EFFECT OF BIDIRECTIONAL EXCITATIONS ON SEISMIC RESPONSE OF RC BUILDINGS

November 24, 2012 17:45 WSPC/S1793-4311/238-JET 1250019

Journal of Earthquake and TsunamiVol. 6, No. 3 (2012) 1250019 (20 pages)c© World Scientific Publishing CompanyDOI: 10.1142/S1793431112500194

EFFECT OF BIDIRECTIONAL EXCITATIONSON SEISMIC RESPONSE OF RC BUILDINGS

AMAN M. MWAFY∗

Department of Civil and Environmental EngineeringUAE University, Al-Ain, P.O. Box 17555, UAE

Received 15 November 2010Accepted 4 October 2011

Published 4 September 2012

This paper investigates the effect of the horizontal and vertical components of groundmotions (HGM and VGM, respectively) on the seismic response of Reinforced Concrete(RC) buildings designed to modern capacity design principles and located in the vicinityof active faults. Fiber-based analytical models are used to monitor the global and localresponse of twelve reference structures, including verifying the response modificationfactor and tracing the member shear supply-demand response using a ductility- and axialforce-sensitive shear strength approach. The simulation models are subjected to near-field earthquake records with increasing severity up to collapse, including and excludingVGM. The results indicate that the lower the contribution of horizontal seismic forcesto the seismic response, the higher is the significance of VGM. The fluctuation of axialforces in vertical structural members significantly increases when including VGM. Thisnot only has direct consequences on tension and compression response but also hasimpact on shear capacity. The diverse range of buildings and performance criteria andlarge number of incremental dynamic analyses confirm the importance of including VGMin seismic design and assessment of contemporary RC buildings, and hence cast doubtson the reliability of pre-code structures located in the vicinity of active faults.

Keywords: Seismic design; RC buildings; failure modes; bidirectional excitation; incre-mental dynamic analysis.

1. Introduction

Since the vertical ground motion (VGM) attenuates faster than its horizontal coun-terparts, the average vertical-to-horizontal peak ground acceleration (V/H) ratiowill be lower than the values conventionally assumed in design at some distance fromthe epicenter. Conversely, there are increasing field evidences that in the vicinityof the causative fault of moderate-to-strong earthquakes the V/H ratio frequentlyexceeds unity, and hence exceeds the design values [Papazoglou and Elnashai, 1996;Kim and Elnashai, 2009]. For instance, for the 1979 Imperial Valley “EO6” and 1984Morgan Hill “G07” events, the V/H ratio was 3.70 and 3.94, respectively. However,these high values do not imply that a structure will suffer severe damage underthese records since either one or both of the two components may be insignificantor they may not coincide in time to cause strong interaction effects. The difference

∗The author is also affiliated with Zagazig, Egypt (on leave).

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http://dx.doi.org/10.1142/S1793431112500194


A. M. Mwafy

in frequency content between the VGM and horizontal ground motion (HGM)when coupled with the difference between the vertical and horizontal dynamiccharacteristics of structures cast doubts regarding the adequacy of the simplifiedapproaches adopted in some design provisions. Recently, new approaches have beensuggested to account for VGM [Collier and Elnashai, 2001; Elgamal and He, 2004],which lead to the adoption of VGM spectra in design provisions [CEN, 2004].

A number of analytical and laboratory studies concluded that structures locatednear active faults may be subjected to unaccounted for demands if VGM was under-estimated [Saadeghvariri and Foutch, 1991; Broderick and Elnashai, 1995; Buttonet al., 2002; Shakib and Fuladgar, 2003; Elnashai et al., 2005; Kianoush and Chen,2006]. Columns may be adversely affected if high compressive forces are developedor if axial forces changed to tension. The ductility demands increase in the presenceof high vertical forces due to second order moments. The shear supply of columnsmay be significantly affected by the variation in axial forces due to the reductionof the axial load contribution to shear strength.

