Dual Plastic Hinge Design Concept for Reducing Higher Mode Effects on Higher Rise Cantilever Wall Buildings

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2009; 38:1359–1380Published online 24 February 2009 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.905

Dual-plastic hinge design concept for reducing higher-mode effectson high-rise cantilever wall buildings

Marios Panagiotou1,∗,†,‡ and Jose I. Restrepo2,§

1Department of Civil and Environmental Engineering, University of California, Berkeley, CA, U.S.A.2Department of Structural Engineering, University of California, San Diego, La Jolla, CA, U.S.A.

SUMMARY

This paper explores the notion of detailing reinforced concrete structural walls to develop base and mid-height plastic hinges to better control the seismic response of tall cantilever wall buildings to strongshaking. This concept, termed here dual-plastic hinge (DPH) concept, is used to reduce the effects ofhigher modes of response in high-rise buildings. Higher modes can significantly increase the flexuraldemands in tall cantilever wall buildings. Lumped-mass Euler–Bernoulli cantilevers are used to model thecase-study buildings examined in this paper. Buildings with 10, 20 and 40 stories are designed accordingto three different approaches: ACI-318, Eurocode 8 and the proposed DPH concept. The buildings aredesigned and subjected to three-specific historical strong near-fault ground motions. The investigationclearly shows the dual-hinge design concept is effective at reducing the effects of the second mode ofresponse. An advantage of the concept is that, when combined with capacity design, it can result inrelaxation of special reinforcing detailing in large portions of the walls. Copyright q 2009 John Wiley &Sons, Ltd.

Received 30 May 2008; Revised 12 January 2009; Accepted 15 January 2009

KEY WORDS: capacity design; high-rise buildings; higher-mode effects; near-fault earthquakes; plastichinges; reinforced concrete; seismic design; structural walls; tall buildings

INTRODUCTION

In 1981 Derecho et al. [1], while examining the results of a comprehensive study on the nonlineardynamic response of reinforced concrete cantilever walls of high-rise buildings, pointed out:The difference between UBC-76 and 0.9 fractile normalized (bending) moments is particularly

∗Correspondence to: Marios Panagiotou, Department of Civil and Environmental Engineering, University of California,Berkeley, CA, U.S.A.

†E-mail: [email protected]‡Assistant Professor.§Professor.

Copyright q 2009 John Wiley & Sons, Ltd.

1360 M. PANAGIOTOU AND J. I. RESTREPO

significant near mid-height. At about two-thirds of the height of the walls, the 0.9 fractile (bending)moments exceed the corresponding UBC moments by as much as 100% for the longer period.Despite this observation, codes in United States have not yet recognized the significant effect thathigher modes have on the bending moment demands in cantilever walls of high-rise buildings. Incontrast, codes like Eurocode 8 (EC8) [2], which has similar design provisions for cantilever wallbuildings to the New Zealand 3101 Concrete Design Standard (NZS-3101) [3] and the CanadianCode CSA A23.3-04 (CSA) [4], do recognize the higher-mode effects. These codes incorporatespecific provisions that stemmed from the pioneering work of Blakeley et al. [5].

Design codes recognize the difficulties in ensuring elastic response of the lateral force resistingsystem in buildings. For this reason codes recommend the use of reduced lateral forces in design.As a result, they recognize the possibility of developing nonlinear deformations in some partsof the structural system during a rare and strong intensity earthquake. Nonlinear deformations incantilever walls occur preferably in flexure in regions defined as plastic hinges. Traditionally, asingle plastic hinge (SPH) has been advocated in the seismic design of each wall in these buildings[2–4, 6, 7]. Plastic hinges are generally selected to develop at the base of the walls in verticallyregular buildings, or at the top of a podium in buildings, with podiums or at the ground floorin buildings with floors below grade. Detailing of the reinforcement in the plastic hinge regionsis critical to ensure deformation demands that have a low probability of exceeding the capacityin these rare events. Thus, codes include prescriptive requirements to ensure a certain degree ofductility in potential plastic hinge regions.

Seismic design codes such as EC8, the NZS-3101 and the CSA use capacity design (CD)to ensure elastic response in regions other than the plastic hinges. In these codes the flex-ural design envelope varies linearly from the expected flexural overstrength at the wall baseto zero at the top. The intention of such linear variation is to consider the effect of thehigher modes. Recently, Panneton et al. [8] and Priestley et al. [9] have found that thelinear variation of bending moment with height does not always preclude the spread of plas-ticity into the upper regions. Priestley et al. proposed a bilinear bending moment envelopeto overcome this shortcoming. This envelope starts at the base with the expected flexuraloverstrength, ends at zero moment at the top and passes through a mid-height moment M◦

H/2given by:

M◦H/2=C1,T �◦ Mu,0 where C1,T =0.4+0.075T1(�/�◦−1)�0.4 (1)

In which �◦ is the wall base expected flexural overstrength factor given by M◦0/Mu,0, where M◦

0is the expected flexural overstrength that accounts for all sources of strength increase above thedesign bending moment, Mu,0 is the design base bending moment, T1 is the fundamental periodand � the displacement ductility factor.

Codes such as ACI-318 [10] are based on the premise that plasticity concentrates at the baseof the walls only [11]. These codes do not restrict the designer to concentrate all the plasticityat the base, but at the same time they do not prompt the designer to check and detail regionsabove the base as probable plastic hinge regions. However, these codes do not use CD, and thusdo not recognize the effect of base overstrength and of higher modes. Thus, plasticity is likely tospread anywhere in the upper levels of the walls as it has been recently pointed out by Moehleet al. [12]. The main problem with the design by this code is that undesirable premature modesof response other than flexure could develop in the upper regions. This is because these regionsare not specially detailed for ductility.

