Seismic performance of a full-scale, reinforced high

Seismic performance of a full-scale, reinforcedhigh-performance concrete building. Part I:Experimental study

Sebastien Mousseau and Patrick Paultre

Abstract: Full-scale tests provide valuable information on the characteristics of building structures that can be used toevaluate design methods, to calibrate modelling techniques, and to determine damage corresponding to loading levels.These tests are scarce due to the enormous requirements in testing space and specialized testing equipment. The seismicbehaviour of a full-scale, two-storey, reinforced high-performance concrete building designed with moderate ductility de-tailing is evaluated by pseudo-dynamic testing, during which increasing seismic loads are applied, resulting in increasinglevels of permanent damage to the structure. To monitor the level of damage, a series of successive forced-vibration testsare also carried out at each step of the process and are used to track changes in the key dynamic properties of the building.The paper presents the design of the test structure according to the new edition of the CSA A23.3-04 Design of concretestructures standard, the series of pseudo-dynamic tests simulating different levels of earthquake excitation consistent withthe 2005 edition of the National building code of Canada, and the evaluation of the performance of the building. It isshown that the detailing requirements of CSA A23.3-04 are more than adequate to provide the ductility and overstrengthexpected.

Key words: high-performance concrete, reinforced concrete, moment-resisting frames, earthquake engineering, forcemodification factors, overstrength, ductility, pseudo-dynamic testing, push-over.

Resume : Les essais a grande echelle fournissent des informations importantes sur les caracteristiques des structures pou-vant etre utilisees pour evaluer les methodes de dimensionnement, pour calibrer des techniques de modelisation, et pourdeterminer l’endommagement correspondant a des niveaux de chargement. La rarete de ces essais est due principalement ala necessite de disposer de grands espaces de laboratoire et d’equipements d’essais specialises. Dans cet article, le compor-tement d’un batiment en vraie grandeur de deux etages est evalue par essais pseudo-dynamiques dans lesquels le batimentest soumis a des niveaux d’excitation sismique croissants causant des dommages de plus en plus importants a la structure.Le batiment est construit en beton a hautes performances pour posseder une ductilite moderee. Des essais en vibration for-cee sont utilisees pour evaluer les changements dans les proprietes dynamiques de la structure. L’article presente le dimen-sionnement de la structure d’apres la nouvelle edition de la norme CSA A23.3-04, Dimensionnement des structures enbeton, la suite des essais pseudo-dynamiques simulant les differents niveaux d’excitation des tremblements de terre consis-tants avec le Code national du batiment du Canada 2005, et l’evaluation de la performance du batiment. On montre queles reglements de la norme CSA A23.3-04 sont tout a fait adequats pour assurer le niveau de ductilite et de surcapacite de-sire.

Mots-cles : beton a hautes performances, beton arme, ossature resistant aux moments, genie parasismique, facteurs demodification de force, surcapacite, ductilite, essai pseudo-dynamique, poussee progressive.

Introduction

Experimental research is the most reliable means of as-sessing seismic performance of structures and is crucial to

the development of new numerical models and design meth-ods. Ultimately, the performance of buildings during actualearthquakes is the only measure of the adequacy of new de-sign procedures and detailing practice. Numerical predic-tions with calibrated models using full-scale test resultsprovide the only choice of systematically evaluating the in-fluence certain parameters have on the likely response ofbuilding structures. This paper reports on a comprehensivetest series performed on a full-scale, two-storey reinforcedhigh-performance concrete (HPC) building. The buildingwas subjected to repeated pseudo-dynamic tests as part of aresearch project on the seismic behaviour of HPC structuresand damage detection. The main objectives of the experi-mental investigation were to carry out pseudo-dynamic testson a two-storey reinforced HPC building to: (i) determinethe damage and performance under increasing seismic loads,

Received 31 May 2007. Revision accepted 9 January 2008.Published on the NRC Research Press Web site at cjce.nrc.ca on30 July 2008.

S. Mousseau. SNC-Lavalin inc, 455 Rene-Levesque BoulevardWest, Montreal, QC H2Z 1Z3, Canada.P. Paultre.1 Department of Civil Engineering, Universite deSherbrooke, Sherbrooke, QC J1K 2R1, Canada.

Written discussion of this article is welcomed and will bereceived by the Editor until 31 December 2008.

1Corresponding author (e-mail: [email protected]).

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Can. J. Civ. Eng. 35: 832–848 (2008) doi:10.1139/L08-017 # 2008 NRC Canada

(ii) investigate the force modification and overstrength fac-tors suitable for the structure that is designed and detailedto exhibit moderate ductility (nominal ductility in past co-des), (iii) investigate whether the concrete compressivestrength limit of 55 MPa in Canadian standard CSA-A23.3-94 (CSA 1994) is too conservative, (iv) investigate the ad-equacy of the design and detailing requirements for moder-ate ductility, (v) provide experimental evidence forpredicting damage under increasing seismic loads, and(vi) evaluate the performance of different inelastic time-history dynamic analyses. This paper focuses on the designof the test structure, the experimental procedures, thepseudo-dynamic and push-over tests, and the test results.A companion paper (Mousseau et al. 2008) compares theexperimental results obtained during the seismic tests withthe predictions of inelastic time-history dynamic analyses.

High-performance concrete in the Canadian standardRecent advances in material technology facilitate the

production of high-performance concrete. The term high-performance concrete encompasses improved mechanicalcharacteristics, increased durability, enhanced workability,better behaviour under loading, etc. In this research project,only the improved mechanical characteristics of the high-performance concrete are considered, especially high-compressive strength and its effects. In this paper, theterms HPC and high-strength concrete (HSC) are used in-terchangeably. High-strength concrete is more fragile thannormal-strength concrete (NSC) and columns made ofHSC need to be properly confined to display the samelevel of ductility as NSC columns. In view of limited ex-perimental results at the time of its publication, the 1994Canadian standard CSA-A23.3 (CSA 1994) limited thespecified concrete compression strength to 55 MPa in seis-mic zones. A large number of experimental works haveshown that HSC columns and beams, when properly de-tailed, can exhibit sufficient ductility. Most, if not all,tested specimens in these experimental works were singlecantilever columns or beams or beam–column–slab sub as-semblages. The present research program, therefore, wasdeveloped to study the behaviour of HSC members in afull-scale reinforced concrete structure designed accordingto the new Canadian standard CSA-A23.3-04 (CSA 2004)under realistic earthquake excitation.

