational limit due to lateral

loading exceeds the rotation capacity of RCC coupling beam with truss reinforcement.Various research works conducted by Paulay (2002), Hindi and Sexsmith (2001),

FEMA356 (2000), Xuan et al. (2008) describe these capacities. ATC 40 (1996),

FEMA 273 (1997), FEMA 356 (2000), Galano and Vignoli (2000), Chao et al. (2006)and Englekirk (2003) describe the following rotational capacities for various types ofcoupling beams considering the behavior controlled by flexure and shear duringearthquake. Table 1, Table 2, Table 3, Table 4, Table 5 and Table 6 show these different

rotational capacities for various coupling beams.

Table 1:Rotation capacities for coupling beams controlled by flexure as perFEMA 273 (1997) and FEMA 356 (2000)

Type of coupling beam

ConditionsPlastic Rotation

Capacity (Radians)

'

cww fLt

Shear

IO LS CP

Conventional

longitudinal

reinforcement wi th

conforming transverse

reinforcement

3 0.006 0.015 0.025

6 0.005 0.010 0.015

Conventional

longitudinal

reinforcement wi th non-


reinforcement

3 0.006 0.012 0.020

6 0.005 0.008 0.010

Diagonal Reinforcement NA 0.006 0.018 0.030

Flexure dominant s teel

coupling beam

ywyf

f

Ft

hand

Ft

b 41852

2

y1 y6 y8

ywyf

f

Ft

hand

Ft

b 64065

2

y25.0

y2 y3

Table 2:Rotation capacities for coupling beams controlled by shear as per

FEMA 273 (1997) and FEMA 356 (2000)



Capacity (Radi ans)

'

cww fLt

Shear IO LS CP

Conventional

longitudinal

reinforcement wi th

conforming trans verse

reinforcement

3 0.006 0.012 0.015

6 0.004 0.008 0.010

Conventional

longitudinal

reinforcement wi th

non-conforming

transversereinforcement

3 0.006 0.008 0.010

6 0.004 0.006 0.007


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Shear dominant steel coupling beam 0.005 0.11 0.14

Table 3:Rotation capacities for coupling beams controlled by flexure as per

ATC 40 (1996)



Capacity (Radians)

'

cw fdb

Shear IO LS CP

Conventional

longitudinalreinforcement wi th


reinforcement

3 0.006 0.015 0.025

6 0.005 0.010 0.015

Conventional

longitudinal

reinforcement wi th non-


reinforcement

3 0.006 0.012 0.020

6 0.005 0.008 0.010

Diagonal Reinforcement NA 0.006 0.018 0.030

Table 4:Rotation capacities for coupling beams controlled by shear as perATC 40 (1996)



Capacity (Radians)

'

cw fdb

Shear IO LS CP

Conventional

longitudinal

reinforcement wi th


reinforcement

3 0.006 0.012 0.015

6 0.004 0.008 0.010

Conventional

longitudinal

reinforcement wi th

non-conforming

trans verse

reinforcement

3 0.006 0.008 0.010

6 0.004 0.006 0.007

Table 5:Rotation capacities for coup ling beams as per Galano and Vignoli (2000)


Aspect

Ratio

Rotation

Capacity

(Radians)

b

b

dL Lu


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Conventional

Reinforcement1.5 0.051

Diagonal


Truss Reinforcement 1.5 0.084

Table 6:Rotation capacities for coupling beams as per Englekirk (2003)

Type of coupling

beam

Aspect

Ratio

Rotation Capacity

(Radians)

b

b

d

L ma x,u

Conventional


Diagonal


Truss


'

cww fLt

Shear or'

cw fdb

Shear 3 or 6 is based on the aspect ratio (b

b

d

L) of coupling beamand

ywyf

f

Ft

hand

Ft

b 41852

2

or

ywyf

f

Ft

hand

Ft

b 64065

2

are the conditions of the flexure

dominant steel coupling beam to prevent local buckling.

Specifications in Tables 1, 2, 3 and 4 can be questioned on the basis of the followingobservations:

1. As per Tables 1 and 2, the rotational capacities of beam depends on size of wall

( ww Lt , ) which is illogical.

2. When shear span to depth ratio 2 or aspect ratio 4bb dL , the behavior of

RCC coupling beams is controlled by shear. For this reason, as aspect ratio

b

b

d

L of

diagonally reinforced beam is less than 1.5, it means that the behavior of diagonally

reinforced beam is controlled by shear. Whereas,Tables 1 and 3 show that diagonally reinforced coupling beam behavior is controlled

by flexure which is not acceptable.

3. Conventional longitudinal reinforcement with non-conforming transversereinforcement is not accepted for new construction.

4. If the behavior of coupling beam is controlled by flexure [aspect ratio

b

b

d

L is greater

than 4], the length of the coupling beam is quite larger. According to

Munshi and Ghosh (2000), weakly coupled shear walls can be obtained for largerspan of the coupling beam and the design results of this type of coupled shear walls

are inconsistent with regard to the ductility and energy dissipat ion during earthquakemotion. Hence, it can be said that rotational capacity of coupling beams controlled


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4-noded quadrilateral elements; material in coupling beam was assigned as SBeta(inelastic), whereas, material in shear wall was assigned as plane stress elastic isotropic.

Investigative model

Figure 1 and Table 7 describe the investigative models considered for

ATENA2D (2006) analysis. The behaviors of all eighteen coupling beams weregoverned by shear. The load (F) was calculated based on the shear force in beam and

other parameters according to the provisions of FEMA 273 (1997) andFEMA 356 (2000).

bw

w

LLLFV (4)

Where, V is shear force in the beam

Figure 1: Initial sketch of the analytical model

The depth of the wall is considered as wL = 4m, thickness of the wall is considered as

wt = 300mm and minimum reinforcement in the shear wall is taken as 0.25% of its

gross area @450 c/c.Here, Youngs modulus for concrete in beam = Ecb= 2.24x10

4MPa, Youngs modulusfor steel in beam = Esb = 2.1x10

5 MPa,

Youngs modulus for concrete in wall = Ecw= 2.24x104MPa and Youngs modulus for

steel in wall = Esw= 2.1x105MPa.