Copyright q 2009 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2009; 38:1359–1380DOI: 10.1002/eqe

DUAL-PLASTIC HINGE DESIGN CONCEPT 1361

One initial problem in the design of cantilever walls in tall buildings is the evaluation of thebending moment and shear force demands. It is a common practice to obtain these demandsfrom a modal response spectrum analysis (MRSA) using an accepted modal combination method.Elastic forces obtained from the modal combinations are reduced by a force reduction factorto obtain design forces. In 2002, Rodriguez et al. [13] suggested that inelastic response at thebase of cantilever walls reduces mainly the first mode of response. Consequently, the relativecontribution of the higher modes to response quantities, such as bending moments and shearforces, increases with an increase in ground motion intensity augmenting the curvature ductilitydemand at the base. For this reason, these researchers challenged the modal superposition methodsdeveloped for calculating design quantities in linear systems and recommended in codes foruse in nonlinear systems. They claimed that such methods produce nonconservative demands.Panneton et al. [8], Priestley et al. [9] and Panagiotou and Restrepo [14] have arrived at similarconclusions.

No experimental evidence exists indicating the potential of development of plastic hingingabove the base of a reinforced concrete wall. The formation of a plastic hinge above the base ofa wall becomes more probable as the height of the building increases and especially when barcurtailment along the height exists. The authors are not aware of experimental results of a wall tallenough to arouse such effects. During the experimental response of the UCSD full-scale 7-storywall test [14], the important effect of the higher modes was observed, though their contributionwas not so adequate to cause formation of a plastic hinge above the base. Regarding historicalevidences, historical records do seem to indicate plastic hinge formation at intermediate heights[15, 16].

This study proposes a dual-plastic hinge (DPH) design approach useful for the design ofhigh-rise-reinforced concrete wall buildings. Note that from the static’s viewpoint the notion ofdual hinges is nearly unthinkable. However, under dynamic excitation, this notion is not onlyconceivable but is believed to be favorable to the system’s response and attractive from the designand constructability viewpoints. This is because the second hinge at an intermediate height in thecantilever wall is specifically intended to reduce the large bending moment demands imposed bythe second mode.

DPH DESIGN APPROACH

Figure 1 shows three possible approaches as to where plasticity can develop in cantilever wallbuildings. Figure 1(a) shows the first approach. Plasticity develops anywhere along the height ofthe walls, and is termed here as extended plasticity (EP) in this paper. The second approach, shownin Figure 1(b), is that of a SPH. This hinge develops only at the wall base. The third approach,proposed by the authors and shown in Figure 1(c), allows two plastic hinges in a wall, one at thebase and the second one at mid-height and is termed as the DPH design approach.

The EP and the SPH approaches have clear disadvantages. In the EP approach, yielding upthe height in walls would typically require special reinforcement detailing along all the heightof the walls. Extended yielding, as inferred in the EP approach, is theoretical in nature. In practicethe longitudinal reinforcement is detailed to show stepped bending moment capacity diagrams thatenvelope the code’s demand. These steps in the capacity diagrams form critical flexural strengthdiscontinuities where inelastic response concentrates. In the SPH approach the rigorous use ofCD to preclude yielding above the plastic hinge region can result in longitudinal reinforcement



H

(c)

Lp1

Lp2

Plastic hinge

(a)

Lp1

(b)

0.5H

Figure 1. Three different cases of plasticity location in an Euler–Bernoulli cantilever: (a) extended plasticity(EP); (b) single plastic hinge (SPH); and (c) dual-plastic hinge (DPH).

ratios that exceed those calculated at the base of the walls. The need for these large ratios will bediscussed later with the design examples chosen.

The DPH design approach, see Figure 1(c), overcomes the disadvantages of EP and SPHapproaches. Like the bottom plastic hinge, the mid-height plastic hinge can be designed to meetspecific objectives such as curvature ductility or strain demands for which design alternatives tothe current force-based approaches may be more suitable. The base and mid-height regions of thewall where plastic hinges will develop are designed following a strength hierarchy. This hierarchyprecludes the first mode of response alone from developing the mid-height plastic hinge. CD issubsequently employed to keep the remaining portion of the walls elastic and to ease the detailingof the reinforcement there. Thus, on the one hand, the performance of the building is controlledas is in the SPH design approach. On the other hand, the ease of detailing and/or reduction inthe longitudinal reinforcement along a significant portion of the walls’ height in the DPH designapproach brings significant optimization to construction compared with the SPH design approach.

NUMERICAL VERIFICATION OF THE DIFFERENT DESIGN APPROACHES

This section examines the design and nonlinear dynamic response of 10, 20 and 40-story repre-senting core-wall buildings. The buildings are designed for the 5% response spectra of specificground motions that have distinct near-fault characteristics. The base moment demand was esti-mated from a MRSA, as prescribed by ASCE 7 [17]. The elastic design quantities were dividedby a force reduction factor R=5. The buildings were designed with three different approaches:ACI-318 building code [10], SPH according to EC8, NZS-3101 or CSA and the proposed DPHdesign approach. Each building was designed for the 5% damped response spectra of each of thethree ground motions for each of the three design approaches. Thus, in total there were 27 casestudies. A nonlinear time-history analysis was carried out for each building using as input thedesign ground motion. The following sections give details about the designs, modeling, groundmotions and summarize the main results obtained.



Gravity ColumnsCore-wall

Lw

Lw/ 2 tw

Lo

Lo

Direction of excitation considered

Lw/ 2

Figure 2. Floor plan view of the buildings.

Building description and designs

The lateral force resistance in buildings studied was solely provided by a reinforced concretecore wall. Figure 2 shows the floor plan view of the core-wall buildings. Table I lists the maincharacteristics of the buildings, including the floor height h, the seismic weight w per floor andaxial load P per floor acting on the wall, as well as the main building and core-wall geometricalproperties and longitudinal reinforcement ratios. The axial stress ratios at the wall bases arealso listed in this table. These ratios are based on a specified concrete compressive strength off ′c=41MPa. The yield curvature of the idealized bi-linear moment–curvature response for thewalls was defined based on moment curvature analysis. For all the wall sections in this study theyield curvature was equal to �y=0.0034/Lw, where Lw is the core-wall length. The longitudinalreinforcement steel ratios, �1,0, provided at the wall base of the design for the different earthquakerecords are listed in Table I. These ratios were calculated from moment–curvature analyses usingthe actual reinforcement provided, specified material properties and a strength reduction factor forbending and axial force equal to 0.9. The wall thickness was chosen in each case to ensure a baselongitudinal reinforcement ratio 0.4%��1,0�1.5%.

