research article a conceptual design approach of coupled...

Hindawi Publishing CorporationISRN Civil EngineeringVolume 2013 Article ID 161502 28 pageshttpdxdoiorg1011552013161502

Research ArticleA Conceptual Design Approach of Coupled Shear Walls

Dipendu Bhunia1 Vipul Prakash2 and Ashok D Pandey3

1 Civil Engineering Group BITS Pilani 333031 India2Department of Civil Engineering IIT Roorkee Roorkee India3 Department of Earthquake Engineering IIT Roorkee Roorkee India

Correspondence should be addressed to Vipul Prakash vipulprakashyahoocom

Received 27 May 2013 Accepted 6 July 2013

Academic Editors N D Lagaros and I Smith

Copyright copy 2013 Dipendu Bhunia et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Earthquake causes considerable damage to a large number of RCC high-rise buildings and tremendous loss of life Thereforedesigners and structural engineers should ensure to offer adequate earthquake resistant provisions with regard to planning designand detailing in high-rise buildings to withstand the effect of an earthquake and minimize disaster As an earthquake resistantsystem the use of coupled shear walls is one of the potential options in comparison with moment resistant frame (MRF) and shearwall frame combination systems in RCC high-rise buildings Furthermore it is reasonably well established that it is uneconomicalto design a structure considering its linear behavior during earthquake Hence an alternative design philosophy needs to be evolvedin the Indian context to consider the postyield behavior wherein the damage state is evaluated through deformation considerationsIn 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

1 Introduction

The growth of population density and shortage of land inurban areas are two major problems for all developing coun-tries including India In order tomitigate these two problemsthe designers resort to high-rise buildings which are rapidlyincreasing in number with various architectural configura-tions and ingenious use of structural materials Howeverearthquakes are the most critical loading condition for allland based structures located in the seismically active regionsThe Indian subcontinent is divided into different seismiczones as indicated by IS 1893 (Part 1) [1] facilitating thedesigner to provide adequate protection against earthquakeA recent earthquake in India on January 26th 2001 causedconsiderable damage to a large number of RCC high-risebuildings (number of storey varies from 4 to 15) and tremen-dous loss of life The reasons were (a) most of the buildingshad soft andweak ground storey that provided open space forparking (b) poor quality of concrete in columns and (c) poordetailing of the structural design (httpwwwniceeorgeqe-iitkuploadsEQR Bhujpdf) Therefore this particular inci-dent has shown that designers and structural engineers

should ensure to offer adequate earthquake resistant provi-sions with regard to planning design and detailing in high-rise buildings to withstand the effect of an earthquake tominimize disaster

As an earthquake resistant system the use of coupledshear walls is one of the potential options in comparisonwith moment resistant frame (MRF) and shear wall framecombination systems in RCC high-rise buildings MRF sys-tem and shear wall frame combination system are controlledby both shear behavior and flexural behavior whereas thebehavior of coupled shearwalls system is governed by flexuralbehavior However the behavior of the conventional beamboth in MRF and shear wall frame combination systemsis governed by flexural capacity and the behavior of thecoupling beam in coupled shear walls is governed by shearcapacity During earthquake infilled brick masonry cracksin a brittle manner although earthquake energy dissipatesthrough both inelastic yielding in beams and columns forMRF and shear wall frame combination systems whereasin coupled shear walls earthquake energy dissipates throughinelastic yielding in the coupling beams and at the base ofthe shear walls Hence amount of dissipation of earthquake

2 ISRN Civil Engineering

energy and ductility obtained from both MRF and shearwall frame combination systems are less than those ofcoupled shear walls system in the high-rise buildings [2ndash11] However the Indian codes of practice governing theearthquake resistant design such as IS 1893 (Part 1) [1] andIS 4326 [12] do not provide specific guidelines with regardto earthquake resistant design of coupled shear walls On theother hand IS 13920 [13] gives credence to the coupled shearwalls as an earthquake resistant option but it has incorporatedvery limited design guidelines of coupling beams that areinadequate for practical applications It requires furtherinvestigations and elaborations before practical use

Further it is reasonably well established that it is uneco-nomical to design a structure considering its linear behaviorduring earthquake as is recognized by the Bureau of IndianStandards [1 12 13] currently in use Hence an alternativedesign philosophy needs to be evolved in the Indian contextto consider the postyield behavior wherein the damage stateis evaluated through deformation considerations

In the present context therefore performance-basedseismic design (PBSD) can be considered to offer significantlyimproved solutions as compared to the conventional designbased on linear response spectrum analysis Performance-based seismic design (PBSD) implies design evaluationand construction of engineered facilities whose performanceunder common and extreme loads responds to the diverseneeds and objectives of owners tenants and societies atlarge The objective of PBSD is to produce structures withpredictable seismic performance In PBSD multiple levelsof earthquake and corresponding expected performancecriteria are specified [16] This aspect emphasizes nonlinearanalyses for seismic design verification of any structure Thisprocedure gives some guidelines for estimating the possiblelocal and global damages of structures A retrofitted structurecan be evaluated with the help of PBSD Similarly economicsin the form of life-cycle cost along with construction cost ofthe structure is inherently included in PBSD [21]

On the basis of the aforesaid discussion an effort has beenmade in this paper to develop a comprehensive procedure forthe design of coupled shear walls

2 Investigation of Coupling Beam

Coupled shear walls consist of two shear walls connectedintermittently by beams along the height The behavior ofcoupled shear walls is mainly governed by the couplingbeams The coupling beams are designed for ductile inelasticbehavior in order to dissipate energy The base of theshear walls may be designed for elastic or ductile inelasticbehaviors The amount of energy dissipation depends on theyield moment capacity and plastic rotation capacity of thecoupling beams If the yield moment capacity is too highthen the coupling beams will undergo only limited rotationsand dissipate little energy On the other hand if the yieldmoment capacity is too low then the coupling beams mayundergo rotations much larger than their plastic rotationcapacitiesTherefore the coupling beams should be providedwith an optimum level of yield moment capacities Thesemoment capacities depend on the plastic rotation capacity

available in beams The geometry rotations and momentcapacities of coupling beams have been reviewed based onprevious experimental and analytical studies in this paper Ananalytical model of coupling beam has also been developedto calculate the rotations of coupling beam with diagonalreinforcement and truss reinforcement

21 Geometry of Coupling Beam The behavior of the rein-forced concrete coupling beam may be dominated by (1)shear or by (2) flexure as per ATC40 [16] FEMA273 [14] andFEMA 356 [15] Shear is dominant in coupling beams when120601 le 2 [5] or 119871119887119889119887 le 4

There are various types of reinforcements in RCC cou-pling beams described as follows

211 Conventional Reinforcement Conventional reinforce-ment consists of longitudinal flexural reinforcement andtransverse reinforcement for shear Longitudinal reinforce-ment consists of top and bottom steel parallel to the longitu-dinal axis of the beam Transverse reinforcement consists ofclosed stirrups or ties If the strength of these ties 1198811199041 ge 34

required shear strength of the beam and the spacing these tiesle 1198893over the entire length of the beam then stable hysteresisoccurs and such transverse reinforcement is said to beconforming to the type nowmandatory for new constructionIf the transverse reinforcement is deficient either in strengthor spacing then it leads to pinched hysteresis and suchreinforcement is said to be nonconforming [14ndash16]

According to IS 13920 [13] the spacing of transversereinforcement over a length of 2119889 at either end of a beam shallnot exceed (a)1198894 and (b) 8 times the diameter of the smallestlongitudinal bar however it need not be less than 100mmElsewhere the beam shall have transverse reinforcement ata spacing not exceeding 1198892 Whereas the shear force to beresisted by the transverse reinforcement shall be the maxi-mum of (1) calculated factored shear force as per analysis and(2) shear force due to formation of plastic hinges at both endsof the beam plus the factored gravity load on the span

212 Diagonal Reinforcement Diagonal reinforcement con-sists of minimum four bars per diagonal It gives a betterplastic rotation capacity compared to conventional couplingbeam during an earthquake when 119871119887119889119887 lt 15 as per Penelisand Kappos [5] The provisions for diagonal reinforcementaccording to different codes have already been shown inTable 1 If the diagonal reinforcement is subjected to compres-sive loading itmay buckle in which case it cannot be relied onto continue resisting compressive loading Under the actionof reversing loads reinforcement that buckles in compressionwith loading in one direction may be stressed in tensionwith loading in the opposite direction This action maylead to low-cycle fatigue failure so that the reinforcementcannot continue to resist tensile forces For this reasonit is necessary to ensure that this reinforcement does notbuckle To prevent buckling due to compressive loading thespacing between two adjacent diagonal bars should be greaterthan (11987111988912) [based on buckling condition of a column]It has also been noticed from Englekirk [3] that diagonal

ISRN Civil Engineering 3

Table 1 Rotation capacities for coupling beams controlled by flexure as per FEMA 273 [14] and FEMA 356 [15]

Type of coupling beam Conditions Plastic Rotation Capacity (Radians)Shear119905119908119871119908radic1198911015840119888 IO LS CP

Conventional longitudinal reinforcement withconforming transverse reinforcement

le3 0006 0015 0025ge6 0005 0010 0015

Conventional longitudinal reinforcement withnon-conforming transverse reinforcement

le3 0006 0012 0020ge6 0005 0008 0010

Diagonal Reinforcement NA 0006 0018 0030

Flexure dominant steel coupling beam1198871198912119905119891 le 52radic119865119910 and ℎ1199051199081015840 le 418radic119865119910 1120579119910 6120579119910 8120579119910

1198871198912119905119891 ge 65radic119865119910 and ℎ1199051199081015840 ge 640radic119865119910 025120579119910 2120579119910 3120579119910

reinforcement should not be attempted in walls that are lessthan 16 in (4064mm) thick Unless strength is an overridingconsideration diagonally reinforced coupling beams shouldnot be used

213 Truss Reinforcement Truss reinforcement represents asignificant and promising departure from traditional cou-pling beam reinforcementsThe primary load transfer mech-anism of the system is represented by the truss taken to itsyield capacity A secondary load path is created by the globalstrut and tie The load transfer limit state will coincide withthe yielding of all of the tension diagonals provided the so-produced compression loads do not exceed the capacity ofthe concrete compression strut The yield strength of theprimary truss is governed by the tensile strength of its diag-onal whereas the primary truss transfer mechanism mustinclude the shear travelling along the compression diagonalAccording to Penelis and Kappos [5] and Galano and Vignoli[17] when 15 le 119871119887119889119887 le 4 truss reinforcement offersbest seismic performance in comparison with conventionaland diagonal reinforcements This type of reinforcement hasnot been used till now Detailing and placement problemsmust be carefully studied if their use is contemplated Clearlyadditional experimentation is required because the systemappears to have merit especially in thin walls [3]

When the postyield rotational level is much highercompared to rotational level for truss reinforcement thensteel beam can be provided as a coupling beamThere are twotypes of steel beams which are provided as coupling beamsbased on the following factors as per Englekirk [3] AISC [26]AISC [27] and AISC [28]

(a) Shear Dominant In this beam the shear capacity 119881119904119901 isattained and the corresponding bending moment is equalto 119881119904119901 times 1198902 which must be less than 08119872119901 The postyielddeformation is accommodated by shear and it is presumed119890 le 16119872119901119881119904119901 where e = clear span of the coupling beam +2 times concrete cover of shear wall 119872119901 = moment capacity ofcoupling beam and 119881119904119901 = shear capacity of coupling beam

(b) Flexure Dominant In this beam the bending momentcapacity119872119901 is attained and the corresponding shear force isequal to 2119872119901119890which must be less than 08119881119904119901 The postyielddeformation is accommodated by flexure and it is presumed119890 ge 26119872119901119881119904119901

22 Moment Capacity of Coupling Beam The bendingmoment capacity of coupling beam depends on the geometryand material property of coupling beam Bending momentcapacity and shear force capacity of the coupling beam arerelated with each other Englekirk [3] Park and Paulay [4]Paulay [29] Harries et al [30] AISC [26] AISC [27] andAISC [28] describe these capacities as follows

221 Reinforced Concrete Coupling Beam Shear capacityof coupling beam with conventional reinforcement can becalculated as

119881119904119901 =

2119872119901

119871119887

=

2119860 119904119891119910 (119889 minus 1198891015840)

119871119887

(1)

Whereas shear capacity of coupling beam with diagonalreinforcement can be calculated as

119881119904119901 = 119881119891 + 1198811198891

=

2119872119901

119871119887

+ 21198791 sin 120579

=

2119860 119904119891119910 (119889 minus 1198891015840)

119871119887

+

411986010158401015840

119904119891119910 ((1198891198872) minus 119889

1015840)