Table 7(a): Investigative Model of Coupling Beam in ATENA2D (2006) as per IS13920(1993), IS456 (2000), SP-16 (1978), FEMA273 (1997) and FEMA356(2000)

Coupling Beam

Type Lb(m) '

cww fLt

Shear F(kN)

Reinforced Steel

Longitudinal Transverse

Conventional

beam withlongitudinal and

transverse

conformingreinforcement

0.63 585.4 8-10 2-legged 16@200 c/c

6 1171 8-20 2-legged 25@200 c/c

0.93 623.5 8-10 2-legged 16@200 c/c

6 1247 8-20 2-legged 25@200 c/c

1.23 661.7 8-10 2-legged 16@200 c/c

6 1323 8-20 2-legged 25@200 c/c

F

F

hs= 3m

Lw LwLb

WallBeam


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Table 7(b): Investigative Model of Coupling Beam in ATENA2D (2006) as per IS13920(1993), IS456 (2000), SP-16 (1978), FEMA273 (1997) and FEMA356 (2000)

Table 7(c): Investigative Model of Coupling Beam in ATENA2D (2006) as per IS13920

(1993), IS456 (2000), SP-16 (1978), FEMA273 (1997) and FEMA356 (2000)

Beam

TypeLb

(m)'

cww fLt

Shear

F (kN)

Reinforced Steel


Beam withtruss

reinforcement

0.6

3 585.48-10+ 4-30as

one truss2-legged 16@200 c/c

6 11718-20+ 4-45as


0.9

3 623.58-10+ 4-30as


6 12478-20+ 4-40as


1.2

3 661.78-10+ 4-30as


6 13238-20+ 4-40as


Coupling Beam

Type Lb

(m)'

cww fLt

Shear

F (kN) Reinforced Steel


Beam with

diagonalreinforcement

0.6

3 585.48-10+ 4-20as one

diagonal2-legged 16@200 c/c

6 11718-20+ 4-30as one


0.9

3 623.58-10+ 4-25as one


6 12478-20+ 4-30as one

diagonal

2-legged 25@200 c/c

1.2

3 661.78-10+ 4-25as one


6 13238-20+ 4-35as one



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Results and Discussions

The results using ATENA2D (2006) have been tabulated in Table 8. It shows thecomparison of rotational limit at CP level among FEMA 273 (1997),

FEMA 356 (2000) and ATENA2D (2006). There are a lot of diffeamong the results of

FEMA 273 (1997), FEMA 356 (2000) and ATENA2D (2006). The comparison has alsobeen extended for considering ATC 40s (1996) provisions. There are also big

differences between the results of ATC 40 (1996) and ATENA2D (2006) shown inTable 9. It may be because of limitations of ATENA2D (2006) software. However, it is

unexpected in FEMA 273 (1997), FEMA 356 (2000) and ATC 40 (1996) that therotational limit is more or less same, whereas, the parameters considered for calculationof shear strength are different. Therefore, it can be said that the parameters given in

FEMA 273 (1997), FEMA 356 (2000) and ATC 40 (1996) are questionable which havealready been discussed in this paper. It has also been observed from

Tables 8 and 9 that crack width in beam is quite significant although the rotationalvalues in ATENA2D (2006) are unexpectedly varying with

FEMA 273 (1997), FEMA 356 (2000) and ATC 40 (1996).


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Table 8: Compare the Modeling Parameters and Numerical Acceptance Criteria with FEMA 273 (1997) and FEMA 356 (2000)

Longitudinal

reinforcement

and transverse

reinforcement

'

cww fLt

Shear

Rotational l imit at collapse prevention level (CP) in radians Crack width in coupling beam at CP level in meters

by ATENA2DMember control led by flexure Member control led by shear ATENA2D

FEMA273 FEMA356 FEMA273 FEMA356 mLb 6.0 mLb 9.0 mLb 2.1

mLb 6.0 mLb 9.0 mLb 2.1

Conventional

longitudinal

reinforcementwith conforming

transverse

reinforcement

3 0.025 0.025 0.015 0.020 0.000881 0.00104 0.002325 0.000263 0.000306 0.000559

6 0.015 0.02 0.010 0.016 0.00348 0.00528 0.00886 0.0007125 0.001726 0.003124

Diagonal3 0.03 0.03 - - 0.00235 .011 .0111 .000494 .004315 .00372

6 0.03 0.03 - - .00292 .00833 .00978 .0005724 .002961 .003228

Truss3 NA NA NA NA .001176 .000422 .00093 .0003144 .0001066 .000204

6 NA NA NA NA .001413 .00297 .0029 .000344 .0007514 .00066

Table 9: Compare the Modeling Parameters and Numerical Acceptance Criteria with ATC 40 (1996)

Longitudinal reinforcement

and transverse reinforcement'

cw fdb

Shear

Rotational limit at collapse prevention level (CP) in radiansCrack width in coupling beam at CP level in

meters by ATENA2DMember controlled by

flexureMember control led by shear ATENA2D

ATC 40 ATC 40 mLb 6.0

mLb 9.0

mLb 2.1

mLb 6.0

mLb 9.0

mLb 2.1

Conventional longitudinal

reinforcement with


reinforcement

3 0.025 0.018 0.0001023 0.000784 0.00198 0.0000001308 0.0005 0.001613

6 0.015 0.012 0.0002423 0.001944 0.00344 0.00163 0.00136 0.00297

Diagonal

3 0.03 - 0.00012 .000416 .00055 .0000194 .0002184 .00021

6 0.03 - .000415 .000422 .001533 .0001795 .0001483 .00093


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Hence, the results obtained from the above study using ATENA2D (2006) were foundunsatisfactory. Therefore, a new model has been created with some assumptions in the following

manner to carryout further study.

Assumptions:

The effect of gravity loads on the coupling beams has been neglected.

Deflection of the coupling beam occurs due to lateral loading.

Contra flexure occurs at the mid-span of the coupling beam. The confined concrete, due to the confining action is provided by closely spaced

transverse reinforcement in concrete, is assumed to govern the strength.

Total elongation in the horizontal direction (Figure 2) due to lateral loading can be written as:

bbb dL (5)

and strain in the concrete,b

bc L

L (6)

Hence, considering Equations (5) and (6) the following equation can be written as:

coupling beam rotation,b

bcb d

L (7)

The results, considering Equation (7) with maximum strain in confined concrete ( cu ) of 0.02[Confining action is provided by closely spaced transverse reinforcement in concrete as per ATC

40 (1996)], have been tabulated in Table 10.

Lb

db

bbd 2

bbd 2

Figure 2: Schematic diagram of coupling beam


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Table 10: Maximum rotations in radians

Type of

Reinforcementb

b

d

L Value as per

Equation (2.7)Galano and Vignoli (2000) Englekirk (2003)

ATC40 (1996),

FEMA273 (1997) andFEMA356 (2000)

Diagonal < 1.5 < 0.03 0.062 0.04 0.03

Truss 1.5 to 4.0 0.03 to 0.08 0.084 0.06 -

It can be observed from Table 10 that the values obtained as per Equation (7) have similar trendwith the values specified by ATC 40 (1996), FEMA 273 (1997),

FEMA 356 (2000), Galano and Vignoli (2000) & Englekirk (2003).Based on the above study, Table 11 has been prepared containing modified parameters governing

the coupling beam characteristics, which are also considered for developments of the design

technique discussed below. As design technique is based on collapse prevention (CP) level ofstructure, plastic rotation capacity given in Table 11 is for CP level only.

