ICE Publishing: All rights reserved

Transcription

1 Volume 1 Issue SB Proeedings of the Institution of Civil Engineers Strutures and Buildings 1 August 15 Issue SB Pages Paper 1 Reeived 3/3/1 Aepted 1//15 Keywords: odes of pratie & standards/onrete strutures/ statistial analysis ICE Publishing: All rights reserved Effet of axial ompression on dutility &1 Y. P. Yuen BEng, PhD Assistant Professor, Department of Civil Engineering, Bursa Orhangazi Üniversitesi, Bursa, Turkey & J. S. Kuang PhD, CEng, FICE, FIStrutE, FHKIE Professor, Department of Civil and Environmental Engineering, The Hong Kong University of Siene and Tehnology, Hong Kong 1 Reinfored onrete (RC) strutural walls an render exellent lateral stability and dutility to medium to high-rise buildings, but are generally subjeted to very high axial ompression loading, whih an redue the inherent dutility. A omprehensive statistial analysis with 7 sets of experimental data was onduted to evaluate and quantify the effet of the axial ompression ratio (ACR) on the strutural performane of RC strutural walls. The stipulated limits on the ACR and the methods of evaluation used in various design odes were ompared. Provisions on the limits of the ACR stipulated in various design odes were ompared, and the expeted attainable dutility fators for RC walls designed to different odes were evaluated. It was found that the provisions on ACR limits in Euroode generally satisfy the target dutility level but a distintion needs to be made between non-squat and squat walls due to their different strutural behaviours. Notation A ross-setional area of onrete setion A gross area of the onrete setion A g ross-setional area of a wall segment A w web area of wall natural axis depth E seismi ation E i Young s modulus of unonfined onrete E l seant modulus from the origin to the peak ompressive stress E y Young s modulus of steel reinforement f uniaxial ompressive strengths of unonfined onrete f design axial ompressive strength of onrete under uniaxial ompression at days f uniaxial ompressive strengths of onfined onrete f d design ylinder strength (with a safety fator of 1 5) of onrete under uniaxial ompression at days f k harateristi axial strength of onrete f u harateristi ube strength of onrete under uniaxial ompression at days f l effetive onfining stress provided by the onfining reinforement f s stress in reinforement steel f si stress in the ith reinforement steel f y uniaxial yield strength of steel total permanent or dead load G k H k L l p l w M N N ED,EC N W,C N W, HK Q k Q ki r di t V p y Δ g Δ sp Δ t Δ u Δ y α V δ u δ y height of wall E i /E il length of wall length of plasti hinge web length of wall bending moment axial ompression design axial fore from the analysis for seismi design fatored axial fore for the wall design axial fore total live load variable ation ombination oeffiient for variable ation i due to the representative gravity load (Equation 1) thikness of wall peak shear fore distane measured from the wall edge ground displaement strain penetration effet displaement at the top of the building relative to the ground ultimate displaement yield displaement vertial aspet ratio ultimate top displaement yield top displaement 55

2 Volume 1 Issue SB ε ε onrete ompressive strain strain at the peak ompressive stress of onfined onrete ε 1 strain at the peak ompressive stress of unonfined onrete ε u ultimate rushing strain of onrete ε sm rupture strain of steel reinforement ε t strain in the extreme tensile fiber ε y steel yielding strain η axial ompression ratio μ φ urvature dutility fator μ Δ displaement dutility fator ν n normalised shear strength ρ v volumetri ratio of the onfinement reinforement σ ompressive stress φ p plasti setional urvature φ u ultimate setional urvature φ y yield setional urvature ψ E,i ombination oeffiient (Equation 1) ω v mehanial onfining reinforement ratio 1. Introdution Catastrophi ollapse of reinfored onrete (RC) buildings learly neessitates the dragging down of vertial strutural members; for instane, the failure of strutural walls an lead to potential overall strutural instability. In view of this, the apaity protetion of walls and primary olumns through speial design and detailing is one of the most ritial issues in seismi design (fib, 1; Kappos and Penelis, 199; Park, 19; Paulay and Priestley, 199). It has been demonstrated in many disastrous earthquakes (Fintel, 199) that well-designed strutural walls an provide exellent lateral stability and drift dutility to medium- to high-rise RC buildings under seismi ation. To ahieve the goal of apaity design, the enhanement and preservation of suffiient dutility of RC strutural walls are ahieved through onfinement details, the requirements of whih are signifiantly influened by the level of the axial fore indued on the walls. The effet of axial fore on the seismi behaviour of RC walls is atually known from experiene, but the fore and behaviour are orrelated in many aspets. Although the urvature dutility of RC setions an be readily evaluated at different levels of axial fore, the relationships between the axial fore and the bukling tendeny of longitudinal reinforing bars and the yli fatigue of the members are quite ompliated, espeially under seismi loading (Paulay and Priestley, 199). However, the axial fore an also have some positive effet on the strutural behaviour, suh as supressing shear sliding and premature anhorage failure (Kappos and Penelis, 199). Hene the atual seismi responses of RC walls under a signifiant axial fore an be ompliated, given that interations between different axial fore effets and failure mehanisms further ompliate the situation. Nonetheless, both researh studies (Su and Wong, 7; Zhang and Wang, ) and disastrous earthquakes (Adebar, 13; Wallae et al., 1) have repeatedly revealed that the adverse effet of axial ompression on RC walls generally overwhelms the benefits introdued. The Chile earthquake in 1 is a good example, showing the effet of high axial fores on the seismi performane of RC walls. Post-earthquake field investigations indiated that thin walls, with thikness ranging from 15 to mm and designed to the modern standards, in newly built high-rise buildings were subjeted to higher axial ompression than thiker walls in the old buildings, and surprisingly suffered more severe damage during the earthquake (EERI, 1). This shows that the use of reinforement detailing annot guarantee desirable seismi performane of walls when they are subjeted to high axial ompression. Modern omplex strutures and super-high-rise skysrapers, both in Chile and in other parts of the developed world, are also often haraterised by high ompression fores in very slender members, as a onsequene of arhitetural designs that maximise lear floor heights and usable floor areas. Reent studies (Su and Wong, ; Wallae et al., 1) have indiated that strutural walls in modern high-rise buildings would sustain an axial ompression ratio (ACR) of or above, whih is muh higher than the typial range of. To avert undesirable brittle failures of RC members, on the basis of the work by Chronopoulos and Vinzileou (1995), Euroode (BSI, ) stipulates the limits for the normalised axial fore, also known as the axial fore ratio, for RC members in various dutility lasses, despite the largely sattered results (Tassios, 199). Chinese (MCPRC, 1) and Hong Kong (HKSAR-BD, 13) design odes impose similar requirements to Euroode. However, not all modern design odes, for instane, New Zealand, Amerian and Canadian odes (ACI, 11; SNZ, ), use the same measure to limit the ACR in the design of RC strutures. There is apparently no onsensus among the different engineering and researh ommunities on whether limiting the ACR is ruial to the dutile or apaity to withstand seismi loading. In view of this, in the present study the effet of the ACR on seismi performane of RC strutural walls was revisited and a statistial analysis undertaken in order to ompare and disuss the rationale of the relevant provisions in various design odes. The aim was to shed light on the justifiation of the use of ACR in the to determine a suitable limit to ontrol the seismi performane of RC strutures.. Failure modes of walls.1 Slender walls Failure modes of walls are governed by the slenderness and axial ompression. It is well reognised that the failure modes and mehanisms of slender and squat walls are very different. Slender walls often fail in the flexural mode, with prominent horizontal raks developing in plasti hinges, usually at the base. Under low axial ompression, the ollapse of slender walls is due either to low-yle fatigue frature of reinforement in the 555