119871119889

(2)

and shear capacity of coupling beamwith truss reinforcementis as

119881119904119901 = 21198811 + 1198812

= 2119879119889 (119889 minus 1198891015840

1198711198891

) + 21198791015840(119889 minus 1198891015840

1198711198892

)

=

211986010158401015840

119904119891119910 (119889 minus 119889

1015840)

1198711198891

+

2 (119860 119904 minus 11986010158401015840

119904) 119891119910 (119889 minus 119889

1015840)

1198711198892

(3)

where 1198711198891 = radic(1198711198872)2+ (119889 minus 119889

1015840)2 and 1198711198892 =

radic(119871119887)2+ (119889 minus 119889

1015840)2 All three shear capacities must

be less than equal to [(0351198911015840

119888119887119887119908(119889 minus 119889

1015840)1198711198891205820] or

[(0351198911015840

119888119887119887(025119871119889)(119889 minus 119889

1015840)1198711198891205820] or [(008119891

1015840

119888119887119887(119889 minus 119889

1015840)1205820]


Table 2 Rotation capacities for coupling beams controlled by shear as per FEMA 273 [14] and FEMA 356 [15]



le3 0006 0012 0015ge6 0004 0008 0010


le3 0006 0008 0010ge6 0004 0006 0007

Shear dominant steel coupling beam 0005 011 014

Table 3 Rotation capacities for coupling beams controlled by flexure as per ATC 40 [16]

Type of coupling beam Conditions Plastic Rotation Capacity (Radians)Shear119887

119908119889radic1198911015840

119888IO LS CP


le3 0006 0015 0025ge6 0005 0010 0015


le3 0006 0012 0020ge6 0005 0008 0010

Diagonal reinforcement NA 0006 0018 0030

which is based on the statement that is capacity of a concretestrut in cylindrical elements will diminish to a level of 30 to35 of 1198911015840

119888as cracking increases where 1205820 is member over

strength factor of 125

222 Shear Dominant Steel Coupling Beam For I-sectiontype of steel coupling beam shear capacity (permissible shearresisted by web only) for shear dominant steel coupling beamis denoted as 119881119904119901 = 061198651199101199051199081015840(119863 minus 2119905119891) and moment capacityis119872119901 = 119885119901119865119910 where 119865119910 is yield stress of structural steel 1199051199081015840is web thickness 119863 is the overall depth of the section 119905119891 isflange thickness and 119885119901 is plastic section modulus

223 Flexure Dominant Steel Coupling Beam The transfer-able shear force (119881119899119891) for flexure dominant steel couplingbeam is the lesser of 2119872119901119890 and119881119904119901 where119872119901 is themomentcapacity which is 119885119901119865119910

23 Rotational Capacity of Coupling Beam The rotationcapacity in coupling beams depends upon the type of cou-pling beam When the rotational demand is greater thanrotational capacity of RCC coupling beam with conventionalflexural and shear reinforcement then diagonal or trussreinforcement type of coupling beam could be provideddepending on the 119871119887119889119887 ratio The steel coupling beam couldbe used when the rotational limit due to lateral loadingexceeds the rotation capacity of RCC coupling beam withtruss reinforcement Various research works conducted byPaulay [31 32] Hindi and Sexsmith [33] FEMA356 [15]Xuan et al [34] describe these capacities ATC 40 [16] FEMA273 [14] FEMA 356 [15] Galano and Vignoli [17] Chao etal [35] and Englekirk [3] describe the following rotationalcapacities for various types of coupling beams considering thebehavior controlled by flexure and shear during earthquake

Tables 1 2 3 4 5 and 6 show these different rotationalcapacities for various coupling beams

Shear119905119908119871119908radic1198911015840119888 or Shear119887119908119889radic1198911015840119888 le 3 or ge 6 is basedon the aspect ratio (119871119887119889119887) of coupling beam and 1198871198912119905119891 le52radic119865119910 and ℎ1199051199081015840 le 418radic119865119910 or 1198871198912119905119891 ge 65radic119865119910 and

ℎ1199051015840

119908ge 640radic119865119910 are the conditions of the flexure dominant

steel coupling beam to prevent local bucklingSpecifications in Tables 1 2 3 and 4 can be questioned on

the basis of the following observations

(1) As per Tables 1 and 2 the rotational capacities of beamdepends on size of wall (119905119908 119871119908) which is illogical

(2) When shear span to depth ratio 120601 le 2 or aspect ratio119871119887119889119887 le 4 the behavior of RCC coupling beams iscontrolled by shear For this reason as aspect ratio(119871119887119889119887) of diagonally reinforced beam is less than15 it means that the behavior of diagonally rein-forced beam is controlled by shear Whereas Tables1 and 3 show that diagonally reinforced couplingbeam behavior is controlled by flexure which is notacceptable

(3) Conventional longitudinal reinforcement with non-conforming transverse reinforcement is not acceptedfor new construction

(4) If the behavior of coupling beam is controlled byflexure [aspect ratio (119871119887119889119887) is greater than 4] thelength of the coupling beam is quite larger Accordingto Munshi and Ghosh [36] weakly coupled shearwalls can be obtained for larger span of the cou-pling beam and the design results of this type ofcoupled shear walls are inconsistent with regard to theductility and energy dissipation during earthquakemotion Hence it can be said that rotational capacity


Table 4 Rotation capacities for coupling beams controlled by shear as per ATC 40 [16]



le3 0006 0012 0015ge6 0004 0008 0010


le3 0006 0008 0010ge6 0004 0006 0007

Table 5 Rotation capacities for coupling beams as per Galano and Vignoli [17]

Type of coupling beam Aspect ratio Rotation Capacity (Radians)119871119887119889119887 120579Lu

Conventional reinforcement 15 0051Diagonal reinforcement 15 0062Truss reinforcement 15 0084

of coupling beams controlled by flexure as per ATC40 [16] FEMA 273 [14] and FEMA 356 [15] cannotbe accepted

Similarly specifications in Tables 5 and 6 can also be ques-tioned on the basis of following observation

For aspect ratio 119871119887119889119887 = 15 Galano and Vignoli [17]show different results regarding the ultimate rotation ofvarious RCC coupling beams in comparison with the resultsmade by Englekirk [3]

24 Analytical Program The above study shows the incon-sistent modeling parameters and inconsistent evaluativeparameters However the behavior of coupled shear walls iscontrolled by the characteristics of various coupling beamsThese characteristics depend on the following parameters

(1) Beam span to depth ratio(2) Reinforcement details

For this reason more study is required to investigate into thelimitations on behavior of coupling beams Since computerprogramme ATENA2D [18] has some advantages in com-parison with other software packages like SAP V 1005 [23]ATENA2D [18] was considered to carry out this study Theadvantages as well as disadvantage of ATENA2D [18] are asfollows

25 Advantages of ATENA2D Are

(i) Material element and reinforcement can bemodeledindividually and

(ii) Geometric andmaterial nonlinearity can be provided

26 Disadvantage of ATENA2D Is

(i) Only static loading in one direction can be applied

27 Reinforcement Layouts There were eighteen RCC cou-pling beams and three different reinforcement layouts con-sidered in the analytical program using ATENA2D [18] (a)

longitudinal with conforming transverse ties (b) diagonalwith conforming transverse ties around themain bars and (c)truss with conforming transverse ties around the main barsFor each layout the cross section of the coupling beam wasconsidered as 600mm (depth 119889119887) times 300mm (width 119887119887) andthe beam span-depth ratio (119871119887119889119887) was considered as 1 15and 2

28 Materials The concrete (M20 grade) and steel (Fe 415grade) were considered as twomaterials tomodel the coupledshear walls The Poissonrsquos ratio was considered as 02 Theunit-weight of concrete was considered as 23 kNm3 andthe unit-weight of steel was considered as 785 kNm3 Bothcoupling beam and shear wall elements were assigned as 4-noded quadrilateral elements material in coupling beamwasassigned as SBeta (inelastic) whereas material in shear wallwas assigned as plane stress elastic isotropic

29 Investigative Model Figure 1 and Table 7 describe theinvestigative models considered for ATENA2D [18] analysisThe behaviors of all eighteen coupling beams were governedby shearThe load (F) was calculated based on the shear forcein beam and other parameters according to the provisions ofFEMA 273 [14] and FEMA 356 [15]

The depth of the wall is considered as 119871119908 = 4m thicknessof the wall is considered as 119905119908 = 300mm and minimumreinforcement in the shear wall is taken as 025 of its grossarea 450 cc

Here Youngrsquos modulus for concrete in beam = 119864119888119887 =

224 times 104MPa Youngrsquos modulus for steel in beam = 119864119904119887 =

21 times 105MPa Youngrsquos modulus for concrete in wall = 119864119888119908 =

224times104MPa and Youngrsquos modulus for steel in wall = 119864119904119908 =

21 times 105MPa

210 Results and Discussions The results using ATENA2D[18] have been tabulated in Table 8 It shows the comparisonof rotational limit at CP level among FEMA 273 [14] FEMA356 [15] and ATENA2D [18] There are a lot of differencesamong the results of FEMA 273 [14] FEMA 356 [15] andATENA2D [18] The comparison has also been extended


Table 6 Rotation capacities for coupling beams as per Englekirk [3]

Type of coupling beam Aspect ratio Rotation Capacity (Radians)119871119887119889119887 120579119906max


Table 7 (a) investigative model of coupling beam in ATENA2D [18] as per IS 13920 [13] IS 456 [19] SP-16 [20] FEMA 273 [14] and FEMA356 [15] (b) investigative model of coupling beam in ATENA2D [18] as per IS 13920 [13] IS 456 [19] SP-16 [20] FEMA 273 [14] and FEMA356 [15] (c) investigative model of coupling beam in ATENA2D [18] as per IS 13920 [13] IS 456 [19] SP-16 [20] FEMA 273 [14] and FEMA356 [15]

(a)

Coupling beam

Type 119871119887 (m) Shear119905119908119871119908radic1198911015840119888 119865 (kN) Reinforced steelLongitudinal Transverse

Conventional beam with longitudinal andtransverse conforming reinforcement

06 le3 5854 8ndash10120601 2-legged 16120601200 ccge6 1171 8ndash20120601 2-legged 25120601200 cc


12 le3 6617 8ndash10120601 2-legged 16120601200 ccge6 1323 8ndash20120601 2-legged 25120601200 cc(b)

Coupling beam


Beam with diagonal reinforcement

06 le3 5854 8ndash10120601 + 4ndash20120601 as one diagonal 2-legged 16120601200 ccge6 1171 8ndash20120601 + 4ndash30120601 as one diagonal 2-legged 25120601200 cc



(c)

Beam


Beam with truss reinforcement

06 le3 5854 8ndash10120601 + 4ndash30120601 as one truss 2-legged 16120601200 ccge6 1171 8ndash20120601 + 4ndash45120601 as one truss 2-legged 25120601200 cc



for considering ATC 40rsquos [16] provisions There are also bigdifferences between the results of ATC40 [16] andATENA2D[18] shown in Table 9 It may be because of the limitations ofATENA2D [18] software However it is unexpected in FEMA273 [14] FEMA 356 [15] and ATC 40 [16] that the rotationallimit ismore or less samewhereas the parameters consideredfor calculation of shear strength are different Therefore itcan be said that the parameters given in FEMA 273 [14]FEMA 356 [15] and ATC 40 [16] are questionable which

have already been discussed in this paper It has also beenobserved from Tables 8 and 9 that crack width in beam isquite significant although the rotational values in ATENA2D[18] are unexpectedly varyingwith FEMA273 [14] FEMA356[15] and ATC 40 [16]

Hence the results obtained from the above study usingATENA2D [18] were found unsatisfactory Therefore a newmodel has been created with some assumptions in themanner shown in Figure 2 to carryout further study


where V is shear force in the beam

WallBeam

F

F

Lw LwLb

hs = 3mV =

F times Lw

Lw + Lb

Figure 1 Initial sketch of the analytical model

db2

times 120579b

db2

times 120579b

Lb

db

Figure 2 Schematic diagram of coupling beam

211 Assumptions

(i) The effect of gravity loads on the coupling beams hasbeen neglected

(ii) Deflection of the coupling beam occurs due to lateralloading

(iii) Contra flexure occurs at the mid-span of the couplingbeam

(iv) The confined concrete due to the confining action isprovided by closely spaced transverse reinforcementin concrete is assumed to govern the strength

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

Δ119871119887 = 119889119887 times 120579119887 (4)

and strain in the concrete

120576119888 =Δ119871119887

119871119887

(5)

Hence considering (4) and (5) the following equation can bewritten as

coupling beam rotation 120579119887 =120576119888 times 119871119887

119889119887

(6)

The results considering (6) withmaximum strain in confinedconcrete (120576cu) of 002 (Confining action is provided by closelyspaced transverse reinforcement in concrete as per ATC 40[16]) have been tabulated in Table 10