Table 11:Modified Parameters governing the coupling beam characteristics controlled by shear

Type ofcoupling

beam

ShearSpan

toDepth

Ratiob

b

d

L Type of detailing

Plastic Rotation

Capacity (Radians)

'

cw fdb

Shear CP

Reinforcedconcretecoupling

beam2

No limit

Conventional longitudinalreinforcement with


reinforcement

3 0.015

6 0.010

< 1.5

Diagonal Reinforcement

(strength is an overridingconsideration and thickness

of wall should be greater than406.4 mm)

- < 0.03

1.5 to 4.0Truss

Reinforcement(additionalexperimentation is required)

- 0.03-0.08

Steel

couplingbeam sp

p

V

Me

6.1 Shear dominant -

bL

15.0

PROPOSED DESIGN TECHNIQUE

In this paper an attempt has been made to develop a technique to design coupled shear wallsconsidering its ideal seismic behavior (stable hysteresis with high earthquake energy

dissipation). For preparing this design technique, symmetrical coupled shear walls have beenconsidered. Design/capacity curve of coupled shear walls is obtained at the collapse mechanismof the structure based on this technique. This technique is applied to both fixed base and pinned

base coupled shear walls. To start with, this technique is useful in selecting the preliminary


17/50

dimensions of symmetrical coupled shear walls and subsequently arrives at a final design stage.Further, this technique is particularly useful for designer, consultant and practicing engineer

who have no access to sophisticated software packages. A case study has been doneimplementing the technique with the help of Microsoft Excel Spreadsheet and the results have

also been validated.

Proposed Formulation

In Figure 3, the coupled shear walls are subjected to a triangular variation of loading withamplitude F1 at the roof level. The value of F1 is obtained corresponding to the CP level of

structure. Subsequently, the base shear and roof displacement can be determined. The procedureinvolving Figure 3, the assumptions, steps and mathematical calculation with initial value of F 1as unity has been illustrated as follows.

Figure 3 (a):Coupled shear walls Figure 3 (b): Free body diagramof coupled shear walls

Assumptions

The following assumptions are adopted for the design technique to obtain the ideal seismic

behavior of coupled shear walls.1. The analytical model of coupled shear walls is taken as two-d imensional entity.

2. Coupled shear walls exhibit flexural behavior.

3.

Coupling beams carry axial forces, shear forces and moments.4. The axial deformation of the coupling beam is neglected.

5. The effect of gravity loads on the coupling beams is neglected.6. The horizontal displacement at each point of wall 1 is equal to the horizontal displacement at

each corresponding point of wall 2 due to the presence of coupling beam.7. The curvatures of the two walls are same at any level.8. The point of contra flexure occurs at mid point of clear span of the beam.

F1

Vw

V

V

V

V

V

V

Wg

H

Lb LW

Wall 2

h

I, A

I, A

Wall 1

db

F1

LW

i

T C = T

Mid-point of Lb

H

M M

V

C/L of Wall 2

Wg

l

C/L of Wall 1

A B

V

V

F1

x

F1(H-hs)/H

F1(H-2hs)/H

F1(H-3hs)/H

F1(H-(N-i)hs)/H

Vw

F1(H-4hs)/H

F1(H-5hs)/H

F1(H-(N-2i)hs)/H

F1(H-(N-3i)hs)/H


18/50

9. The seismic design philosophy requires formation of plastic hinges at the ends of thecoupling beams. All coupling beams are typically designed identically with identical plastic

moment capacities. Being lightly loaded under gravity loads they will carry equal shearforces before a collapse mechanism is formed. All coupling beams are, therefore, assumed to

carry equal shear forces.

10.

In the collapse mechanism for coupled shear walls, plastic hinges are assumed to form at thebase of the wall and at the two ends of each coupling beam. In the wall the elastic

displacements shall be small in comparison to the d isplacements due to rotation at the base ofthe wall. If the elastic displacements in the wall are considered negligible then a triangular

displaced shape occurs. This is assumed to be the distributiondisplacement/velocity/acceleration along the height. The acceleration times the mass/weightat any floor level gives the lateral load. Hence, the distribution of the lateral loading is

assumed as a triangular variation, which conforms to the first mode shape pattern.

Steps

The following iterative steps are developed in this thesis for the design of coupled shear walls.

1)

Selection of a particular type of coupling beam and determining its shear capacity.2) Determining the fractions of total lateral loading subjected on wall 1 and wall 2.

3) Determining shear forces developed in coupling beams for different base conditions.4) Determining wall rotations in each storey.5) Checking for occurrence of plastic hinges at the base of the walls when base is fixed. For

walls pinned at the base this check is not required.6) Calculating coupling beam rotation in each storey.

7) Checking whether coupling beam rotat ion lies at collapse prevention level.8) Calculating base shear and roof displacement.9) Modifying the value of F1for next iteration starting from Step (2) if Step (7) is not satisfied.

Mathematical Calculation

The steps which are described in above have been illustrated in this section as follows:

Step 1

The type of coupling beam can be determined as per Table 11 and shear capacity can becalculated as per section Moment Capacity of Coupling Beam.

Step 2

In Figure 3(b), free body diagram of coupled shear walls has been shown; and are fractionsof total lateral loading incident on wall 1 and wall 2, respectively, such that,

+=1.0 (8)For symmetrical coupled shear walls, moments of inertias of two walls are equal for equal depthsand thicknesses at any level. Further, curvatures of two walls are equal at any level. Hence based

on the Assumption (7), Equation (8) can be written as:== 0.5 (9)


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Step 3

In this step, it is explained how to calculate the shear force developed in the coupling beams fordifferent types of boundary conditions. CSA (1994) and Chaallal et al. (1996) defined the degree

of coupling which is written as,

otM

lTDC

(10)

where, bw LLl ; T is the axial force due to lateral loading; Mot is total overturning moment at

the base of the wall produced due to lateral loading. For fixed base condition DC varies from 0 to1 and Equation (10) can also be written as:

cbb

w

a

b

LL

dkDC

(10a)

The above Equation (10a) is proposed by Chaallal et al. (1996); Nis the total number of storeys,k is constant and a, b and c are exponents which are given in

Table 12.Table 12:Values of constant k and exponents a, b and c

N k a b c

6 2.976 0.706 0.615 0.698

10 2.342 0.512 0.462 0.509

15 1.697 0.352 0.345 0.279

20 1.463 0.265 0.281 0.190

30 1.293 0.193 0.223 0.106

40 1.190 0.145 0.155 0.059

So based upon the above criteria and considering Equations (10) and (10a), shear forcedeveloped in the coupling beam could be determined as follows:

Fixed base condition:For fixed base condition following equation can be written as:

cb

b

w

a

botN

i

iLL

dk

l

MVTC

1

(11)

where,Motis total overturning moment at the base due to the lateral loading.