3 Volume 1 Issue SB tensile zone, or to onrete rushing followed by bukling of vertial reinforement in the ompression zone. For slender walls subjeted to high axial ompression, ompression failure (Figure 1(a)) or lateral bukling is likely to our after suffiient horizontal raks have developed during the yli loading.. Squat walls For squat walls, little or no flexural yielding will our before shear failure, resulting in non-dutile strutural behaviour. Shear failure of squat walls an be in the form of diagonal tension, diagonal ompression or sliding shear. Diagonal tension failure, where diagonal shear raks develop aross the entire length of the wall, is likely to our in walls having little horizontal reinforement and low axial ompression (Figure 1()). On the other hand, diagonal ompression failure or web rushing, where loalised onrete rushing ours at one end of the diagonal strut, often takes plae in walls subjeted to high axial ompression. Sliding shear failure is also likely to our in walls having low axial ompression and aspet ratio. Horizontal sliding planes are reated when the raks from one side interset those from the other side during reversed yli loading. (a) (b) Figure 1. Failure modes of a shear wall: (a) ompression failure of a wall in the 19 Alaska earthquake; (b) lateral bukling of a wall during the 1 Chile earthquake; () shear failure of a wall during the 1999 Izmit earthquake. (Courtesy of Vitelmo V. Bertero for (a), M. Franiso for (b) and Andrew S. Whittaker for (); aquired from the NISEE e-library, EERC, University of California, Berkeley, CA, USA) () 55

4 Volume 1 Issue SB 3. Axial ompression ratio 3.1 Definition of ACR To parametrise the axial ompression effet on the strutural performane of RC walls, in the literature the axial ompression is generally normalised using the onrete uniaxial ompressive strength multiplied by the setional area of the onrete member. That is, the ACR η is defined as 1: η ¼ N f A where N is the axial ompression, f is uniaxial ompressive strength of onrete, and A is the ross-setional area of the onrete setion. Besides the onfinement detailing, aspet ratios, lap and splies et., the ACR is a very important fator in evaluating the expeted dutility and fragility of RC walls during earthquakes. However, it should not be onfused with limit-state design onepts, as the ACR alone annot represent or be used to assess the atual seismi performane of RC strutural walls. 3. Axial ompression effet on dutility Axial fore plays a ruial role in governing the drift dutility of RC walls. An apparent and instant effet at higher axial ompression is a redution in the urvature dutility of the walls (Paulay and Priestley, 199; Priestley et al., 7). The relationship between the urvature dutility ϕ u and the axial ompression is illustrated in Figure. The urvature dutility is diretly inversely proportional to the natural axis depth, whih in turn is a monotonially inreasing funtion of the axial ompression. Hene, the urvature dutility, as well as the total drifts dutility of the wall of height H (Figure 3) dereases with inreasing axial ompression. If the strain penetration effet Δ sp is deemed to be negligible, and assuming a plasti hinge length of l p 5l w, the normalised drift apaity and dutility of flexurally ontrolled wall segments an then be estimated as : Δ u H ¼ ε y α V 15 1 þ ε ul w 3: μ Δ ¼ Δ u 1 þ 1 75 l w Δ y α V εu ε y 15 where α V is the vertial aspet ratio H/l w, and μ Δ is the displaement dutility fator. Equation 3 further indiates that the aspet ratio α V, onrete rushing strain ε u and steel yielding strain ε y are also effetive parameters for representing the drift dutility of a wall segment, and the natural axis depth is an influential parameter. The auray of Equations and 3 was tested against experimental data from the SLDRCE Database (Zhou and Lu, 1). The predited results for the drift dutility and ultimate drift ratio are plotted against the experimental data in Figure. Linear regressions of the predited results N M y l w Axial fore balane i si l w N f f y d ε t ε y Movement balane f y φ u ε u φ u i εu l w M f y f y y si i d Ultimate and yield urvatures of walls (Priesley et al., 7) ε φ u l y w f Curvature dutility of walls f s µ φ εulw ε y Figure. Relationship between the urvature dutility and the internal fores in the walls 557