Moment-resisting frame with moderate ductilityThe 1984 version of Canadian standard A23.3 (CSA 1984)

introduced new requirements for the design and detailing ofconcrete structures in seismic zones, particularly for frameswith what was then called nominal ductility. This new duc-tility level is between the ductile structures built accordingto capacity design procedures to dissipate energy in speciallydetailed members and all the other structures.

The suitability of the new requirements for nominal duc-tility was confirmed by results from reversed cycling load-ing tests on full-scale beam–slab–column subassemblagesand by inelastic time-history dynamic analyses (Paultre etal. 1989; Paultre and Mitchell 1987). Ductility level was ac-counted for by using a force-modification factor, R, varyingfrom 1 to 4 for concrete structures in the 1985 version of theNational building code of Canada (NBCC) (NRCC 1985). A

value of R = 2.0 was assigned to a frame with nominal duc-tility, which did not change up to the 1995 version of theNBCC (NRCC 1995). One of the objectives of this researchprogram was to study the possibility of increasing the force-modification factor for moment-resisting frames with nomi-

Fig. 1. Full-scale two-storey reinforced high-performance concretebuilding with reaction wall.

Fig. 2. Plan and elevation views of the building.

Mousseau and Paultre 833

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nal ductility from 2.0 to 2.5 to do justice to these type ofstructures, which, as was judged by many designers andmembers of the CSA A23.3 committee, possess more ductil-ity than the factor 2.0 implied. It is important to note that,when this research program began, the change of the forcemodification factor from 2.0 to 2.5 had not been made.Therefore, this research was a part of the process of makingthat change.

Design and description of the buildingThe two-storey reinforced concrete building used for this

research project has a 5 m bay in the east–west (E–W) di-rection and a 4 m bay in the north–south (N–S) direction.The storey height from top of slab to top of slab was 3 m.The columns were all 300 mm � 300 mm. The two-wayslab floor system consisted of a 150 mm thick slab sup-ported by beams 300 mm � 300 mm on all four sides. Thespecified concrete strength was 70 MPa and the specifiedsteel yield strength was 400 MPa. Plan and elevation viewsof the building are shown in Figs. 1 and 2.

The design of the building is summarized below; morecomplete information can be found in Mousseau and Paultre(2005). The design forces used are in accordance with the1995 edition of the NBCC (NRCC 1995) for a site locatedin Montreal. The moment-resisting frame concrete structurewas designed for nominal ductility with a seismic forcemodification factor R = 2.0. Table 1 presents the loads usedin the design process. Load combinations, as prescribed bythe 1995 NBCC, were used to calculate the design forces.

The seismic base shear, V, was calculated from the fol-lowing equation:

½1� V ¼ Ve

RU

where U = 0.6 is a calibration factor and Ve is the elasticbase shear given by:

½2� Ve ¼ vSIFW

where v is the zonal velocity ratio, I is the seismic impor-tance factor, F is a foundation factor, and W is the seismicweight (100% of the dead load plus 25% of the design snowload). S is the seismic response factor (Table 2), which is afunction of the period of vibration of the building and the

acceleration-related seismic zone (Za), and the velocity-related zone (Zv). For the building located in Montreal,v = 0.10, I = 1.0, F = 1.0, Za = 4.0, Zv = 2, and W =759.4 kN.

Significant changes were introduced in the 2005 editionof the NBCC (NRCC 2005) to determine the seismic baseshear, as given by:

½3� V ¼ SðTaÞMvIEW

RdRo

� Sð2:0ÞMvIEW

RdRo

where S(Ta) is the design spectral response acceleration forthe fundamental lateral period of vibration of the buildingTa, Mv is a factor to account for higher mode effects onbase shear, IE is an earthquake importance factor for thestructure, W is the seismic weight (100% of the dead loadplus 25% of the design snow load), Rd is a ductility-relatedforce-modification factor, and Ro is an overstrength-relatedforce-modification factor. The NBCC 2005 also specifiesthat, for structures with Rd ‡ 1.5, V need not be taken asbeing greater than two thirds of the value calculated forTa = 0.2 s, i.e.,

½4� V � 2

3

Sð0:2ÞIEWRdRo

Figure 3 compares the base shear coefficients formoment-resisting frames with moderate (called nominal inprevious codes and standards) ductility built in Montreal ac-cording to the NBCC 1995 and 2005 in the form of baseshear coefficients (V/W) as a function of the fundamentallateral period of vibration (T). The base shear was calculatedfor a structure located on site classification C, which is thereference site classification in the NBCC 2005, hence Fa =

Table 1. Specified loads used in design.

Dead loads, DWeight of structural members 24 kN/m3

Mechanical services, floor finishing, and partition loading for the first floor 1.70 kN/m2

Mechanical services and insulation weight loading for the roof 2.10 kN/m2

Walls, cladding, and insulation 2.40–3.60 kN/m2

Live load, LOffice building (first floor) 2.40 kN/m2

Snow load, SBuilding located in Montreal 2.32 kN/m2

Earthquake load, EBase shear: V = 0.1260 W (NRCC 1995) 95.69 kN

Wind load, WTotal pressure on building 0.866 kN/m2

Table 2. Seismic response coefficient.

Period, T (s) Za/Zv ST £ 0.25 <1.0 2.1

= 1.0 3.0>1.0 4.2

0.25 < T < 0.50 <1.0 2.1= 1.0 3.0 – 3.6(T – 0.25)>1.0 4.2 – 8.4(T – 0.25)

T‡ 0.50 All values 1:5=ffiffiffiffiT

p

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Fv = 1.0. The other parameters were Rd = 2.5, Ro = 1.4, IE =1.0, and Mv = 1.0. The 5% damped spectral response accel-eration values for the Montreal site are Sa(0.2) = 0.69g,Sa(0.5) = 0.34g, Sa(1.0) = 0.14g, Sa(2.0) = 0.048g. The de-sign spectral acceleration values, S(T), are equal to the cor-responding Sa(T) values as Fa = Fv = 1.0, with the additionalvalues S(T ‡ 4.0) = 0.024g.

The equations given in the NBCC 2005 to determine thefundamental lateral period of vibration of moment-resistingframes are:

½5� Ta ¼ 0:075h3=4n

for concrete frames, and

½6� Ta ¼ 0:1N

for all other moment frames; where hn is the total height ofthe building above the base and N is the total number ofstoreys above exterior grade. The same expressions werealso specified in the NBCC 1995, except that eq. [6] canalso be used for any moment frames.

Figure 3 shows that the seismic forces calculated with theNBCC 2005 are slightly higher than those calculated withthe NBCC 1995 for structures having a fundamental periodlower than 1.0 s located on site classification C. For thebuilding being studied, the base shear coefficient is 4.3%higher according to the NBCC 2005.