Therefore, based on the Assumption (9) shear force in coupling beam at each storey is,

N

V

V

N

i

i 1 (12)

Pinned base condition:

In this study, pinned base condition has been introduced as one of the possible boundaryconditions for coupled shear walls. It can be constructed by designing the foundation for axial

load and shear force without considering bending moment. It is expected that stable hysteresiswith high earthquake energy dissipation can be obtained for considering this kind of basecondition.

DC is 1 for pinned base condition from the equation (10). Hence, the equation can be written as:

l

MVTC ot

N

i

i 1

(13)

Therefore, based on the Assumption (9) shear force in coupling beam at each storey is,


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N

V

V

N

i

i 1 (14)

Step 4

After obtaining , and V at each storey for the particular value of F1, bending moment valuesin each storey could be determined for each wall. Subsequently, curvature diagram for each wallis generated by using moment area method as adopted in the Microsoft excel spreadsheet; whichis required to determine the wall rotation in each storey. The following equations are considered

to calculate the wall rotation.Overturning moment at a distance x from base with respect to each wall can be written as:

iN

j

ssot jhxHjhHH

FxM

0

15.0 (15)

where, i is storey number and it is considered from the base as 0, 1, 2, 3 N.

Resisting moment in wall due to shear force in the coupling beam at a d istance x from base canbe written as:

N

ij

jbw

wr VLL

xM22

(16)

where, net moment in the wall at a distance x from base, generated due to overturning momentand moment due to shear force in the coupling beam, can be written as:

Mnet(x) = Mot(x) xMwr (17)Wall rotation at i thstorey for fixed base can be written as:

IE

dxxM

c

ih

net

wi

s

0 (18)

where,12

3

ww LtI

(19)

For plastic hinge rotation at the fixed base of wall or rotation at the pinned base of wall, Equation(18) could be written as:

0

0

w

c

ih

net

wiIE

dxxMs

(20)

where,0w is the plastic hinge rotation at the fixed base of wall or rotation at the pinned base of

wall.

Step 5

i. Tensile forces at the base of wall 1 (T) as well as compressive forces at the base of wall 2 (C)are calculated due to lateral loading.

ii. Compressive loads at the bases of wall 1 and wall 2 are calculated due to gravity loading.


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iii.Net axial forces at the bases of wall 1 and wall 2 are calculated, i.e.Net axial force = Tensile or Compressive force due to lateral loading (T or C)

Compressive load due to gravity loading.iv. Then, according to these net axial forces for the particular values of fck, bb, dandp, the yield

moment values at the bases of wall 1 and wall 2 can be determined from

P-M interaction curve [IS 456 (1978) & Jain (1999)]. Wherefck, bb, dandpare yield strengthof concrete, breadth of a section, depth of that section and percentage of minimum

reinforcement in that particular section, respectively; and P is the axial force and M is themoment; here net axial force is considered as P in the

P-M interaction curve.v. Therefore, if calculated bending moment value at any base of the two walls is greater than

yield moment value, plastic hinge at that base would be formed, otherwise no plastic hinge

would be formed.

Step 6

The rotation of coupling beam in each storey is determined as follows:

Rotation of coupling beam at i thstorey for symmetrical walls [Englekirk (2003)] as per Figure 4

is given by

b

wwibi

L

L1 (21)

where, wi is rotation of wall at i th storey and can be calculated as per Equation (18), wL =

depth of wall,b

L = length of coupling beam.

For plastic hinge rotation at the fixed base of wall or real hinge rotation at the pinned base of

wall, Equation (21) could be written as:

wiwbbi L (22)

Lw LwLb

2

bL

wi

wi

bi

Figure 4:Deformed shape of a i thstorey symmetrical coupled shear walls


22/50

where, wi can be calculated as per Equation (20) for fixed base of wall or for pinned base of

wall and

wbL =

b

w

L

L1 (23)

Step 7

The rotational limit for collapse prevention level of different types of RCC coupling beams andsteel beams are given in Table 11. The task was to check whether the rotations of beams attained

their rotational limit of CP level at the collapse mechanism of the structure simultaneously.

Step 8

The roof displacement can be calculated as per the following equations:

N

i

wisroof h0

(24)

where, displacement at i thstorey can be calculated as:

i

j

wjsi h0

(25)

The base shear can be calculated as follows:

2

11 NF

VB (26)

Step 9

The F1 is modified as follows when the condition of Step 7 is not satisfied:To obtain the collapse mechanism of the structure, it is required to increase F1 with equal

increment until all coupling beams attain their rotation limit of CP level simultaneously.

Validation of the Proposed Design Technique

The following numerical example has been considered to validate the propose design technique.In this study plan and elevation with dimensions and material properties of the coupled shear

walls have been adopted as given in Chaallal et al. (1996).

Numerical Example

The coupled shear walls considered here is part of a 20-storey office building(Figure 5). It is subjected to triangular variation of lateral loading. The dimension and material

properties are tabulated in Table 13. Dead loads and live loads are discussed in the followingsection. A comparison of the results regarding design/capacity curve

(Figure 7) and ductility [Equation (27)] obtained from the proposed design technique with theresults obtained in SAP V 10.0.5 (2000) and DRAIN-3DX (1993) software packages may, thus,


23/50

be required. For obtaining more perfection about the results, these two softwares have beenconsidered here simultaneously.

Table 13: Dimensions and material properties of coupled shear walls for validation of proposeddesign technique

Depth of the wall (Lw) 4 mWidth of coupling beam

(bb) 300 mm

Length of coupling

beam (Lb)1.8 m Storey height (hs) 3.0 m

Depth of coupling

beam (db)600 mm

Modulus of concrete (Ec) 27.0 GPa

Modulus of steel (Es) 200.0 GPa

Number of storeys (N) 20Steel yield strength (fy) 415 MPa

Wall thickness (tw) 300 mm

Figure 5(a) and Figure 5(b) show the plan and sectional elevation of the coupled shear wallbuilding, respectively.

Figure 5(a): Plan view of building Figure 5(b): Coupled shear walls atsection a-a

Loading Consideration

Dead loads (DL) of 6.7 kN/m2 and live loads (LL) of 2.4 kN/m2 have been considered assuggested in Chaallal et al. (1996). Total gravity loading on coupled shear walls at section a -a

has been calculated as the sum of dead load plus 25 % LL as perIS 1893 (part 1) (2002) for floor; however, in case of roof only dead load is considered.