For the MRSA, the effective flexural rigidity of EIe=0.5EIg recommended by FEMA 356 [18]formed the basis for estimating the design lateral forces. Table II lists the design base momentsand base shear forces. It is noted that because of the large variation of the spectral accelerationsat period T =1s the minimum base shear requirement of Equation 12.8-6 of ASCE-7 was notconsidered in the design of the 40-story buildings.

Designs based on ACI-318 2005 building code

The bending moment envelopes for the ACI-318 design were obtained from a MRSA. In the 10-and 20-story buildings, the expected flexural strengths at the core-wall base are 20% greater thanthe design moments. Expected flexural strengths are calculated from first principles of concretemechanics using the reinforcement as detailed. Furthermore, calculations assume that the actualconcrete compressive and reinforcing steel yield strengths are 8% greater than those specifiedand the strength reduction factor is one. The longitudinal reinforcement in these buildings is



TableI.Maincharacteristicsof

build

ings

considered.

10-story

20-story

40-story

SYLOV

TAK

RIN

SYLOV

TAK

RIN

SYLOV

TAK

RIN

360

090

228

360

090

228

360

090

228

Floo

rheight

h(m

)3.4

3.4

3.4

Buildingheight

H(m

)33

.567

.113

4.1

Floo

rplan

view

dimension

Lo(m

)12

.224

.445

.7

Axial

load

/flo

or�P

(kN)

516

633

817

1653

6614

Baseaxialstress

P/(f′ cAg)

0.03

0.03

0.03

0.08

0.14

Seismic

weigh

t/flo

orw

(kN)

1183

1301

1484

4322

1599

6

Core-wallleng

thLw

(m)

4.6

8.2

15.2

Core-wallthickn

esst w

(m)

0.21

0.30

0.46

0.30

0.76

Core-wallarea

Aw

(m2)

3.7

5.2

7.5

9.7

44.1

Core-wallgrossmom

entof

inertia

I(m

4)

11.8

15.9

21.5

101.3

1545

.9Core-wallyieldcurvature

�y(rad

/m)

0.00

078

0.00

043

0.00

023

Lon

gitudinalreinforcem

entsteelratio

at1.0

1.3

1.4

1.4

1.4

0.8

0.4

wallbase

� l,0(%

)

Lon

gitudinalreinforcem

entsteelratio

at0.5

0.6

0.7

0.6

0.6

0.4

0.4

mid-heigh

tforDPH

design

� l,H

/2(%

)



Table II. Normalized design base bending moment and base shear force from MRSA.

SYLOV TAK RIN360 090 228

Normalized base bending moment Mu,0/(WH)10-story 0.089 0.138 0.19320-story 0.047 0.048 0.03540-story 0.014 0.013 0.019

Normalized base shear force Vu,0/W10-story 0.127 0.193 0.25820-story 0.117 0.093 0.08840-story 0.055 0.054 0.082

cut-off at four locations ensuring the nominal flexural strength envelope is greater than the designenvelope following current recommended practice [19]. For the 10-story buildings, the longitudinalreinforcement layout in the walls changes at floors 2, 4 and 6, except for the building designedfor the SYLOV360 ground motion, which has minimum longitudinal reinforcement from level 6upwards. For the 20-story buildings, the longitudinal reinforcement layouts in the walls changeat floors 4, 8 and 12. Expected flexural strengths at these elevations are also 20% greater thanthe design bending moments there. From the axial force bending moment interaction diagram,the reduction flexural strength per level caused by the change in axial force is approximated to0.45Lw�P, where �P is the axial load change per floor. The longitudinal reinforcement of the 40-story walls at the base is just above the minimum. Boundary elements meet ACI-318 requirementsand extend a distance equal to 19, 13 and 6% of the building height from the base of the wallsfor the 10, 20 and 40-story buildings, respectively.

SPH design approach

The design bending moment at the base of the core walls is identical to the ACI-318 design.The remaining portion of the core walls is assumed elastic. This assumption is made to prove theadequacy of the current CD design recommendations in EC8 and NZS-3101 concerning the effectof higher modes, and of the recent proposal made by Priestley et al. [9] and given by Equation (1).

DPH design approach

For comparative purposes the expected flexural strength at the base of the core wall in this designis the same like the previous two approaches. We note that this is done despite that MRSA shouldnot be used as the basis for the design of cantilever beams with the dual-hinge approach. Thisis because this design directly considers the effects of the first and second modes independently.To ensure the development of the base plastic hinge, the flexural design at the location of themid-height plastic hinge follows a design hierarchy, described below, whereas those portions ofthe walls away from the plastic hinges are assumed elastic. Thus, design bending moments for themid-height plastic hinge are computed as follows:

(i) Calculate the expected flexural overstrength at the base of the wall M◦0 . In this study the

expected flexural overstrength M◦0 =My,0�h at the wall base is calculated as the product of



Figure 3. Mass and flexural rigidity distributions of a 20-story lumped-mass Euler–BernoulliSPH cantilever: (a) mass distribution; (b) flexural rigidity distribution; and (c) idealized

moment–curvature hysteretic response.

the expected flexural strength and the strain hardening overstrength factor. The latter factor isgiven by �h =1+r(��−1), see Figure 3(c). With r=2% and assuming �� =16→�h =1.3.

(ii) Determine the design mid-height bending moment derived from the first mode lateral forces

MH/2=�M◦0 (2)

where factor � is the ratio of the mid-height bending moment to the base bending momentestimated from a first mode lateral force distribution. An analysis of Euler–Bernoullicantilever beams with different number of equal lumped masses indicates factor � varieslittle [20]. A value of factor �=0.33 was chosen in this study. The bending moment calcu-lated from Equation (2) was used for the design for flexure and combined axial force at thestem of the mid-height plastic hinge. Based on Equation (2) and considering that the expectedflexural strength of the mid-height plastic hinge My,H/2=1.2 MH/2 the expected flexuralstrength there is My,H/2=0.52 My,0 where My,0 is the expected base flexural strength. Forthe 40-story buildings, where minimum reinforcement requirements governed, the actualreinforcement detailed was 10% above the minimum. This resulted in My,H/2=0.59 My,0.

