Seismic behaviour of multistorey RC wall–frame system versus bare ductile frame system

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2002; 31:79–97 (DOI: 10.1002/eqe.99)

Seismic behaviour of multistorey RC wall–frame systemversus bare ductile frame system

Yong Lu∗;†

School of Civil and Structural Engineering; Nanyang Technological University; Nanyang Avenue;Singapore 639798

SUMMARY

The wall–frame systems have many known advantages, namely increase of the system’s lateral strengthand sti7ness thereby allowing for a good tangential inter-storey drift control, and the retention ofa satisfactory energy dissipation capacity. However, rocking of the wall could occur as a result ofuplifting wall base or concentrated plastic hinge deformations. Problems arising from this phenomenonhave signi;cant impact on the system behaviour and hence require extended study. This paper focuseson the wall-rocking phenomenon due to the concentrated plastic hinge rotation at the wall base. Tofacilitate a comprehensive evaluation, a six-storey three-bay RC wall–frame structure is investigatedwith comparison to a bare ductile frame by means of earthquake simulation tests. The results revealedthat, despite a superior performance over the ductile frame under low to moderate seismic actions, thewall–frame structure deteriorated more rapidly than the bare frame during advanced inelastic response.The increasingly signi;cant rocking of the wall resulted in severe material damage at localized criticalregions. Mitigating the wall rocking is seen to be a key to the further improvement of the systemperformance, and the extent to which this may be achieved by incorporating the three-dimensionale7ects is explicitly illustrated by an analytical evaluation. Copyright ? 2001 John Wiley & Sons, Ltd.

KEY WORDS: RC wall; ductile frame; plastic hinge; failure mechanism; three-dimensional e7ects;earthquake simulation

1. INTRODUCTION

In modern seismic design of building structures, ductile RC walls are widely used to incorpo-rate with frames to form the wall–frame structural system. Such a system is known to combinethe advantages of the ductile moment-resisting frame and the relatively sti7 wall [1–5]. Duc-tile frames, interacting with walls, can provide a substantial amount of energy dissipation. On

∗Correspondence to: Yong Lu, School of Civil and Structural Engineering, Nanyang Technological University,Nanyang Avenue, Singapore 639798.

†E-mail: [email protected] 28 November 2000Revised 26 February 2001

Copyright ? 2001 John Wiley & Sons, Ltd. Accepted 21 March 2001

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the other hand, the addition of the wall to the frame signi;cantly increases its lateral strengthand sti7ness. The increase in lateral sti7ness provides a good tangential inter-storey driftcontrol thereby decreasing the damage to the structure as a whole.

However, traces of potential problems with the wall–frame systems can also be found fromsome previous experimental investigations [6; 7], and these problems are primarily related tothe rocking motion of the wall. Rocking of the wall occurs when the wall footing on thetension side uplifts; it may also result from the concentration of the inelastic deformation atthe bottom end of the wall. Whereas in both cases the wall rocking can have profound e7ectson the behaviour of the entire system, in the latter case considerable compressive strain coulddevelop in the outer layer of the compression zone at the wall base, causing crushing of theconcrete while rupture of the wall vertical reinforcement takes place on the tension side. Suchhighly localized material failure can lead to the loss of wall constraint at the base and thusaccelerate the deterioration of the entire structural system. A thorough understanding of theextent of such wall rocking mechanism is necessary in an attempt to seek e7ective remedies,and this requires dedicated research e7orts.

A planar wall–frame system is purposely selected for the current experimental investigation.In the absence of the 3-dimensional (3-D) e7ects which are not mandatory in the design ofthe wall–frame structures according to the relevant design provisions, this system, being code-compatible, ultimately demonstrated the wall rocking phenomenon due to the plastic hingerotation and the associated response and damage mechanism. The observations on such aplanar wall–frame system, combined with an analytical evaluation of the potential 3-D e7ectsas described later, provide a broader angle for judging the system behaviour and understandingthe e7ective ways to improve the design.