Modeling of Coupled Shear Walls in Proposed Design Technique

The modeling of coupled shear walls involving Figure 3, assumptions and steps withmathematical calculation is already described in Section Proposed Formulation.

5m

5m

9m9m9m9m

Lw

Lw

Lb

a

a

H

Lb

Wall 2

hs

I, A I, A

Wall 1

db

L LW


24/50

Modeling of coupled shear wal ls in SAP and DRAI N-3DX

Wide column frame analogy [Mcleod (1966)] has been considered for modeling of coupled shearwalls in SAP V 10.0.5 (2000) and DRAIN-3DX (1993) as given in

Figure 6. In this analogy, shear walls are represented as two line elements (centre line of shearwall) and beams are represented as line elements (centre line of beam) by joining with each otherwith rigid link. Beam column elastic element (Type-17) and inelastic element (Type-15) are

considered for modeling.

Figure 6:Modeling in SAP V 10.0.5 (2000) and DRAIN-3DX (1993)

Calculation of Ducti li ty

The obtained design/capacity curve from the proposed design technique,

SAP V 10.0.5 (2000) and DRAIN-3DX (1993) is bilinearized. The bilinear representation isprepared in the following manner based on the concepts given inATC 40 (1996).

Figure 7: Bilinear Representation for Capacity Curve

Coupling beam

Rigid link

0.5Lw Lb 0.5Lw

Capacity


25/50

It can be seen from Figure 7 that bilinear representation can be due to the basis of initial tangentstiffness and equal energies (Area a1 = Area a2). Subsequently, ductility of the coupled shear

walls has been calculated as:

yieldroof

CProof

,

,

(27)

where, CProof, and yieldroof, can be calculated from the Equation (24); is the ductility which

represents how much earthquake energy dissipates during an earthquake.

Results and Discussions

Coupled shear walls at section a-a as shown in Figure 5 are considered for conducting thestudy.

RCC coupling beam with Conventional longitudinal reinforcement and conformingtransverse reinforcement: RCC coupling beam with Conventional longitudinal reinforcement

and conforming transverse reinforcement in each storey has been selected as per Step 1 for thestudy. The results of this study for fixed base as well as pinned base conditions have been shownin the following manner.

Figure 8(a): Figure 8(b):Capacity curve for fixed base condition Capacity curve for pinned base condition

Table 14: Ductility of coupled shear walls considering different approaches

Method

Ductility

Fixed base Pinned base

Proposed Design Technique 7 7.5

DRAIN-3DX (1993) 6.75 7.45

SAP V 10.0.5 (2000) 6.92 7.47

0 0.1 0.2 0.3

1500

1000

500

0

SAP V 10.0.5

DRAIN-3DX

DESIGN

Roof Displacement (m)

0 0.1 0.2 0.3

900

600

300

0

SAP V 10.0.5

DRAIN-3DX

DESIGN

Roof Displacement (m)

0.4


26/50

Discussions of numerical results:

Figure 8(b) shows that the results obtained from proposed design technique for pinned baseconditions are almost similar with the results obtained from DRAIN-3DX (1993) and SAP V

10.0.5 (2000). Whereas, Figure 8(a) is showing a bit differences about the results obtained fromproposed design technique, DRAIN-3DX (1993) and SAP V 10.0.5 (2000) although samedimensions, same material properties and same loading were considered in all the three

techniques. However, the differences were not very high (5-10%). Table 14 is showing theresults about ductility obtained for fixed and pinned base conditions with the help of the Figures

8(a) and 8(b) and Section Calculation of Ductility. It is noticed that ductility for pinned basecondition is greater than fixed base conditions. It means that stable hysteresis with highearthquake energy dissipation can be obtained for coupled shear walls with pinned base.

The results obtained from the proposed design technique are satisfactory. However, it isnecessary to find the limitations of the proposed design technique. Therefore, in the following

section, parametric study is elaborately discussed to detect the limitations of the proposed designtechnique.

PARAMETRIC STUDYIt has been observed from the CSA (1994) and Chaallal et al. (1996) that the behavior of the

ductile coupled shear walls depends on degree of coupling, where degree of coupling dependsupon depth and length of the coupling beam as well as depth and height of the coupled shearwalls [Park and Paulay (1975) & Paulay and Priestley (1992)].

Therefore, this study has been restricted on length of the coupling beam and number of storiesas basic variables and other parameters are considered as constant. These parameters have been

considered in proposed method to make out effect on the behavior of coupled shear walls.Further, modifications to achieve ideal seismic behavior according to the proposed method havebeen included in this study.

Model for Parametric Study

A typical building with symmetrical coupled shear walls is shown inFigures 9(a) and (b). Coupled shear walls at section a-a have been considered to carry out theparametric study.


27/50

Figure 9(a): Plan view of building with Figure 9(b):Coupled shear walls

symmetrical coupled shear at section a-awalls

Loading Consideration

Dead loads (DL) of 6.7 kN/m2and live loads (LL) of 2.4 kN/m2have been considered as per thesuggestions made by in Chaallal et al. (1996). Total gravity loading on coupled shear walls at

section a-a has been calculated as the sum of dead loadplus 25 % LL as per IS 1893 (part 1) (2002) for floor; however, in case of roof only dead load isconsidered.

Parameters

Table 15 mentions the different parameters with dimensions and material properties which havebeen considered to carry out the parametric study.

Table 15:Dimensions and material properties of coupled shear walls for parametric study

Depth of the wall(Lw)

4 mWidth of coupling beam

(bb)300 mm

Length of beam (Lb) 1 m, 1.5 m and 2 m Storey height (hs) 3.6 m

Depth of beam (db) 800 mm Modulus of concrete (Ec) 22.4 GPa

Number of stories(N)

10, 15 and 20 Yield strength of steel(fy)

415 MPa


Analysis Using Proposed Design Technique

The above mentioned building has been studied by the design technique. The results for different

parameters have been described in this section.

5m

5m

9m9m9m9m

Lw

Lw

Lb

a

a

H

Lb

Wall 2

hs

I, A I, A

Wall 1

db

LW LW


28/50

Observed Behavior

To study the influence of length of the coupling beam (Lb) on the behavior of coupled shearwalls, length of the coupling beam is considered as 1 m, 1.5 m and 2 m for both fixed and pinned

base conditions. RCC coupling beam with conventional longitudinal reinforcement withconforming transverse reinforcement has been selected. Shear capacity in the coupling beam iscalculated as per Step 1. The rotational limit of coupling beam has been selected as per Step 7.

The study has been performed for coupled shear walls with number of stories 20, 15 and 10 forboth fixed and pinned base conditions.