Equation (2) uses the first mode lateral force distribution to establish the required strength of themid-height plastic hinge. This implies that in cases where the response is dominated by the firstmode and the corresponding lateral force distribution is valid, the second plastic hinge will developwhen the base plastic has already been developed and experiences 30% flexural overstrength there.In cases where the response is dominated by the second mode of response there is the possibilitythat the mid-height plastic hinge will develop before or even without the formation of a base plastichinge. This case becomes more probable as we consider taller buildings. As it will be shown beloweven for 40-story buildings and ground motions with significant second mode spectral accelerationsfor these buildings, Equation (2) gave an adequate strength of the mid-height plastic hinge. Havingdetermined the mid-height plastic hinge flexural strength based on Equation (2) the wall can beanalyzed to verify or further adjust the strength of the mid-height plastic hinge in order to meetspecific performance objectives.



Analytical model

Because of the exploratory nature of the approach, simple nonlinear analytical tools and simplemodels are used in this investigation. All floors have identical lumped masses. One-componentGiberson beam elements [21] model the core walls. One such beam element represents a core-wallsegment between two consecutive floors. The plastic hinge length at each end is assumed to be halfthe element length. Models use expected flexural strengths. With the expected flexural strengthMy and the yield curvature �y, the flexural rigidity of the beam element is given by EIe=My/�y.In this study the elastic portion of the walls in the SPH and DPH designs uses the flexural rigiditiesdetermined from the expected flexural strengths at a height of 0.3H. The hysteretic responsein the plastic hinges is represented by the simple Clough hysteretic moment–curvature rule, seeFigure 3(c). A post-yield flexural rigidity ratio r =0.02 is assumed in the model. Note that withthis model, the flexural rigidity ignores completely the tension stiffening effect. Tension stiffeningaffects the initial period of the buildings and can also affect the response, especially in casesof limited nonlinear response or lightly reinforced walls. Two further simplifications are: (i) thestiffness of the gravity load system is not considered and (ii) all walls were fixed at the base.A limitation of the Giberson beam elements is that they do not consider the spread of plasticitycaused by flexure–shear interaction in reinforced concrete [22]. Consequently, curvatures obtainedfrom the analyses should be taken as approximate only. The effect of shear deformations wasignored in this study. In addition, the lumped-plasticity model used does not consider the effectof axial force-bending moment-shear force interaction in the nonlinear hysteretic behavior of thewalls. In addition, no strength and stiffness degradation was considered in the hysteretic behaviorof the walls.

The computer program Ruaumoko [23] was used to estimate modal properties as well as toperform the nonlinear dynamic time-history analyses (NDTHA). Table III lists the first two modalperiods for all the case studies. The periods obtained from each design approach vary within asmall range. Such variation is due to the different amounts of longitudinal reinforcement providedin the elastic portions of the walls. Large displacement theory was selected for the analyses andthe P-Delta effect caused by the displaced floor weights was conservatively assumed to be resistedby the core wall. Caughey constant 2% viscous damping ratio was used in all the modes [23, 24].

Table III. Modal periods obtained ignoring concrete tension stiffening.

Design for MRSAbased on 0.5Ig ACI-318 Eurocode 8 DPH concept

T1(s) T2(s) T1(s) T2(s) T1(s) T2(s) T1(s) T2(s)

10-story SYLOV360 1.0 0.2 2.1 0.4 2.0 0.3 2.1 0.3TAK090 0.9 0.2 1.7 0.4 1.6 0.3 1.7 0.3RIN228 0.9 0.1 1.4 0.3 1.4 0.2 1.4 0.2





0 5 10 15 20-1

0

1

a g(g

)a g

(g)

a g(g

)

SYLOV360

0 5 10 15 20-1

0

1TAK090

0 5 10 15 20-1

0

1

t (sec)

RIN228

0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

Acc

eler

atio

n, S

a (g

)

Period, T (sec)

SYLOV360

TAK090RIN228

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

Dis

plac

emen

t, S d

(m

)

Period, T (sec)

SYLOV360

TAK090RIN228

(a)

(b)

(c)

Figure 4. Earthquake ground motions time histories, acceleration and displacement responseelastic spectra for 5% damping: (a) time histories; (b) acceleration response spectra; and

(c) displacement response spectra.

Ground motions

Each building was analyzed for the near-fault ground motion as it was designed for. The groundacceleration time histories and the 5% damped acceleration and displacement response spectra aredepicted in Figure 4. Two of them, the SYLOV360 and the RIN228 were recorded in the Mw 6.61994 Northridge earthquake. The third record is the TAK090 from the Mw 7.2 1995 Great Hanshinearthquake. All the three records have large spectral accelerations between T =0 and 1.6 s, whichis the period range of the second mode in all cases. The SYLOV360 record is characterized by astrong pulse of two cycles resulting in maximum spectral accelerations at T=0.35s. The RIN228motion has a strong one-cycle pulse with predominant period of about Tp=0.8s. The TAK090motion has multiple cycles of Tp=0.35 and 1.2 s resulting in large spectral accelerations at theseperiods.

The motions used in this study have distinct strong pulses with significant frequency contentin the period range of the second mode for the buildings considered. The destructiveness of thesemotions in terms of second, and higher, mode excitation is due to the fact that results not only in



0 0.15 0.30

5

10Le

vel

SYLOV360

0 0.15 0.30

5

10

TAK090

10-story

0 0.15 0.30

5

10

20-story

RIN228

0 0.05 0.10

10

20

Leve

l

0 0.05 0.10

10

20

40-story

0 0.05 0.10

10

20

0 0.03 0.060

20

40

Leve

l

0 0.03 0.060

20

40

0 0.03 0.060

20

40

Mi / (WtH)Mi / (WtH)Mi / (WtH)

MRSA

ACI-Exp.

ACI-NDTHA

Figure 5. Normalized bending moment envelopes for ACI designs.

large second mode spectral, but also in significant first mode spectral accelerations that are highlycorrelated in the time domain with the second modal accelerations.