5 Volume 1 Issue SB t 3 5 Zhou and Lu (1) 3 Critial region l p H Predited drift dutility y 5x 15 against the experimental data, also plotted in Figure, have slopes lose to unity, whih indiates that the drift dutility and ultimate drift ratio of RC walls an be losely predited using Equations and 3. As an illustrative example to show the effet of the ACR, onfinement and aspet ratios on dutility, a group of four RC walls having the same ross-setion (17 γ mm) but different aspet ratios (,, and ) was onsidered. The walls were longitudinally reinfored with two layers of R1 bars spaed at mm on the entre, as shown in Figure together with various boundary elements details. The onrete over was 5 mm. The material properties of the unonfined onrete were f =3MPa, E i =33 GPa, ε l = 3 and ε u = 35, and the material properties of the reinforement were f y = 5 MPa, E y = GPa and ε sm = 15. The onrete stress strain urve is defined based on the fib Model Code 1 ( fib, 1) as follows : σ kη η ¼ f 1 þðk Þη where σ is the ompressive stress, η=ε /ε l and k=e i /E l. Based on Mander et al. (19) and Park and Paulay (1975), the onfined onrete properties in the boundary elements at different values of the mehanial onfining reinforement ratio (ω v =ρ v f y /f ) are alulated as 5: f ¼ f 15 þ 5 : ε ¼ ε 1 ½1 þ 5ðf =f 1ÞŠ g l w φ p φ y Curvature distribution Figure 3. Drift and plasti hinge region in antilever RC walls under seismi ation sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 79f l f f l f! Predited ultimate drift Experimental data (a) Experimental data: % (b) 7: ε u ¼ þ 1ω v ε sm f =f Zhou and Lu (1) where f l is the effetive onfining stress provided by the onfining reinforement. By assuming the walls fail in the flexural mode and the onrete onfinement effetiveness is 7 for the boundary elements, the influene of the ACR on the displaement apaity and dutility an be evaluated, as shown in Figures 5 and, respetively. The handy alulation shown above learly demonstrates the indispensable need for an ACR limit, in view of the diminishing effetiveness of onfinement on enhaning the displaement apaity at high values of the ACR. It an be seen from Figures 5 and that there is a quite drasti drop in the displaement apaities, whih follows the inrease in the ACR from 1% to 3%, after whih the relationship urves stagnate and tend to onverge to the same value of dutility or ultimate displaement, and thus the onfinement details beome irrelevant thereafter. Meanwhile, it is interesting to note that high aspet ratios have a negative effet y 3x Figure. Predited drift dutility and ultimate drift ratio plotted against experimental data (Zhou and Lu, 1) 55

6 Volume 1 Issue SB Ultimate displaement ratio, u / H : % 1 α v ω v % ω v 5% ω v 1% ω v % 1 α v Ultimate displaement ratio, u / H : % α v α v Axial ompression ratio: % Axial ompression ratio: % Figure 5. Effet of the ACR on the ultimate displaement dutility of RC walls on the dutility but are benefiial to the ultimate displaement, although the latter is less sensitive to the value of the aspet ratio than is the dutility. However, the real relationship between the ACR and the displaement apaity is far more ompliated, as will be seen later, owing to the fat that eah influening fator an interat with the others, resulting in omplex overall strutural behaviour (e.g. various fators, inluding the axial fore, aspet ratio, stiffness and raks, an ome into play in the elasto-plasti bukling of walls). Furthermore, it should be noted that the above alulation is based on the assumption of flexural ontrol, whih may not be valid for squat walls with an aspet ratio lower than 1 5. Wallae and Elwood () over the evaluation of the seismi apaity of squat walls. 3.3 Statistial analysis Besides the onfinement detailing, aspet ratio and axial ompression, the dutility and general seismi performane of RC olumns an be influened by various other fators, suh as the anhorage, loading pattern et., the effets of whih in turn interat with the onfinement and axial load effet. In view of this ompliated behaviour, the quantifiation of the effet of axial ompression on the seismi performane of RC walls has relied heavily on experimental data. Therefore, a omprehensive statistial study was undertaken to evaluate and quantify the effet of the axial fore ratio on the seismi performane of RC walls. A non-linear regression analysis was performed using the Levenberg Marquardt Flether algorithm (Flether, 1971). A total of 7 sets of data, omprising experimental results for small to full-sale RC walls of various shapes and detailing methods, were olleted from the literature (Adebar et al., 7; Ali and Wight, 1991; Barda et al., 1977; Birely, 11; Bohl and Adebar, 11; Borg et al., 1; Cardenas and Magura, 1973; Carrillo and Aloer, 1a, 1b; Dazio et al., 9; Devi et al., 11; Ghorbani-Renani et al., 9; Han et al., ; Hidalgo et al., ; Hirosawa, 1975; Kazaz et al., 1; Kuang and Ho, ; Lefas and Kotsovos, 199; Lefas et al., 199; Liao et al., 9; Morgan et al., 19; Oesterle, 19; Pilakoutas and Elnashai, 1995; Qian and Chen, 5; Qian et al., 1; Riva and Franhi, 1; Salonikios et al., 1999; 559