It can be observed from Table 10 that the values obtainedas per (6) have similar trend with the values specified by ATC40 [16] FEMA 273 [14] FEMA 356 [15] Galano and Vignoli[17] and Englekirk [3]

Based on the above study Table 11 has been preparedcontaining modified parameters governing the couplingbeam characteristics which are also considered for thedevelopments of the design technique discussed below Asdesign technique is based on collapse prevention (CP) levelof structure plastic rotation capacity given in Table 11 is forCP level only

3 Proposed Design Technique

In this paper an attempt has beenmade to develop a techniqueto design coupled shear walls considering its ideal seismicbehavior (stable hysteresis with high earthquake energy dis-sipation) For preparing this design technique symmetricalcoupled shear walls have been considered Designcapacitycurve of coupled shear walls is obtained at the collapsemechanism of the structure based on this technique Thistechnique is applied to both fixed base and pinned basecoupled shear walls To start with this technique is useful inselecting the preliminary dimensions of symmetrical coupledshear walls and subsequently arrives at a final design stageFurther this technique is particularly useful for designerconsultant and practicing engineer who have no access tosophisticated software packages A case study has been doneimplementing the technique with the help of Microsoft ExcelSpreadsheet and the results have also been validated

31 Proposed Formulation In Figure 3 the coupled shearwalls are subjected to a triangular variation of loading withamplitude 1198651 at the roof level The value of 1198651 is obtainedcorresponding to the CP level of structure Subsequently thebase shear and roof displacement can be determined Theprocedure involving Figure 3 the assumptions steps andmathematical calculation with initial value of1198651 as unity havebeen illustrated as in Figure 3


Table8Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

FEMA273[14

]and

FEMA356[15]

Long

itudinalreinforcementand

transverse

reinforcem

ent

Shear119905119908119871119908radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

berc

ontro

lled

byflexu

reMem

berc

ontro

lled

byshear

ATEN

A2D

[18]

FEMA

273[14

]FE

MA

356[15]

FEMA

273[14

]FE

MA

356[15]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon

gitudinalreinforcement

with

conformingtransverse

reinforcem

ent

le3

0025

0025

0015

0020

000

0881

000104

0002325

000

0263

000

0306

000

0559

ge6

0015

002

0010

0016

000348

000528

000886

000

07125

0001726

0003124

Diagonal

le3

003

003

mdashmdash

000235

0011

00111

000

0494

000

4315

000372

ge6

003

003

mdashmdash

000292

000833

000

978

000

05724

0002961

0003228

Truss

le3

NA

NA

NA

NA

000117

6000

0422

000

093

000

03144

000

0106

6000

0204

ge6

NA

NA

NA

NA

0001413

000297

00029

000

0344

000

07514

000

066


Table9Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

ATC40

[16]

Long


transverse

reinforcem

ent

Shear119887119908119889radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

ber

controlled

byflexu

re

Mem

ber

controlled

byshear

ATEN

A2D

[18]

ATC40

[16]

ATC40

[16]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0018

000

01023

000

0784

000198

000

00001308

000

050001613

ge6

0015

0012

000

02423

0001944

000344

000163

000136

000297

Diagonal

le3

003

mdash000

012

000

0416

000

055

000

00194

000

02184

000

021

ge6

003

mdash000

0415

000

0422

0001533

000

01795

000

01483

000

093


Wall 2

Wall 1

F1

F1 times (H minus hs)H

F1 times (H minus 2hs)H




F1 times (H minus (N minus 3i)hs)H


F1 times (H minus (N minus i)hs)H

I A

I A

db

hs

H

i

Lw LwLb

(a)

l

Mid-point of Lb

CL of wall 1 CL of wall 2120572F1 V

V

V

V

V

V

V

V

V

120573F1

Wg

Wg

H

x

MMVw Vw

B

T C = T

A

(b)

Figure 3 (a) Coupled shear walls (b) Free body diagram of coupled shear walls

Table 10 Maximum rotations in radians

Type ofreinforcement 119871119887119889119887 Value as per (6) Galano and

Vignoli [17] Englekirk [3]ATC40 [16] FEMA273 [14] and FEMA

356 [15]Diagonal lt15 lt003 0062 004 003Truss 15 to 40 003 to 008 0084 006 mdash

32 Assumptions The following assumptions are adopted forthe design technique to obtain the ideal seismic behavior ofcoupled shear walls

(1) The analytical model of coupled shear walls is takenas two-dimensional 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 eachcorresponding point of wall 2 due to the presence ofcoupling 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(9) The seismic design philosophy requires formation of

plastic hinges at the ends of the coupling beamsAll coupling beams are typically designed identicallywith identical plasticmoment capacities Being lightlyloaded under gravity loads they will carry equal shear

forces before a collapse mechanism is formed Allcoupling beams are therefore assumed to carry equalshear forces

(10) In the collapse mechanism for coupled shear wallsplastic hinges are assumed to form at the base of thewall and at the two ends of each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base of the wall If the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs This is assumed to be thedistribution displacementvelocityacceleration alongthe height The acceleration times the massweightat any floor level gives the lateral load Hence thedistribution of the lateral loading is assumed as atriangular variation which conforms to the firstmodeshape pattern

33 Steps The following iterative steps are developed in thisthesis for the design of coupled shear walls

(1) Selection of a particular type of coupling beam anddetermining its shear capacity

(2) Determining the fractions of total lateral loadingsubjected on wall 1 and wall 2

(3) Determining shear forces developed in couplingbeams for different base conditions


Table 11 Modified parameters governing the coupling beam characteristics controlled by shear

Type of couplingbeam Shear span to depth ratio 119871119887119889119887 Type of detailing Plastic Rotation Capacity (Radians)

Shear119887119908119889radic1198911015840119888 CP

Reinforced concretecoupling beam 120601 le 2

No limit Conventional longitudinal reinforcementwith conforming transverse reinforcement

le3 0015ge6 0010

lt15Diagonal Reinforcement (strength is anoverriding consideration and thickness ofwall should be greater than 4064mm)

mdash lt003

15 to 40 Truss Reinforcement (additionalexperimentation is required) mdash 003ndash008

Steel coupling beam 119890 le 16119872119901119881119904119901 Shear dominant mdash 015119871119887

(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 thebase this check is not required

(6) Calculating coupling beam rotation in each storey(7) Checking whether coupling beam rotation lies at

collapse prevention level(8) Calculating base shear and roof displacement(9) Modifying the value of 1198651 for next iteration starting

from Step (2) if Step (7) is not satisfied

34Mathematical Calculation Thestepswhich are describedabove have been illustrated in this section as follows

Step 1 The type of coupling beam can be determined asper Table 11 and shear capacity can be calculated as perSection 22

Step 2 In Figure 3(b) free body diagram of coupled shearwalls has been shown 120572 and 120573 are fractions of total lateralloading incident on wall 1 and wall 2 respectively such that

120572 + 120573 = 10 (7)

For symmetrical coupled shear walls moments of inertiasof two walls are equal for equal depths and thicknesses atany level Further curvatures of two walls are equal at anylevel Hence based on the Assumption (7) equation (7) canbe written as

120572 = 120573 = 05 (8)

Step 3 In this step it is explained how to calculate the shearforce developed in the coupling beams for different typesof boundary conditions CSA [25] and Chaallal et al [37]defined the degree of coupling which is written as

DC =119879 times 119897

119872ot (9)

where 119897 = 119871119908 + 119871119887 119879 is the axial force due to lateral loadingand 119872ot is total overturning moment at the base of the wallproduced due to lateral loading For fixed base condition DCvaries from 0 to 1 and (9) can also be written as

DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)

Table 12 Values of constant 1198961015840 and exponents 119886 119887 and 119888

119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059

The above equation (10) is proposed by Chaallal et al [37]119873is the total number of storeys 1198961015840 is constant and 119886 119887 and 119888are exponents which are given in Table 12So based upon the above criteria and considering (9) and(10) shear force developed in the coupling beam could bedetermined as follows

For fixed base condition following equation can bewritten as

119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)

where119872ot is total overturningmoment at the base due to thelateral loading

Therefore based on the Assumption (9) shear force incoupling beam at each storey is

119881 =sum119873

119894=1119881119894

119873 (12)

Pinned Base Condition In this study pinned base condi-tion has been introduced as one of the possible boundaryconditions for coupled shear walls It can be constructedby designing the foundation for axial load and shear forcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained for considering this kind of base condition

DC is 1 for pinned base condition from (9) Hence theequation can be written as

119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)

Step 4 After obtaining 120572 120573 and 119881 at each storey for theparticular value of 1198651 bending moment values in each storeycould be determined for each wall Subsequently curvaturediagram for each wall is generated by using moment areamethod as adopted in the Microsoft excel spreadsheet whichis required to determine the wall rotation in each storeyThe following equations are considered to calculate the wallrotation

Overturning moment at a distance ldquo119909rdquo from base withrespect to each wall can be written as

119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651

119867(119867 minus 119895ℎ119904) (119867 minus 119909 minus 119895ℎ119904) (15)

where 119894 is storey number and it is considered from the baseas 0 1 2 3 119873

Resisting moment in wall due to shear force in thecoupling beam at a distance ldquo119909rdquo from base can be written as

119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)

where net moment in the wall at a distance ldquo119909rdquo from basegenerated due to overturning moment and moment due toshear force in the coupling beam can be written as

119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)

Wall rotation at 119894th storey for fixed base can be written as

120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)

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

120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)

where 1205791199080 is the plastic hinge rotation at the fixed base of wallor rotation at the pinned base of wall

Step 5 Consider (i) Tensile forces at the base of wall 1 (119879)as well as compressive forces at the base of wall 2 (119862) arecalculated due to lateral loading

(ii) Compressive loads at the bases of wall 1 and wall 2 arecalculated due to gravity loading

Lw Lb Lw

120579wi

120579wi120579bi

Lb

2

Figure 4 Deformed shape of a 119894th storey symmetrical coupled shearwalls

(iii) Net axial forces at the bases of wall 1 and wall 2 arecalculated that is Net axial force = Tensile or Compressiveforce due to lateral loading (119879 or 119862) plusmn Compressive load dueto gravity loading

(iv) Then according to these net axial forces for theparticular values of 119891119888119896 119887119887 119889 and 119901 the yield moment valuesat the bases of wall 1 and wall 2 can be determined from119875-119872 interaction curve [2 19] Where 119891119888119896 119887119887 119889 and 119901 areyield strength of concrete breadth of a section depth of thatsection and percentage of minimum reinforcement in thatparticular section respectively and 119875 is the axial force and119872 is the moment here net axial force is considered as 119875 inthe 119875-119872 interaction curve

(v) Therefore if calculated bending moment value at anybase of the two walls is greater than yield moment valueplastic hinge at that base would be formed otherwise noplastic hinge would be formed

Step 6 The rotation of coupling beam in each storey isdetermined in Figure 4

Rotation of coupling beam at 119894th storey for symmetricalwalls [3] as per Figure 4 is given by

120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)

where 120579119908119894 is rotation of wall at 119894th storey and can becalculated as per (18) 119871119908 = depth of wall 119871119887 = length ofcoupling beam

For plastic hinge rotation at the fixed base of wall or realhinge rotation at the pinned base of wall (21) could bewrittenas

120579119887119894 = 119871119908119887 120579119908119894 (22)

where 120579119908119894 can be calculated as per (20) for fixed base of wallor for pinned base of wall and

119871119908119887 = (1 +119871119908

119871119887

) (23)

Step 7 The rotational limit for collapse prevention level ofdifferent types of RCC coupling beams and steel beams aregiven in Table 11 The task was to check whether the rotationsof beams attained their rotational limit of CP level at thecollapse mechanism of the structure simultaneously


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)

Figure 5 (a) Plan view of building (b) Coupled shear walls at section ldquoa-ardquo

Step 8 The roof displacement can be calculated as per thefollowing equations

Δ roof = ℎ119904 times (

119873

sum

119894=0

120579119908119894) (24)

where displacement at 119894th storey can be calculated as

Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)

The base shear can be calculated as follows

119881119861 =1198651 times (119873 + 1)

2 (26)

Step 9 The 1198651 is modified as follows when the condition ofStep 7 is not satisfied

To obtain the collapse mechanism of the structure itis required to increase 1198651 with equal increment until allcoupling beams attain their rotation limit of CP level simul-taneously

35 Validation of the Proposed Design Technique The follow-ing numerical example has been considered to validate thepropose design technique In this study plan and elevationwith dimensions andmaterial properties of the coupled shearwalls have been adopted as given in Chaallal et al [37]

36 Numerical Example The coupled shear walls consideredhere are part of a 20-storey office building (Figure 5) Itis subjected to triangular variation of lateral loading Thedimension and material properties are tabulated in Table 13Dead loads and live loads are discussed in the following sec-tion A comparison of the results regarding designcapacitycurve (Figure 7) and ductility (27) obtained from the pro-posed design technique with the results obtained in SAPV 1005 [23] and DRAIN-3DX [22] software packages maythus be required For obtaining more perfection about theresults these two softwares have been considered in Table 13simultaneously