Results of the analyses

Figures 5 and 6 plot the bending moment envelopes for the ACI-318 and SPH design approaches,respectively. Figure 7 compares the bending moment envelopes obtained from the NDTHA for theACI-318, SPH and DPH designs. An analysis of the different responses for each design approachwill follow.

Each plot in Figure 5 shows three bending moment envelopes: (i) MRSA; (ii) expected flexuralstrength established from the final design, labeled ACI-Exp.; and (iii) demand obtained from theNDTHA, labeled ACI–NDTHA. The bending moment envelopes have been normalized by theproduct of the total seismic weight and height of the structure, WtH. We observe that the bendingmoment envelopes obtained from the NDTHA reach or exceed the expected flexural strength notonly at the base, but also in at least another region up in the walls. In the 10- and 20-storybuildings the demand exceeds the expected capacity in those regions of the walls that have flexuraldiscontinuities due to termination of longitudinal reinforcement. In the 40-story buildings plasticityis also observed up in the walls. It will be shown later that the curvature ductility demands in thoseplastic regions in the upper portions of the walls are not negligible. This observation is significant



0 0.15 0.30

5

10Le

vel

SYLOV360

0 0.15 0.30

5

10

TAK090

10-story

0 0.15 0.30

5

10

20-story

RIN228

0 0.05 0.10

10

20

Leve

l

0 0.05 0.10

10

20

40-story

0 0.05 0.10

10

20

0 0.03 0.060

20

40

Leve

l

0 0.03 0.060

20

40

0 0.03 0.060

20

40

Mi / (WtH)Mi / (WtH)Mi / (WtH)

MRSA

EC8

Priestley

SPH-NDTHA

Figure 6. Normalized bending moment envelopes for SPH design case. Comparison with design bendingmoment envelopes based on MRSA, EC8 [2], Priestley et al. [9] and obtained from NDTHA.

because in practice plasticity up the height in the walls is not expected by practicing engineerswhen using the ACI-318 design approach.

Figure 6 plots the bending moment envelopes for with the SPH design approach. Each plotincludes four envelopes: (i) MRSA; (ii) design envelope prescribed by EC8 or NZS-3101, labeledEC8; (iii) design envelope proposed by Priestley et al. [9] and given by Equation (1); and(iv) demand obtained from NDTHA, labeled SPH–NDTHA. The bending moment envelopes havebeen normalized by the product of the total seismic weight and total height of the structure,WtH. The design envelope given by Equation (1) and plotted in Figure 6 was computed with anoverstrength factor �◦ =1.56, a displacement ductility �=5 and the fundamental periods listed inTable III for each building. Factor �◦ was calculated as �◦ =�h My,0/Mu,0, where �h=1.3 andMy,0/Mu,0=1.2. The displacement ductility � was made equal to the R factor, thus accepting theassumption of equal elastic and inelastic displacement demands for long-period single-degree-of-freedom oscillators [6, 24]. For the 40-story buildings, where just above minimum reinforcementwas detailed, �◦ was larger than 1.56 because the expected flexural strength at the base My,0 wasmore than 1.2 times larger than the design moment Mu,0.

Figure 6 shows clearly that there are very large differences between the shapes of the bendingmoment envelopes obtained from the MRSA and the NDTHA, and the differences become morepronounced in the 20- and 40-story buildings. As pointed out by others [5, 8, 9, 13, 14], the secondand other higher modes are not greatly affected by the base plasticity as inferred by the MRSA



0 0.15 0.30

5

10Le

vel

SYLOV360

0 0.15 0.30

5

10

TAK090

10-story

0 0.15 0.30

5

10

20-story

RIN228

0 0.05 0.10

10

20

Leve

l

0 0.05 0.10

10

20

40-story

0 0.05 0.10

10

20

0 0.03 0.060

20

40

Leve

l

Mi / (WtH) Mi / (WtH) Mi / (WtH)0 0.03 0.06

0

20

40

0 0.03 0.060

20

40

ACI

SPH

DPH

Figure 7. Bending moment envelopes obtained from the NDTHA for the three design approaches.

and this is the main reason for the differences in shapes. This figure also shows that the bendingmoment envelopes obtained from the NDTHA reaches or exceeds the EC8 linear design envelopesin all cases. Thus, the present study confirms the observations made by Panneton et al. [8] andPriestley et al. [9] that the current linear design envelope recommended by EC8 and other similarcodes does not provide sufficient protection against yielding in the upper portions of the wallsas intended in CD. Figure 6 also shows that the bending moment envelopes obtained from theNDTHA are all within or just above the design envelope proposed by Priestley et al. except forone of the 20-story buildings.

A main finding of the analysis for the SPH design approach is the practical difficulty thatarises when trying to ensure elastic response in the walls except at the base. For example, ifthe 20-story walls are designed in accordance with the envelope proposed by Priestley et al.[9], the required longitudinal reinforcement ratios at mid-height are �1,H/2=3.5, 3.5 and 2.3%for the SYLOV360, TAK090 and RIN228 design motions, respectively. Similarly, for the 40-storybuildings the reinforcement ratios required at mid-height are �1,H/2=4.2, 4.3 and 4.3% for thesame design motions. These reinforcement ratios are large to excessive. The reason for the largeratios is the larger bending moment demands combined with smaller axial forces acting on thewalls at mid-height. In summary, the SPH design approach requires large amounts of longitudinalreinforcement in the intermediate portion of the walls and this is associated with significantcongestion and higher cost.



0 9 180

5

10

Leve

lSYLOV360

0 9 18

TAK090

10-story

0 9 18

RIN228

20-story

0 9 180

10

20

Leve

l

0 9 18 0 9 18

40-story

0 9 180

20

40

Leve

l

μφ i

0 9 18μφ i

0 9 18μφ i

ACI

SPH

DPH

Figure 8. Curvature ductility envelopes obtained from NDTHA for the three design approaches.

The reduction in bending moment demands in the DPH design approach is observed in Figure 7,where the bending moment envelopes obtained from the NDTHA for the ACI-318, SPH and DPHdesign approaches for the nine buildings are compared. As in previous two figures, the bendingmoment envelopes have been normalized by the product of the total seismic weight and totalheight of the structure, WtH. As expected, the SPH design approach consistently shows the greatestbending moment demands in the intermediate portion of the walls. In contrast, the DPH designapproach effectively limits these demands. Limiting the intermediate height bending moments inthe DPH design approach makes it possible to obtain longitudinal reinforcement ratios that aresmaller than those at the wall base, see Table I.