7 Volume 1 Issue SB u y Displaement dutility / α v ω v % ω v 5% ω v 1% ω v % α v u y Displaement dutility / α v Axial ompression ratio: % α v Axial ompression ratio: % Figure. Effet of the ACR on the displaement dutility of RC walls Shiu et al., 191; Su and Wong, 7; Takahashi et al., 13; Thomsen and Wallae, 1995; Vallenas et al., 1979; Wallae and Elwood, ; Wallae and Moehle, 1991; Wang et al., 1975; Yuen et al., ; Zhang and Wang, ; Zhou and Lu, 1). The load displaement data gathered were then analysed using definitions of yield displaement, ultimate displaement and displaement dutility of the loading urves based on the work by Park (199). In the olleted database, more than % of the tests had been onduted under a relatively low axial fore ratio (< 5), while only about 15% and 7% were tested with an axial fore ratio above 15 and 3, respetively. Nonetheless, these high axial fore tests demonstrated that RC walls will fail in a very partiular manner, suh as out-of-plane bukling, resembling the observed modes of damage to walls seen in the 1 Chile earthquake. RC walls that have failed in outof-plane bukling are generally very brittle and exhibit low dutility, so the lassial methods of evaluating dutility, whih assuming in-plane flexural failure, are no longer appliable. The relationship between the ultimate displaement apaity and the ACR for various types of RC shear walls having different aspet ratios H/L is plotted in Figure 7(a). The statistial analysis followed the design odes in defining the ACR limit, in that no differentiation was made between different types of walls. Nonetheless, it is reognised that the failure behaviour of different types of wall an be very different even under the same ACR. Hene, the data were disaggregated further into two groups squat and non-squat walls for individual statistial analysis. Similar to the analytial results shown in Figure, for slender walls there is a trend of diminishing ultimate displaement apaity with inreasing ACR (Figure 7(b)), owing to the redution in the neutral axial depth, the low-yle fatigue effet as well as potential out-of-plane bukling. Conversely, the ultimate displaement apaity of squat walls tends to inrease with inreasing ACR (Figure 7()). This reversed trend is atually due to the fat that the shear strength and sliding resistane of raks in squat walls are enhaned by axial ompression. Furthermore, it an be seen that the standard deviation varies with the ACR. Suh variation is onsistent with the physial and mehanial behaviour of the walls. When the ACR is low, the failure behaviour an be strongly influened by the reinforement detailing, resulting in a large 5

8 Volume 1 Issue SB Ultimate displaement ratio, δ u / H : % Ultimate displaement ratio, δ u / H : % Ultimate displaement ratio, δ u / H : % Axial fore ratio, N /( f A g ): % (a) Axial fore ratio, N /( f A ): % Axial fore ratio, N /( f A ): % g g (b) () Retangular ( H / L 1 5) Retangular ( H / L 1 5) Composite boundary elements plus one standard deviation minus one standard deviation Retangular ( H / L 1 5) plus one standard deviation minus one standard deviation Retangular ( H / L 1 5) plus one standard deviation minus one standard deviation Figure 7. Relationship between the ultimate displaement apaity and the ACR: (a) various types of RC wall; (b) non-squat walls (H/L>1 5); () squat walls (H/L 1 5) variation in the data. But when the ACR is high, ompression failure or bukling dominate the wall failure, and hene the reinforement detailing has little influene on the failure behaviour, resulting in little variation in the data. Figure (a) shows the relationship between the drift dutility and the axial fore ratio for RC walls of various kinds. It an be seen that RC walls an easily ahieve a high dutility fator (μ Δ ) at a low axial fore ratio (η 1%) as long as the 51

9 Volume 1 Issue SB boundary elements are well detailed and designed. However, when the ACR inreases to above %, the RC walls an only just maintain moderate dutility ( < μ Δ ), and speial detailing methods suh as omposite-reinfored boundary elements are neessary in order to aquire high dutility. It has been reported that above 35% ACR the dominant failure mode an be pre-emptive out-of-plane bukling (Su and Wong, 7; Zhang and Wang, ), resulting in the RC walls not being able to u y Displaement dutility, δ / δ Retangular ( H / L 1 5) Retangular ( H / L 1 5) Composite boundary elements plus one standard deviation minus one standard deviation Axial fore ratio, N /( f A ): % (a) 1 g u y Displaement dutility, δ / δ 1 1 Retangular ( H / L 1 5) plus one standard deviation minus one standard deviation Axial fore ratio, N /( f A ): % g (b) 1 u y Displaement dutility, δ / δ 1 1 Retangular ( H / L 1 5) plus one standard deviation minus one standard deviation Axial fore ratio, N /( f A ): % Figure. Relationship between the displaement dutility fator and the ACR: (a) various types of RC wall; (b) non-squat walls (H/L > 1 5); () squat walls (H/L 1 5) g () 5

10 Volume 1 Issue SB provide lateral and vertial resistane in seismi design. It is reognised that squat RC walls with aspet ratios (H/L) lower than 1 5 will be prone to shear failure, in partiular sliding shear failure (rather than flexural failure), but the displaement dutility is not neessarily redued by the inrease in axial ompression. In ontrast to non-squat walls (Figure (b)), the dutility of squat walls is less influened by the ACR and the dutility fators generally stay within the range < μ Δ, as shown in Figure (). For shear-ontrolled walls, little or no flexural yielding will our before shear failure (Wallae and Elwood, ). On the one hand, high axial ompression an suppress the flexural yielding, and hene redue the dutility of squat walls. On the other hand, axial ompression an inrease the shear frition on the rak faes in the walls (Wallae and Elwood, ), favouring the overall behaviour and ultimate drift apaity of the walls. Hene, the drift dutility ACR and drift apaity ACR relationships show different trends, as an be seen in Figures 7() and (). Another important strutural property of RC walls related to the axial ompression is the shear strength. For omparison purposes, the peak base shears reported for the tests inluded in the database were further normalised using : ν n ¼ V p f 5 A w where A w is web area of the wall. Figure 9 shows the relationship between the normalised shear strength and the ACR. Higher axial ompression tends to inrease the shear strength of all types of RC walls, in partiular squat RC walls, as shown in Figure 9(). This is beause axial ompression an enhane not only the shear strength of walls but in some ases also the moment resistane (Kappos and Penelis, 199; Wallae et al., 1).. Code provisions for the ACR In view of the adverse effet of axial ompression on the seismi performane of RC strutural walls (as illustrated in the last setion), most of the modern design odes of pratie for RC strutures stipulate upper limits of the ACR. RC walls with an ACR beyond the limits are generally deemed to be ineffetive in resisting seismi ation, even with onfinement detailing in the ritial regions (expeted plasti hinges) of the members. The aim of these provisions, in addition to onfinement detailing, is to ensure that suffiient drift dutility and axial fore arrying apaity an be retained in RC strutures during earthquakes or other exeptional load ases..1 Euroode (BS EN 199-1:) Euroode (BSI, ) stipulates upper limits of the ACR (normalised axial fore) for dutile walls and olumns designed for dutility lasses moderate and high (DCM and DCH), but no restritions for dutility lass low (DCL), as follows 9: N ED;EC f d A 35 DCH >< DCM >: DCL ðbs EN : Þ where N ED,EC is the design axial fore from the analysis for seismi design equal to 1: N ED;EC ¼ G k þ X i ψ E;i Q ki þ E in whih ψ E,i is the ombination oeffiient ( 1) for variable ation Q ki and E is the seismi ation; and f d is the design ylinder strength (fatored with a safety fator of 1 5) of onrete under uniaxial ompression at days, A is the gross area of the onrete setion and G k is the total permanent or dead load. The design axial fore alulated using Equation 9 onsists of two major parts: the axial fore indued by representative gravity ation, and the axial fore indued by seismi ation. It also inludes the effet of seismi ations on RC walls. Although axial fores inurred in antilever walls by seismi ations are relatively minor as ompared with permanent gravity ation in general, oupled shear walls would have to bear signifiant extra axial fores inurred by seismi ations, due to the oupling ation aggregated from the shear fores of the oupling beams, whih obviously has a nonnegligible effet on the seismi performane of the walls. Therefore, the definition of the ACR in Euroode an be onsidered the most appropriate desription of realisti stress states experiened by RC strutures during earthquakes. In fat, the limits of the ACR stipulated in Euroode an be readily ompared with experimental studies to see whether the provisions an ensure suffiient dutility of RC members.. Chinese seismi design ode 1 (GB511-1) In the Chinese seismi design ode (MCPRC, 1), the upper limits of the ACR for RC shear walls (setional aspet ratio L/t > ) take different values under different design fortifiation earthquake intensities and struture grades (four lasses, I to IV: for grade I strutures have high drift dutility, grade II and III strutures have moderate to high drift dutility, and grade IV strutures have relatively low drift dutility) as follows 11: Grade I; intensity 9 N >< W;C 5 Grade I; intensity 7 or f A Grade II or III >: Grade IV ðgb511-1þ 53