To enhance the evaluation, a bare ductile frame was also designed and tested under similarconditions to allow a systematic comparison of the response between the two di7erent systems.Both structures were designed to satisfy the requirements for ductility class “Medium” ac-cording to Eurocode 8 [8], with design peak ground acceleration of 0:3g. For the experiment,models at 1 : 5:5 scale of the prototype structures were constructed conforming to necessarysimilitude laws and they were tested under simulated earthquakes on a large earthquake sim-ulator. The experimental results demonstrate a distinctive response pattern of the wall–framesystem as compared to the ductile frame, while the development path of the eventual failuremechanism is also clearly observed.

It is generally recognized that in real 3-D dual systems, the upward movement of the wallcould trigger reactions in the transverse beam–Moor system which is bene;cial to the wallbehaviour. In order to give an explicit idea on the extent to which the wall response might bea7ected by such 3-D outriggering e7ects, an analytical evaluation is carried out on the basisof the relevant measured response and the details are discussed in the last part of this paper.

EXPERIMENTAL PROGRAMME

Test structures

The con;guration and dimensions of the wall–frame model (designated as SWF) and theductile bare frame model (designated as BFR) are shown in Figure 1. Both models had sixstoreys and three bays, and their overall dimensions were identical. The cross-section sizes

Copyright ? 2001 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2002; 31:79–97

RC WALL–FRAME SYSTEM VS BARE DUCTILE FRAME SYSTEM 81

Figure 1. Geometry and reinforcement arrangement of two model structures. (a) Wall-framemodel SWF, (b) Bare frame model BFR.


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Table I. Strength and natural frequency characteristics of test models.

Model Design base shear Achieved base shear Fundamental frequency (Hz)∗

EL0.10 EL0.30 EL0.60 EL0.90

SWF 18:9 kN (0:22W ) 57:9 kN (0:67W ) 5.57 3.82 3.12 2.47BFR 11:8 kN (0:15W ) 37:5 kN (0:47W ) 3.44 2.98 2.29 2.06

∗Measured after the respective test.

of the beam–column members were varied for the two models to better suit the respectivedetailing requirements. The RC wall was located across the mid-span of model SWF andextended throughout the entire structure height, with a height–length ratio of 5.8. Takinginto account the capacity limitation of the testing facilities, the scale chosen for the modelstructures was 1 : 5:5.

The test structures were designed in their prototype scale to satisfy the relevant design re-quirements for ductility class “Medium” according to EC8. The design peak ground accelerationwas 0:3g. Soil pro;le “A” was assumed when determining the design response spectrum. Otherdesign assumptions included

• Dead load (additional to self-weight): 1:5 kN=m2

• Live load: 2:0 kN=m2 (30 per cent of it was considered in the seismic load combination)• Perpendicular span length: 4:0 m• Concrete: Class 20 (characteristic cylinder compressive strength 20 MPa)• Flexural reinforcement for beams and columns: Grade S400 (yield strength 400 MPa)• Wall reinforcement and beam–column transverse reinforcement: Grade S220

The total design base shear was found to be 0:22W for SWF and 0:15W for BFR, with “W ”being the total dead weight plus 30 per cent of the live load of the structure. Compared tothe actually achieved base shear strength during the tests (Table I), an overstrength factor ofapproximately 3 was observed for both models. In fact, similar level of overstrength was alsoobserved in many previous shaking table tests of model structures [9–11], and the contributingfactors were identi;ed to include the material overstrength, surplus amount of reinforcement,structural redundancy, etc. For the main purpose of the current investigation, however, itwas most important that the relative overstrength was maintained almost the same for thetwo models which allowed for a direct comparison of the observed responses. The modelreinforcement was deduced from the prototype design on a one-to-one basis, and it is alsoshown in Figure 1. For model SWF, the reinforcement ratio was 1.02 and 1.69 per cent inbeams and columns, respectively, and it was 0.78 per cent for vertical reinforcement and0.63 per cent for horizontal reinforcement in the wall panel. The reinforcement ratio rangedbetween 0.95–1.35 per cent in beams and 0.90–2.76 per cent (5–6 storeys) in columns inmodel BFR.