For Number of Stor ies N = 20

Figure 10(a):Storey displacement for fixed base condition

at CP level

Figure 10(b):Storey displacement for pinned base conditionat CP level

Figure 11(a):Wall rotation for fixed base condition at CP

level

Figure 11(b):Wall rotation for pinned base condition at CP

level

Reduced

Reduced

Reduced

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m


29/50

Figure 13(a):

Capacity curve for fixed base conditionFigure 13(b):Capacity curve for pinned base condition

Discussion of results for N = 20

The deflection for the case of pinned base condition is much higher than the case of fixed base

(Figure 10); however, the base shear for the case of pinned base condition is lower than the caseof fixed base (Figure 13). It shows satisfactory results based on the behavior of coupled shearwalls. Because, coupled shear walls with pinned base deflected more subjected to lesser lateral

loading in comparison with the coupled shear walls with fixed base and base shear is directlyvarying with the lateral loading (Equation 26). Since wall rotation is directly varying with the

length of the beam (Figure 11) and deflection is the summation of the wall rotation (Equation25), deflection is directly varying with the length of the beam (Figure 10). It has been alsoobserved that all beams reach to their rotational limit of CP level for pinned base condition;

however, very few beams reach to their rotational limit of CP level for fixed base condition(Figure 12). Hence, it can be said that coupled shear walls is behaving as a rigid body motion for

pinned base condition; which is expected.The explanations for fixed base condition (Figure 12)are given in the following manner:

Figure 12(a):Beam rotation for fixed base condition at CP

level

Figure 12(b):

Beam rotat ion for p inned base condition at CPlevel

Reduced

Reduced

Reduced

Reduced

Reduced

Reduced

Reduced

Reduced

Reduced

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m


30/50

i) The rotation of the cantilever wall is maximum at the free end of the wall. This rotationdecreases towards the base of the wall and is zero at the base for fixity.

ii) Fixed base coupled shear walls with short span coupling beam is behaving as a cantileverwall (Lb = 1m of Figure 11). It is also one of the behaviors of a coupled shear walls.

However, fixed base coupled shear walls with long span coupling beam does not show

cantilever wall (Lb= 1.5m and Lb= 2m of Figure 11) behavior.iii) Beam rotation is proportional to the wall rotation.

Therefore, it can be said from the above observations that coupled shear walls with short spancoupling beam (Lb= 1m) can be acceptable in comparison with the long span coupling beam (Lb

= 1.5m and Lb= 2m) although the behavior of all three coupling beams is governed by shearaccording to Table 11.With the help of Section Calculation of Ductility and Figure 13, ductility for pinned base

condition and fixed base condition has been calculated in the following table.

Table 16: Ductility of coupled shear walls for N = 20

Base

condition

Length of the coupling beam

(Lb) Values

Fixed

1m 3.33

1.5m 4.8

2m 6.3

Pinned1m 5.11

1.5m 6.35

2m 7.1

It has been observed from the above table that ductility is more for pinned base condition in

comparison with the fixed base condition and ductility increases with increase in length of the

coupling beam (Equations 24 and 27, Figures 10, 11 & 13).


Figure 14(a):

Storey displacement for fixed base conditionat CP level

Figure 14(b):

Storey displacement for pinned base conditionat CP level

Reduced

Reduced

Reduced

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m


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Figure 15(a):Wall rotation for fixed base condition at CP

level

Figure 15(b):Wall rotation for p inned base condition at CP

level

Figure 16(a):

Beam rotation for fixed base condition at CPlevel

Figure 16(b):

Beam rotation for pinned base condition at CPlevel

Figure 17(a):

Capacity curve for fixed base condition

Figure 17(b):

Capacity curve for pinned base condition

Reduced

Reduced

Reduced

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m


32/50


With the help of Section Calculation of Ductility and Figure 17, ductility for pinned base

condition and fixed base condition has been calculated in the following table.

Table 17: Ductility of coupled shear walls for N = 15

Base condition Length of the coupling beam (Lb) Values

Fixed

1m 2.93

1.5m 4.0

2m 5.9

Pinned

1m 4.5

1.5m 5.85

2m 6.87

It has been observed from Figures 14 to 17 and Table 17 that the results obtained for N=15 aresimilar with the results of N = 20 for fixed base condition and pinned base condition.


Figure 18(a):

Storey displacement for fixed basecondition at CP level

Figure 18(b):Storey displacement for pinned base condition

at CP level

Reduced

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m


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Figure 19(a):Wall rotation for fixed base condition at

CP level

Figure 19(b):Wall rotation for pinned base condition at

CP level

Figure 20(a):Beam rotation for fixed base condition at

CP level

Figure 20(b):Beam rotation for pinned base condition at

CP level

Figure 21(a):Capacity curve for fixed base condition

F

Figure 21(b):Capacity curve for pinned base condition

Reduced

Reduced

Reduced

Reduced

Reduced

Reduced

Reduced

Reduced

ReducedReduced

Reduced

Reduced

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m

Lb= 1m

Lb= 1.5 m

Lb= 2 m


34/50


Figures 20 and 21 show that beam rotat ion and capacity curve reach CP level for the case of Lb=

1 m with pinned base condition only. However, beam rotation and capacity curve do not reachthe CP level for the other cases while shear capacities in all coupling beams have been achieved.

It means that ideal seismic behavior (stable hysteresis with high earthquake energy dissipation)of coupled shear walls has only been achieved for Lb= 1 m with pinned base condition. Proposeddesign technique does not show ideal seismic behavior of coupled shear walls for Lb= 1 m, 1.5

m and 2 m with fixed base condition and Lb= 1.5 m and 2 m with pinned base condition. Now,remedial action has been considered in the following manner to obtain the ideal seismic

behavior.

Remedial Action for N = 10

The remedy for the cases of Lb = 1 m, 1.5 m and 2 m with fixed base condition and

Lb= 1.5 m and 2 m with pinned base condition to achieve CP level is mentioned below (Figures22 to 25). To obtain the CP level, it is required to increase the wall rotation. Since wall rotation[Equations (18) and (19)] is inversely varying to the Lw

3, it is required to decrease the Lw. It has

been observed from Figure 25 that the ideal seismic behavior of coupled shear walls has beenachieved.

Figure 22(a):

Storey displacement for fixed basecondition at CP level

Figure 22(b):Storey displacement for pinned base condition

at CP level

Reduced demand

response spectra

Reduced

demandReduced


35/50

Figure 23(a):Wall rotat ion for fixed base condition at CP

level

Figure 23(b):Wall rotation for pinned base condition at CP

level

Figure 24(a):

Beam rotation for fixed base condition at CPlevel

Figure 24(b):Beam rotat ion for pinned base condition at CP

level

Figure 25 (a): Figure 25(b):

Capacity curve for fixed base condition Capacity curve for pinned base condition


36/50

Discussion of the above results

Figures 24 and 25 show that beam rotation and capacity curve reach CP level for all cases

although the results are not satisfactory for fixed base condition according to the explanationsgiven in Section For Number of Stories N = 20.