11 Volume 1 Issue SB Normalised shear strength, V /( f A ) 5 w p Normalised shear strength, V /( f A 5 w ) p Normalised shear strength, V /( f A 5 w ) p Axial fore ratio, N /( f A ): % Axial fore ratio, N /( f A ): % Axial fore ratio, N /( f A ): % g g g (a) (b) () Retangular ( H / L 1 5) Retangular ( H / L 1 5) Composite boundary elements plus one standard deviation minus one standard deviation Retangular ( H / L 1 5) plus one standard deviation minus one standard deviation Retangular ( H / L 1 5) plus one standard deviation minus one standard deviation Figure 9. Relationship between the normalised shear strength and the ACR: (a) various types of RC wall; (b) non-squat walls (H/L>1 5); () squat walls (H/L 1 5) 5

12 Volume 1 Issue SB where N W,C is the fatored axial fore for the wall equal to 1: N W;C ¼ 1ðG k þ X i r di Q ki Þ in whih r di is the ombination oeffiient ( 1) for variable ation i due to the representative gravity load, and f is the design axial ompressive strength of onrete under uniaxial ompression at days (equal to the harateristi axial strength of onrete f k divided by the safety fator 1 ). The harateristi axial strength f k is determined in a mm prism ompression test, whih in this ode an be onservatively taken as 7 of the harateristi ube strength f u,k. The average value of the ratio f k /f u,k, the soalled effetiveness fator, is around 7, based on experimental studies (Nielsen, 1999; Zhang, 1993). More stringent provisions are set for short-pier RC shear walls (<L/t ), suh that the values of the ACR for grades I, II and III shortpier walls should not exeed 5, 5 and 55, respetively, in the ritial regions (MCPRC, 1). The axial fore in Equation 11 is alulated using the representative gravity ation, rather than the ultimate gravity ation, whih the struture is expeted to take during earthquakes, and the multiplying fator of 1 is used to aount for additional axial fore inurred by unforeseen and exluded ations on the walls. In the alulation of the representative gravity ation, the ombination oeffiient r di is used to onsider the redued likelihood that full variable ations are present during earthquakes; for instane, r di for a residential floor live load is 5..3 Hong Kong onrete ode 13 In the Hong Kong onrete ode (HKSAR-BD, 13), the upper limit of the ACR for RC strutural walls is speified as follows 13: N W;HK 5f u A 75 where N W, HK is the design axial fore equal to 1: N W;HK ¼ 1G k þ 1Q k in whih G k is the total permanent or dead load and Q k is the total live load, for the wall due to gravity load; f u is the harateristi ube strength of onrete under uniaxial ompression at days, and A is the gross area of the onrete setion. Note that the safety fator for the onrete ompressive strength used in the HK ode is 1 5, and dividing the harateristi onrete strength by this fator gives the design strength. The onstant 5 = 7/1 5 in the denominator onverts the harateristi onrete strength into the equivalent design ompressive strength for the setions subjeted to dominant flexural bending ation, wherefore another multiplying fator 7 is used. Meanwhile, the axial fore in the numerator takes the ultimate load value due to sole gravity ation, without onsideration of possible non-permanent live load redution or representative gravity ation during rare events with exeptional loading ations suh as earthquakes.. New Zealand and other design odes The New Zealand onrete ode (SNZ, ) does not have similar provisions regarding the axial fore ratios as in the European, Chinese and Hong Kong odes, but limiting setional urvatures or strains in potential plasti hinge regions are speified for different RC members (lause..1.3., NZS 311.1&:). Limiting material strains is apparently the most diret method to ontrol urvature dualities of RC members; however, whether it is suffiient to prevent the lowyle fatigue phenomenon or rapid strength and stiffness degradation of RC members under yli loading is unertain. It is also worth mentioning here that the US onrete design ode ACI 31-11:11 (ACI, 11) also does not introdue similar limits on the ACR for RC olumns and walls. Nevertheless, a US standard for the seismi rehabilitation of buildings, ASCE/SEI 1-:7 (ASCE, 7; Park, 199), states that RC walls with axial loads greater than 35% of the nominal axial load strength P shall not be onsidered effetive in resisting seismi fores. The Canadian onrete ode, CSA A3.3- (CSA, 1), also states that flexural members with fatored axial loads in exess of 35 P shall have a nominal resistane greater than the indued member fore, (i.e. not to be designed to form potential plasti hinges and dissipate energy in any irumstanes under seismi effets)..5 Comparison of ode provisions Although the definitions of the axial fore ratios in the European, Chinese and Hong Kong odes are somewhat dissimilar, partiularly with regard to the axial fores in the numerators, the ompressive strength terms in the denominators an be readily transformed to give a harateristi ylindrial strength f = f u = f d /1 5 for omparison purposes. Table 1 summarises the key omparisons of the provisions on the ACR defined in the three odes. The ACR limits stipulated in the Chinese ode resemble those in Euroode but, as mentioned before, the ombinations of ations for alulating the axial fores are different in the two odes. For antilever walls, the Chinese ode is more stringent beause a safety fator of 1 is used to amplify the ation. However, for oupled shear walls, it is not onlusive whih of the two odes is more onservative, as the fator of 1 may not be suffiient to over the exeeding axial fores indued by the oupling ation. Nevertheless, Euroode provides a more realisti assessment for these ases by taking into onsideration seismi or generally lateral fore effets. At first sight, looking at the last row 55