In order to ensure a satisfactory reproduction of the prototype response, extensive modelmaterial investigation as well as model member tests [12] were conducted prior to embark-ing on the model construction. The ;nal mix design adopted for the microconcrete was:cement (Portland II)=sand=coarse aggregate (crushed limestone with maximum particle size



Figure 2. Stress–strain curves for (a) model reinforcement and (b) microconcrete (cylinder compression).

of 5 mm) = 1=2:2=4:5, with water-to-cement ratio 0.645. Upon testing the models, the con-trol specimens prepared during the model construction gave an average cylinder compressivestrength of 30 MPa, and a splitting tensile-to-compressive strength ratio of about 1=10. Forthe Mexural reinforcement in the beam–column members of the models, the conventionallydeformed 6-mm bars with annealing treatment were used to approach the expected GradeS400 reinforcement properties, while 3-mm smooth wire (S220) was used for the stirrupsand wall reinforcement. The bond strength of the main 6-mm bars embedded in the modelconcrete was found to be 25–30 per cent of the concrete compressive strength, slightly lowerthan that expected for normal size deformed bars.

The representative stress–strain curves for the model microconcrete and the 6-mm mainreinforcing bars are shown in Figure 2.

The model structures were cast in their vertical standing position following typicalconstruction procedures. At all Moor levels, 300-mm wide Manges were provided on bothsides of the frame to represent the Moor slab e7ects and also to accommodate the additionalmasses required by the similitude laws. Extended beam stubs were provided at the exteriorjoints to allow for a straight anchorage of the beam reinforcement. The entire model structurewas built on a strong base girder to facilitate a proper attachment of the test model to theearthquake simulator platform.

Test set-up and instrumentation

The model structures were mounted on the earthquake simulator platform as schematicallyillustrated in Figure 3. A side-support system was installed which essentially guaranteed thetest model to respond to the unidirectional excitations within its plane.

As the test models were of reduced scale, their structural masses had to be augmentedso that the static normal stress as well as the stress induced by inertia forces in the modelswere similar to those in the respective prototype structures [13]. The total additional massesweighed about 7800 kg for model SWF and 6900 kg for BFR, and they were distributed and;xed on the Moor slabs through bolts.

The instrumentation was organized to cover both overall and critical local response measure-ments, namely: displacements and accelerations at all Moor levels; critical column rotations;and reinforcement strains at critical regions. For model SWF, local response measurements


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Figure 3. (a) Test set-up and (b) instrumentation.

also included the wall rotation in the base region, the diagonal displacement of the ;rst-storeywall panel, as well as the wall sliding displacement relative to the base girder. Additionalinstruments were installed to monitor the out-of-plane motion as well as the ;xity of the basegirders on the simulator platform. A sketch of the instrumentation is given in Figure 3(b).

As can be seen, the wall rotation was measured over three gauge lengths to allow for anobservation of average curvature distribution. The rotations over the lowest two sequentialgauge lengths (200 and 120 mm, respectively), starting from the base, were measured byLVDTs aligned vertically along the two side faces of the wall. The rotation over the entire



Figure 4. Typical achieved base motion. (a) Time history, (b) response spectra.

;rst storey height was measured by a pair of string transducers, which actually measured theupward=downward motion of the wall at the ;rst level along the wall edges.

Test scheme

The models were tested for various levels of earthquake simulations, modelled after the ElCentro 1940 N-S record. The time scale of the simulated earthquakes was compressed by thesquare of the model length scale factor (

√5:5). In the description which follows, each earth-

quake simulation is labelled by “EL” followed by a number denoting the corresponding peakacceleration in terms of “g”, namely EL0.30, EL0.60, and so forth. The test programme con-sisted of the following consecutive earthquake simulations: EL0.10, EL0.30, EL0.60, EL0.90and EL1.20. It is noted that EL1.20 was not performed on model BFR due to an accidentalset-up problem. Figure 4 shows the typical achieved base acceleration time history and thecorresponding response spectrum. Complementary random vibration tests were performed aftereach major earthquake simulation to determine the change of the natural frequencies of themodels.