Figures 5(a) and 5(b) show the plan and sectional eleva-tion of the coupled shear wall building respectively

Table 13Dimensions andmaterial properties of coupled shearwallsfor validation of proposed design technique

Depth of the wall (119871119908) 4mLength of coupling beam (119871119887) 18mDepth of coupling beam (119889119887) 600mmNumber of storeys (119873) 20Wall thickness (119905

119908) 300mm

Width of coupling beam (119887119887) 300mmStorey height (ℎ119904) 30mModulus of concrete (119864119888) 270GPaModulus of steel (119864119904) 2000GPaSteel yield strength (119891119910) 415Mpa

361 Loading Consideration Dead loads (DL) of 67 kNm2and live loads (LL) of 24 kNm2 have been considered assuggested in Chaallal et al [37] Total gravity loading oncoupled shear walls at section ldquoa-ardquo has been calculated as thesum of dead load plus 25 LL as per IS 1893 (part 1) [1] forfloor however in case of roof only dead load is considered

362 Modeling of Coupled Shear Walls in Proposed DesignTechnique The modeling of coupled shear walls involvingFigure 3 assumptions and steps with mathematical calcula-tion are already described in Section 31

363 Modeling of Coupled Shear Walls in SAP and DRAIN-3DX Wide column frame analogy [38] has been consideredfor modeling of coupled shear walls in SAP V 1005 [23]and DRAIN-3DX [22] as given in Figure 6 In this analogyshear walls are represented as two line elements (centre lineof shear wall) and beams are represented as line elements(centre line of beam) by joining with each other with rigidlink Beam column elastic element (Type-17) and inelasticelement (Type-15) are considered for modeling

364 Calculation of Ductility The obtained designcapacitycurve from the proposed design technique SAP V 1005[23] and DRAIN-3DX [22] is bilinearized The bilinear


Coupling beam

Rigid link

05Lw Lb 05Lw

Figure 6 Modeling in SAP V 1005 [23] and DRAIN-3DX [22]

Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2

Δ roofyield Δ roofCP

Figure 7 Bilinear representation for Capacity Curve

representation is prepared in the manner shown in Figure 7based on the concepts given in ATC 40 [16]

It can be seen from Figure 7 that bilinear representationcan be due to the basis of initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility of thecoupled shear walls has been calculated as

120583Δ =Δ roofCP

Δ roofyield (27)

whereΔ roofCP andΔ roofyield can be calculated from (24)120583Δ isthe ductility which represents how much earthquake energydissipates during an earthquake

37 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 5 are considered for conducting thestudy

38 RCC Coupling Beam with Conventional LongitudinalReinforcement and Conforming Transverse Reinforcement

Table 14 Ductility of coupled shear walls considering differentapproaches

Method DuctilityFixed base Pinned base

Proposed Design Technique 7 75DRAIN-3DX [22] 675 745SAP V 1005 [23] 692 747

RCC coupling beam with Conventional longitudinal rein-forcement and conforming transverse reinforcement in eachstorey has been selected as per Step 1 for the studyThe resultsof this study for fixed base as well as pinned base conditionshave been shown in Figure 8 and Table 14

381 Discussions of Numerical Results Figure 8(b) showsthat the results obtained from proposed design technique forpinned base conditions are almost similar with the resultsobtained from DRAIN-3DX [22] and SAP V 1005 [23]Whereas Figure 8(a) is showing a bit differences about theresults obtained from proposed design technique DRAIN-3DX [22] and SAP V 1005 [23] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (5ndash10) Table 14 is showing the results aboutductility obtained for fixed and pinned base conditions withthe help of the Figures 8(a) and 8(b) and Section 364 It isnoticed that ductility for pinned base condition is greater thanfixed base conditions Itmeans that stable hysteresis with highearthquake energy dissipation can be obtained for coupledshear walls with pinned base

The results obtained from the proposed design techniqueare satisfactoryHowever it is necessary to find the limitationsof the proposed design techniqueTherefore in the followingsection parametric study is elaborately discussed to detectthe limitations of the proposed design technique

4 Parametric Study

It has been observed from theCSA [25] andChaallal et al [37]that the behavior of the ductile coupled shear walls depend ondegree of coupling where degree of coupling depends upondepth and length of the coupling beam as well as depth andheight of the coupled shear walls [4 10]

Therefore this study has been restricted on length of thecoupling beam and number of stories as basic variables andother parameters are considered as constant These param-eters have been considered in proposed method to makeout effect on the behavior of coupled shear walls Furthermodifications to achieve ideal seismic behavior according tothe proposed method have been included in this study

41 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 9(a)and 9(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study


0 01 02 03

1500

1000

500

0

SAP V 1005Drain-3DXDesign technique

Roof displacement (m)

Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0

Roof displacement (m)04

Base

shea

r (kN

)

(b)

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

9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)

Figure 9 (a) Plan view of building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo

42 Loading Consideration Dead loads (DL) of 67 kNm2and live loads (LL) of 24 kNm2 have been considered asper the suggestions made by in Chaallal et al [37] Totalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum of dead load plus 25 LL as per IS1893 (part 1) [1] for floor however in case of roof only deadload is considered

43 Parameters Table 15 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study

44 Analysis Using Proposed Design Technique The abovemen-tioned building has been studied by the design tech-nique The results for different parameters have beendescribed in this section

45 Observed Behavior To study the influence of length ofthe coupling beam (119871119887) on the behavior of coupled shearwalls length of the coupling beam is considered as 1m 15m

Table 15Dimensions andmaterial properties of coupled shearwallsfor parametric study

Depth of the wall (119871119908) 4mLength of beam (119871

119887) 1m 15m and 2m

Depth of beam (119889119887) 800mmNumber of stories (119873) 10 15 and 20Wall thickness (119905119908) 300mmWidth of coupling beam (119887119887) 300mmStorey height (ℎ119904) 36mModulus of concrete (119864119888) 224GPaYield strength of steel (119891119910) 415MPa

and 2m for both fixed and pinned base conditions RCCcoupling beamwith conventional longitudinal reinforcementwith conforming transverse reinforcement has been selectedShear capacity in the coupling beam is calculated as per Step 1The rotational limit of coupling beam has been selected as perStep 7The study has been performed for coupled shear walls


with number of stories 20 15 and 10 for both fixed and pinnedbase conditions

451 For Number of Stories 119873 = 20 For more details seeFigures 10 11 12 and 13

452 Discussion of Results for 119873 = 20 The deflection forthe case of pinned base condition is much higher than thecase of fixed base (Figure 10) however the base shear for thecase of pinned base condition is lower than the case of fixedbase (Figure 13) It shows satisfactory results based on thebehavior of coupled shear walls Because coupled shear wallswith pinned base deflected more subjected to lesser lateralloading in comparisonwith the coupled shearwalls with fixedbase and base shear is directly varying with the lateral loading(26) Since wall rotation is directly varying with the lengthof the beam (Figure 11) and deflection is the summation ofthe wall rotation (25) deflection is directly varying with thelength of the beam (Figure 10) It has been also observedthat all beams reach to their rotational limit of CP level forpinned base condition however very few beams reach totheir rotational limit of CP level for fixed base condition(Figure 12) Hence it can be said that coupled shear walls arebehaving as a rigid body motion for pinned base conditionwhich is expected The explanations for fixed base condition(Figure 12) are given in the following manner

(i) The rotation of the cantilever wall is maximum at thefree end of the wall This rotation decreases towardsthe base of the wall and is zero at the base for fixity

(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (119871119887 =

1m of Figure 11) It is also one of the behaviors ofa coupled shear walls However fixed base coupledshear walls with long span coupling beam does notshow cantilever wall (119871119887 = 15m and 119871119887 = 2m ofFigure 11) behavior

(iii) Beam rotation is proportional to the wall rotationTherefore it can be said from the above observations thatcoupled shear walls with short span coupling beam (119871119887 =1m) can be acceptable in comparison with the long spancoupling beam (119871119887 = 15m and 119871119887 = 2m) although thebehavior of all three coupling beams is governed by shearaccording to Table 11

With the help of Section 364 and Figure 13 ductility forpinned base condition and fixed base condition has beencalculated in Table 16

It has been observed from Table 16 that ductility is morefor pinned base condition in comparison with the fixed basecondition and ductility increases with increase in length ofthe coupling beam ((24) and (27) Figures 10 11 and 13)


454 Discussion of Results for 119873 = 15 With the help ofSection 364 and Figure 17 ductility for pinned base condi-tion and fixed base condition has been calculated in Table 17

Table 16 Ductility of coupled shear walls for119873 = 20

Base condition Length of the coupling beam (119871119887) Values

Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687

It has been observed from Figures 14 to 17 and Table 17that the results obtained for 119873 = 15 are similar with theresults of 119873 = 20 for fixed base condition and pinned basecondition


456 Discussion of Results for 119873 = 10 Figures 20 and21 show that beam rotation and capacity curve reach CPlevel for the case of 119871119887 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level for the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) of coupled shear walls has only beenachieved for 119871119887 = 1mwith pinned base condition Proposeddesign technique does not show ideal seismic behavior ofcoupled shear walls for 119871119887 = 1m 15m and 2m with fixedbase condition and 119871119887 = 15m and 2m with pinned basecondition Now remedial action has been considered in thefollowing manner to obtain the ideal seismic behavior

457 Remedial Action for 119873 = 10 The remedy for the casesof 119871119887 = 1m 15m and 2m with fixed base condition and119871119887 = 15m and 2m with pinned base condition to achieveCP level is mentioned in (Figures 22 23 24 and 25) To obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((18) and (19)) is inversely varying to the 1198713

119908

it is required to decrease the 119871119908 It has been observed fromFigure 25 that the ideal seismic behavior of coupled shearwalls has been achieved

458 Discussion of the Above Results Figures 24 and 25show that beam rotation and capacity curve reach CP levelfor all cases although the results are not satisfactory for


Stor

ey h

eigh

t (m

)

0 01 02 03 04Displacement (m)

Lb = 1mLb = 15mLb = 2m

0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)

Figure 10 (a) Storey displacement for fixed base condition at CP level (b) Storey displacement for pinned base condition at CP level

0

24

48

72

Stor

ey h

eigh

t (m

)

0 0002 0004 0006 0008Wall rotation (rad)


(a)

0

24

48

72St

orey

hei

ght (

m)



(b)

Figure 11 (a) Wall rotation for fixed base condition at CP level (b) Wall rotation for pinned base condition at CP level


0

24

48

72

Stor

ey h

eigh

t (m

)

0 001 002 003Beam rotation (rad)

(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)

Figure 12 (a) Beam rotation for fixed base condition at CP level (b) Beam rotation for pinned base condition at CP level



0

600

1200Ba

se sh

ear (

kN)

0 02 04Roof displacement (m)

(a)


0

375

750

Base

shea

r (kN

)

0 01 02 03 04 05Roof displacement (m)

(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)

0 028 056Displacement (m)


(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 0016 0032Beam rotation (rad)

(b)


0

500

1000

1500

2000

Base

shea

r (kN

)

0 01 02 03Roof displacement (m)


(a)

Base

shea

r (kN

)

Roof displacement (m)0 02 04

0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)

Displacement (m)0 004 008 012


(b)



0

18

36

Stor

ey h

eigh

t (m

)

0 00004 00008Wall rotation (rad)


(a)

0

18

36

Stor

ey h

eigh

t (m

)

Wall rotation (rad)0 00055 0011


(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)


ISRN Civil Engineering 21St

orey

hei

ght (

m)

0 02 04 06Displacement (m)

Lb = 1m and Lw = 2m for fixed and 4 m for pinnedLb = 15m and Lw = 3mLb = 2m and Lw = 3m

0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)


22 ISRN Civil EngineeringBa

se sh

ear (

m)

0

500

1000

0 03 06Roof displacement (rad)


(a)

Base

shea

r (m

)

Roof displacement (rad)

0

425

850

0 01 02 03


(b)


Table 18Dimensions andmaterial properties of coupled shearwallsfor nonlinear static analysis

Depth of the wall (119871119908) 4mLength of beam (119871119887) 1mDepth of beam (119889119887) 800mmNumber of stories (119873) 20 and 15Wall thickness (119905119908) 300mmWidth of coupling beam (119887119887) 300mmStorey height (ℎ119904) 36mModulus of concrete (119864119888) 224GPaModulus of steel (119864119904) 2000GPaSteel yield strength (119891119910) 415MPa

fixed base condition according to the explanations given inSection 451

Hence it can be said from the above results that proposeddesign technique is useful to design the coupled shear wallsduring earthquake motion To confirm it more nonlinearstatic analysis is considered in the following manner to assessthe proposed design technique