13 Volume 1 Issue SB Euroode (BS EN 199-1:) Chinese ode (GB511-1) Hong Kong onrete ode 13 N ED;EC N W;C N W;HK Definition of ACR f d A f A 5f u A Grade I; intensity 9 < 35 DCH >< a 5 Grade I; intensity 7 or a Limit DCM : GradeII or III a 75 DCL >: Grade IV Seismi/lateral fores effet 3 Variable load redution 3 3 Grade I; intensity 9 N < 3 DCH ED;E N >< W;C Grade I; intensity 7 or N W;HK ACR limit renormalised vs f DCM f A : f DCL A 3 Grade II or III f >: A Grade IV a Limits for grades I, II and III short-pier RC shear walls ( < H/B ) are 5, 5 and 55, respetively Table 1. Comparison of ode provisions for the ACR of RC walls in Table 1, the Hong Kong ode has the least stringent limit on the ACR for RC walls ompared with the other two odes. But it should be noted that the axial fore in the numerator is generally muh larger, given that full ultimate gravity ation is onsidered instead of representative gravity ation. The relationship between the displaement dutility fator and ACR shown in Figure 7 is re-plotted with the ode-speified limits on the ACR in Figure 1(a), where the expeted ahievable dutility of RC walls an be learly seen. In Euroode, for multi-storey unoupled RC-walled buildings with a fundamental period T 1 longer than the period T at the upper limit of the onstant aeleration region of the responses spetrum, the displaement dutility fator μ δ is equal to the behaviour fator q (BSI, ), the basi values of whih are 3 and for DCM and DCH, respetively. Euroode provisions undoubtedly satisfy this target level of dutility, provided that the boundary elements are properly detailed. The grade I strutures designed to the Chinese ode an also satisfy this target but the grade II or III strutures may have only restrited inherent dutility and are suseptible to out-of-plane bukling. However, the Hong Kong ode limit is somewhat unjustifiable in the sense that the target is to ontrol the dutility. It is noted that walls having different reinforement detailing would attain different dutility, even if they were subjet to the same ACR. However, under high values of the ACR the use of reinforement detailing is no longer effetive in enhaning the dutility, as the failure mode hanges from flexural to ompression or bukling. In this sense, reinforement detailing plays a minor role in defining the ACR limit, whih is used to ontrol the failure mode of walls. Nevertheless, the wall onfiguration and aspet ratio do play an important role in ontrolling the behaviour of walls even under high values of the ACR. The data in Figure 1(a) an be split into data for non-squat (H/L >1 5) and squat (H/L 1 5) walls, as done previously, and the resultant plots are shown in Figure 1(b) and 1(). For non-squat walls, it an be seen that there is still room for the ACR limits stipulated in Euroode to be relaxed, for instane to 5 and 3 for DCH and DCM, respetively, whereas for squat walls the ACR has apparently little effet on wall dutility. However, as shown in Figure 7(), the axial fore tends to inrease the ultimate displaement of squat RC walls, whih is learly benefiial in the state-of-the-art displaement-based design methods (Priestley et al., 7). It may be onluded that squat walls are not suitable to be designed to allow inelasti deformation or as an energy-dissipating element. 5. Conlusion In the design of medium and high-rise buildings, RC shear walls are often used to provide exellent lateral stability and dutility to the strutures under the ation of wind or earthquakes. In general, shear walls are subjeted to very high axial ompression, whih has been pushing the limits of onventional design and analysis theories. A omprehensive statistial analysis of 7 sets of experimental data was onduted to investigate the effet of the ACR on the strutural performane of various types of RC walls. It was shown that the dutility of the walls redues generally with inreasing ACR. This trend is partiularly notieable for nonsquat walls having an aspet ratio H/L >1 5. Provisions on the limits of the ACR stipulated in various design odes of pratie were ompared, and the expeted attainable dutility of RC 5