The present study focuses on investigating the importance or otherwise ofincluding VGM in design and assessment of code-compliant RC buildings designedto the modern capacity design requirements and located near active faults. Widerange of buildings, realistic fiber-based modeling and incremental dynamic analysesare adopted to study the impact of near-source VGM on seismic response at variousearthquake intensities. Natural earthquake records are selected on the basis of thesite-to-source distance and the V/H ratio. Ground motions with unusual V/H ratioswere avoided, aiming to arrive at practical, rather than extreme, conclusions. Theselected earthquake records are normalized to possess equal velocity spectrum inten-sity in the period range of the buildings. This scaling approach reduces the responsevariability under different excitations, thus allowing the use of fewer ground motionsin analysis. A total of 700 inelastic response history analyses are carried out fortwelve reference structures to trace their response at different limit states using awide range of global and local response parameters, including the assessment of theresponse modification factor (R) and structural members shear response.

2. Analytical Models, Response Criteria, and Ground Motions

Twelve buildings are selected in the current study to represent medium-rise RCbuildings designed to modern seismic codes. Different building heights (24–36m)and structural systems (moment-resisting frames and dual frame-wall systems) aswell as structural regularity are taken into consideration. The buildings are splitinto three sets based on their structural system, as shown in Table 1. The geometriccharacteristics of the structures are illustrated in Fig. 1. The overall plan dimensionsof the reference buildings are 20×15m. The total heights are 25.5, 36, and 24m forthe IF, RF, and FW sets, respectively, with equal story heights of 3m except thefirst story of the IF set, which is 4.5m. The lateral force resisting system for theIF and RF sets is moment frames, while it comprises of both moment frames and

1250019-2


Effect of Bidirectional Excitations on Seismic Response

Table

1.

Chara

cter

isti

csofth

ein

ves

tigate

dst

ruct

ura

lsy

stem

s.

IFR

FFW

Gro

up

Buildin

gIF

-H-

IF-M

-IF

-M-

IF-L

-R

F-H

-R

F-M

-R

F-M

-R

F-L

-FW

-H-

FW

-M-

FW

-M-

FW

-L-

Ref

eren

ce030

030

015

015

030

030

015

015

030

030

015

015

Eig

ht

Tw

elve

Eig

ht

No.ofst

ori

esD

esig

nD

uct

ility

HM

ML

HM

ML

HM

ML

Des

ign

PG

A(g

)0.3

00.3

00.1

50.1

50.3

00.3

00.1

50.1

50.3

00.3

00.1

50.1

5T

H(s

)0.6

74

0.6

54

0.7

19

0.7

23

0.8

57

0.8

93

0.9

20

0.9

13

0.5

38

0.5

33

0.5

92

0.5

88

TV

(s)

0.0

75

0.0

73

0.0

86

0.0

87

0.0

89

0.0

89

0.0

88

0.0

88

0.0

70

0.0

70

0.0

82

0.0

82

Note

:T

H:E

last

icper

iod

inhori

zonta

ldir

ecti

on.

TV

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last

icper

iod

inver

tica

ldir

ecti

on.

H:H

igh

des

ign

duct

ility;M

:M

ediu

m;L:Low

.

1250019-3


A. M. Mwafy

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a central core in the FW set. While the second and third sets are regular in planand in elevation, the IF set exhibits two sources of irregularity in elevation. Thefirst story has a greater height than the remaining ones and the discontinuity atthe ground story of some intermediate columns, which are supported by long spanbeams. The floor system is solid slab in the IF and RF sets, and a waffle slab inthe FW set. The buildings were assumed to be founded on medium soil type.

The reference structures were designed and detailed in accordance with theEurocodes [Fardis, 1994]. The characteristic compressive strength of concrete andyield strength of reinforcing steel are 25MPa and 500MPa, respectively. The cross-sectional dimensions of columns and walls were kept constant at various storiesto eliminate any potential plastic hinge development at column bottoms in inter-mediate stories due to tapering [Fardis, 1994]. The column reinforcing steel variesalong the height of the buildings according to the imposed actions from gravity andseismic loads.