EXPERIMENTAL RESULTS AND DISCUSSION

Cracking pattern and failure modes

The cracking patterns of the two test models at several test stages are compared in Figure 5.For model SWF, a few minor cracks appeared at some beam-ends framing into the wall

following test EL0.30, which corresponded to the design intensity. It was noticed during theexcitation that a marked wall rotation occurred at the base. Despite that no visible crackingwas found at the wall–foundation interface after this test; the measured fundamental frequencyof the model decreased by approximately 30 per cent from that before the test (Table I),indicating that appreciable cracking had occurred.

Cracks were observed to spread into beams at almost all levels, in regions close to thewall, after test EL0.60. At the wall base, major horizontal cracks appeared across the entiresection. Several horizontal cracks also appeared on higher levels of the wall (between 3 and 6storeys), and this was attributable to the higher-modes contribution, combined with the e7ectsof opposing displacement shapes between the wall (bending) and the frame (shear). Substantial


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Figure 5. Observed crack patterns of two models. (a) Model SWF, (b) Model BFR.

upward motion on the alternating tension side of the wall was observed in association withsigni;cant rocking during the excitation. It was apparent that most of the vertical reinforcementin the wall experienced very large tensile strain, while only a small compression zone remainedon the wall bottom section at the peak responses.

For test EL0.90, the response of model SWF appeared to be overwhelmed by severe con-centration of the wall deformation in the bottom region and subsequent wall rocking arounda point close to the compressive edge at the wall base. Inspection after the test revealed thata majority of the wall vertical reinforcing bars had ruptured, while severe crushing of concreteoccurred at the wall bottom corner and extended towards the wall web. In a broader perspec-tive, rocking of the wall imposed large rotation demands on the beam-ends that framed intothe wall, resulting in extensive cracking in these beam regions throughout the entire structuralheight. Excessive beam rotation relative to the wall further generated a severe stress conditionin the beam–wall adjoining areas, resulting in what appeared to be the anchorage failure atalmost all beam–wall connections. Such a chain reaction eventually produced a distinctivefailure mechanism as can be clearly observed from the ;nal damage pattern for test EL1.20:the wall was almost completely cut free from the base girder; the connection failure occurredat beam–wall adjoining areas at almost all levels. Meanwhile, the horizontal cracking on theupper levels of the wall developed further.

As for the bare frame BFR, only a few scattered minor cracks were detected after testEL0.30. The crack distribution following test EL0.60 showed a mixed pattern (on beams aswell as some columns) along the height of the frame, while slight spalling of concrete occurred



Figure 6. Measured displacement, inter-storey drift and lateral force pro;les.

in the ;rst storey beams near the exterior joints. For test EL0.90, the overall response of themodel essentially remained stable, however cracking and yielding intensi;ed substantially,and spalling of concrete occurred in various beam and column members in the lowest storeys.These evidences suggested that the model response was approaching the onset of mechanismformation. The maximum crack width which appeared on the ;rst storey beam exceeded1:0 mm (model scale). Nevertheless, no critical material failures of the kind observed onmodel SWF at comparable test level, such as the rupture (or buckling) of steel bars andcrushing of core concrete, were observed on model BFR. Therefore it may be said that thebare frame model BFR performed in a somewhat more satisfactory manner than model SWFat this advanced inelastic stage should the critical material failures be considered as a maincriterion.

Measured displacements and lateral forces

The displacement pro;les and inter-storey drifts measured during various tests for the twomodel structures are plotted in Figure 6. The ;rst-mode dominance in the displacement re-sponse can be readily observed from these pro;les. It is worth noting, however, that bothframes exhibited a “kink” in the displaced shapes at the ;fth storey, indicating appreciablehigher-mode contributions. The severer “kink” at the ;fth storey of frame BFR was alsoattributable to the rather abrupt discontinuity of the storey strength and sti7ness at the corre-sponding level (Figure 1(b)). This in fact con;rms the importance of maintaining a smoothstrength-sti7ness distribution along the structure height.