Design and detailing of the members of the structure werein agreement with the special provisions for seismic designof CSA A23.3-94 Design of concrete structures (CSA1994), but accounted for the new requirements of CSAA23.3-04 (CSA 2004), which were then in a preliminarystage. Hence, the strong column – weak beam concept andnew requirements for the design of confinement reinforce-ment were all incorporated into the design. These new con-finement requirements state that the total effective area ineach of the principal directions of the cross section within aspacing s of rectangular hoop reinforcement, Ash, shall notbe less than the larger of:

½7� Ash ¼ 0:15knkpAg

Ach

f 0cfyh

shc

½8� Ash ¼ 0:09f 0cfyh

shc

where kn = n‘/(n‘ – 2) is a factor accounting for the effec-tiveness of the transverse reinforcement arrangement (wheren‘ is the total number of longitudinal bars in the columncross section that are laterally supported by the corner ofhoops or by hooks of seismic crossties), kp = Pf /Po is a fac-tor accounting for the level of axial load (where Pf is themaximum factored axial load for earthquake loading casesand Po is the nominal axial load resistance at zero eccentri-city), Ag is the gross area of section, Ach is the cross-sectional area of core, f 0c is the specified compressive con-crete strength, fyh is the specified yield strength of hoopreinforcement, s is the spacing of transverse reinforcement,and hc is the dimension of concrete core of rectangularsection measured perpendicular to the direction of thehoop bars to outside of peripheral hoop. The total effectivearea of rectangular hoops reinforcement is based on the

Fig. 3. Base shear coefficient (V/W) for reinforced concrete moder-ately ductile moment-resisting frames in Montreal.

Fig. 4. Summary of detailing requirements for reinforced concretemoderately ductile moment-resisting frames. ‘n, clear height of col-umn; c, column dimension; d, effective height; dbh, diameter of thehoop bars; db‘, diameter of the smallest longitudinal bars; h, mem-ber depth.


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curvature ductility demand and is, therefore, a function ofthe axial load, effectiveness of the transverse reinforce-ment, concrete strength, and the yield strength of hoop re-inforcement. General detailing requirements for moderatelyductile moment-resisting frames are summarized in Fig. 4.

Figures 5 and 6 show the reinforcement details of thebeams, columns, and slabs, and Fig. 7 shows a picture of abeam–slab–column connection of the two-storey framestructure being studied.

Casting of the building took place in seven stages. Thepedestals were first installed on the strong floor and castingproceeded for the columns of the first storey, two columnsat a time, followed by casting of the first-floor slab. Theprocedure was then repeated for the second storey. The con-

crete formulation is shown in Table 3. A large number of100 mm � 200 mm and 150 mm � 300 mm cylinders and100 mm � 100 mm � 400 mm prisms were made at thetime of casting to determine concrete compressive and ten-sile strengths at different ages. The average compressiveand tensile (modulus of rupture) concrete strengths at 28 dwere 63 and 5.5 MPa, respectively. At the time of testing,the average compressive strength had increased to 66 MPafor the low seismic excitation tests (April 2001) and was73 MPa during very severe seismic excitation tests (Sep-tember 2004).

Tension tests were performed on at least three steel sam-ples of each bar diameter for each batch of steel bars. Forthe 10M bars, the average values of yield strength, tensilestrength, and Young’s modulus were fy = 436 MPa, fu =555 MPa, and Es = 205 300 MPa, respectively. For the 15Mbars, the average values were fy = 401 MPa, fu = 631 MPa,and Es = 200 200 MPa.

Fig. 6. Reinforcement details of slabs: (a) roof reinforcement and(b) first floor reinforcement. E–W, east–west; N–S, north–south.All dimensions in millimetres.

Fig. 5. Reinforcement details of beams and columns. E–W, east–west; N–S, north–south. All dimensions in millimetres.

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Pseudo-dynamic and push-over testingprogram

The analysis of buildings subjected to seismic loadingshas always proved to be a delicate task. The inelastic behav-iour of these structures is often complex to model despitethe availability of different kinds of structural analysis soft-ware. Therefore, experimental investigation remains themost reliable method to predict seismic performance ofcivil-engineering structures and to calibrate numerical mod-els.

Shake-table tests make it possible to obtain the responseof a structure subjected to seismic loadings. The structuresare usually small-scale specimens due to limitations of theshaking tables. Therefore, size effects cannot be reproducedand detailing of reinforced concrete structures becomesproblematic. Consequently, shake-table studies are generallylimited to very simplified models or scaled structures requir-ing scaling laws that poorly represent the behaviour of rein-

forced concrete buildings. The rapid development ofcomputer-assisted computations over the last 30 years aswell as the possibility of realising a complete on-linecomputer-controlled acquisition system and data processingallowed the development of new hybrid experimental techni-ques, such as the pseudo-dynamic testing method (PSD)(Takanashi 1975).

Pseudo-dynamic testing methodologyGiven a discrete parameter model, the equations of mo-

tion for a structural system can be written in matrix form as

½9� M€u ðtÞ þ C_uðtÞ þ frðtÞ ¼ fðtÞ

where M and C are the mass and viscous damping matricesof the structure, _uðtÞ and €uðtÞ are the vectors of nodal rela-tive velocity and acceleration, t is time, fr(t) is the nodal re-storing force vector, and f(t) is the external excitation vectorapplied to the system. If a shear-type structure is subjectedto a horizontal ground acceleration €ugðtÞ, the force vectorf(t) = –Mr€ugðtÞ, where r is an influence vector with eachelement equal to one in the case of the tested building.

In an elastic system, the restoring force is fr(t) = Ku(t),where K is the stiffness matrix and u(t) is the displacementvector. For inelastic systems, more complex models are re-quired to represent the relation between restoring forces anddisplacements. The solution of eq. [9] can be approximatedusing direct step-by-step integration techniques where thetime is divided into n equal steps �t = td/n, where td is thetotal time of the external excitation, giving

½10� M€u i þ C_ui þ fri ¼ fi

in which €ui = €uði�tÞ, _ui ¼ _uði�tÞ, and fi = f(i�t).Pseudo-dynamic testing involves an interactive closed-

loop testing procedure that simulates dynamic loading. Acomputer program, which predicts the incremental displace-ments to be imposed on the structure after receiving nonlin-ear force response feedback ( fri) from the actual structure,models the interactive dynamic response. This process iscarried out for the duration (td) of a particular input accel-erogram ( fi). Therefore, measurements of the actual stiffnessproperties of the structure provide a realistic simulation ofthe dynamic response histories. Whereas inertial (M€ui) andviscous (C_ui) damping forces are modeled analytically withknown and measured quantities, respectively, the nonlinearstructural restoring forces are measured experimentally be-cause of the difficulty in modeling them accurately (Fig. 8).In this way, the process automatically accounts for the hys-teretic damping due to inelastic deformation of the rein-forcement and irreversible damage of the concrete material,which are the two major sources of energy dissipation.