Eurocode 8 allows for adjusting seismic design forces through the use of threeductility classes [CEN, 2004]. The value of the behavior factor (response modifica-tion factor) increases and rigorous design requirements are imposed by Eurocode 8for higher ductility classes. The level of ductility varies from “Low”, requiring nospecial detailing or capacity design requirements, to “High”, dictating rigorous stan-dards on member detailing. Structures designed to ductility class “Low” are notintended to dissipate large amount of hysteretic energy. Structures designed anddetailed to ductility class “Medium” can exceed the yield limit state well withoutdeveloping brittle failure modes. Eurocode 8 ensures that structures designed anddetailed to ductility class “High” will develop stable mechanisms associated withhigh levels of hysteretic energy dissipation. Combinations of three design ductilityclasses (High, Medium, and Low) and two design ground accelerations (0.15 and0.30 g) lead to the four investigated cases within each of the investigated groups.The selection of the three groups of structures was motivated by the desire toinvestigate the effect of VGM on structures designed to different ductility and PeakGround Acceleration (PGA) levels. The elastic fundamental periods obtained fromfree vibration analyses confirm that the horizontal periods of the selected build-ings (0.53–0.92 s) cover a broad spectral amplification rang. Sample reinforcementdetails of the frame buildings designed to a ductility class “Medium” and a PGAof 0.30 g are depicted in Fig. 2.

The assessment of the seismic behavior of RC structures subjected to strongmultiple component of excitations requires the resolution of some fundamentaldifficulties. VGM mainly increases the fluctuation of axial forces in columns, whichis superimposed on the forces generated from overturning. Since flexural and shearbehavior of structural elements are strongly dependent on the axial force level,the fluctuation in axial forces may cause a significant variation in stiffness andstrength. Therefore, detailed fiber-based analytical models of the entire buildingswere developed using the verified inelastic analysis platform Zeus-NL [Elnashaiet al., 2010]. This Finite Elements package is capable of predicting the large

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A. M. Mwafy

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1250019-6



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(Continued

)

1250019-7


A. M. Mwafy

displacement behavior of space frames under static and dynamic loading, takinginto account both geometric nonlinearities and material inelasticity. The programhas a large library of material models and three-dimensional elements that canbe used with a wide range of concrete, steel, and composite sections. The programexplicitly accounts for the spread of inelasticity along the member length and acrossthe section depth through the fiber modeling approach, which enables the accu-rate estimation of damage accumulation. This technique is more accurate than thepoint–hinge modeling approach used in other programs, especially when large axialforce variations exist. This structural simulation platform was originally developedand thoroughly tested at Imperial College London [Izzuddin and Elnashai, 1993;Izzuddin et al., 1994]. The further development and verification of the program withfull scale test results have continued at University Illinois at Urbana-Champaignto deliver a state-of-the-art simulations platform for inelastic static and dynamicanalysis [Jeong and Elnashai, 2005; Kim et al., 2011]. Several research projects cov-ering high-rise buildings and complex bridges have adopted this verified analysisplatform [Kwon and Elnashai, 2008; Mwafy et al., 2010; Mwafy, 2011].

Each structural member is idealized using a number of cubic-elasto-plastic ele-ments capable of representing the spread of inelasticity within the member cross-section and along the member length. This elasto-plastic element employs a cubicshape function to calculate transverse displacement. The formulation is intended torepresent the inelastic cyclic response of RC members, considering material and geo-metrical nonlinearities. Large displacements/rotations and large independent defor-mations relative to the frame element’s chord are taken into account. The inelasticresponse of the element is evaluated through the use of the fiber approach. Theelement cross-sections are divided into a number of fibers. The appropriate mate-rial stress-strain relationships are applied for each fiber, and strains and stressesare monitored. The response of cross-sections is assembled from the response ofindividual fibers.