5 Assessment of Proposed Design TechniqueUsing Nonlinear Static Analysis

In this paper nonlinear static analysis is carried out todetermine the response reduction factors of coupled shearwalls at different earthquake levels

51 Design Example The following design example is pre-sented for carrying out the nonlinear static analysis ofcoupled shear walls These walls are subjected to triangularvariation of lateral loading The base of the walls isassumed as fixed Table 18 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 26(a) and 26(b)

show the plan and sectional elevation of the coupled shearwall building respectivelyTheplace considered for this studyis Roorkee and soil type for this place is medium (Type II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered for the study

52 Loading Consideration Dead loads (DL) of 67 kNm2and live loads (LL) of 24 kNm2 have been considered asgiven in Chaallal et al [37] Total gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum ofdead load plus 25 LL as per IS 1893 (part 1) [1] for floorhowever in case of roof only dead load is considered

53 Results and Discussions The results and discussions aredescribed in Figure 27

531 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 024 as per IS 1893 (part 1) [1] 5 damped elasticresponse spectra as per IS 1893 (part 1) [1] are consideredhere as demand curve DBE and MCE levels are consideredfor calculation of performance point (pp) Capacity curvesare already obtained in Figure 27The performance point hasbeen calculated with the help of capacity spectrummethod ofATC 40 [16] which is shown in Figure 28

In this case modal mass co-efficient 1205721 = 0616 andMode participation factor PF1 = 151 derived with the help ofmodal analysis in SAP V 1005 [23] Figure 28 shows that ppis the performance point The base shear at the performancepoint (pp) 119881bpp = 11731 kN and roof displacement at theperformance point (pp) Δ roofpp = 031m

In this casemodalmass co-efficient1205721 = 0616 andModeparticipation factor PF1 = 151 Figure 29 shows that pp isthe performance point The base shear at the performancepoint (pp) 119881bpp = 9576 kN and roof displacement at theperformance point (pp) Δ roofpp = 0097m


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)

Figure 26 (a) Plan view of building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo

0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)

0 01 02 03 04Roof displacement (m)

(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)

Figure 27 (a) Capacity curve for119873 = 20 (b) Capacity curve for119873 = 15

0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp

Straight linetangent to thecapacity curve

5 demandresponse spectra

Capacity curve

Reduced demandspectra

Figure 28 Performance point at the MCE level for119873 = 20


pp

Straight line tangent to the Capacity curve

5 demand response spectra

Capacity curve

Reduced demand response spectra

0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd

Figure 29 Performance point at the DBE level for119873 = 20

Straight line tangent to the capacity curve


Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd



Table 19 Response Reduction Factors for DBE and MCE levels

Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]

119877120583IDRS [Firstmethod of

Energy-DuctilityBased ResponseReduction] [24]

119877120583IDRS [Secondmethod of


119877119889 as per CSA[25]

119873 = 20DBE 104 1004 102 104 1004 15 or 2 for coupled

shear walls withconventionalreinforced couplingbeam

MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122



532 Calculation of Response Reduction Factor at the Per-formance Point Table 19 shows different response reductionfactors for MCE and DBE levels These are calculated atdifferent performance points (Figures 28ndash31)

FromTable 19 response reduction factor of coupled shearwalls is varying between 122 to 205 for maximum consid-ered earthquake (MCE) level which is almost same as theprovision of CSA [25] for coupling beam with conventionalreinforcement

6 Conclusions

From the above studies the following recommendations havebeen made for the design of coupled shear walls underearthquake motion

(i) Design technique should be adopted for fixing thedimensions of coupled shear walls

(ii) Coupled shear walls with 119873 ge 15 with equal storeyheight ℎ119904 = 36m can be designed with an optimumratio of 119871119887119871119908 = 025 for 119871119887119889119887 = 125 and 119868119887119868 = 8times

10minus03 to obtain consistency between the behaviorwith

respect to the wall rotation and earthquake energydissipations

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

(iv) The behavior of coupling beam should be governed byshear

Notations

119860 Area of symmetrical coupled shear walls119860119888119908 Area of concrete section of an Individual pier

horizontal wall segment or coupling beamresisting shear in in2 as per ACI 318 [39]

119860119892 Gross area of concrete section in in2 For ahollow section 119860119892 is the area of the concreteonly and does not include the area of thevoid(s) as per ACI 318 [39]

11986010158401015840

119904 Reinforcing steel in one diagonal as per

Englekirk [3]119860 119904 Area of nonprestressed tension reinforcement

as per Englekirk [3]119860 119904119889 Reinforcement along each Diagonal of

Coupling beam as per IS 13920 [13]119860V119889 Total area of reinforcement in each group of

diagonal bars in a diagonally reinforcedcoupling beam in in2 as per ACI 318 [39]

119887119887 Width of coupling beam119887119891 Flange width of I-beam as per FEMA 273 [14]

and FEMA 356 [15]119887119908 Web width of the coupling beam as per FEMA

273 [14] and FEMA 356 [15]119862 Compressive axial force at the base of wall 2CP Collapse prevention level119863 Overall depth of the steel I-coupling beam

sectionDC Degree of couplingDL Dead loadsDBE Design basis earthquake119889 Effective depth of the beam119889119887 Depth of the coupling beam1198891015840 Distance from extreme compression fiber to

centroid of compression reinforcement as perEnglekirk [3]

Δ 119887 Displacement at 119881119887Δ 119890 Elastic displacement (rArr 119881119890)Δ 119897 Displacement at limiting responseΔ roof Roof displacementΔ roofCP Roof displacement at CP levelΔ roofyield Roof displacement at yield levelΔ 119906 Displacement at ultimate strength capacityΔ 119910 Displacement at yield strength capacityΔ 119910119886

Actual displacement at 119881119910119886


119864c Modulus of elasticity of concrete119864119888119887 Youngrsquos modulus for concrete in beam119864cw Youngrsquos modulus for concrete in wallEPP Elastic-perfectly-plasticEQRD Earthquake resistant design119864119904 Modulus of elasticity of steel as per FEMA 273

[14] and FEMA 356 [15]119864119904119887 Youngrsquos modulus for steel in beam119864119904119908 Youngrsquos modulus for steel in wall119890 Clear span of the coupling beam + 2 times concrete

cover of shear wall as per Englekirk [3]120576119888 Strain in concrete119865 Force1198651 Maximum amplitude of triangular variation of

loadingFEMA Federal emergency management agency119865119906 Ultimate force119865119910 Yield stress of structural steel1198911015840

119888 Specified compressive strength of concrete

cylinder119891119888119896 Characteristic compressive strength of concrete

cube119891119910 Specified yield strength of reinforcement119867 Overall height of the coupled shear wallsℎ Distance from inside of compression flange to

inside of tension flange of I-beam as per FEMA273 [14] and FEMA 356 [15]

ℎ119904 Storey height119868 Moment of inertia of symmetrical coupled

shear walls119868119887 Moment of inertia of coupling beamIO Immediate occupancy level119894 Storey number119896 Unloading stiffness1198961 Postyield stiffness119896119890 Elastic stiffness119896119894 Initial stiffness119896sec Secant stiffness119871119887 Length of the coupling beam119871119889 Diagonal length of the memberLL live loadsLS Life safety level119871119908 Depth of coupled shear walls119897 Distance between neutral axis of the two walls1205820 Member over strength factor as per Englekirk

[3]119872 Moment of symmetrical coupled shear walls1198721 Moment at the base of the wall 11198722 Moment at the base of the wall 2MCE Maximum considered earthquakeMDOF Multi-degree of freedom119872119899 Nominal flexural strength at section in lb-in as

per ACI 318 [39]119872119901 Moment capacity of coupling beam as per

Englekirk [3]119872ot Total overturning moment due to the lateral

loadingMRF Moment resistant frame

120583 Displacement ductility capacity relied on in thedesign as per NZS 3101 [40]

120583Δ Ductility120583Δ1198901 Energy based proposal for ductility under

monotonic loading and unloading120583Δ1198902 Energy based proposal for ductility under

cyclic loading119873 Total number of storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure119875 Axial force as per IS 456 [19]PBSD Performance based seismic design119901 Percentage of minimum reinforcement120601 Shear span to depth ratiopp Performance point119877 Response reduction factorRCC Reinforced cement concrete119877119889 Ductility related force modification factor119877120583 Ductility factor119877119877 Redundancy factor119877119904 Overstrength factor119878119886 Spectral acceleration119878119889 Spectral displacementSDOF Single-degree of freedom119879 Tensile axial force at the base of wall 11198791 Tensile strength of One diagonal of a diagonal

reinforced coupling beam119879119889 Tensile strength of truss reinforced coupling

beamrsquos diagonal as per Englekirk [3]1198791015840 The residual chord strength as per Englekirk [3]

119905119891 Flange thickness of steel I-coupling beam as perEnglekirk [3]

120579 Inclination of diagonal reinforcement incoupling beam

120579119887 Coupling beam rotation120579119897119906 Rotational value at ultimate point120579119906max Maximum rotational value120579119908 Wall rotation120579119910 Yield rotation as per FEMA 273 [14] and FEMA

356 [15]119905119908 Wall thickness1199051199081015840 Web thickness of steel I-coupling beam119881 Shear force in the coupling beam1198811 The shear or vertical component of one

diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [3]

1198812 The shear in a secondary truss produced by theresidual tension reinforcement activated theload transfer mechanism as per Englekirk [3]

119881119861 Base shear119881119887 Non-factored design base shear119881119889 Factored design base shear may be less than or

greater than 119881119910119886

119881119890 Base shear for elastic response119881119897 Base shear at limiting response119881119899 Nominal shear strength in lb as per ACI 318

[39]


119881119899119891 The transferable shear force for flexuredominant steel coupling beam as per Englekirk[3]

119881119904119901 Shear capacity of coupling beam as perEnglekirk [3]

1198811199041 Shear strength of closed stirrups as per ATC 40[16] FEMA 273 [14] and FEMA 356 [15]

119881119906 Capacity corresponding to Δ 119906 (may be themaximum capacity)

1198811199061 Factored shear force as per IS 13920 [13]1198811199062 Factored shear force at section in lb as per ACI

318 [39]119881119908 Shear force at the base of the shear wall1198811199081 Shear force at the base of wall 11198811199082 Shear force at the base of wall 2119881119910 Base shear at idealized yield level119881119910119886

Actual first yield levelV119899 Total nominal shear stress in MPa as per NZS

3101 [40]119882119892 Total gravity loading for symmetrical coupled

shear walls119908 Compressive strut width as per Englekirk [3]119885 Zone factor119885119901 Plastic section modulus of steel coupling beam

References

[1] Bureau of Indian Standards ldquoCriteria for earthquake resistantdesign of structures part 1 general provisions and buildingsrdquoTech Rep IS-1893 part 1 Bureau of Indian Standards NewDelhi India 2002

[2] A K Jain Reinforced Concrete Limit State Design Nem Chandamp Bros Roorkee India 1999

[3] R E Englekirk Seismic Design of Reinforced and PrecastConcrete Buildings John Wiley New York NY USA 2003

[4] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 1975

[5] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 1997

[6] B S Smith and A Coull Tall Building Structures (Analysis andDesign) John Wiley and Sons New York NY USA 1991

[7] P J Fortney and B M Shahrooz ldquoBoundary detailing ofcoupled core wall system wall piersrdquo Advances in StructuralEngineering vol 12 no 3 pp 299ndash310 2009

[8] K A Harries and D S McNeice ldquoPerformance-based designof high-rise coupled wall systemsrdquo Structural Design of Tall andSpecial Buildings vol 15 no 3 pp 289ndash306 2006

[9] S El-Tawil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design of hybrid coupled wall systems stateof the artrdquo Journal of Structural Engineering vol 122 no 12 pp1453ndash1458 2010

[10] T Paulay and M J N Priestley Seismic Design of ReinforcedConcrete andMasonry Buildings JohnWiley amp Sons New YorkNY USA 1992

[11] F Naiem The Seismic Design Handbook Kluwer AcademicBoston Mass USA 2001

[12] Bureau of Indian Standards ldquoEarthquake resistant design andconstruction of buildingsmdashcode of practicerdquo Tech Rep IS-4326 Bureau of Indian Standards New Delhi India 1993

[13] Bureau of Indian Standards ldquoDuctile detailing of reinforcedconcrete structures subjected to seismic forcesmdashcode of prac-ticerdquo Tech Rep IS-13920 Bureau of Indian Standards NewDelhi India 1993

[14] Federal Emergency Management Agency ldquoNEHRP guidelinesfor the seismic rehabilitation of buildingsrdquo Tech Rep FEMA-273 Federal Emergency Management Agency WashingtonDC USA 1997