To simulate the earthquake response of a structure, a re-cord of an actual or artificially generated earthquake groundacceleration history is used as input data for the computerrunning the pseudo-dynamic algorithm. The horizontal dis-placements of the control degrees-of-freedom (DOF) wherethe mass of the structure is considered concentrated arecalculated for a small time-step using a suitable time-integration algorithm. These displacements are then appliedto the test structure by servo-controlled hydraulic actuatorsreacting against a stiff reaction wall. Load cells on the ac-

Fig. 7. First floor joint reinforcement.

Table 3. Concrete formulation.

Mixing water 155 kg/m3

Cement, type 10-SF* 470 kg/m3

Natural sand 830 kg/m3

Coarse aggregate, 2.5–10 mm 980 kg/m3

Superplasticizers (EUCON 37) 5 L/m3

Water reducer (EUCON DX) 250 mL/100 kg

Mass density 2435 kg/m3

Water to cement ratio 0.33

*Approximately 7.5% of silica-fume content.


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tuators return the forces necessary to reach the requireddisplacements and these structural restoring forces are usedby the computer program to predict the next time-step dis-placement increment. A typical flowchart for the pseudo-dynamic test method is illustrated in Fig. 9.

InstrumentationPseudo-dynamic tests require essentially the same equip-

ment as conventional quasi-static tests, in which prescribedhistories of load or displacement are imposed on specimenstructures by means of displacement-controlled hydraulic ac-tuators. As shown in Figs. 1 and 10, the lateral seismic loadswere applied to the building by four double-acting,dynamic-rated servo-hydraulic actuators with a strokeof ±400 mm and 500 kN capacity reacting on a large-capacity vertical reaction wall. Two actuators were placedat each floor level and were attached at mid-span of theslabs and spandrel beams running in the E–W direction.The imposed displacements were measured with respect totwo independent steel frames (Fig. 10) using displacementtransducers. The two-storey building was fully instru-mented with strain gauges and displacement transducers tomeasure the deformations in the longitudinal reinforcementin the beams, columns, and slabs, and in the transverse re-inforcement in the columns and beams.

Undamaged dynamic propertiesAs the pseudo-dynamic testing method requires the devel-

opment of a precise numerical model for the structure,forced-vibration tests (FVT) were carried out to calibratethis model and to evaluate its performance (Paultre et al.2003). The FVT consisted of subjecting the structure to asinusoidal horizontal harmonic load generated by aneccentric-mass shaker. The recorded acceleration responseswere then used to extract various vibration properties (reso-

nant frequencies, mode shapes, and modal damping). Con-crete blocks were used on each floor to simulate the addedmass representing the combined dead and live loads. TheE–W axis was chosen for the pseudo-dynamic earthquakeloading as well as the FVT. The shaker was placed on theroof in a position chosen to excite both flexural and tor-sional modes of vibration. Low-frequency force-balancedaccelerometers were used on each floor to record horizontalaccelerations in two orthogonal directions (parallel and per-pendicular to the simulated earthquake loads). The FVTwere carried out with the shaker operating from 1 to 16 Hz,with increments of 0.01 Hz.

Figure 11 illustrates typical frequency responses for thebuilding in the undamaged state, i.e., before any seismic ex-citations were applied. Accelerations are plotted with respectto frequency. The building’s resonant frequencies (flexureand torsion) can be readily identified from the peaks ofthese frequency response curves. The amplitude recorded atposition TNEW (top floor, northeast corner, measuring axisparallel to the shaker force in the E–W direction) is plottedin Fig. 11a. The building’s two resonant flexural frequenciesin the E–W direction (2.47 and 7.56 Hz) and the two tor-sional frequencies (4.14 and 12.59 Hz) can be identified.The corresponding modal damping ratios are then obtainedusing the half-power bandwidth method and range from0.76% of critical damping for the second flexural frequencyto 1.57% for the first flexural frequency. Response obtainedat position TNEN in the orthogonal axis (same position, butaxis perpendicular to the shaker force) is also illustrated inFig. 11b. The torsional modes identified in the top graph(Fig. 11a) have a relatively stronger perpendicular compo-nent in the N–S direction and exhibit larger resonant ampli-tudes in that direction (4.14 and 12.59 Hz). The tworesonant flexural frequencies in the N–S directions thatwere barely visible in graph (Fig. 11a) are now clearly appa-

Fig. 8. Simplified representation of the pseudo-dynamic method. DOF, degrees of freedom; LVDT, linear voltage displacement transducer.

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rent (2.80 and 8.34 Hz). Table 4 presents the complete set ofundamaged dynamic properties for building.

Test procedureRepeated pseudo-dynamic tests were carried out to ob-

serve the behaviour of the structure under increasing simu-lated earthquake loading. At the end, a push-over test wasperformed to evaluate the structure’s overstrength and struc-tural ductility. After each level of seismic load applied tothe structure, the dynamic characteristics of the buildingwere obtained by forced-vibration tests. The structural signa-ture was, therefore, obtained for each loading step and wasrelated to the level of damage in the structure (Paultre et al.2007). Table 5 presents the chronology of the tests per-formed on the building.

The lumped mass matrix for the pseudo-dynamic test is a2 � 2 diagonal matrix with the masses concentrated at thefloor levels. The mass of the structure was provided by eight1300 mm � 1300 mm concrete blocks, four on each floor.The thickness of the blocks was determined to representprobable loading on the floor, i.e., 100% of design deadloads and 50% of design live loads. Hence, the mass matrix

consisted of a 20 050 kg mass at DOF 1 and a 18 730 kgmass at DOF 2. An initial damping matrix and stiffness ma-trix need to be specified at the beginning of the pseudo-dy-namic test. The damping matrix was based on results fromthe FVT obtained from the structure in the undamaged state.This initial damping matrix was computed to give dampingratios of 1.57% and 0.76% in the two flexural modes in theE–W direction (Table 4). The initial stiffness matrix for thestructure was determined by carrying out a static displace-ment test on the building and the results were confirmed byparameter identification after the first dynamic test.