14 Volume 1 Issue SB u y Displaement dutility, δ / δ Euroode : DCH. GB511: grade 1 (intensity 9) Euroode : DCM GB511: grade 1 (intensity 7/) GB511: grade II/III Hong Kong onrete ode 13 walls designed to different odes was evaluated against the results of the statistial analysis. Based on the results of the analysis, it was found that Euroode provisions on the ACR limits for RC strutural walls generally satisfy the target level for dutility. However, the ACR limits may take different values for non-squat and squat walls due to their distint strutural behaviours. It was found in this study that the ACR limits for non-squat walls an be relaxed. However, there is obviously a need to ondut more experimental studies on squat walls under high axial ompression loading before definite onlusions an be drawn. u y Displaement dutility, δ / δ u y Displaement dutility, δ / δ Axial fore ratio, N /( f A g ): % (a) Euroode : DCH. GB511: grade 1 (intensity 9) Euroode : DCM GB511: grade 1 (intensity 7/) GB511: grade II/III Hong Kong onrete ode Axial fore ratio, N /( f A g ): % (b) Euroode : DCH. GB511: grade 1 (intensity 9) Euroode : DCM GB511: grade 1 (intensity 7/) Axial fore ratio, N /( f A g ): % () Figure 1. Relationship between ode-speified ACR limits and the expeted displaement dutility: (a) various types of RC wall; (b) non-squat walls (H/L>1 5); () squat walls (H/L 1 5) GB511: grade II/III Hong Kong onrete ode 13 Aknowledgements The support of the Hong Kong Researh Grand Counil (HK-RGC) under grant number 111 and the Sientifi and Tehnologial Researh Counil of Turkey (TÜBİTAK) under projet number 1M3 is gratefully aknowledged. REFERENCES Adebar P (13) Compression failure of thin onrete walls during 1 Chile earthquake: lessons for Canadian design pratie. Canadian Journal of Civil Engineering (): Adebar P, Ibrahim AMM and Bryson M (7) Test of high-rise ore wall: effetive stiffness for seismi analysis. ACI Strutural Journal 1(5): Ali A and Wight JK (1991) RC strutural walls with staggered door openings. Journal of Strutural Engineering 117(5): ACI (Amerian Conrete Institute) (11) ACI 31-11:11: Building ode requirements for strutural onrete and ommentary. ACI, Farmington Hills, MI, USA. ASCE (Amerian Soiety of Civil Engineers) (7) ASCE/SEI 1-:7: Seismi rehabilitation of existing buildings. ASCE, Reston, VA, USA. Barda F, Hanson J and Corley W (1977) Shear strength of lowrise walls with boundary elements. In Reinfored Conrete Strutures in Seismi Zones. Amerian Conrete Institute, Farmington Hills, MI, USA, SP 53-, pp Birely AC (11) Seismi Performane of Slender Reinfored Conrete Strutural Walls. PhD thesis, University of Washington, Seattle, WA, USA. Bohl A and Adebar P (11) Plasti hinge lengths in high-rise onrete shear walls. ACI Strutural Journal 1(S15): Borg RC, Rossetto T and Varum H (1) The effet of the number of response yles on the behaviour of reinfored onrete elements subjet to yli loading. The 15th World Conferene on Earthquake Engineering, Lisbon, Portugal. BSI () BS EN 199-1:: Euroode : Design of strutures for earthquake resistane. Part 1: General rules, seismi ations and rules for buildings. BSI, London, UK. 57

15 Volume 1 Issue SB Cardenas AE and Magura DD (1973) Strength of high-rise shear walls retangular ross setions.in Response of Multistory Conrete Strutures to Lateral Fores. Amerian Conrete Institute, Farmington Hills, MI, USA, SP-3, pp Carrillo J and Aloer SM (1a) Aeptane limits for performane-based seismi for low-rise housing. Earthquake Engineering & Strutural Dynamis 1 (15): 73. Carrillo J and Aloer SM (1b) Bakbone model for performane-based seismi for low-rise housing. Earthquake Spetra (3): Chronopoulos MP and Vinzileou E (1995) Confinement of RC olumns. In European Seismi Design Pratie (Elnashai AS (ed.)). Balkema, Rotterdam, the Netherlands pp CSA (Canadian Standard Assoiation) (1) CSA:A3.3- (R1): Design of onrete strutures. CSA, Ontario, Canada. Dazio A, Beyer K and Bahmann H (9) Quasi-stati yli tests and plasti hinge analysis of RC strutural walls. Engineering Strutures 31(7): Devi GN, Subramanian K and Santakumar AR (11) Experimental investigations on reinfored onrete lateral load resisting systems under lateral loads. Experimental Tehniques 35(): EERI (Earthquake Engineering Researh Institute) (1) Learning from Earthquakes. The Mw Chile Earthquake of February 7, 1. EERI, Oakland, CA, USA, Speial Earthquake Report. fib (Fédération Internationale Du Béton) (1) Model Code 1 Bulletin. fib, Lausanne, Switzerland, vol.. Fintel M (199) Need for shear walls in onrete buildings for seismi resistane: observations on the performane of buildings with shear walls in earthquakes of the last thirty years. In Conrete Shear in Earthquake (Hsu TTC and Mau ST (eds)). Elsevier, London, UK, pp. 3. Flether R (1971) A Modified Marquardt Subroutine for Nonlinear Least Squares. United Kingdom Atomi Energy Authority, Harwell, UK, Report AERE-R 799. Ghorbani-Renani I, Velev N, Tremblay R et al. (9) Modeling and testing influene of saling effets on inelasti response of shear walls. ACI Strutural Journal 1(3): Han SW, Oh YH and Lee LH () Seismi behaviour of strutural walls with speifi details. Magazine of Conrete Researh 5(5): Hidalgo PA, Ledezma CA and Jordan RM () Seismi behavior of squat reinfored onrete shear walls. Earthquake Spetra 1(): 7 3. Hirosawa M (1975) Past Experimental Results on Reinfored Conrete Shear Walls and Analysis on Them. Building Researh Institute, Ministry of Constrution, Tokyo, Japan, Kenhiku Kenkyu Shiryo No. (in Japanese). HKSAR-BD (Government of the Hong Kong Speial Administrative Region Buildings Department) (13) Code of Pratie for Strutural Use of Conrete 13. HKSAR-BD, Hong Kong. Kappos A and Penelis GG (199) Earthquake Resistant Conrete Strutures. CRC Press, Boa Raton, FL, USA. Kazaz I, Gülkan P and Yakut A (1) Deformation limits for strutural walls with onfined boundaries. Earthquake Spetra (3): Kuang JS and Ho YB () Seismi behavior and dutility of squat reinfored onrete shear walls with nonseismi detailing. ACI Strutural Journal 15(): Lefas ID and Kotsovos MD (199) Strength and deformation harateristis of reinfored onrete walls under load reversals. ACI Strutural Journal 7(): Lefas ID, Kotsovos MD and Ambrasseys NN (199) Behaviour of RC strutural walls: strength, deformation harateristis and failure mehanism. ACI Strutural Journal 7(1): Liao FY, Han LH and Tao Z (9) Seismi behaviour of irular CFST olumns and RC shear wall mixed strutures: experiments. Journal of Construtional Steel Researh 5( 9): Mander JB, Priestley MJN and Park P (19) Theoretial stress strain model for onfined onrete. Journal of Strutural Engineering 11(): 1 1. Morgan BJ, Hiraishi H and Corley WG (19) US Japan Quasi Stati Test of Isolated Wall Planar Reinfored Conrete Struture. PCA Report. Constrution Tehnology Division, Skokie, IL, USA. Nielsen MP (1999) Limit Analysis and Conrete Plastiity, nd edn. CRC Press, Boa Raton, FL, USA. MCPRC (Ministry of Constrution of the People s Republi of China) (1) National Standard of People s Republi of China: Code for seismi design of buildings. China Arhiteture & Building Press, Beijing, China, GB Oesterle RG (19) Inelasti Analysis for In-plane Strength of Reinfored Conrete Shear Walls. PhD dissertation, Northwestern University, Evanston, IL, USA. Park R (19) Dutile design approah for reinfored onrete frames. Earthquake Spetra (3): Park R (199) Evaluation of dutility of strutures and strutural assemblages from laboratory testing. Bulletin of the New Zealand Soiety for Earthquake Engineering (3): Park R and Paulay T (1975) Reinfored Conrete Strutures. Wiley, New York, NY, USA. Paulay T and Priestley MJN (199) Seismi Design of Reinfored Conrete and Masonry Buildings. Wiley, New York, NY, USA. Pilakoutas K and Elnashai AS (1995) Cyli behaviour of RC antilever walls. Part I: experimental results. ACI Strutural Journal 9(3): Priestley MJN, Calvi GM and Kowalsky MJ (7) Displaement-Based Seismi Design of Strutures. IUSS Press, Pavia, Italy. 5