[15] Federal Emergency Management Agency ldquoPrestandard andcommentary for the seismic rehabilitation of buildingsrdquo TechRep FEMA-356 Federal Emergency Management AgencyWashington DC USA 2000

[16] Applied Technology Council ldquoSeismic evaluation and retrofitof concrete buildingsrdquo Tech Rep ATC-40 Applied TechnologyCouncil Redwood City Calif USA 1996 Volume I

[17] L Galano and A Vignoli ldquoSeismic behavior of short couplingbeams with different reinforcement layoutsrdquo ACI StructuralJournal vol 97 no 6 pp 876ndash885 2000

[18] ATENA2D Version 3303Nonlinear Finite Element IntegratedAnalysis Cervenka Consulting Praha Czech Republic 2006

[19] Bureau of Indian Standards ldquoPlain and reinforced concretemdashcode of practicerdquo Tech Rep IS-456 Bureau of Indian StandardsNew Delhi India 2000

[20] Bureau of Indian Standards IS-456 ldquoDesign aids for reinforcedconcreterdquo Tech Rep SP-16 Bureau of Indian Standards NewDelhi India 1978

[21] V Prakash ldquoWhither performance-based engineering inIndiardquo ISET Journal vol 41 no 1 pp 201ndash222 2004

[22] V Prakash G H Powell and S Campbell DRAIN-3DXBase Program User Guide Version 110 Structural EngineeringMechanics andMaterials Department of Civil EngineeringUCBerkeley Calif USA 1993

[23] SAP2000 Advanced 1005 Static and Dynamic Finite ElementAnalysis of Structures Computers and Structures Inc BerkeleyCalif USA 2006

[24] S M Pore Performance Based Seismic Design of Low toMediumRise RC Framed Buildings for India Department of EarthquakeEngineering IIT Roorkee Roorkee India 2007

[25] Canadian Standards Association ldquoDesign of concrete struc-tures for buildingsrdquo CSA CAN3-A23 3-M94 Canadian Stan-dards Association Rexdale Canada 1994

[26] American Institute of Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute of SteelConstruction Inc Chicago Ill USA 1997

[27] American Institute of Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 2 AmericanInstitute of Steel Construction Inc Chicago Ill USA 2000


[29] T Paulay ldquoThe design of ductile reinforced concrete structuralwalls for earthquake resistancerdquo Earthquake Spectra vol 2 no4 pp 783ndash823 1986

[30] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response of steel beams coupling concrete wallsrdquoJournal of Structural Engineering vol 119 no 12 pp 3611ndash36291993

[31] T Paulay ldquoA displacement-focused seismic design of mixedbuilding systemsrdquo Earthquake Spectra vol 18 no 4 pp 689ndash718 2002


[32] T Paulay ldquoThe displacement capacity of reinforced concretecoupled wallsrdquo Engineering Structures vol 24 no 9 pp 1165ndash1175 2002

[33] R A Hindi and R G Sexsmith ldquoA proposed damage model forRC bridge columns under cyclic loadingrdquo Earthquake Spectravol 17 no 2 pp 261ndash281 2001

[34] G Xuan B M Shahrooz K A Harries and G A RassatildquoA performance-based design approach for coupled core wallsystems with diagonally reinforced concrete coupling beamsrdquoAdvances in Structural Engineering vol 11 no 3 pp 265ndash2802008

[35] S Chao K Khandelwal and S El-Tawil ldquoDuctile web fractureinitiation in steel shear linksrdquo Journal of Structural Engineeringvol 132 no 8 pp 1192ndash1200 2006

[36] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign for coupled wall systemsrdquo Earthquake Spectra vol 16no 3 pp 621ndash642 2000

[37] O Chaallal D Gauthier and P Malenfant ldquoClassificationmethodology for coupled shear wallsrdquo Journal of StructuralEngineering vol 122 no 12 pp 1453ndash1458 1996

[38] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment of Civil Engineering GlasgowUniversity GlasgowUK 1966

[39] American Concrete Institute ldquoBuilding code requirements forreinforced concrete and commentaryrdquo Tech Rep ACI 318-05ACI 318R-05 American Concrete Institute FarmingtonHills Mich USA 2005

[40] New Zealand Standard ldquoThe design of concrete structuresrdquoTech Rep NZS 3101 (part 1) New Zealand Standard Welling-ton New Zealand 1995

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energy and ductility obtained from both MRF and shearwall frame combination systems are less than those ofcoupled shear walls system in the high-rise buildings [2ndash11] However the Indian codes of practice governing theearthquake resistant design such as IS 1893 (Part 1) [1] andIS 4326 [12] do not provide specific guidelines with regardto earthquake resistant design of coupled shear walls On theother hand IS 13920 [13] gives credence to the coupled shearwalls as an earthquake resistant option but it has incorporatedvery limited design guidelines of coupling beams that areinadequate for practical applications It requires furtherinvestigations and elaborations before practical use

Further it is reasonably well established that it is uneco-nomical to design a structure considering its linear behaviorduring earthquake as is recognized by the Bureau of IndianStandards [1 12 13] currently in use Hence an alternativedesign philosophy needs to be evolved in the Indian contextto consider the postyield behavior wherein the damage stateis evaluated through deformation considerations

In the present context therefore performance-basedseismic design (PBSD) can be considered to offer significantlyimproved solutions as compared to the conventional designbased on linear response spectrum analysis Performance-based seismic design (PBSD) implies design evaluationand construction of engineered facilities whose performanceunder common and extreme loads responds to the diverseneeds and objectives of owners tenants and societies atlarge The objective of PBSD is to produce structures withpredictable seismic performance In PBSD multiple levelsof earthquake and corresponding expected performancecriteria are specified [16] This aspect emphasizes nonlinearanalyses for seismic design verification of any structure Thisprocedure gives some guidelines for estimating the possiblelocal and global damages of structures A retrofitted structurecan be evaluated with the help of PBSD Similarly economicsin the form of life-cycle cost along with construction cost ofthe structure is inherently included in PBSD [21]

On the basis of the aforesaid discussion an effort has beenmade in this paper to develop a comprehensive procedure forthe design of coupled shear walls

2 Investigation of Coupling Beam

Coupled shear walls consist of two shear walls connectedintermittently by beams along the height The behavior ofcoupled shear walls is mainly governed by the couplingbeams The coupling beams are designed for ductile inelasticbehavior in order to dissipate energy The base of theshear walls may be designed for elastic or ductile inelasticbehaviors The amount of energy dissipation depends on theyield moment capacity and plastic rotation capacity of thecoupling beams If the yield moment capacity is too highthen the coupling beams will undergo only limited rotationsand dissipate little energy On the other hand if the yieldmoment capacity is too low then the coupling beams mayundergo rotations much larger than their plastic rotationcapacitiesTherefore the coupling beams should be providedwith an optimum level of yield moment capacities Thesemoment capacities depend on the plastic rotation capacity

available in beams The geometry rotations and momentcapacities of coupling beams have been reviewed based onprevious experimental and analytical studies in this paper Ananalytical model of coupling beam has also been developedto calculate the rotations of coupling beam with diagonalreinforcement and truss reinforcement

21 Geometry of Coupling Beam The behavior of the rein-forced concrete coupling beam may be dominated by (1)shear or by (2) flexure as per ATC40 [16] FEMA273 [14] andFEMA 356 [15] Shear is dominant in coupling beams when120601 le 2 [5] or 119871119887119889119887 le 4

There are various types of reinforcements in RCC cou-pling beams described as follows

211 Conventional Reinforcement Conventional reinforce-ment consists of longitudinal flexural reinforcement andtransverse reinforcement for shear Longitudinal reinforce-ment consists of top and bottom steel parallel to the longitu-dinal axis of the beam Transverse reinforcement consists ofclosed stirrups or ties If the strength of these ties 1198811199041 ge 34

required shear strength of the beam and the spacing these tiesle 1198893over the entire length of the beam then stable hysteresisoccurs and such transverse reinforcement is said to beconforming to the type nowmandatory for new constructionIf the transverse reinforcement is deficient either in strengthor spacing then it leads to pinched hysteresis and suchreinforcement is said to be nonconforming [14ndash16]

According to IS 13920 [13] the spacing of transversereinforcement over a length of 2119889 at either end of a beam shallnot exceed (a)1198894 and (b) 8 times the diameter of the smallestlongitudinal bar however it need not be less than 100mmElsewhere the beam shall have transverse reinforcement ata spacing not exceeding 1198892 Whereas the shear force to beresisted by the transverse reinforcement shall be the maxi-mum of (1) calculated factored shear force as per analysis and(2) shear force due to formation of plastic hinges at both endsof the beam plus the factored gravity load on the span

212 Diagonal Reinforcement Diagonal reinforcement con-sists of minimum four bars per diagonal It gives a betterplastic rotation capacity compared to conventional couplingbeam during an earthquake when 119871119887119889119887 lt 15 as per Penelisand Kappos [5] The provisions for diagonal reinforcementaccording to different codes have already been shown inTable 1 If the diagonal reinforcement is subjected to compres-sive loading itmay buckle in which case it cannot be relied onto continue resisting compressive loading Under the actionof reversing loads reinforcement that buckles in compressionwith loading in one direction may be stressed in tensionwith loading in the opposite direction This action maylead to low-cycle fatigue failure so that the reinforcementcannot continue to resist tensile forces For this reasonit is necessary to ensure that this reinforcement does notbuckle To prevent buckling due to compressive loading thespacing between two adjacent diagonal bars should be greaterthan (11987111988912) [based on buckling condition of a column]It has also been noticed from Englekirk [3] that diagonal





le3 0006 0015 0025ge6 0005 0010 0015


le3 0006 0012 0020ge6 0005 0008 0010











119881119904119901 =

2119872119901

119871119887

=

2119860 119904119891119910 (119889 minus 1198891015840)

119871119887

(1)


119881119904119901 = 119881119891 + 1198811198891

=

2119872119901

119871119887

+ 21198791 sin 120579

=

2119860 119904119891119910 (119889 minus 1198891015840)

119871119887

+

411986010158401015840

119904119891119910 ((1198891198872) minus 119889

1015840)

119871119889

(2)


119881119904119901 = 21198811 + 1198812

= 2119879119889 (119889 minus 1198891015840

1198711198891

) + 21198791015840(119889 minus 1198891015840

1198711198892

)

=

211986010158401015840

119904119891119910 (119889 minus 119889

1015840)

1198711198891

+

2 (119860 119904 minus 11986010158401015840

119904) 119891119910 (119889 minus 119889

1015840)

1198711198892

(3)


1015840)2 and 1198711198892 =

radic(119871119887)2+ (119889 minus 119889



119888119887119887119908(119889 minus 119889

1015840)1198711198891205820] or

[(0351198911015840

119888119887119887(025119871119889)(119889 minus 119889

1015840)1198711198891205820] or [(008119891

1015840

119888119887119887(119889 minus 119889

1015840)1205820]





le3 0006 0012 0015ge6 0004 0008 0010


le3 0006 0008 0010ge6 0004 0006 0007




119908119889radic1198911015840

119888IO LS CP


le3 0006 0015 0025ge6 0005 0010 0015


le3 0006 0012 0020ge6 0005 0008 0010










ℎ1199051015840












le3 0006 0012 0015ge6 0004 0008 0010


le3 0006 0008 0010ge6 0004 0006 0007
























21 times 105MPa







(a)

Coupling beam






Coupling beam






(c)

Beam











WallBeam

F

F

Lw LwLb

hs = 3mV =

F times Lw

Lw + Lb


db2

times 120579b

db2

times 120579b

Lb

db


211 Assumptions






Δ119871119887 = 119889119887 times 120579119887 (4)


120576119888 =Δ119871119887

119871119887

(5)



119889119887

(6)








Table8Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

FEMA273[14

]and

FEMA356[15]

Long


transverse

reinforcem

ent

Shear119905119908119871119908radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

berc

ontro

lled

byflexu

reMem

berc

ontro

lled

byshear

ATEN

A2D

[18]

FEMA

273[14

]FE

MA

356[15]

FEMA

273[14

]FE

MA

356[15]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0025

0015

0020

000

0881

000104

0002325

000

0263

000

0306

000

0559

ge6

0015

002

0010

0016

000348

000528

000886

000

07125

0001726

0003124

Diagonal

le3

003

003

mdashmdash

000235

0011

00111

000

0494

000

4315

000372

ge6

003

003

mdashmdash

000292

000833

000

978

000

05724

0002961

0003228

Truss

le3

NA

NA

NA

NA

000117

6000

0422

000

093

000

03144

000

0106

6000

0204

ge6

NA

NA

NA

NA

0001413

000297

00029

000

0344

000

07514

000

066


Table9Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

ATC40

[16]

Long


transverse

reinforcem

ent

Shear119887119908119889radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

ber

controlled

byflexu

re

Mem

ber

controlled

byshear

ATEN

A2D

[18]