The pseudo-dynamic tests were carried out in quasi-staticcondition to prevent the generation of inertial forces(accounted for in the computer model) and a maximumvelocity was specified for each actuator to control force re-laxation during the test (Thewalt and Mahin 1991). Hence,a maximum speed of 0.2 mm/s was used to move thebuilding. The time-integration scheme adopted is based onthe �-method (Hilber et al. 1977), which is an uncondi-tionally stable implicit algorithm. A time step of 0.02 swas used with the algorithm.

Ground motion time historiesTwo different accelerograms were used for the pseudo-

dynamic test. The first ground motion was the S00Ecomponent of the accelerogram recorded in El Centro,California, during the 18 May 1940, Imperial Valley earth-quake. The first 30 s time history for the input motion isshown in Figs. 12b and 13e. This ground motion wasscaled to different intensities to meet the objectives of theinvestigation.

The second time history used to carry out the PSD testswas the M7R70A1 accelerogram generated for Montrealand having a probability of exceedance of 2% in 50 years(Atkinson and Beresnev 1998). This ground motion is com-patible with the uniform hazard spectra (UHS) used in theNBCC 2005 (NRCC 2005, Adams and Halchuk 2003). Thistime history (Figs. 12a and 14c) was generated for a mo-ment magnitude 7.0 earthquake at a hypocentral distance of70 km. The peak ground acceleration (PGA) is 0.271g. Fig-ure 12 presents 5% damped pseudo-acceleration responsespectra (PSA) for the ground motion used in the tests. Thislast figure also illustrates the uniform hazard spectra (UHS)for a very dense soil and soft rock (class C) site located inMontreal according to the NBCC 2005.

Pseudo-dynamic and push-over test results

The earthquake responses of the structure, in terms ofstorey displacements and base shear forces, are presented inFigs. 13 and 14, respectively, for different seismic excitationlevels of the Imperial Valley earthquake (El Centro accel-erogram). Figure 15 presents the response to the M7R70A1accelerogram. The force–displacement hysteretic curves forall seismic excitations are shown in Figs. 16 and 17 forboth floors (interstorey drift versus storey shear) and inFigs. 18 and 19, where the global hysteretic behaviour ofthe building is depicted in terms of base shear versus roofdisplacement. Table 6 presents the maximum response ob-tained during the pseudo-dynamic tests carried out on the

Fig. 9. Pseudo-dynamic flowchart.


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building. The results are presented in chronological order ofthe tests.

Response to low seismic excitationThe responses of the building to the El Centro ground

motion scaled to 0.078g PGA were basically within the line-arly elastic range. According to the NBCC 1995 (NRCC1995), this level of seismic loading corresponds to a 1% in1 year probability level for Montreal. The storey displace-ment time history is shown in Fig. 13a and the storey shear

versus displacement responses and the base shear versusroof displacement are plotted in Figs. 16a and 18a, respec-tively.

The maximum interstorey drifts were 6.5 and 5.2 mm forthe first and second storeys, which correspond to drift ratiosof 0.22% and 0.20%, respectively. According to the NBCC2005 (NRCC 2005), drift ratios shall be limited to 1% forpost-disaster buildings, 2% for schools, and 2.5% for all otherbuildings. The maximum base shear, V0max, was 68.1 kN dur-ing the test.

The global behaviour of the building during the low seis-mic excitation test was excellent. The inspection of thestructure after testing did not reveal any major cracks otherthan hairline cracks due to the preliminary forced-vibrationtests, which had been performed before the first PSD test toobtain initial dynamic properties (frequencies and modeshapes).

Response to moderate seismic excitationModerate seismic excitation was achieved by scaling the

El Centro ground motion to 0.180g PGA. The structure’searthquake responses are shown in Figs. 13b, 15b, 16b, and18b. Some period elongation can be observed from the re-sponse history. All floor-displacement time histories are inphase, pointing to a dominant first-mode participation.

Under this seismic input, the structure exhibited signifi-cant cracking in the beams, columns, and slabs, but per-formed with no measured yielding of the reinforcement and

Fig. 10. Experimental setup for pseudo-dynamic tests.

Fig. 11. Measured frequency response functions, horizontal accel-eration: (a) east–west direction, north frame and (b) north–southdirection, east frame.

Table 4. Dynamic characterization results for undamaged building.

ModeFrequency,f (Hz)

Period,T (s)

Damping,� (%)

First flexural (E–W) 2.47 0.405 1.57First flexural (N–S) 2.80 0.358 1.56First torsional 4.14 0.242 1.21Second flexural (E–W) 7.56 0.132 0.76Second flexural (N–S) 8.34 0.120 0.86Second torsional 12.59 0.079 1.14

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no spalling of the concrete covers. The building displayed amaximum first-storey displacement of 24.5 mm and a maxi-mum top-storey displacement of 52.4 mm. Maximum storey

drifts were 24.5 and 28.3 mm for the first and second stor-eys, respectively, which are about 82% and 94% of the max-imum 1% interstorey drift ratio allowed by the NBCC 2005(NRCC 2005) for post-disaster buildings. Note that the max-imum base shear measured just reached the design baseshear (99.8 kN) in the NBCC 2005 (NRCC 2005). The hys-teretic curves confirm that no evident yielding had occurredat this level of excitation. This PSD test indicates that HPCperforms well up to this moderate seismic excitation withvery little damage.

Response to severe seismic excitationTwo different PSD tests were carried out at severe seismic

excitations. The first test was done with the El Centro groundmotion scaled to 0.270g PGA. As can be seen in Fig. 12b, thepseudo-acceleration response spectra for this level of excita-tion at the measured periods of vibration of the building isclearly higher than the design spectrum for Montreal.

The responses of the structure for the first test are shownin Figs. 13c, 15c, 16c, and 18c. A vibration period of ap-proximately 0.68 s can be observed from the storey dis-placement time history. Maximum interstorey drifts were34.6 and 41.9 mm for the first and second storeys, whichcorrespond to drift ratios of 1.15% and 1.40%, respectively.These values exceed the drift ratio allowed by the NBCC2005 (NRCC 2005) for post-disaster buildings, but are lowerthan the drift ratios for schools and for all other buildings.Maximum base shear developed during the test was165.1 kN, which is significantly higher than the design baseshear (99.8 kN).

The severe seismic excitation test caused the first meas-ured yielding of reinforcement steel. Measured strains in thelongitudinal reinforcement at the bottom of the first storeycolumn reached 1.18�y, where �y is the yield strain of rein-forcing bars. At the time of the first yielding, the base shearwas 144.4 kN.

Table 5. Chronology of the tests carried out on the building.