Hence, it can be said from the above results that proposed design technique is useful to designthe coupled shear walls during earthquake motion. To confirm it more, nonlinear static analysisis consisdered in the following manner to assess the proposed design technique.

ASSESSMENT OF PROPOSED DESIGN TECHNIQUE USING NONLINEAR STATIC

ANALYSIS

In this paper, nonlinear static analysis is carried out to determine the response reduction factorsof coupled shear walls at different earthquake levels.

Design Example

The following design example is presented for carrying out the non linear static analysis ofcoupled shear walls. These walls are subjected to triangular variation of lateral loading. The baseof the walls is assumed as fixed. Table 18 mentions the different parameters with dimensions and

material properties which have been considered to carry out the study. Figure 26(a) and Figure26(b) show the plan and sectional elevation of the coupled shear wall building, respectively. Theplace considered for this study is Roorkee and soil type for this place is medium (Type II);

maximum considered earthquake (MCE) level and design basis earthquake level (DBE) areconsidered for the study.

Table 18: Dimensions and material properties of coupled shear walls for nonlinear static

analysis

Depth of the wall (Lw) 4 mWidth of coupling beam

(bb)300 mm

Length of beam (Lb) 1 m Storey height (hs) 3.6 m

Depth of beam (db) 800 mm

Modulus of concrete (Ec) 22.4 GPa

Modulus of steel (Es)200.0

GPa

Number of stories (N) 20 and 15Steel yield strength (fy) 415 MPa



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Figure 26(a): Plan view of building with Figure 26(b):Coupled shear walls

coupled shear walls at section a-a

Loading considerationDead loads (DL) of 6.7 kN/m2and live loads (LL) of 2.4 kN/m2have been considered as givenin Chaallal et al. (1996). Total gravity loading on coupled shear walls at section a-a has been

calculated as the sum of dead load plus 25 % LL as perIS 1893 (part 1) (2002) for floor; however, in case of roof only dead load is considered.

Results and discussions

The results and discussions are described in the following manner.

Figure 27(a): Capacity curve for N = 20 Figure 27(b):Capacity curve for N = 15

5m

5m

9m9m9m9m

Lw

Lw

Lb

a

a

H

Lb

Wall 2

hs

I, A I, A

Wall 1

db

L LW


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Calculation of performance point

Place considered here is Roorkee which belongs to the seismic zone IV and Z is 0.24 as per IS1893 (part1) (2002). 5% damped elastic response spectra as per

IS 1893 (part1) (2002) are considered here as demand curve. DBE and MCE levels areconsidered for calculation of performance point (pp). Capacity curves are already obtained inFigure 27. The performance point has been calculated with the help of capacity spectrum method

of ATC 40 (1996) which is as follows:

Figure 28: Performance point at the MCE level for N = 20

In this case, modal mass co-efficient 1 = 0.616 and Mode participation factor

PF1 = 1.51 derived with the help o f modal analysis in SAP V 10.0.5 (2000). Figure 28 shows thatpp is the performance point. The base shear at the performance point (pp), Vb,pp= 1173.1 kN androof displacement at the performance point (pp), roof, pp= 0.31 m.


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Figure 29: Performance point at the DBE level for N = 20


PF1 = 1.51. Figure 29 shows that pp is the performance point. The base shear at the performancepoint (pp), Vb,pp= 957.6 kN and roof displacement at the performance point (pp), roof,pp= 0.097

m.

Figure 30: Performance point at the MCE level for N = 15

Straight line

tangent to the

5% demand response

spectra

Capacity curve

Reduced demand

response spectra

Straight line tangent to

the ca acit curve

5% demand response

s ectra

Capacity curve

Reduced demand

res onse s ectra


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In this case, modal mass co-efficient 1 = 0.644 and Mode participation factorPF1 = 1.485. Figure 30 shows that pp is the performance point. The base shear at the performance

point (pp), Vb,pp = 1455.3 kN and roof displacement at the performance point (pp), roof,pp =0.259 m.

Figure 31: Performance point at the DBE level for N = 15


PF1 = 1.485. Figure 31 shows that pp is the performance point. The base shear at the performancepoint (pp), Vb,pp = 1251.5 kN and roof displacement at the performance point (pp), roof,pp =0.101 m.

Calculation of r esponse reduction factor at the per formance point

Table 19 shows different response reduction factors for MCE and DBE level. These arecalculated at different performance points (Figures 28-31).

pp

Straight line tangent to the

5% demand response

Capacity curve

Reduced demand response

spectra


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Table 19:Response Reduction Factors for DBE and MCE levels

Parameters 1e [Pore

(2007)]

2e [Pore(2007)]

R [Pore

(2007)]IDRSR

[First Method of Energy-

Ductility Based Response

Reduction] [Pore (2007)]

IDRSR

[Second Method of

Energy-Ductility Based

Response Reduction]

[Pore (2007)]

dR as per CSA

(1994)

N=20

DBE 1.04 1.004 1.02 1.04 1.004

1.5 or 2 for coupled

shear walls with

conventional

reinforced coupling

beam

MCE 2.05 1.2 1.58 2.05 1.34

N=15

DBE 1.01 1.00 1.002 1.01 1.00

MCE 1.87 1.13 1.39 1.87 1.22

From the above table, response reduction factor of coupled shear walls is varying between

05.2to22.1 for maximum considered earthquake (MCE) level; which is almost same as the

provision of CSA (1994) for coupling beam with conventional reinforcement.

CONCLUSIONS

From the above studies, the following recommendations have been made for the design of

coupled shear walls under earthquake motion.

(i)Design technique should be adopted for fixing the dimensions of coupled shear walls.

(ii)Coupled shear walls withN 15 with equal storey height m6.3h s can be designed with

an optimum ratio of 25.0L

L

w

b for 25.1d

L

b

b and 03108 I

Ib to obtain consistency

between the behavior with respect to the wall rotation and earthquake energy dissipation.

(iii)Pinned base condition can be provided at the base of the shear wall as this type of basecondition offers better nonlinear behavior in compare to the fixed base condition.

(iv)The behavior of coupling beam should be governed by shear.