The extent and magnitude of plasticity in the walls can be observed through the curvatureductility demands. The authors discussed above the approximation made in the analytical curvaturesgiven by the Giberson beam elements. Figure 8 shows the curvature ductility demands for the casesstudied. Curvature ductilities were computed as the maximum absolute curvature obtained fromthe NDTHA divided by the yield curvature. Figure 8 clearly illustrates the concentration of theplasticity in regions along the wall height in the ACI-318 designs, labeled ACI in this figure. Thecurvature ductility demand in the upper part of the 10-story buildings reaches 14 in one case and17 in another, which if upon model refinement is found to be correct, requires special detailing tosustain such a demand. For one of the 20-story buildings the curvature ductility demand observed



at 60% of the height reaches the large value of 12. For another of the 20-story and for one ofthe 40-story buildings, the curvature ductility demand observed at 60% of the height reaches themoderate value of 9. The remaining 20-story and all the 40-story buildings also yield a height ofabove 0.6H, although the ductility demands there are moderately low and may be attained if somedetailing of the reinforcement designed for these regions. We note that in all analyses yieldingtakes place in the upper portions of the walls well above the boundary elements mandated by ACI-318. From the observations made, the authors recommend a revision of the ACI-318 requirementsfor determining the extent of well-detailed boundary elements or a revision of the entire designapproach.

The SPH design has, in seven out of the nine cases, the largest base curvature ductility demands,see Figure 8. This is due to constraining plasticity to a SPH. The DPH design approach concentratesthe plasticity at two specific regions along the height not exceeding 0.2 of the total buildingheight, see Figure 8. For the 10-story buildings the DPH design significantly reduces the extentand magnitude of curvature ductility demand in the upper part of the building in comparison withACI-318, and in all cases the curvature ductility demands are small or modest. For the 20-storybuildings the DPH design significantly reduces the extent and in one case also the magnitude ofcurvature ductility demand in the upper part of the building in comparison with ACI-318, and inall cases except for RIN228 the curvature ductility demands are small or modest. For the 20-storybuilding for the RIN228 case a curvature ductility demand equal to 14 was computed, which canbe achieved with proper detailing. For the 40-story buildings the mid-height plastic hinge does notcompletely spread throughout the allocated length Lp2=0.1H. This is because of the significanteffect of axial load on the flexural strength of the lightly reinforced 40-story walls. At the baseof the walls the DPH design results in curvature ductility demands in between or even smallerthan the demands obtained from the other two approaches. The curvature ductility demands inthe 40-story buildings are greater for the DPH design approach than for the ACI-318 design andreaches a maximum of 12 for the RIN228 motion. In all these cases curvature ductility demandscan be achieved with proper detailing.

We note that in the 20-story buildings responding to SYLOV360 and TAK090, the curvatureductility demand at the base is small. This is because the designs followed the FEMA 356recommendations of using an effective section flexural rigidity equal to 0.5EIg. This value issignificantly larger than the flexural rigidities between 0.15 and 0.25EIg, calculated from the finaldesigns. This is a characteristic of force-based design provisions, which can result in overestimationof the required base strength in some cases.

Panagiotou et al. [7] observed experimentally shear force amplifications during the shaketable testing of a full-scale structural wall. Such amplifications have been observed by otherresearchers through analytical work [1, 5, 9, 14, 25–28] and were observed also in this study.Figure 9 presents the shear force envelopes obtained from the NDTHA. These forces have beennormalized by the total seismic weight Wt. A close comparison of the shear force envelopesobtained for the buildings in each design approach SPH in 6 out of the 9 times results in thehighest shear forces. In general, the DPH design approach does not result in significant reductionof the shear forces in cantilever wall buildings when compared with the other two approaches.Furthermore, for all cases the base shear forces range between 2 and 5 times the design base shearforces calculated from the MRSA. This is because in the reduction of the higher-mode spectralaccelerations with the large value of R=5 used in the MRSA. The authors concur with Pannetonet al. [8] in that shear forces obtained fromMRSA are no indication of the force demands in inelasticwalls.



0 0.3 0.60

5

10Le

vel

SYLOV360

0 0.3 0.6

10-story

TAK090

0 0.3 0.6

20-story

RIN228

0 0.25 0.50

10

20

Leve

l

0 0.25 0.5

40-story

0 0.25 0.5

0 0.2 0.40

20

40

Leve

l

Vi / W Vi / W Vi / W0 0.2 0.4 0 0.2 0.4

MRSA

ACI

SPH

DPH

Figure 9. Normalized shear force envelopes obtained from NDTHA.

Figure 10 plots the normalized lateral displacement envelopes for each of the cases analyzed.Lateral displacements have also been normalized by the total height. The maximum roof drift ratio,defined as the maximum roof lateral displacement at the top of the wall over the wall height, ispractically independent of the design approach, save the cases of the 10-story building designed forand subjected to SYLOV360 motion and the 20-, 40-story building designed for and subjected toRIN228 motion. This is due to the similar first modal periods for the different design approaches, inmost cases, and to the almost constant spectral displacements for the periods of interest. Differencesin the lateral displacement envelopes are observed primarily for the 10-story buildings. The SPHdesign results in quasi-linear displacement envelopes. This is because of the concentration plasticrotation of the wall around its SPH at the base. In contrast, the ACI-318 design approach results inthe more curved displacement envelope due to the propagation of yielding along the wall height.