Date Type of test Description of testSeptember 2000 Forced vibration Preliminary dynamic characterization of the buildingSeptember 2000 Forced vibration Dynamic characterization without the actuator bracketsJanuary 2001 Forced vibration Dynamic characterization with the actuator bracketsApril 2001 Pseudo dynamic Test with the El Centro* recording (ugmax = 0.078g)April 2001 Pseudo dynamic Test with the El Centro recording (ugmax = 0.129g)April 2001 Forced vibration Dynamic characterization after PSD (ugmax = 0.129g)July 2002 Pseudo dynamic Test with the El Centro recording (ugmax = 0.180g)August 2002 Forced vibration Dynamic characterization after PSD (ugmax = 0.180g)October 2003 Forced vibration Dynamic characterization after PSD (ugmax = 0.180g){

April 2004 Forced vibration Dynamic characterization after PSD (ugmax = 0.180g){

July 2004 Pseudo dynamic Test with the El Centro recording (ugmax = 0.270g)July 2004 Forced vibration Dynamic characterization after PSD (ugmax = 0.270g)September 2004 Pseudo dynamic Test with the M7R70A1 accelerogram (ugmax = 0.271g)September 2004 Pseudo dynamic Test with the El Centro recording (ugmax = 0.430g)September 2004 Forced vibration Dynamic characterization after PSD (ugmax = 0.430g)November 2004 Push over Push-over test until �� = 3.62November 2004 Forced vibration Dynamic characterization after push-over test

Note: ugmax, maximum ground acceleration; PSD, pseudo-dynamic testing method; ��, maximum structuralductility ratio.*El Centro, Calif., during the 18 May 1940, Imperial Valley earthquake{New equipment.{New accelerometer positions.

Fig. 12. Spectral accelerations of (a) M7R70A1, and (b) El Centroearthquake north–south component scaled at different levels. PSA,pseudo-acceleration response spectra.


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The structure performed very well during the test. Fewnew cracks developed, but existing cracks widened. Neitherspalling of the cover nor local instabilities of reinforcementwere observed.

The second test was carried out with the M7R70A1 accel-erogram generated for Montreal (see Fig. 12a). The peakground acceleration of the accelerogram is 0.271g. The PSDtest results obtained with the accelerogram are shown in

Figs. 14, 17, and 19. The maximum interstorey drifts were17.7 and 21.6 mm for the first and second storeys, respec-tively. These values are less than the limits imposed by theNBCC 2005 (NRCC 2005) for all types of structures. Fur-thermore, as shown in Fig. 14, the maximum base shear de-veloped was only 76.3 kN, significantly lower than thedesign base shear (99.8 kN) in the NBCC 2005.

No new cracks appeared during the severe seismic excita-tion test. Existing cracks opened (and closed) in the criticalregions of the beams and columns according to the displace-ments imposed on the structure by the seismic forces. Meas-ured displacements and storey shears were clearly lowerthan those measured during the PSD test with the El Centroground motion scaled to 0.270g PGA, even though the max-imum ground accelerations of these two seismic functionsare almost identical. This result highlights that the high fre-quency content of Eastern Canada earthquakes are not crit-ical for flexible structures.

Response to very severe seismic excitationThe last pseudo-dynamic test was performed with the El

Centro ground motion scaled to 0.43g PGA. The PGA levelcorresponds to a 2% in 50 year probability level for Mon-treal (Adams and Halchuk 2003). Even though the PGAvalue is in accordance with the prescribed acceleration forMontreal, the pseudo-acceleration response spectra for thevery severe seismic excitation is clearly higher than the de-

Fig. 13. Time histories of first floor and roof displacements for ElCentro earthquake, N–S component scaled to (a) 0.078g peakground acceleration (PGA), (b) 0.180g PGA, (c) 0.270g PGA,(d) 0.430g PGA, and (e) N–S component of horizontal ground ac-celeration of El Centro earthquake.

Fig. 14. Time histories of first floor, roof displacements, and baseshear for the M7R70A1 time history scaled to 0.271g peak groundacceleration.

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sign spectra of Montreal for all given frequencies (Fig. 12b).This excitation level was used to study the behaviour of thestructure under very severe seismic excitation.

The earthquake responses of the structure are shown inFigs. 13d, 15d, 16d, and 18d. An important period elonga-tion can be observed from the response history. The meas-ured vibration period is about 0.85 s. The maximuminterstorey drifts were 50.9 and 67.5 mm for the first and

second storeys, which corresponds to drift ratios of 1.70%and 2.25%, respectively. The values exceed the drift ratio al-lowed by the NBCC 2005 (NRCC 2005) for post-disasterbuildings. Furthermore, the interstorey drift of the secondfloor also exceeds the limit of 2% imposed on school build-ings. On the other hand, the limit concerning all other build-ing categories was not exceeded. Maximum base shear was204.3 kN during the test, which is more than twice the de-sign base shear.

The hysteretic curves in Fig. 16d show a light pinching ofthe hysteresis. Furthermore, analysis of the curves revealsthe structure has significant inelastic behaviour. The longitu-dinal reinforcement in the beams, near the column faces,and at the base of the first-storey columns suffered inelastictensile strains. The column longitudinal bars, below the first-floor beam–column joints, and all the longitudinal bars inthe second-storey columns remained in the elastic range ofthe steel reinforcement.

This intensity level caused some damage to the structure.Several new cracks in the beams, columns, slabs, and jointsappeared and most of the existing cracks widened signifi-cantly. On the other hand, no spalling of the cover was ob-served and, hence, it can be implied that no localinstabilities of reinforcement took place. Despite the veryhigh level of excitation, the building preserved its structuralintegrity and its capacity to sustain gravity loads.

Response to push-overAfter the last very severe seismic excitation PSD test, a

push-over test was carried out on the building. The objectiveof the test was to verify the ultimate capacity of the struc-ture, thereby measuring its overstrength and ductility levels.The structure was tested for incrementally increasing lateralloads. The shape of the lateral load distribution applied tothe structure was calculated as combinations (square root ofsum of squares) of the lateral load distributions obtainedfrom modal analyses of the structure with the NBCC 2005(NRCC 2005) design spectra.

Figure 20 illustrates the building’s response during thepush-over test. It shows the overall hysteretic behaviour ofthe building in terms of lateral load versus roof displace-ment. The maximum positive displacement of the roof was183.1 mm, with a corresponding base shear of 237.6 kN. Incontrast, the maximum negative roof displacement was203.3 mm, with a corresponding base shear of 233.7 kN.Obviously, these displacements exceeded the drift ratio al-lowed by the NBCC 2005 for all buildings. The recordedbase shear was 2.38 times greater than the design base shearand surpassed the base shear recorded during the pseudo-dynamic test with the El Centro ground motion scaled to0.43g PGA.