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NOTATIONS

A Area of Symmetrical Coupled Shear Walls

cwA Area of Concrete Section of an Individual Pier, Horizontal Wall

Segment, or Coupling Beam Resisting Shear in in2as per

ACI 318 (2005)

gA Gross Area of Concrete Section in in2For a Hollow Section, Agis

the Area of The Concrete Only and does not Include the Area of

the Void(S) as per ACI 318 (2005)

"

sA Reinforcing Steel in One Diagonal as per Englekirk (2003)

sA Area of Nonprestressed Tension Reinforcement as per Englekirk (2003)

sdA Reinforcement along each Diagonal of Coupling Beam as per

IS 13920 (1993)

vdA Total Area of Reinforcement in Each Group of Diagonal Bars in

a diagonally reinforced coupling beam in in2as per

ACI 318(2005)

bb Width of Coupling Beam

fb Flange width of I-beam as per FEMA 273 (1997) and FEMA 356 (2000)

wb Web Width of the Coupling Beam as per FEMA 273 (1997) and

FEMA 356 (2000)

C Compressive Axial Force at the Base of Wall 2

CP Collapse Prevention Level

D Overall Depth of the Steel I-Coupling beam Section

DC Degree of Coupling

DL Dead Loads

DBE Design Basis Earthquake


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d Effective Depth of the Beam

bd Depth of the Coupling Beam

d Distance from Extreme Compression Fiber to Centroid of CompressionReinforcement as Per Englekirk (2003)

b Displacement at Vb

e Elastic displacement (Ve)

l Displacement at Limiting Response

roof Roof Displacement

CProof, Roof Displacement at CP Level

yieldroof, Roof Displacement at Yield Level

u Displacement at Ultimate Strength Capacity

y Displacement at Yield Strength Capacity

ay Actual displacement at

ayV

Ec Modulus of Elasticity of Concrete

cbE Youngs Modulus for Concrete in Beam

cwE Youngs Modulus for Concrete in Wall

EPP Elastic-Perfectly-Plastic

EQRD Earthquake Resistant Design

sE Modulus of Elasticity of Steel as per FEMA 273 (1997) and

FEMA 356 (2000)

sbE Youngs Modulus for Steel in Beam

swE Youngs Modulus for Steel in Wall

e Clear Span of the Coupling Beam+2Concrete Cover of Shear Wall as perEnglekirk (2003)

c Strain in Concrete


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F Force

1F Maximum Amplitude of Triangular Variation of Loading

FEMA Federal Emergency Management Agency

uF Ultimate Force

yF Yield stress of Structural Steel

'

cf Specified Compressive Strength of Concrete Cylinder

ckf Characteristic Compressive Strength of Concrete Cube

yf Specified Yield Strength of Reinforcement

H Overall Height of the Coupled Shear Walls

h Distance from inside of compression flange to inside of tension flange of

I-beam as per FEMA 273 (1997) and FEMA 356 (2000)

sh Storey Height

I Moment of Inertia of Symmetrical Coupled Shear Walls

bI Moment of Inertia of Coupling Beam

IO Immediate Occupancy Level

i Storey Number

k Unloading Stiffness

1k Post Yield Stiffness

ek Elastic Stiffness

ik

Initial Stiffness

seck Secant Stiffness

bL Length of the Coupling Beam

dL Diagonal Length of the Member

LL Live Loads


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LS Life Safety Level

Lw Depth of Coupled Shear Walls

l Distance between Neutral Axis of the Two Walls

0 Member Over strength factor as per Englekirk (2003)

M Moment of Symmetrical Coupled Shear Walls

M1 Moment at the Base of the Wall 1

M2 Moment at the Base of the Wall 2

MCE Maximum Considered Earthquake

MDOF Multi-Degree of Freedom

nM Nominal Flexural Strength at Section in lb- in as per

ACI 318 (2005)

pM Moment Capacity of Coupling Beam as per Englekirk (2003)

Mot Total Overturning Moment due to the Lateral Loading

MRF Moment Resistant Frame

Displacement Ductility Capacity Relied on in the Design as per

NZS 3101 (1995)

Ductility

1e Energy based proposal for ductility under monotonic loading and

Unloading

2e Energy based proposal for ductility under Cyclic Loading

N Total Number of Storeys

NA Not Applicable

NEHRP National Earthquake Hazard Reduction Program

NSP Non-linear Static Procedure

P Axial Force as per IS 456 (1978)

PBSD Performance Based Seismic Design


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p Percentage of Minimum Reinforcement

Shear span to depth ratio

pp Performance Point

R Response Reduction Factor

RCC Reinforced Cement Concrete

dR Ductility Related Force Modification Factor

R Ductility Factor

RR Redundancy Factor

Rs Overstrength Factor

aS Spectral Acceleration

dS Spectral Displacement

SDOF Single-Degree of Freedom

T Tensile Axial Force at the Base of Wall 1

1T Tensile Strength of One Diagonal of a Diagonal Reinforced Coupling Beam

dT Tensile Strength of Truss Reinforced Coupling Beams Diagonal as per

Englekirk (2003)

'T The Residual Chord Strength as per Englekirk (2003)

ft Flange Thickness of Steel I-Coupling beam as per Englekirk (2003)

Inclination of Diagonal Reinforcement in Coupling Beam

b Coupling Beam Rotation

Lu

Rotat ional Value at Ultimate Point

max,u Maximum Rotational Value

w Wall Rotation

y Yield Rotation as per FEMA 273 (1997) and FEMA 356 (2000)

wt Wall Thickness


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'wt Web Thickness of Steel I-Coupling beam

V Shear Force in the Coupling Beam

1V The Shear or Vertical Component of One Diagonal in a Primary Truss Travelled

along the Compression Diagonal as per Englekirk (2003)

2V The Shear in a Secondary Truss produced by the Residual Tension

Reinforcement Activated the Load Transfer Mechanism as per

Englekirk (2003)

BV Base Shear

bV Non-factored des ign base shear

dV Factored design base shear may be less than or greater thana

yV

eV Base shear for elastic response

lV Base shear at limiting response

nV Nominal Shear Strength in lb as per ACI 318 (2005)

nfV The transferable shear force for flexure dominant steel coupling beam as per

Englekirk (2003)

sp

V Shear Capacity of Coupling Beam as per Englekirk (2003)

1sV Shear Strength of Closed Stirrups as per ATC 40 (1996),

FEMA 273 (1997) and FEMA 356 (2000)

uV Capacity corresponding to u (may be the maximum capacity)

1uV Factored Shear Force as per IS 13920 (1993)

2uV Factored Shear Force at Section in lb as per ACI 318 (2005)

wV Shear Force at the Base of the Shear Wall

1wV Shear Force at the Base of Wall 1

2wV Shear Force at the Base of Wall 2

yV Base shear at idealized yield level


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ayV Actual first yield level

nv Total Nominal Shear Stress in MPa as per NZS 3101 (1995)

gW Total Gravity Loading for Symmetrical Coupled Shear Walls

w Compressive Strut Width as per Englekirk (2003)

Z Zone Factor

pZ Plastic Section Modulus of Steel Coupling Beam

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conceptual design of coupled shear wall

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