The storey shear envelopes for both models during various tests are also given in Figure 6.The storey shear force was inferred from the measured inertial forces of reactive masses. Thedistribution of the design storey shear forces is also shown in the ;gure. As can be seen, the


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Figure 7. Comparison of envelope base shear vs. roof displacement relations.

measured envelope storey shear force in model SWF fairly resembled the design distributionthroughout the tests. For model BFR, however, the ratio between the shear force at the topstorey and the base shear appears to increase with the increase in the inelastic response,clearly indicating an intensifying “whipping” e7ect. This observation justi;es the adoption ofa concentrated lateral load, say, 20 per cent of the total base shear, to the top level while therest of the base shear is distributed in the usual way for the design of ductile frames.

For a comparison of the strength and overall ductility parameters, Figure 7 illustrates theenvelope base shear vs. roof displacement relationships for the two models. The design baseshear forces are also shown in the ;gure. As can be seen, despite the fact that model SWFexhibited much higher absolute base shear resistance than model BFR, the overstrength factor(actual base shear divided by design base shear) was practically the same for the two models.The increase of the lateral sti7ness in model SWF resulted in an increased base shear demand,as observed during the elastic response, which tended to cancel the advantage of the wall–frame system regarding the strength for the case herein.

Based on Figure 7, an estimation of the overall ductility demands, de;ned as the ratio ofthe measured maximum top displacement to the top displacement at yield, can be made forthe two models during various test stages. The relationships shown in the ;gure do not havea well-de;ned yielding point though, as an alternative the yield displacement was determinedat the intersection between a straight line passing through the origin and the point where 75per cent of the ultimate strength is reached, and a horizontal line on top of the curve [14].The ductility demands in model BFR are found to be 2.5 for test EL0.60 and 3.9 for EL0.90as compared to the reduced ductility demands of 1.6 and 3.2, respectively, in model SWF.The ductility demand in SWF sharply increased to 5.9 during test EL1.20.

Hysteretic behaviour

For a comparison of the relative energy dissipation capacities, Figure 8 shows the base momentvs. roof displacement hysteretic relations of the two models.



Figure 8. Comparison of primary hysteretic loops between two model structures.

As can be seen, despite the highly localized inelastic deformation and eventually failureat some critical regions, model SWF exhibited more desirable overall hysteretic behaviourthan model BFR. The hysteresis energy was apparently greater and pinching appeared tobe less pronounced. To provide a quantitative comparison, the equivalent hysteretic dampingcoeRcients were calculated for the two models in accordance with the following expression:

�e =Ehys

4�Eel(1)

where Ehys and Eel are the hysteretic and elastic strain energy of the system for a givendisplacement, respectively. It has to be pointed out that the current models were tested withgradually increased intensity, therefore the energy dissipated during a speci;c large displace-ment cycle (hence the hysteretic damping coeRcient) is expectedly smaller than in the casewhere the initial structure is subjected straightaway to the displacement cycle of similar mag-nitude. The damping coeRcient thus obtained for model SWF was between 9.3 and 11.9 percent while the roof drift (roof displacement=frame height) varied from 0.8 to 3.2 per cent,and it was notably smaller, between 6.1 and 9.9 per cent, for BFR when the roof drift variedin a similar range.

Local response

The wall bottom region was instrumented extensively during the tests. This allowed for acomprehensive evaluation of the response at this critical region which largely a7ected theperformance of the entire system. It is noted that, among the local measurements acquired, thediagonal deformation was found to be less signi;cant due to the predominant bending natureof the wall response in this particular model. The measured wall rotations, the elongation ofthe wall along the tension edge, as well as the wall slip displacement are discussed in whatfollows.

Figure 9 shows the distribution of the nominal wall curvature, obtained as the measuredrotation divided by the respective gauge length, along the ;rst storey height. As can be clearlyseen, the concentration of wall deformation was initiated at a very early stage and it took


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Figure 9. Distribution of wall curvature along ;rst-storey height.

Figure 10. Variation in the neutral axis of wall and average strain at wall edge withincrease of base motion intensity.

place within the lowest wall segment measuring 200 mm long or approximately 20 per centof the storey height. With the increase of the inelastic response, the concentration of walldeformation continuously intensi;ed, while the curvature in the remaining portion of this partof the wall appeared to remain constant. Dividing the LVDT readings for the lowest segmentby the 200-mm gauge length yields the average strains at both wall edges near the bottom,from which the location of the neutral axis could be identi;ed. The shift of the neutral axisduring the course of tests provides another viewpoint of the development of the inelasticdeformation within the wall critical region, as illustrated in Figure 10.