ATC40

[16]

ATC40

[16]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0018

000

01023

000

0784

000198

000

00001308

000

050001613

ge6

0015

0012

000

02423

0001944

000344

000163

000136

000297

Diagonal

le3

003

mdash000

012

000

0416

000

055

000

00194

000

02184

000

021

ge6

003

mdash000

0415

000

0422

0001533

000

01795

000

01483

000

093


Wall 2

Wall 1

F1









I A

I A

db

hs

H

i

Lw LwLb

(a)

l

Mid-point of Lb


V

V

V

V

V

V

V

V

120573F1

Wg

Wg

H

x

MMVw Vw

B

T C = T

A

(b)

























Shear119887119908119889radic1198911015840119888 CP



le3 0015ge6 0010


mdash lt003











120572 + 120573 = 10 (7)


120572 = 120573 = 05 (8)


DC =119879 times 119897

119872ot (9)


DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)


119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)



119881 =sum119873

119894=1119881119894

119873 (12)



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













le3 0006 0015 0025ge6 0005 0010 0015


le3 0006 0012 0020ge6 0005 0008 0010











119881119904119901 =

2119872119901

119871119887

=

2119860 119904119891119910 (119889 minus 1198891015840)

119871119887

(1)


119881119904119901 = 119881119891 + 1198811198891

=

2119872119901

119871119887

+ 21198791 sin 120579

=

2119860 119904119891119910 (119889 minus 1198891015840)

119871119887

+

411986010158401015840

119904119891119910 ((1198891198872) minus 119889

1015840)

119871119889

(2)


119881119904119901 = 21198811 + 1198812

= 2119879119889 (119889 minus 1198891015840

1198711198891

) + 21198791015840(119889 minus 1198891015840

1198711198892

)

=

211986010158401015840

119904119891119910 (119889 minus 119889

1015840)

1198711198891

+

2 (119860 119904 minus 11986010158401015840

119904) 119891119910 (119889 minus 119889

1015840)

1198711198892

(3)


1015840)2 and 1198711198892 =

radic(119871119887)2+ (119889 minus 119889



119888119887119887119908(119889 minus 119889

1015840)1198711198891205820] or

[(0351198911015840

119888119887119887(025119871119889)(119889 minus 119889

1015840)1198711198891205820] or [(008119891

1015840

119888119887119887(119889 minus 119889

1015840)1205820]





le3 0006 0012 0015ge6 0004 0008 0010


le3 0006 0008 0010ge6 0004 0006 0007




119908119889radic1198911015840

119888IO LS CP


le3 0006 0015 0025ge6 0005 0010 0015


le3 0006 0012 0020ge6 0005 0008 0010










ℎ1199051015840












le3 0006 0012 0015ge6 0004 0008 0010


le3 0006 0008 0010ge6 0004 0006 0007
























21 times 105MPa







(a)

Coupling beam






Coupling beam






(c)

Beam











WallBeam

F

F

Lw LwLb

hs = 3mV =

F times Lw

Lw + Lb


db2

times 120579b

db2

times 120579b

Lb

db


211 Assumptions






Δ119871119887 = 119889119887 times 120579119887 (4)


120576119888 =Δ119871119887

119871119887

(5)



119889119887

(6)








Table8Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

FEMA273[14

]and

FEMA356[15]

Long


transverse

reinforcem

ent

Shear119905119908119871119908radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

berc

ontro

lled

byflexu

reMem

berc

ontro

lled

byshear

ATEN

A2D

[18]

FEMA

273[14

]FE

MA

356[15]

FEMA

273[14

]FE

MA

356[15]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0025

0015

0020

000

0881

000104

0002325

000

0263

000

0306

000

0559

ge6

0015

002

0010

0016

000348

000528

000886

000

07125

0001726

0003124

Diagonal

le3

003

003

mdashmdash

000235

0011

00111

000

0494

000

4315

000372

ge6

003

003

mdashmdash

000292

000833

000

978

000

05724

0002961

0003228

Truss

le3

NA

NA

NA

NA

000117

6000

0422

000

093

000

03144

000

0106

6000

0204

ge6

NA

NA

NA

NA

0001413

000297

00029

000

0344

000

07514

000

066


Table9Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

ATC40

[16]

Long


transverse

reinforcem

ent

Shear119887119908119889radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

ber

controlled

byflexu

re

Mem

ber

controlled

byshear

ATEN

A2D

[18]

ATC40

[16]

ATC40

[16]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0018

000

01023

000

0784

000198

000

00001308

000

050001613

ge6

0015

0012

000

02423

0001944

000344

000163

000136

000297

Diagonal

le3

003

mdash000

012

000

0416

000

055

000

00194

000

02184

000

021

ge6

003

mdash000

0415

000

0422

0001533

000

01795

000

01483

000

093


Wall 2

Wall 1

F1









I A

I A

db

hs

H

i

Lw LwLb

(a)

l

Mid-point of Lb


V

V

V

V

V

V

V

V

120573F1

Wg

Wg

H

x

MMVw Vw

B

T C = T

A

(b)

























Shear119887119908119889radic1198911015840119888 CP



le3 0015ge6 0010


mdash lt003











120572 + 120573 = 10 (7)


120572 = 120573 = 05 (8)


DC =119879 times 119897

119872ot (9)


DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)


119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)



119881 =sum119873

119894=1119881119894

119873 (12)



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













le3 0006 0012 0015ge6 0004 0008 0010


le3 0006 0008 0010ge6 0004 0006 0007




119908119889radic1198911015840

119888IO LS CP


le3 0006 0015 0025ge6 0005 0010 0015


le3 0006 0012 0020ge6 0005 0008 0010










ℎ1199051015840












le3 0006 0012 0015ge6 0004 0008 0010


le3 0006 0008 0010ge6 0004 0006 0007
























21 times 105MPa







(a)

Coupling beam






Coupling beam






(c)

Beam











WallBeam

F

F

Lw LwLb

hs = 3mV =

F times Lw

Lw + Lb


db2

times 120579b

db2

times 120579b

Lb

db


211 Assumptions






Δ119871119887 = 119889119887 times 120579119887 (4)


120576119888 =Δ119871119887

119871119887

(5)



119889119887

(6)








Table8Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

FEMA273[14

]and

FEMA356[15]

Long


transverse

reinforcem

ent

Shear119905119908119871119908radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

berc

ontro

lled

byflexu

reMem

berc

ontro

lled

byshear

ATEN

A2D

[18]

FEMA

273[14

]FE

MA

356[15]

FEMA

273[14

]FE

MA

356[15]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0025

0015

0020

000

0881

000104

0002325

000

0263

000

0306

000

0559

ge6

0015

002

0010

0016

000348

000528

000886

000

07125

0001726

0003124

Diagonal

le3

003

003

mdashmdash

000235

0011

00111

000

0494

000

4315

000372

ge6

003

003

mdashmdash

000292

000833

000

978

000

05724

0002961

0003228

Truss

le3

NA

NA

NA

NA

000117

6000

0422

000

093

000

03144

000

0106

6000

0204

ge6

NA

NA

NA

NA

0001413

000297

00029

000

0344

000

07514

000

066


Table9Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

ATC40

[16]

Long


transverse

reinforcem

ent

Shear119887119908119889radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

ber

controlled

byflexu

re

Mem

ber

controlled

byshear

ATEN

A2D

[18]

ATC40

[16]

ATC40

[16]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0018

000

01023

000

0784

000198

000

00001308

000

050001613

ge6

0015

0012

000

02423

0001944

000344

000163

000136

000297

Diagonal

le3

003

mdash000

012

000

0416

000

055

000

00194

000

02184

000

021

ge6

003

mdash000

0415

000

0422

0001533

000

01795

000

01483

000

093


Wall 2

Wall 1

F1









I A

I A

db

hs

H

i

Lw LwLb

(a)

l

Mid-point of Lb


V

V

V

V

V

V

V

V

120573F1

Wg

Wg

H

x

MMVw Vw

B

T C = T

A

(b)

























Shear119887119908119889radic1198911015840119888 CP



le3 0015ge6 0010


mdash lt003











120572 + 120573 = 10 (7)


120572 = 120573 = 05 (8)


DC =119879 times 119897

119872ot (9)


DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)


119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)



119881 =sum119873

119894=1119881119894

119873 (12)



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













le3 0006 0012 0015ge6 0004 0008 0010


le3 0006 0008 0010ge6 0004 0006 0007
























21 times 105MPa







(a)

Coupling beam






Coupling beam






(c)

Beam











WallBeam

F

F

Lw LwLb

hs = 3mV =

F times Lw

Lw + Lb


db2

times 120579b

db2

times 120579b

Lb

db


211 Assumptions






Δ119871119887 = 119889119887 times 120579119887 (4)


120576119888 =Δ119871119887

119871119887

(5)



119889119887

(6)








Table8Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

FEMA273[14

]and

FEMA356[15]

Long


transverse

reinforcem

ent

Shear119905119908119871119908radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

berc

ontro

lled

byflexu

reMem

berc

ontro

lled

byshear

ATEN

A2D

[18]

FEMA

273[14

]FE

MA

356[15]

FEMA

273[14

]FE

MA

356[15]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0025

0015

0020

000

0881

000104

0002325

000

0263

000

0306

000

0559

ge6

0015

002

0010

0016

000348

000528

000886

000

07125

0001726

0003124

Diagonal

le3

003

003

mdashmdash

000235

0011

00111

000

0494

000

4315

000372

ge6

003

003

mdashmdash

000292

000833

000

978

000

05724

0002961

0003228

Truss

le3

NA

NA

NA

NA

000117

6000

0422

000

093

000

03144

000

0106

6000

0204

ge6

NA

NA

NA

NA

0001413

000297

00029

000

0344

000

07514

000

066


Table9Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

ATC40

[16]

Long


transverse

reinforcem

ent

Shear119887119908119889radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

ber

controlled

byflexu

re

Mem

ber

controlled

byshear

ATEN

A2D

[18]

ATC40

[16]

ATC40

[16]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0018

000

01023

000

0784

000198

000

00001308

000

050001613

ge6

0015

0012

000

02423

0001944

000344

000163

000136

000297

Diagonal

le3

003

mdash000

012

000

0416

000

055

000

00194

000

02184

000

021

ge6

003

mdash000

0415

000

0422

0001533

000

01795

000

01483

000

093


Wall 2

Wall 1

F1









I A

I A

db

hs

H

i

Lw LwLb

(a)

l

Mid-point of Lb


V

V

V

V

V

V

V

V

120573F1

Wg

Wg

H

x

MMVw Vw

B

T C = T

A

(b)

























Shear119887119908119889radic1198911015840119888 CP



le3 0015ge6 0010


mdash lt003











120572 + 120573 = 10 (7)


120572 = 120573 = 05 (8)


DC =119879 times 119897

119872ot (9)


DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)


119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)



119881 =sum119873

119894=1119881119894

119873 (12)



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














(a)

Coupling beam






Coupling beam






(c)

Beam











WallBeam

F

F

Lw LwLb

hs = 3mV =

F times Lw

Lw + Lb


db2

times 120579b

db2

times 120579b

Lb

db


211 Assumptions






Δ119871119887 = 119889119887 times 120579119887 (4)


120576119888 =Δ119871119887

119871119887

(5)



119889119887

(6)








Table8Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

FEMA273[14

]and

FEMA356[15]

Long


transverse

reinforcem

ent

Shear119905119908119871119908radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

berc

ontro

lled

byflexu

reMem

berc

ontro

lled

byshear

ATEN

A2D

[18]

FEMA

273[14

]FE

MA

356[15]

FEMA

273[14

]FE

MA

356[15]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0025

0015

0020

000

0881

000104

0002325

000

0263

000

0306

000

0559

ge6

0015

002

0010

0016

000348

000528

000886

000

07125

0001726

0003124

Diagonal

le3

003

003

mdashmdash

000235

0011

00111

000

0494

000

4315

000372

ge6

003

003

mdashmdash

000292

000833

000

978

000

05724

0002961

0003228

Truss

le3

NA

NA

NA

NA

000117

6000

0422

000

093

000

03144

000

0106

6000

0204

ge6

NA

NA

NA

NA

0001413

000297

00029

000

0344

000

07514

000

066


Table9Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

ATC40

[16]

Long


transverse

reinforcem

ent

Shear119887119908119889radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

ber

controlled

byflexu

re

Mem

ber

controlled

byshear

ATEN

A2D

[18]

ATC40

[16]