Figure 11 compares the inter-story drift ratio envelopes. The ACI-318 design results in thehighest values of inter-story drift in eight out of the nine cases in the upper part of the walls. Thereare six cases where the ACI-318 design exceeds 3% inter-story drift ratio. This is due to localizedyielding that occurs at about 0.6H. Further, the maximum inter-story drift values in the DPH designare consistently smaller than those computed for the ACI-318 design approach. Finally, the SPH



0 1 20

5

10

Leve

lSYLOV360

0 1 20

5

10

10-story

TAK090

0 1 20

5

10

20-story

RIN228

0 1 20

10

20

Leve

l

0 1 20

10

20

40-story

0 1 20

10

20

0 1 20

20

40

Leve

l

Δ i (m) Δ i (m) Δ i (m) 0 1 2

0

20

40

0 1 20

20

40

ACI

SPH

DPH

33 3

1.5 5.15.1

0.75 0.75 0.75

Δ i / H (%) Δi / H (%) Δi

/ H (%)

Figure 10. Lateral displacement response envelopes obtained from NDTHA.

design approach gives in eight out of nine cases the smallest values of inter-story drift in the upperpart of the building.

Residual lateral displacements should be an important design objective in tall building design.Figure 12 plots the residual lateral displacement profiles observed for the case studies. ACI-318designs result in the highest values of residual roof displacement for the 20-and 40-story buildings.In the ACI-318 designs, residual displacements increase very significantly above a height of 0.6H,where the maximum curvature ductility demand was computed. The DPH design approach showslarge residual roof displacements in one of the 40-story buildings.

From the results of this study, the authors suggest decreasing the ductility demand in the mid-height plastic hinges in the taller buildings. This will also cause reduction of the residual displace-ments and can be achieved by increasing the flexural strength of the mid-height plastic hinges.

SUMMARY AND CONCLUSIONS

This paper discussed the effect of higher modes, and especially of the second mode, on thenonlinear dynamic response of cantilever-reinforced concrete wall buildings. It proposed a DPHapproach to better control the seismic response of these buildings to strong shaking. This paper



0 2 4 6 70

5

10Le

vel

SYLOV360

0 2 4 6 70

5

10

TAK090

10-story

0 2 4 6 70

5

10

RIN228

20-story

0 2 4 6 70

10

20

Leve

l

0 2 4 6 70

10

20

40-story

0 2 4 6 70

10

20

0 2 4 6 70

20

40

Leve

l

Θi (%)

0 2 4 6 70

20

40

Θi (%)

0 2 4 6 70

20

40

Θi (%)

ACI

SPH

DPH

Figure 11. Inter-story drift ratio envelopes obtained from NDTHA.

investigated numerically the seismic response of cantilever wall buildings designed using threedifferent approaches: (i) ACI-318; (ii) a SPH concentrated at the base of the walls according toEC8, NZS-3101 or the CSA; and (iii) the proposed dual-hinge approach where one plastic hingeconcentrated at the wall base and another develops near mid-height. Nonlinear dynamic analysesof these buildings were carried out for three strong near-fault ground motions. The investigationled to the following conclusions:

1. Near-fault ground motions including strong pulses, characterized by large elastic spectralaccelerations in the range of the second translational mode in high-rise cantilever buildingsare likely to have a significant influence on the bending moment and shear force demandsin the walls. Currently, design codes do not address such large demands explicitly.

2. The second mode response is not significantly affected by the development of plasticity atthe base of the walls as is often assumed when performing a code-based MRSA. In light ofthis observation it is concluded that modal superposition approaches, which are appropriatefor obtaining design parameters in linear systems, be revised for appropriate use in nonlinearsystems considered herein like cantilever flexural walls.

3. Based on this numerical study, designs of cantilever wall buildings following the current ACI-318 building code may result in unintended concentration of nonlinear deformations higherup in the walls where elastic response is generally expected. Current detailing requirements



0 0.15 0.30

5

10

Leve

lSYLOV360

0 0.15 0.30

5

10

TAK090

10-story

0 0.15 0.30

5

10

RIN228

20-story

0 0.8 1.60

10

20

Leve

l

0 0.8 1.60

10

20

40-story

0 0.8 1.60

10

20

0 0.3 0.60

20

40

Leve

l

Δi,r

(m) 0 0.3 0.6

0

20

40

Δi,r

(m) 0 0.3 0.6

0

20

40

Δi,r

(m)

ACI

SPH

DPH

Figure 12. Lateral residual displacement response envelopes obtained from NDTHA.

may not ensure controlled flexural response in such regions. This study also observed largeinter-story drift ratios as well as a large concentration of residual rotations at about 60% ofthe walls’ height in the ACI-318 designs.

4. Codes like EC8, NZS-3101 and CSA allow the development of plastic hinges at the wallbases only. The results presented in this paper indicate that, under the near-fault groundmotions considered, bending moment demands at intermediate height in walls developingbase plastic hinges compare closely or even exceed the base bending moments. Suchintermediate height moment demands are not recognized in the code prescriptive require-ments for CD. Hence, elastic response up the height in walls may not actually occur asintended. It is recommended that current design provisions be examined and appropriatelyrevised.

5. The proposed DPH design approach, in which plastic hinges are allowed to form at thewall base and near mid-height while ensuring elastic response elsewhere, was found to havesignificant advantages: reduction in the amount of longitudinal reinforcement when comparedwith the EC8, NZS-3101 and CSA designs, and ease of detailing along most of the height.This approach can be easily implemented in design, bringing a reduction in the amountof longitudinal reinforcement and of confinement reinforcement in a significant portion ofthe walls.



6. The flexural strength of the mid-height plastic hinge can be adjusted above a minimum value,proposed in Equation (2) of this study, to meet specific performance objectives in high-risebuildings.

7. This study concurs with studies reported in the literature on the effect of higher modes ofresponse on the shear force demands in cantilever wall buildings. Shear force demands incantilever wall buildings can be much greater than those determined from modal responsespectrum analyses. In this study the shear force demand from NDTHA was up to 5 timeslarger than the one obtained fromMRSA and reduced with a uniform force reduction factor R.