The selected reinforced concrete sections from the Zeus-NL library for mod-eling of structural members allow the geometric definition of the steel, confinedand unconfined concrete regions within the section. Confinement factors are evalu-ated as described in Eurocode 8, and varied along the member length according tothe arrangement of transverse reinforcements. The inelastic response of the crosssection is assembled from contributions of different concrete and steel fibers forwhich inelastic cyclic material constitutive relationships are applied. The concreteresponse is represented in the Zeus-NL models using a uniaxial constant confine-ment concrete model, which includes enhanced cyclic degradation rules, inelasticstrain and shape of unloading branches [Mart́ınez-Rueda and Elnashai, 1997]. Anelasto-plastic model is also selected to represent the reinforcing steel [Elnashai andIzzuddin, 1993]. In this model, a kinematic hardening rule for the yield surfacedefined by a linear relationship is assumed in the post-elastic range [Elnashai et al.,2010]. The parameters used in the material models are the actual (mean) valuesrather than nominal (characteristic) material strengths.

1250019-8



The adopted modeling approach explicitly accounts for the interaction betweenaxial force and bending moment and monitors the shear supply-demand ratio duringthe multi-step analysis. Based on anticipated critical response, dynamic analyses areconducted along the global X-axis for the frame buildings, and along the Y -axis forthe frame-wall structures. The self-weight of structural members and superimposeddead loads are calculated and applied in the inelastic analyses before seismic actions.To account for inertia effects during dynamic analysis, masses are calculated in amanner consistent with gravity loads and are represented by lumped mass elements.The columns and walls of the twelve reference structures are considered to be fixedat the foundation level [ASCE, 2010].

In addition to permanent loads, structures are subjected to transient loads,which consist of multi-axial accelerations that vary in the real time domain. Anumerical direct integration scheme must be employed in order to solve the sys-tem of equations of motion. Either the Newmark time integration scheme or theHilber–Hughes–Taylor integration algorithm can be utilized in Zeus-NL. The latternumerically-dissipative algorithm, for which accuracy is not affected by the timestep length, is adopted in the present study since it allows effective response predic-tions for highly inelastic structures [Broderick et al., 1994]. A detailed descriptionof the Zeus-NL capabilities is discussed elsewhere [Elnashai et al., 2010].

Three limit state criteria are utilized to monitor global structural failure. Theseare: (i) an upper limit of interstory drift ratio (IDR) equal to 3%, (ii) formation ofa column hinging mechanism, and (iii) a drop in the overall lateral resistance bymore than 10%. Two additional failure criteria on the member level are employed:(i) exceeding ultimate curvature or (ii) shear failure. The latter is evaluated usingan experimentally-verified ductility- and axial force-sensitive shear strength model[Priestley et al., 1994]. The ductility effect is estimated in the present study based onthe curvature ductility, which is a better indicator of the degradation in the concretecomponent of shear resistance, rather than the displacement ductility formulationintroduced in the latter study. An enhanced approach for estimating the ductilityeffect of RC beams is also adopted [Priestley et al., 1996]. Moreover, the design codeshear strength is monitored after eliminating design safety factors for comparisonwith the Priestley et al. shear strength model.

The adopted performance criteria are implemented in a post-processor todirectly monitor capacities and demands of shear and curvature and apply theperformance parameters during the response history analysis. This algorithm wasdeveloped to trace the continuous variation of supply and demand in different struc-tural members during multi-step analysis. The instantaneous curvature ductility(µφ = φmax/φy) is needed for the evaluation of the shear supply from the modelof Priestley et al. [1994]. Yielding in critical regions should be achieved to obtainφy. This is carried out using inelastic pushover analysis by applying the incremen-tal lateral loads twice, in the positive and in the negative directions, up to a highdrift limit. Hence, two yield curvature values are calculated for all critical sections,corresponding to yielding of the top and bottom reinforcement. The post-processor

1250019-9


A. M. Mwafy

employs the φy values to calculate the instantaneous curvature ductility (µφ) duringtime history analysis. This algorithm also monitors the satisfaction of other limitstates adopted in the current study to provide insight into the level of damage atthe member and the structure levels.