Spalling of the cover was observed at the base of the first-floor column during the push-over test. Furthermore, severespalling of the concrete cover occurred in the spandrelbeams of the first floor perpendicular to the loading (N–S)under significant diagonal torsional compression stresses.This is indicative of torsional yielding, which limits the ef-fective width of the slab contributing to the negative bend-ing resistance of the main beam in the seismic loadingdirection as was explained by Di Franco et al. (1995). Evenat this level of loading and after several pseudo-dynamic

Fig. 15. Time histories of base shear for El Centro earthquakenorth–south (N–S) component scaled to (a) 0.078g peak ground ac-celeration (PGA), (b) 0.180g PGA, (c) 0.270g PGA, (d) 0.430gPGA, and (e) N–S component of horizontal ground acceleration ofEl Centro earthquake.


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Fig. 16. Shear-displacement response for first storey and second storey for El Centro earthquake north–south component scaled to(a) 0.078g peak ground acceleration (PGA), (b) 0.180g PGA, (c) 0.270g PGA, and (d) 0.430g PGA.

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tests, the building maintained its structural integrity andgravity-load-carrying capacity. In addition, according to theshape of the hysteretic curve, the structure had reservestrength and ductility at the end of the push-over test.

Analysis of test resultsAccording to Table 6, the base shear increased from

68.1 kN (9.0%W) to 204.3 kN (26.9%W) during the pseudo-dynamic tests carried out on the building, representing a300% increase. For the same tests, roof displacement in-creased by approximately 1000%. Structural displacementductility demand for the PSD tests progressed from 0.21 to2.11. Even with the very severe seismic excitation test, thebuilding’s overall behaviour was still very good.

Table 7 presents the maximum interstorey drift ratios re-corded during the pseudo-dynamic tests. The drift limit of1% for post-disaster buildings was exceeded during the0.180g PGA test with the El Centro ground motion, and thedrift ratio for schools (2%) was reached at the second storeyduring the PSD test with 0.43g PGA. As for the 2.5% limitprescribed for the category of all other buildings, it wasnever exceeded during the pseudo-dynamic tests carried outon the building.

OverstrengthThe experimental estimation of overstrength for a com-

plete building with several degrees of freedom is linked to

the definition of the concept itself. A very conservative ap-proach is to consider the base shear recorded during firstyielding of a member. In this experimental investigation,first yielding occured in a ground-storey column at a baseshear of 144.4 kN during the PSD test with the El Centroground motion scaled to 0.270g PGA. Therefore, a conser-vative overstrength factor is equal to 144.4/99.8 = 1.45. Onthe other hand, this approach does not take into account thefact that, even after yielding of some structural elements,buildings have important reserve strength and the capacityto sustain additional loads. Mitchell and Paultre (1994) esti-mated the overstrength of reinforced concrete structureswhen the drift ratios reached the limit permitted by theNBCC. In the 2005 edition of the code (NRCC 2005), thelimit for all other buildings is 0.025 times the storey height.This interstorey drift was obtained during the push-over test(Fig. 20). The corresponding base shear was 225.6 kN. Us-ing this value of base shear, the overstrength factor is 225.6/99.8 = 2.26. For a moderately ductile moment-resistingframe, the overstrength-related force-modification factor,Ro, is 1.4 in the NBCC 2005. Experimental results ob-tained in this investigation seem to confirm the validityand safety of this factor.

Displacement ductilityDisplacement ductility, as used in this paper, is equal to

the ratio of maximum displacement reached by the roof tothe displacement at general yielding as used in Mitchell andPaultre (1994). The general yielding level was determinedby using a bilinear idealization of the building response(Fig. 21). The initial stiffness was determined as the averageof the initial force–displacement slope of the first three low-level pseudo-dynamic test results. The second segment ofthe bilinear representation was determined as the tangent tothe post-yield force–displacement response obtained fromthe push-over test. With the bilinear idealization, the roofdisplacement corresponding to general yielding, �y, was56.1 mm. Using this displacement, the maximum structuralductility ratio, �� can be obtained from

½11� �� ¼ �max

�y

where Dmax is the maximum measured displacement at rooflevel.

During the push-over test, the structural displacementductility reached 3.62, which is more than the ductility-re-lated force-modification factor, Rd. This factor is 2.5 in theNBCC 2005 (NRCC 2005) for a moment-resisting framewith moderate ductility.

During the pseudo-dynamic tests, the structural displace-ment ductility demand progressed from 0.21 to 2.11(Table 6). After these tests, a push-over test was carried outon the structure. The structural ductility reached �� = 3.62.At this level, the interstorey drift limit for all building usagewas exceeded. When considering this limit, the structuralductility was 2.67. All these values exceed the ductility-related force-modification factor, Rd, in the NBCC 2005for this seismic-force-resisting system chosen. Furthermore,these results demonstrate that the appropriate use of high-strength concrete in seismic zones seems safe and justified

Fig. 17. Shear–displacement response for (a) first storey and(b) second storey for M7R70A1 time history scaled to 0.271g peakground acceleration.


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if the applicable standards and particularly the detailing re-quirements are respected. During the last PSD test (ElCentro ground motion scaled at 0.43g PGA) and push-overtest, the average compressive strength of the concrete usedin the building was 73 MPa. Despite the very high level ofexcitation and the high compressive strength of the con-

crete, the building has shown excellent ductility withoutshowing signs of major failure.

Conclusions

Forced vibrations were used to extract the key dynamic

Fig. 18. Base shear–roof displacement response for El Centro earthquake north–south component scaled to (a) 0.078g peak ground accel-eration (PGA), (b) 0.180g PGA, (c) 0.270g PGA, and (d) 0.430g PGA. VNBCC-05, design base shear according to the 2005 NBCC (NRCC2005).

Fig. 19. Base shear-roof displacement response for M7R70A1 timehistory scaled to 0.271g peak ground acceleration.

Fig. 20. Base shear–roof displacement response for push-over test.

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properties of the structure (vibration frequencies and modeshapes as well as modal damping ratios) to be used in PSDtests and to set the initial state of the structure. A suite ofPSD tests with increasing seismic excitations demonstratedthe excellent performance of the high-strength concretestructure designed using the new CSA A23.3-04 Design ofconcrete structures standard (CSA 2004) under earthquakeexcitations. In particular, displacement ductility and over-strength are higher than the prescribed values in the newNBCC 2005 (NRCC 2005). The HSC columns designedwith the new requirements of the A23.3-04 standard per-formed very well under PSD tests and push-over testing,even at drift levels significantly larger than the limits al-lowed by the NBCC 2005. These results confirm the appro-priateness of the new CSA A23.3-04 standard, in particular(i) the new strong column – weak beam requirements and(ii) the new confinement requirements for columns. The testresults also confirm the safe values of the ductility-re-lated force-modification factor and the overstrength-re-lated force-modification factor. These unique test resultscan be used for the calibration of numerical models and

as gauges for expected damage levels corresponding tosectional behaviour.