Figure 11. Measured wall edge elongation and bottom sliding displacement amplitudes.(b) Wall edge growth, (b) Wall sliding.

As it is seen, the neutral axis shifted rapidly towards the wall edge as a result of crackpropagation with an increase of the response amplitude up to EL0.60. After that, the neutralaxis tended to shift backward, clearly signifying the deterioration of the outer layer concreteunder compression. This was consistent with the observation that crushing of concrete wasinitiated from the edge layer of the wall and propagated inwards. The average reinforcementstrain over the ;rst 200-mm gauge length on the wall tension edge reached 4.85 per cent fortest EL0.90. Taking into account the observation that the most critical damage further con-centrated within a 50-mm narrow strip at the wall bottom, the actual maximum reinforcementstrain was much higher than the above average value; thus, the eventual rupture of the wallvertical reinforcing bars became inevitable even though the reinforcement was already highlyductile.

With regard to the wall elongation along the tension edge and its sliding relative to the basegirder, Figure 11 shows the wall elongation, measured between the ;rst Moor and the base,and the sliding displacements during various tests. As can be seen, sensible wall elongationand sliding occurred as soon as major cracking appeared at the wall base (EL0.60), and theyincreased progressively with the increase of the inelastic response. In test EL0.90 for example,the wall elongation approached 12 mm or about 1.5 per cent of the storey height, whereasthe wall sliding displacement reached 3 mm which was approximately 15 per cent of thecorresponding ;rst-storey drift (22 mm). The shortening of the wall along the compressiveedge appeared to be insigni;cant compared to the overwhelming tension growth.

EVALUATION OF SYSTEM PERFORMANCES

Comparison of two di/erent resistance mechanisms: local and global perspectives

The response described in the previous sections clearly demonstrated two di7erent resistancemechanisms for the two models. To the extent represented by these particular models, themechanism of the wall–frame system was characterized by bending and particularly, rockingof the wall about the wall base. On the one hand, this resulted in the highly concentratedinelastic deformation at the bottom region of the wall; on the other hand, large rotation


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Figure 12. Comparison of amplitude displacements between SWF and BFR.

demands on beams framing into the wall developed. Consequently, premature material failureoccurred at the respective regions. For the ductile frame model, however, the overall damageexhibited a rather uniform distribution over the entire frame. Due to the distributed inelasticdeformation, no premature critical material failure seemed to have occurred in model BFRthroughout the tests. These observations tended to suggest that, if indeed severe localizedmaterial failures are considered as a major criterion for “collapse” [8], then the wall–framemodel SWF had reached “collapse” during test EL0.90 for which the ductile frame BFRappeared to still remain intact. The implication for the seismic design veri;cation is thatthe wall–frame system may not be able to hold the advantage over the ductile frame at theadvanced inelastic response stage.

The comparison of the roof displacements and critical inter-storey drifts measured duringcomparable earthquake simulations gives another perspective of the performance of the twomodels, as shown in Figure 12.

As can be readily seen, for earthquake simulations up to EL0.60, both roof displacementand the critical ;rst-storey drift of model SWF were about 60 per cent of the correspondingresponse of model BFR, indicating an e7ective drift control due to the presence of the wall, upto that response level (overall ductility is about 1.6 for SWF and 2.5 for BFR). With furtherincrease in the earthquake intensity, however, the displacement in model SWF increased at amuch steeper rate and eventually approached the respective response amplitudes in the bareframe model. This phenomenon apparently was due to the intensi;ed wall rocking followingthe plastic hinge formation, and the increased displacement response in turn made the situationat the respective critical regions deteriorate further.

All the above observations tend to indicate a pertinent weakness at the system level forthe wall–frame structures and the consequences are likely to surface during advanced inelasticresponse, with a threshold overall ductility demand on the order of 3.0 based on the currenttest results. It has to be pointed out, however, that the severity of the problem could di7er fromcase to case depending on the system con;guration and the proportioning details. Nevertheless,in order that a satisfactory system performance can extend into advanced inelastic stage,e7ective counter-measures against the wall rocking are deemed necessary. Discussion follows.