Four input combinations of the horizontal and vertical components of the 1989Loma Prieta “SAR” and 1995 Kobe (Hyogo-ken Nanbu) “KBU” events are usedin the incremental dynamic collapse analyses. The selected earthquake recordswere recorded near the source (9–25km) and have moderately high V/H ratios(1.09–1.56) compared with records with extreme V/H ratios. The accelerationresponse spectra of the natural records used in analysis are compared with thedesign spectrum in Fig. 3. The average inelastic fundamental periods of vibra-tion of the three groups of structures (1.40, 1.75, and 0.9 s, respectively) are alsodepicted in Fig. 3. Figure 4 explains the normalization approach of the selectedearthquake records to possess equal velocity spectrum intensity in the period rangeof the buildings. This scaling approach is adopted to reduce the response variabil-ity under different excitations, thus allowing the use of fewer input ground motionsin analysis. It is clear that the spectral acceleration of Loma Prieta HGM at theperiod range 0.1–0.5 sec is significantly higher than Kobe. Amplifications of highermode effects are therefore anticipated under the former record. It is also noteworthythat the VGM spectral amplifications of Kobe and Lome Prieta were comparablebefore scaling. Employing the HGM scale factors to normalize VGM suppresses theVGM spectrum of Kobe, as shown from Fig. 3. This scaling approach is adoptedto avoid changing the V/H ratio of the records. The impact of Lome Prieta VGMis therefore expected to be more pronounced compared with Kobe VGM.

3. Effect of VGM on Seismic Response

3.1. Vertical periods of vibration

The ratio of horizontal-to-vertical fundamental period (TH/TV ) reported in the lit-erature of RC moment resisting frames up to eight stories high varies from 2.5 to 7.0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2

Period (sec)

Spec

tral

Acc

eler

atio

n (g

)

Design code elastic spectrum

Loma Prieta (SAR) - H

Loma Prieta (SAR) - V

IF

RF

FW

0 0.5 1 1.5 2

Design code elastic spectrum

Kobe (KBU) - H

Kobe (KBU) - V

IF

RF

FW

Inelastic period range of the buildings

Inelastic period range of the buildings

Fig. 3. Elastic response spectra (5% damping) of input ground motions scaled to a PGA of 0.30 galong with the average inelastic period of the three groups of buildings IF, RF, and FW.

1250019-10



Fig. 4. Scaling of input ground motions for inelastic analysis of the RF group of buildings accord-ing to the velocity spectrum intensity and inelastic periods.

(a) 4th Mode (b) 5th Mode (c) 4th Mode

Fig. 5. Vertical modes of vibration of the three groups of buildings: (a) IF group; (b) RF group;(c) FW group.

[Papazoglou and Elnashai, 1996]. The results of the present study indicate that theratios of horizontal-to-vertical “elastic” period of the three groups of structures are8.6, 10.1, and 7.4, respectively. The periods of vibration of the reference buildingsare given in Table 1, while the vertical mode shapes are shown in Fig. 5. It is clearthat the TH/TV ratio is related to the height and the vertical stiffness of the struc-ture. The maximum TH/TV ratio and the longest vertical period are for the tallestbuildings (the 12-story group of buildings), while the minimum ratio and shortestperiod is for the stiffest and lowest structural system (the 8-story FW structures).