AcknowledgementsThe authors gratefully acknowledge the financial support

of the Natural Sciences and Engineering Research Councilof Canada. They would also like to thank Claude Aube, Se-bastien Gauthier, and Laurent Thibodeau, technicians in thestructural laboratory of the Department of Civil Engineeringat the University of Sherbrooke, for their role in the testpreparation. The help of Martin Beauvilliers, Najib Bouaa-nani, Jean-Christophe Kombila, and Olivier Lefebvre is alsoacknowledged. Charles Savard and Tommy Prevost partici-pated in the design and construction of the structure. Thisresearch was carried out as part of the work by the secondauthor on the CSA A23.3-04 seismic design subcommittee.

ReferencesAdams, J., and Halchuk, S. 2003. Fourth-generation seismic hazard

maps of Canada: Values for over 650 Canadian localities in-tended for the 2005 National Building Code of Canada. OpenFile 4459, Structural engineering series. Earthquakes Canada,Geological Survey of Canada, Ottawa, Ont.

Atkinson, G.M., and Beresnev, I.A. 1998. Compatible ground-motion time histories for new national seismic hazard maps.Canadian Journal of Civil Engineering, 25(2): 305–318.doi:10.1139/cjce-25-2-305.

CSA. 1984. Design of concrete structures for buildings. CSA stan-dard CSA-A23.3-84. Canadian Standards Association, Rexdale,Ont.

CSA. 1994. Design of concrete structures. CSA standard CSA-A23.3-94. Canadian Standards Association, Rexdale, Ont.

CSA. 2004. Design of concrete structures. CSA standard CSA-A23.3-04. Canadian Standards Association, Mississauga, Ont.

Di Franco, M.A., Mitchell, D., and Paultre, P. 1995. Role of span-drel beams in slab-beam-column connections subjected to seis-mic loading. Journal of Structural Engineering, ASCE, 121(3):408–419. doi:10.1061/(ASCE)0733-9445(1995)121:3(408).

Hilber, H.M., Hughes, T.J.R., and Taylor, R.L. 1977. Improved nu-merical dissipation for time integration algorithms in structuraldynamics. Earthquake Engineering & Structural Dynamics,5(3): 283–292. doi:10.1002/eqe.4290050306.

Mitchell, D., and Paultre, P. 1994. Ductility and overstrength inseismic design of reinforced concrete structures. Canadian Jour-nal of Civil Engineering, 21(6): 1049–1060. doi:10.1139/l94-109.

Mousseau, S., and Paultre, P. 2005. Esssais pseudo-dynamiques etdynamiques d’un batiment de deux etages en beton a hautes per-formances. CRGP-2005/01. Centre de recherche en genie para-sismique et en dynamique des structures, Departement of Civil

Table 6. Maximum response parameters recorded during pseudo-dynamic testing method tests.

Accelerogramu1max

(mm)u2max

(mm)(u2–u1)max

(mm)f1max

(kN)f2max

(kN)V0max

(kN)M0max

(kN�m) ��

El Centro (ugmax = 0.078g) 6.5 11.8 5.2 39.2 42.5 68.1 306.4 0.21El Centro (ugmax = 0.180g) 24.5 52.4 28.3 68.0 104.1 123.8 661.5 0.93El Centro (ugmax = 0.270g) 34.6 75.9 41.9 93.3 130.5 165.1 837.1 1.35M7R70A1 (ugmax = 0.271g) 17.7 39.2 21.6 68.7 66.9 76.3 384.8 0.70El Centro (ugmax = 0.430g) 50.9 118.4 67.5 110.5 169.0 204.3 1031.4 2.11

Note: u1max, maximum displacement of DOF 1 (first floor); u2max, maximum displacement of DOF 2 (roof); f1max, maximum firststorey shear; f2max, maximum second storey shear; M0max, maximum base overturning moment.

Table 7. Maximum interstorey drift ratios recorded.

Interstorey drift ratios (%)

Accelerogram Storey 1 Storey 2El Centro (ugmax = 0.078g) 0.22 0.20El Centro (ugmax = 0.180g) 0.82 0.94El Centro (ugmax = 0.270g) 1.15 1.40M7R70A1 (ugmax = 0.271g) 0.59 0.72El Centro (ugmax = 0.430g) 1.70 2.25

Fig. 21. Bilinear idealization of building behavior for push-overtest. PSD, pseudo-dynamic testing method.


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Engineering, Universite de Sherbrooke, Sherbrooke, Que. [InFrench.]

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Paultre, P., and Mitchell, D. 1987. Evaluation of seismic perfor-mance of concrete frame structures in Canada. Structural engi-neering series, Report 87–4. McGill University, Montreal, Que.

Paultre, P., Castele, D., Rattray, S., and Mitchell, D. 1989. Seismicresponse of reinforced concrete frame subassemblages — a Ca-nadian code perspective. Canadian Journal of Civil Engineering,16(5): 627–649. doi:10.1139/l89-097.

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2003. Pseudo-dynamic and forced vibration tests of a full-sizetwo-story reinforced high-performance concrete building. InLarge-scale structural testing, SP-211. Edited by M.A. Issa andY.L. Mo. American Concrete Institute, Farmington Hills, Mich.Paper SP-211-7, pp. 135–160.

Paultre, P., Weber, B., Mousseau, S., and Proulx, J. 2007. Measur-ing earthquake damages in a high-strength concrete structure.Report CRGP-2007/05. Centre de recherche en genie parasismi-que et en dynamique des structures, Universite de Sherbrooke,Que.

Takanashi, K. 1975. Nonlinear earthquake response analysis ofstructures by a computer-actuator on line system. Bulletin ofthe Earthquake Resistant Structure Research Center. No. 8. Insti-tute of Industrial Science, University of Tokyo, Tokyo, Japan.pp. 205–219.

Thewalt, C.R., and Mahin, S.A. 1991. The pseudo-dynamic testmethod: Verification and extensions. In Experimental and nu-merical methods in earthquake engineering. Edited by J. Doneaand P. M. Jones. Kluwer Academic Publishers, the Netherlands.pp. 101–118.

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Seismic performance of a full-scale, reinforced high