16 Volume 1 Issue SB Qian J and Chen Q (5) A maro model of shear walls for push-over analysis. Proeedings of the ICE Strutures and Buildings 15(): Qian J, Jiang Z and Ji X (1) Behavior of steel tube-reinfored onrete omposite walls subjeted to high axial fore and yli loading. Engineering Strutures 3(3): Riva P and Franhi A (1) Behavior of reinfored onrete walls with welded wire mesh subjeted to yli loading. ACI Strutural Journal 9(3): Salonikios T, Kappos A, Tegos I and Penelis G (1999) Cyli load behavior of low-slenderness reinfored onrete walls: design basis and test results. ACI Strutural Journal 9(): 9. Shiu KN, Daniel JI, Aristizabal JD, Fiorato AE and Corley WG (191) Earthquake Resistant Strutural Walls Tests of Walls With and Without Openings. Portland Cement Assoiation, Skokie, IL, USA. SNZ (Standards New Zealand) () NZS 311.1&:: Conrete strutures standard. NZS, Wellington, New Zealand. Su RKL and Wong SM () A survey on axial load ratios of medium-rise residential buildings in Hong Kong. HKIE Transations 1(3):. Su RKL and Wong SM (7) Seismi behaviour of slender reinfored onrete shear walls under high axial load ratio. Engineering Strutures 9(): Takahashi S, Yoshida K and Ihinose T (13) Flexural drift apaity of reinfored onrete wall with limited onfinement. ACI Strutural Journal 11(Suppl 1): Tassios TP (199) Advanes in earthquake-resistant design onrete strutures. 11th World Conferene on Earthquake Engineering, Aapulo, Mexio, paper No Thomsen JH and Wallae JW (1995) Displaement-Based Design of Reinfored Conrete Strutural Walls: An Experimental Investigation of Walls with Retangular and T-Shaped Cross-Setions. Department of Civil and Environmental Engineering, Clarkson University, Potsdam, NY, USA, Report No. CU/CEE-95/. Vallenas MV, Bertero VV and Popov EP (1979) Hystereti Behaviour of Reinfored Conrete Strutural Walls. Earthquake Engineering Researh Center, University of California, Berkeley, CA, USA, UCB/EERC Report 79/. Wallae JW and Elwood KJ () An axial load apaity model for shear ritial RC wall piers, Proeedings, th US National Conferene on Earthquake Engineering, San Franiso, CA, USA, Paper 15. Wallae JW and Moehle JP (1991) Dutility and detailing requirements of bearing wall buildings. Journal of Strutural Engineering 11(): Wallae JW, Massone LM, Bonelli Pet al. (1) Damage and impliations for seismi design of RC strutural wall buildings. Earthquake Spetra (Suppl 1): 1 S99. Wang TY, Bertero VV and Popov EP (1975) Hystereti Behavior of Reinfored Conrete Framed Walls. Earthquake Engineering Researh Center, University of California, Berkeley, CA, USA, UCB/EERC Report 75/3. Yuen H, Choi C and Lee L () Earthquake performane of high-strength onrete strutural walls with boundary elements. 13th World Conferene on Earthquake Engineering, Vanouver, BC, Canada. Zhang QX (1993) Conrete Struture Design: Basi Theory, Methods and Examples. Jiangsu Siene and Tehnology Publishing House, Jiangsu, China. Zhang Y and Wang Z () Seismi behaviour of reinfored onrete shear walls subjeted to high axial loading. ACI Strutural Journal 97(5): Zhou Y and Lu X (1) Shear Wall Database from Tongji Univsersity. See (aessed 11//15). WHAT DO YOU THINK? To disuss this paper, please up to 5 words to the editor at journals@ie.org.uk. Your ontribution will be forwarded to the author(s) for a reply and, if onsidered appropriate by the editorial panel, will be published as disussion in a future issue of the journal. Proeedings journals rely entirely on ontributions sent in by ivil engineering professionals, aademis and students. Papers should be 5 words long (briefing papers should be 1 words long), with adequate illustrations and referenes. You an submit your paper online via where you will also find detailed author guidelines. 59