1250019-11


A. M. Mwafy

Comparison of the TH/TV ratio of the first and the third groups, which havethe same number of stories but different vertical stiffness values, indicates thatthis ratio is not significantly influenced by structural characteristics. The resultsimply that a wide range of medium-rise buildings experiences approximately thesame dynamic amplification during vertical excitation. The vertical periods of thetwelve reference structures and those reported in previous studies suggest that theseperiods are less than 0.15 s for the majority of medium-rise RC buildings. The effectof VGMs, which have high amplification in the short period range, as shown fromFig. 3, is likely to be important for a wide range of buildings. This observationsuggests that medium-rise RC buildings near active faults should be conservativelydesigned according to the maximum amplification of VGM.

3.2. Global seismic response

Global response results of the twelve reference structures are compared for the casesof analysis with and without VGM at different levels of PGA up to collapse. A largeincrease in top displacement, IDR and base shear is observed in several cases. Themaximum increase in these response parameters at the design intensity is 14%, 22%,and 15%, while at twice the design PGA it is 12%, 12%, and 13%, respectively. Themaximum impact of VGM is observed on the global response of the FW buildings.This is attributed to the lower contribution of the lateral seismic loads to the globalresponse of these stiff buildings, particularly to deformations. Including VGM inanalysis does not though show a consistent trend in increasing or decreasing theglobal response. As expected, Loma Pieta (SAR) causes higher response comparedwith Kobe (KBU), particularly for the second and the third groups of building.The results confirm that the V/H ratio does not reflect the actual contribution ofVGM, which depends on the combined characteristics of the structure, VGM andHGM.

The incremental dynamic collapse analyses yields several interesting observa-tions. For instance, the interstory drift collapse limit state is frequently exceededunder a lower PGA when employing VGM and HGM in analysis. This is coupledin several cases with an increase in the roof displacement and the base shear by upto 20%. The incremental dynamic analyses also enable tracing the effect of VGMat different PGA levels. Sample results are presented in Figs. 6 and 7 for the rela-tionship between PGA and global response parameters (roof displacement, IDR,and base shear) with and without VGM. It is observed that VGM may lead toa reduction in deformation demands at a certain PGA range, while significantlyamplifies these demands at higher ground motion intensities due to the increase insecond order (P -∆) moment, as shown from Fig. 6. The variability in the responseat higher levels of seismic forces is due to the elongation in the horizontal and ver-tical periods of vibration, which results in significant changes in the contributionof both VGM and HGM to the overall response according to the shape of theirresponse spectra.

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0.0 0.2 0.4 0.6 0.8 1.0 1.20

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[1] Loma Prieta (H) [2] Loma Prieta (H+V)Polynomial Fit of [1]Polynomial Fit of [2]PGA (g)T

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Fig. 6. Tracing the effect of VGM on the global response of the RF-M-030 building using incre-mental dynamic analysis: (a) top displacement; (b) interstory drift; (c) base shear.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60

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Building: FW-M030Record: Loma Prieta

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Fig. 7. Tracing the effect of VGM on the global response of the FW-M-030 building using incre-mental dynamic analysis: (a) top displacement; (b) interstory drift; (c) base shear.

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The response of the dual structural system shown in Fig. 7 is different thanthat of the frame structures. It is observed that the relationship between PGA andglobal response is almost linear. This is attributed to the lateral response of shearwalls, which remain nearly elastic except at the base and dominate the responseof FW buildings due to their higher stiffness compared with lateral force resistingframes.

3.3. Member seismic response

Sample results depicting the impact of VGM on the axial force response of a plantedcolumn are shown in Fig. 8. The deterioration in the response of this column undercyclic loading at twice the design PGA is clear, while the maximum axial compres-sive forces increase by 35%. Although VGM slightly increases the variation in shearsupply of planted columns, it does not have notable effect on the shear demand-supply response. Figure 9 depicts the axial and shear force demand-supply responsehistories of a second story internal column in one of the 12-story structures at twicethe design PGA. It is shown that VGM increases the maximum axial compressiveforces by 45%. Tensile forces are generated only when VGM is included in the anal-ysis. However, this has a marginal effect on the shear strength, which only decreasesby 6%. It is clear that the margin of safety, estimated as the supply-to-demand ratiousing the shear strength model of Priestley et al. [1994], is high due to the capacitydesign provisions imposed by the Eurocode provisions.