ATC40

[16]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0018

000

01023

000

0784

000198

000

00001308

000

050001613

ge6

0015

0012

000

02423

0001944

000344

000163

000136

000297

Diagonal

le3

003

mdash000

012

000

0416

000

055

000

00194

000

02184

000

021

ge6

003

mdash000

0415

000

0422

0001533

000

01795

000

01483

000

093


Wall 2

Wall 1

F1









I A

I A

db

hs

H

i

Lw LwLb

(a)

l

Mid-point of Lb


V

V

V

V

V

V

V

V

120573F1

Wg

Wg

H

x

MMVw Vw

B

T C = T

A

(b)

























Shear119887119908119889radic1198911015840119888 CP



le3 0015ge6 0010


mdash lt003











120572 + 120573 = 10 (7)


120572 = 120573 = 05 (8)


DC =119879 times 119897

119872ot (9)


DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)


119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)



119881 =sum119873

119894=1119881119894

119873 (12)



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











WallBeam

F

F

Lw LwLb

hs = 3mV =

F times Lw

Lw + Lb


db2

times 120579b

db2

times 120579b

Lb

db


211 Assumptions






Δ119871119887 = 119889119887 times 120579119887 (4)


120576119888 =Δ119871119887

119871119887

(5)



119889119887

(6)








Table8Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

FEMA273[14

]and

FEMA356[15]

Long


transverse

reinforcem

ent

Shear119905119908119871119908radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

berc

ontro

lled

byflexu

reMem

berc

ontro

lled

byshear

ATEN

A2D

[18]

FEMA

273[14

]FE

MA

356[15]

FEMA

273[14

]FE

MA

356[15]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0025

0015

0020

000

0881

000104

0002325

000

0263

000

0306

000

0559

ge6

0015

002

0010

0016

000348

000528

000886

000

07125

0001726

0003124

Diagonal

le3

003

003

mdashmdash

000235

0011

00111

000

0494

000

4315

000372

ge6

003

003

mdashmdash

000292

000833

000

978

000

05724

0002961

0003228

Truss

le3

NA

NA

NA

NA

000117

6000

0422

000

093

000

03144

000

0106

6000

0204

ge6

NA

NA

NA

NA

0001413

000297

00029

000

0344

000

07514

000

066


Table9Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

ATC40

[16]

Long


transverse

reinforcem

ent

Shear119887119908119889radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

ber

controlled

byflexu

re

Mem

ber

controlled

byshear

ATEN

A2D

[18]

ATC40

[16]

ATC40

[16]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0018

000

01023

000

0784

000198

000

00001308

000

050001613

ge6

0015

0012

000

02423

0001944

000344

000163

000136

000297

Diagonal

le3

003

mdash000

012

000

0416

000

055

000

00194

000

02184

000

021

ge6

003

mdash000

0415

000

0422

0001533

000

01795

000

01483

000

093


Wall 2

Wall 1

F1









I A

I A

db

hs

H

i

Lw LwLb

(a)

l

Mid-point of Lb


V

V

V

V

V

V

V

V

120573F1

Wg

Wg

H

x

MMVw Vw

B

T C = T

A

(b)

























Shear119887119908119889radic1198911015840119888 CP



le3 0015ge6 0010


mdash lt003











120572 + 120573 = 10 (7)


120572 = 120573 = 05 (8)


DC =119879 times 119897

119872ot (9)


DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)


119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)



119881 =sum119873

119894=1119881119894

119873 (12)



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table8Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

FEMA273[14

]and

FEMA356[15]

Long


transverse

reinforcem

ent

Shear119905119908119871119908radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

berc

ontro

lled

byflexu

reMem

berc

ontro

lled

byshear

ATEN

A2D

[18]

FEMA

273[14

]FE

MA

356[15]

FEMA

273[14

]FE

MA

356[15]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0025

0015

0020

000

0881

000104

0002325

000

0263

000

0306

000

0559

ge6

0015

002

0010

0016

000348

000528

000886

000

07125

0001726

0003124

Diagonal

le3

003

003

mdashmdash

000235

0011

00111

000

0494

000

4315

000372

ge6

003

003

mdashmdash

000292

000833

000

978

000

05724

0002961

0003228

Truss

le3

NA

NA

NA

NA

000117

6000

0422

000

093

000

03144

000

0106

6000

0204

ge6

NA

NA

NA

NA

0001413

000297

00029

000

0344

000

07514

000

066


Table9Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

ATC40

[16]

Long


transverse

reinforcem

ent

Shear119887119908119889radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

ber

controlled

byflexu

re

Mem

ber

controlled

byshear

ATEN

A2D

[18]

ATC40

[16]

ATC40

[16]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0018

000

01023

000

0784

000198

000

00001308

000

050001613

ge6

0015

0012

000

02423

0001944

000344

000163

000136

000297

Diagonal

le3

003

mdash000

012

000

0416

000

055

000

00194

000

02184

000

021

ge6

003

mdash000

0415

000

0422

0001533

000

01795

000

01483

000

093


Wall 2

Wall 1

F1









I A

I A

db

hs

H

i

Lw LwLb

(a)

l

Mid-point of Lb


V

V

V

V

V

V

V

V

120573F1

Wg

Wg

H

x

MMVw Vw

B

T C = T

A

(b)

























Shear119887119908119889radic1198911015840119888 CP



le3 0015ge6 0010


mdash lt003











120572 + 120573 = 10 (7)


120572 = 120573 = 05 (8)


DC =119879 times 119897

119872ot (9)


DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)


119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)



119881 =sum119873

119894=1119881119894

119873 (12)



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table9Com

pare

theM

odelingParametersa

ndNum

ericalAc

ceptance

Criteria

with

ATC40

[16]

Long


transverse

reinforcem

ent

Shear119887119908119889radic1198911015840 119888

Rotatio

nallim

itatcollapsep

reventionlevel(CP

)inradians

Crackwidth

incoup

lingbeam

atCP

levelinmetersb

yAT

ENA2D

[18]

Mem

ber

controlled

byflexu

re

Mem

ber

controlled

byshear

ATEN

A2D

[18]

ATC40

[16]

ATC40

[16]

119871119887=06m

119871119887=09m

119871119887=12m

119871119887=06m

119871119887=09m

119871119887=12m

Con

ventionallon


with


reinforcem

ent

le3

0025

0018

000

01023

000

0784

000198

000

00001308

000

050001613

ge6

0015

0012

000

02423

0001944

000344

000163

000136

000297

Diagonal

le3

003

mdash000

012

000

0416

000

055

000

00194

000

02184

000

021

ge6

003

mdash000

0415

000

0422

0001533

000

01795

000

01483

000

093


Wall 2

Wall 1

F1









I A

I A

db

hs

H

i

Lw LwLb

(a)

l

Mid-point of Lb


V

V

V

V

V

V

V

V

120573F1

Wg

Wg

H

x

MMVw Vw

B

T C = T

A

(b)

























Shear119887119908119889radic1198911015840119888 CP



le3 0015ge6 0010


mdash lt003











120572 + 120573 = 10 (7)


120572 = 120573 = 05 (8)


DC =119879 times 119897

119872ot (9)


DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)


119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)



119881 =sum119873

119894=1119881119894

119873 (12)



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Wall 2

Wall 1

F1









I A

I A

db

hs

H

i

Lw LwLb

(a)

l

Mid-point of Lb


V

V

V

V

V

V

V

V

120573F1

Wg

Wg

H

x

MMVw Vw

B

T C = T

A

(b)

























Shear119887119908119889radic1198911015840119888 CP



le3 0015ge6 0010


mdash lt003











120572 + 120573 = 10 (7)


120572 = 120573 = 05 (8)


DC =119879 times 119897

119872ot (9)


DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)


119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)



119881 =sum119873

119894=1119881119894

119873 (12)



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Shear119887119908119889radic1198911015840119888 CP



le3 0015ge6 0010


mdash lt003











120572 + 120573 = 10 (7)


120572 = 120573 = 05 (8)


DC =119879 times 119897

119872ot (9)


DC = 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (10)


119873 1198961015840

119886 119887 119888

6 2976 0706 0615 069810 2342 0512 0462 050915 1697 0352 0345 027920 1463 0265 0281 019030 1293 0193 0223 010640 1190 0145 0155 0059



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897

times 1198961015840 (119889119887)

119886

(119871119908)119887times (119871119887)

119888 (11)



119881 =sum119873

119894=1119881119894

119873 (12)



119862 = 119879 =

119873

sum

119894=1

119881119894 =119872ot119897 (13)



119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119881 =sum119873

119894=1119881119894

119873 (14)



119872ot (119909) =119873minus119894

sum

119895=0

05 times1198651




119872wr (119909) = (119871119908

2+119871119887

2)

119873

sum

119895=119894

119881119895 (16)


119872net (119909) = 119872ot (119909) minus 119872wr (119909) (17)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868 (18)

where

119868 =119905119908 times 119871

3

119908

12 (19)


120579119908119894 =

int119894ℎ119904

0119872net (119909) 119889119909

119864119888119868+ 1205791199080

(20)




Lw Lb Lw

120579wi

120579wi120579bi

Lb

2







120579119887119894 = 120579119908119894 (1 +119871119908

119871119887

) (21)



120579119887119894 = 119871119908119887 120579119908119894 (22)


119871119908119887 = (1 +119871119908

119871119887

) (23)



9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

H

db

hs

(b)




119873

sum

119894=0

120579119908119894) (24)


Δ 119894 = ℎ119904 times (

119894

sum

119895=0

120579119908119895) (25)


119881119861 =1198651 times (119873 + 1)

2 (26)








119908) 300mm







Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Coupling beam

Rigid link

05Lw Lb 05Lw


Base

shea

r

Roof displacement

Capacity

VByield

Ki

o

Area a1

Area a2





120583Δ =Δ roofCP

Δ roofyield (27)










4 Parametric Study





0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 01 02 03

1500

1000

500

0



Base

shea

r (kN

)

(a)


0 01 02 03

900

600

300

0


Base

shea

r (kN

)

(b)


9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)








119887) 1m 15m and 2m

















Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























Fixed1m 33315m 482m 63

Pinned1m 51115m 6352m 71



Fixed1m 29315m 402m 59

Pinned1m 4515m 5852m 687





119908




Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Stor

ey h

eigh

t (m

)



0

24

48

72

(a)

Stor

ey h

eigh

t (m

)



0

24

48

72

(b)


0

24

48

72

Stor

ey h

eigh

t (m

)



(a)

0

24

48

72St

orey

hei

ght (

m)



(b)



0

24

48

72

Stor

ey h

eigh

t (m

)


(a)


0

24

48

72

Stor

ey h

eigh

t (m

)


(b)




0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

600

1200Ba

se sh

ear (

kN)


(a)


0

375

750

Base

shea

r (kN

)


(b)


0

18

36

54

Stor

ey h

eigh

t (m

)

0 01 02 03 04 05 06Displacement (m)


(a)

0

18

36

54St

orey

hei

ght (

m)



(b)



0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)




0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

18

36

54

Stor

ey h

eigh

t (m

)


(a)


0

18

36

54

Stor

ey h

eigh

t (m

)


(b)


0

500

1000

1500

2000

Base

shea

r (kN

)



(a)

Base

shea

r (kN

)


0

375

750


(b)


0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)



0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

18

36

Stor

ey h

eigh

t (m

)



(a)

0

18

36

Stor

ey h

eigh

t (m

)



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

0

18

36St

orey

hei

ght (

m)



(b)


Base

shea

r (kN

)


0

500

1000


(a)

Base

shea

r (kN

)


0

425

850


(b)



orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










orey

hei

ght (

m)



0

18

36

(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Stor

ey h

eigh

t (m

)

0

18

36



(b)


Stor

ey h

eigh

t (m

)

0

18

36



(a)

Beam rotation (rad)

Stor

ey h

eigh

t (m

)

0

18

36

0 0008 0016 0024


(b)



se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










se sh

ear (

m)

0

500

1000



(a)

Base

shea

r (m

)


0

425

850

0 01 02 03


(b)
















9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










9 m 9 m 9 m 9 m

5 m

5 m

a

a

Lw

Lw

Lb

(a)

Wall 2

Wall 1

Lw LwLb

I A

I A

db

hs

H

(b)


0

200

400

600

800

1000

1200

1400

Base

shea

r (kN

)


(a)

Base

shea

r (kN

)


0

500

1000

1500

2000

(b)


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp



Capacity curve




pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Capacity curve


0

1

2

3

4

5

6

7

Sa

0 01 02 03 04 05 06 07 08 09Sd

pp


pp



Capacity curve


0

05

1

15

2

25

3

35

Sa

0 005 01 015 02 025 03 035 04 045Sd




Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Parameters 120583Δ1198901[24] 120583Δ1198902 [24] 119877120583120585 [24]





119877119889 as per CSA[25]



MCE 205 12 158 205 134

119873 = 15DBE 101 100 1002 101 100

MCE 187 113 139 187 122





6 Conclusions








Notations




11986010158401015840









































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





































greater than 119881119910119886


[39]











References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article a conceptual design approach of coupled...

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