Figure 13. Schematic illustration of the 3-D outriggering e7ects.

Improvement of wall–frame system performance: bene2ting from 3-D e/ects

A seemingly e7ective remedy to wall rocking is to incorporate the structural wall into ductilespace frame in a way such that the rocking of the wall would trigger 3-D reaction e7ects inthe transverse beams and Moor slabs [4]. Such 3-D outriggering forces act back on the wall,providing a constraint on the wall rocking as schematically illustrated in Figure 13.

An estimation of the extent of such outriggering e7ects on the wall response can be ob-tained by means of a simpli;ed analysis based on model SWF. Prior to this analysis, themoment resistance, maximum axial force and the base shear undertaken by the wall duringthe experiment were estimated. The planar model is then hypothetically incorporated into aspace frame, i.e., it is rigidly connected through transverse beams to two adjacent frames asindicated in Figure 13. For simplicity, the transverse beams are assumed to have the samecross-section dimension and reinforcement as the beams in the primary plane. The perpendic-ular span length is 0:73 m (4 m in full scale).

As was observed from the experiment (Figure 11), the wall shortening on the compressionside remained insigni;cant compared to the elongation (upward motion) on the tension side.Therefore, it is reasonable to assume that only the transverse beams connecting the tensionside of the wall contribute to the 3-D e7ects. For these beams, the vertical displacement atthe far end may be neglected as the axial deformation along the interior column lines of theadjacent frames is expected to be small compared to the wall growth. Hence, the relativevertical displacement between the two ends of the transverse beams is approximately equalto the absolute wall growth. The associated torsion in the transverse beams is not accountedfor in this analysis.

Based on Figure 11, the wall growth on the tension edge reached 12 mm at the peakresponse during test EL0.90. This means that at this response level the transverse beams


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would deform vertically by a drift of 12=730=1:64 per cent, which even after considering asuRcient reduction as a result of the 3-D e7ects, is large enough for the full Mexural strength ofa normal beam member to develop. The yield bending moment for the hypothetical transversebeam herein is 1:5 kN m. Correspondingly, a shear force equal to 2×1:5=0:73=4:1 kN wouldresult in each single e7ective transverse beam. It is these shear forces that act back on thewall to provide the anticipated counter-reaction on the wall growth and rocking within thewall plane.

For the six-storey model to connect to two adjacent frames, a total vertical force of 12 ×4:11=49:3 kN, acting downward along the centreline of the wall boundary column, can beexpected. This eccentric vertical force is equivalent to a compressive axial force and a bendingmoment on the wall section, written in a general form as

SN = −∑(2Myt=‘t)

SM = SN ‘w=2(2)

where Myt, ‘t are the yield bending moment and length of the e7ective transverse beams,respectively, and ‘w the distance between the centrelines of the wall boundary columns. Forthe model case herein, ‘w =0:275 m, SN =−49:3 kN, and hence SM =−13:6 kN m. Thenegative sense of the moment indicates that it acts in the reverse direction of the activemoment induced by the base excitation.

Besides the above direct con;ning bending moment, the increase of the axial compressiveforce further results in an increase of the Mexural strength of the wall. For the particularcase herein, the yield moment of the wall is calculated to increase to 50:7 kN m compared to37:5 kN m without the additional axial compressive force. Together with the con;ning momentSM; the total increase of the wall moment resistance reaches (50:7+13:6)−37:5=25:8 kNm,i.e., by more than 70 per cent. Assuming a uniform distribution of lateral forces, such anincrease of the wall moment resistance would enable an increase of the maximum base shearforce carried by the wall by 35 per cent compared to that in the planar model SWF. Thedevelopment of the above e7ects can be schematically illustrated in Figure 14. The shaded arearepresents the estimated cracking shear strength of the particular wall according to EC2 [15].