The effect of VGM on the variation of axial forces in shear walls is less significantsince the stiff walls already attract high levels of axial forces from HGM (similarto the case of external columns). Nevertheless, a significant increase in curvatureductility demands (up to 58%) is observed in the coupling beams when includingthe VGM in analysis, particularly at upper stories as shown in Table 2. It is alsonoteworthy that although axial forces in columns are more influenced by VGM atupper stories due to the lower contribution of gravity and lateral seismic forces,no shear failure is observed in these columns. This is attributed to the constant

Fig. 8. Effect of VGM on the axial force variation of a planted column at twice the design PGA.

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Fig. 9. Effect of VGM on shear response of a second story internal column.

Table 2. Maximum curvature ductility demand in the couplingbeams of the frame-wall buildings at twice the design intensity.

Reference Loma Prieta (H) Loma Prieta (H + V )

MCDD Location MCDD Location

FW-H030 8.45 8th floor 9.94 8th floorFW-M030 6.66 8th floor 10.49 8th floorFW-M015 2.98 7th floor 3.83 8th floorFW-L015 4.41 8th floor 4.76 8th floor

Note: H: Only HGM is used in analysis.H + V : HGM and VGM are used in analysis.

column cross-sections used along the height of the reference structures, which wasadopted to eliminate any potential plastic hinging at intermediate stories due totapering. Clearly, this design approach increases overstrength and unintentionallyprotects the columns from shear failure modes.

The adverse effects of VGM on the response of vertical structural membersare more pronounced at high levels of PGA. As shown in Fig. 10, axial compressiveforces increase by 15% and tensile forces develop in an internal ground story columnwhen VGM is considered. The variability of axial force and shear supply significantlyincreases at the time interval corresponding to the VGM peaks. The vulnerabilityof vertical structural members to failure due to the reduction in shear strength

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Fig. 10. Effect of VGM on shear response of a ground story internal column.

is anticipated if the instances of minimum axial compressive force and maximumshear demand coincide. Moreover, it is observed from the incremental dynamicanalyses that neglecting VGM may result in a gross error in predicting failuremodes. Ultimate concrete strain is exceeded at a PGA of 0.75 g when the KobeVGM is included in the analysis of IF-L-015, while this failure mode is observedat a PGA of 0.97 g under the effect of HGM only. Figure 11 also confirms thatVGM causes shear failure in the walls of FW-M-030; hence higher PGA is neededto arrive at this failure mode if VGM is excluded from analysis.

3.4. Effect of VGM on response modification factor

As shown from the results presented above, yield and collapse may occur underlower PGA when the structure is subjected to both HGM and VGM. This mayreduce the response modification factor (R), leading to higher seismic design forces.The mean values of the R factor “supply” for the twelve reference structures arepresented in Table 3. The results indicate that the mean R factor of IF-M-015 isreduced by 18% under the effect of VGM. The presented sample results confirmthe inadequacy of the response modification factor calculations in the absence ofVGM.

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Fig. 11. Effect of VGM at first indication of shear failure in walls.

Table 3. Effect of VGM on the response modification factor (R).