LIST OF SYMBOLS

ag ground accelerationAw cross section area of core wallC1,T mid-height bending moment amplification factorEI section flexural rigidityEIe effective section flexural rigidityEIg gross section flexural rigidityEIr reloading flexural rigidity of Clough hysteretic ruleh floor heighthi elevation heightH wall heighti floor numberI cross section moment of inertia of core wallLp1 equivalent plastic hinge length at baseLp2 equivalent plastic hinge length near mid-heightLw length of wallLo floor plan view dimensionm lumped-seismic mass per floorM bending momentMi bending moment at floor iM◦

0 base expected bending moment at overstrengthMH/2 design bending moment of mid-height plastic hingeM◦

H/2 expected mid-height bending moment at overstrength for use in Equation (1)Mu,0 design base bending momentMt total massMy,0 reference yield moment or expected base momentn number of floors and lumped massesP base axial load acting on the wallr post-yield stiffness ratioR lateral force reduction factorSa spectral accelerationSd spectral displacementt timetw thickness of wallT period



T1 first modal periodT2 second modal periodV shear forceVi shear force at floor iV0 base shear forceVu,0 design base shear forceWt total seismic weightw seismic weight per floor�i lateral displacement at floor i�i,r residual lateral displacement at floor i�P axial load per floorεy steel yield strain�i inter-story drift ratio� displacement ductility factor�� curvature ductility factor��,i curvature ductility factor at floor i�l,0 longitudinal reinforcing steel ratio�l,H/2 longitudinal reinforcing steel ratio of mid-height plastic hinge

of the DPH design approach�◦ expected flexural overstrength to design moment ratio�y yield curvature�u ultimate curvature� ratio of mid-height to base first modal bending moment�h overstrength factor due to strain hardening

ACKNOWLEDGEMENTS

The authors sincerely thank the Portland Cement Association who provided financial support to the firstauthor for his Doctoral studies. The authors also thank Professors F. J. Crisafulli, M. E. Rodriguez,A. Rutenberg and M. J. N. Priestley and the anonymous reviewers for their very useful comments.

REFERENCES

1. Derecho AT, Iqbal M, Ghosh SK, Fintel M, Corley WG, Scanlon A. Structural walls in earthquake-resistantbuildings dynamic analysis of isolated structural walls development of design procedure—design force levels.Portland Cement Association (PCA) R & D Serial No. 0665, 1981.

2. CEN EC8. Design of Structures for Earthquake Resistance. European Committee for Standardization: Brussels,Belgium, 2004.

3. NZS 3101. New Zealand Standard, Part 1—The Design of Concrete Structures. Standards New Zealand,Wellington, New Zealand, 2006.

4. CSA Standard A23.3-04. Design of Concrete Structures. Canadian Standard Association: Rexdale, Canada, 2005;214.

5. Blakeley RWG, Cooney RC, Megget LM. Seismic shear loading at flexural capacity in cantilever wall structures.Bulletin New Zealand National Society Earthquake Engineering 1975; 8:278–290.

6. Paulay T, Priestley MJN. Seismic Design of Reinforced Concrete and Masonry Buildings. Wiley: Hoboken, NJ,1992.

7. Panagiotou M, Restrepo JI, Conte JP. Shake table test of a 7-story full scale reinforced concrete structural wallbuilding slice phase I: rectangular wall. SSRP 07-07 Report, Department of Structural Engineering, Universityof California at San Diego, 2007.



8. Panneton M, Leger P, Tremblay R. Inelastic analysis of a reinforced concrete shear wall building according tothe national building code of Canada 2005. Canadian Journal of Civil Engineering 2006; 33:854–871.

9. Priestley MJN, Calvi GM, Kowalsky MJ. Displacement Based Seismic Design of Structures. IUSS Press: Pavia,Italy, 2007.

10. ACI 318-05. Building code requirements for structural concrete and commentary. ACI Committee 318, FarmingtonHills, 2005.

11. Wallace JW, Orakcal K. ACI 318-99 provisions for seismic design of structural walls. ACI Structural Journal2002; 99(4):499–508.

12. Moehle J, Bozorgnia Y, Yang TY. The tall buildings initiative. Proceedings of the SEAOC Convention, SquawCreek, CA, 2007; 315–324.

13. Rodrıguez ME, Restrepo JI, Carr AJ. Earthquake-induced floor horizontal accelerations in buildings. EarthquakeEngineering and Structural Dynamics 2002; 31:693–718.

14. Panagiotou M, Restrepo JI. Lessons learnt from the UCSD full-scale shake table testing on a 7-story residentialbuilding slice. Proceedings of the SEAOC Convention, Squaw Creek, CA, 2007; 57–73.

15. Hidalgo PA, Jordan RM, Martinez MP. An analytical model to predict the inelastic seismic behavior of shear-wall,reinforced concrete structures. Engineering Structures 2002; 24:85–98.

16. ABS Consulting. Flash Report on The Niigata-ken Chuetsu-oki Earthquake, Online reference; accessed 2008.17. ASCE 7-2005. Minimum design loads for buildings and other structures. ASCE/SEI 7-05, American Society of

Civil Engineers, Reston, VA, 2006.18. FEMA 356. Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Federal Emergency

Management Agency: Washington, DC, 2000.19. NEHRP. NEHRP Recommended Provisions: Design Examples. Washington, DC, 2006.20. Panagiotou M, Restrepo JI. Design and computational model for the UCSD 7-story structural wall building slice.

SSRP 07-09 Report, Department of Structural Engineering, University of California at San Diego, 2007.21. Giberson MF. Two nonlinear beams with definitions of ductility. Journal of the Structural Division (ASCE) 1969;

95(ST2):137–157.22. Hines EM, Restrepo JI, Seible F. Force–displacement characterization of well-confined bridge piers. ACI Structural

Journal 2004; 101(4):537–548.23. Carr AJ. Ruaumoko—A Program for Inelastic Time-History Analysis. Department of Civil Engineering, University

of Canterbury, New Zealand, 1998.24. Chopra AK. Dynamics of Structures: Theory and Applications to Earthquake Engineering. Prentice-Hall: Upper

Saddle River, NJ, 2001.25. Park R, Paulay T. Reinforced Concrete Structures. Wiley: Hoboken, NJ, 1975.26. Eberhard MO, Sozen MA. Member behavior-based method to determine design shear in earthquake-resistant

walls. Journal of Structural Engineering 1993; 119(2):619–640.27. Filiatrault A, D’Aronco D, Tinawi R. Seismic shear demand of ductile cantilever walls: a Canadian code

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Documents

Dual Plastic Hinge Design Concept for Reducing Higher Mode Effects on Higher Rise Cantilever Wall Buildings