The above analysis clearly demonstrates that considerable increase in the wall resistanceagainst rocking, and subsequently a reduction of the inelastic deformation and ductility de-mand, can be obtained by incorporating the 3-D e7ects. More satisfactory results may beachieved if the transverse beams framing into the wall are deliberately strengthened to en-hance the con;ning e7ects. In this connection, however, care should be exercised to dealwith the possible side e7ects on the adjacent frame members. The subsequent increase in theshear force carried by the wall should also be encountered properly when detailing the wall.In these respects, more explicit code guidelines are needed. Where such Code guidelines arenot available, it is recommended that the following simple procedure be considered in theveri;cation of the seismic design of regular 3-D wall–frame systems:

(i) Compute the yield bending moment of the transverse beams which are e7ective in con-;ning the wall rocking (more complex computation may be necessary if the slab contri-bution is considered).

(ii) Calculate the con;ning force SN and moment SM on the wall according to Equa-tion (2).



Figure 14. 3-D outriggering e7ects on wall moment and shear resistance.

(iii) Calculate the total (equivalent) increase of the wall moment resistance.(iv) Calculate the increase of the wall shear force and the subsequent increase of the overall

base shear strength.(v) Verify the shear design of the wall.(vi) Evaluate the percentage reduction of the ductility demand. As an approximation, it may

be taken equal to the percentage increase of the overall base shear strength of the struc-ture.

CONCLUSIONS

Experimental investigation and associated analytical evaluation have been carried out to studythe seismic behaviour of a wall–frame structure with comparison to a ductile bare frame inthis paper. The results allow for the following conclusions to be drawn:

(1) Both the wall–frame and the bare frame models withstood a peak base acceleration of 0:9g,three times that of the design intensity, without apparent loss of the overall stability. Thecorresponding overall ductility demands were approximately 3.2 (SWF) and 3.9 (BFR)for the two models, respectively. Considering the fact that the base shear overstrengthwas the order of 3 for both models under the rather deterministic conditions, the designanticipations (medium ductility) according to EC8 proved to be adequate.


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(2) The planar wall–frame structure exhibited superior performance over the bare ductile frameduring low to moderate response (up to an overall ductility demand on the order of 2) dueto a substantial increase in the lateral sti7ness. The displacement amplitudes were observedto reduce by approximately 40 per cent from those of the bare frame for comparableearthquakes.

(3) As the structure responded to an advanced inelastic stage, the response of the wall–framesystem was observed to deteriorate more rapidly than the ductile frame, and the advantageof a good drift control with the wall–frame system tended to diminish with the increase ofinelastic deformation. This phenomenon can primarily be attributed to the rocking of thewall and the associated mechanism which involved highly localized inelastic deformationat the wall base region, and the ampli;ed rotation demands on beams framing into thewall. Consequently, premature material failures occurred at the wall base, resulting inthe eventual loss of wall base constraint while anchorage failure occurred at the beam–wall adjoining regions. Comparatively, the ductile frame experienced less severe materialdamage at the critical regions due to the distribution of inelastic deformation throughoutthe entire frame.

(4) The key to further improvement of the inelastic behaviour of the wall–frame system lieson the mitigation of the wall rocking. To achieve this, an e7ective incorporation andpossibly an enhancement of the 3-D e7ects can play a profound role. As illustrated inthe paper, for the particular wall–frame model herein, an increase in the wall momentresistance by 70 per cent and subsequently an increase in its lateral load carrying capacityby 35 per cent can be readily achieved if the planar system were to be incorporated intoa 3-D dual structure. In this respect, Codes should stipulate explicit guidelines on therespective analysis and design considerations. A simpli;ed evaluation of the 3-D e7ectsmay be considered following the tentative procedure outlined in the paper.

ACKNOWLEDGEMENTS

The experimental work was conducted at the National Technical University of Athens, Greece, underthe supervision of Prof. T.P. Tassios. Dr G.-F. Zhang participated in the preparation and implemen-tation of the shaking table tests. Assistance received from Prof. P. Carysis, Prof. E. Vintzileou andDr H. Mouzakis during the experiment is greatly acknowledged.

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Seismic behaviour of multistorey RC wall–frame system versus bare ductile frame system