Reference R(H) R(H + V ) R(H + V )/R(H)

L G F L G F L G F

IF-H-030 8.27 5.35 8.27 9.75 5.89 9.39 1.18 1.10 1.13IF-M-030 4.96 3.97 4.96 5.05 4.83 5.05 1.02 1.22 1.02IF-M-015 15.22 8.81 14.23 12.53 8.91 12.53 0.82 1.01 0.88IF-L015 3.52 5.68 3.52 3.69 6.31 3.69 1.05 1.11 1.05

RF-H-030 13.11 8.16 13.11 13.21 7.10 13.21 1.01 0.87 1.01RF-M-030 11.76 5.23 14.58 11.13 4.90 12.85 0.95 0.94 0.88RF-M-015 9.33 6.93 9.33 8.39 6.95 8.39 0.90 1.00 0.90RF-L-015 6.41 6.25 6.41 6.22 6.13 6.22 0.97 0.98 0.97

FW-H-030 5.47 8.69 5.47 5.83 8.50 5.83 1.07 0.98 1.07FW-M-030 4.46 6.81 4.46 4.54 6.68 4.54 1.02 0.98 1.02FW-M-015 5.39 8.43 5.39 4.95 9.12 4.95 0.92 1.08 0.92FW-L-015 4.59 7.59 4.59 4.33 7.76 4.33 0.94 1.02 0.94

Note: R = (PGA at collapse/PGA at yield) x overstrength.H: Only HGM is considered.H + V : HGM and VGM are considered.L: Local limit states are used to estimate R.G: Global limit states are used to estimate R.F : First observed yield and collapse criteria are employed to calculate R.

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4. Conclusions

The impact of bidirectional seismic excitations, namely horizontal and verticalground motions (HGM and VGM, respectively) on the local and global response ofmodern code-compliant RC buildings in the vicinity of active faults was inves-tigated in this paper. Application to a wide range of contemporary buildingsusing detailed fiber-based analytical modeling, dynamic-to-collapse analyses, andthoroughly-defined response parameters lend weight to the observations of thisstudy. The assessed parameters included the response modification factor (R) andtracing the shear capacity-demand response of all structural members using a real-istic time-dependent ductility- and axial force-sensitive assessment approach ofinstantaneous shear capacity. Dynamic simulations under horizontal-only and hori-zontal plus vertical component were undertaken using natural ground motions withmoderately high vertical-to-horizontal PGA (V/H) ratios.

It is concluded that VGM has an important impact on the seismic responseon both the member and structure levels. It is suggested to conservatively designmedium-rise RC buildings near active faults according to the maximum amplifica-tion of VGMs, which apparently match the predominant vertical periods of thesestructures. The V/H ratio did not clearly reflect the anticipated effect of VGM,which mainly depends on the combined characteristics of HGM and VGM, hori-zontal and vertical dynamic characteristics of the structure and PGA level. Theeffect of VGM increases in irregular structures and when the contribution of thelateral seismic action is relatively small, such as at higher stories.

The results indicated that global response parameters increased by up to 22% atthe design PGA when VGM is considered. The interstory drift collapse limit statewas reached at lower earthquake intensities with VGM. This was coupled with anincrease in the roof displacement and the base shear by up to 20%. The contributionof VGM to global response was not constant at various PGA levels. VGM mayreduce the response at lower intensity levels, while significantly increasing it athigher PGAs due to P -∆ effects. The impact of VGM on the member responsewas more pronounced. The axial compressive forces in vertical structural membersincreased by up to 45% and tensile forces were detected only when VGM wasconsidered. VGM increased the curvature ductility demand of coupling beams byup to 58%. It also reduced the PGA that caused local failure by up to 23% and themean values of the R factors by up to 18%, potentially leading to the need to specifyhigher seismic design forces. The results confirmed the inadequacy of R factorcalculations in the absence of VGM and the pressing need to realistically verify thedesign of new structures and assess the seismic response of existing buildings in thevicinity of active faults using bidirectional seismic excitations.

Acknowledgments

The author is indebted to Professor A.S. Elnashai, Head of the Civil and Environ-mental Engineering Department at the University of Illinois at Urbana-Champaign,

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for his comments on this study. This help is gratefully acknowledged. This studywas partially supported by the UAE University under a contract no. 1554-07-01-10.

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EFFECT OF BIDIRECTIONAL EXCITATIONS ON SEISMIC RESPONSE OF RC BUILDINGS

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