Flexural Drift Capacity of Reinforced Concrete Wall with Limited Confinement

Transcription

1 ACI STRUCTURAL JOURNAL TECHNICAL PAPER Title no. 110-S10 Flexural Drift Capaity of Reinfored Conrete Wall with Limited Confinement by S. Takahashi, K. Yoshida, T. Ihinose, Y. Sanada, K. Matsumoto, H. Fukuyama, and H. Suwada The flexural drift apaity of reinfored onrete (RC) walls is disussed in this study based on the test results of 10 speimens. The test parameters were wall length, thikness, detailing, and axial fore. The detailing of the ties did not satisfy the ACI requirements. Eah speimen had a olumn at one end where an axial fore was applied. All speimens failed in flexural ompression after yielding of the longitudinal bars. The observed flexural drift apaity was between 0.4 and 1.2%. A set of equations to predit the drift apaity is proposed wherein the hinge zone length is assumed to be 2.5 times that of the wall thikness. Keywords: boundary element; ompressive failure; onfinement; drift apaity; plasti hinge; reinfored onrete wall. INTRODUCTION ACI requires speial detailing for boundary elements of reinfored onrete (RC) walls to prevent flexural ompressive failure under seismi fores. One of the approahes to the detailing is based on the displaementbased onept. 2 If the ompressive strain of onrete is expeted to be larger than 0.003, the ompressive zone is required to be reinfored aording to the requirement of the speial boundary element for onfinement. This requirement is verified by Thomsen and Wallae, 3 who tested walls with retangular- and T-shaped ross setions. The Japanese Code 4 presribes the dutility of RC walls based mainly on the ratio of the neutral axis depth to the wall thikness. This presription is based on several experimental studies, inluding those by Tabata et al., 5 who tested RC walls with retangular ross setions and large shear-span ratios. The plasti hinge length L p is important for estimating drift apaity. Researhers have proposed various approahes. In the study by Wallae and Orakal, 2 whih was the basis of the seismi requirements of ACI , 1 the plasti hinge length was assumed as one half of the wall length (L p = l w /2). Tabata et al. 5 assumed L p = 0.3l w. On the other hand, Kabeyasawa et al. 6 idealized the wall, assuming that the strain of eah boundary element is uniform within eah story; this idealization is almost equivalent to the assumption of L p = h, where h is story height. Orakal and Wallae 7 divided the wall into eight segments in the diretion of the height; this idealization is almost equivalent to the assumption of L p = h/8. Paulay and Priestley 8 assumed that L p = 0.20l w a from the test results of antilever walls, where a is shear span length. Takahashi et al. 9 showed that the presription of the Japanese Code 4 is impliitly based on the assumption of L p = 2.5t, where t is wall thikness. The objetive of this paper is to propose a set of equations to predit the drift apaity of RC walls based on the assumption of L p = 2.5t. To verify this assumption, 10 speimens were tested. The detailing of these speimens does not satisfy the seismi requirements of ACI , 1 but suh detailing may be preferred for ease of onstrution. The test parameters were wall length, thikness, detailing, and axial fore. The details of this experiment are available elsewhere. 10,11 RESEARCH SIGNIFICANCE There are many RC buildings that do not satisfy the requirements of ACI , 1 inluding those in Chile. Most of the wall damage aused by the 2010 Chile earthquake was related to the onfiguration and reinforement detailing of wall boundary elements. 12 The damage indiated that the performane of these walls was brittle, as expeted. On the other hand, there may have been many buildings that resisted the earthquake, although they did not satisfy the requirements of ACI The ACI requirements are quite strit about the boundary element; it may be suffiient to ensure large dutility of walls. However, the findings of this researh may lead to simpler detailing for walls where a relatively smaller ompressive strain is expeted. The findings of this researh may also be used to evaluate the seismi apaity of buildings with walls that do not satisfy the ACI requirements. EXPERIMENTAL PROGRAM Speimens Ten RC wall speimens with a boundary olumn on only one side were prepared to investigate the differenes in deformation apaity. Figure 1 shows the ross setions of the speimens used in this researh. Eah speimen is named as follows: 1. Perpendiular end wall: The first letter of the speimen s name P or N means with or without a perpendiular wall, respetively. For example, Speimen PM5 in Fig. 1(g) has a perpendiular end wall 130 mm (5.1 in.) long and 60 mm (2.4 in.) thik. All the perpendiular end walls have single-layer reinforement (D4 at 80 mm [3.15 in.], where D4 is a deformed bar with a nominal diameter of 4 mm [0.16 in.]) and do not have onfinement. 2. The ratio of wall panel length to wall thikness (l wp /t): The seond letter of the speimen s name S, M, or L expresses that the l wp /t ratio is 6, 12, or 18, respetively, where the wall panel length l wp is defined, exluding the olumn. For example, the ratio of Speimen PM5 in Fig. 1(g) is 1200/100 = The ratio of neutral axis depth to wall thikness (/t): The vertial arrows in Fig. 1 indiate the loation of the ACI Strutural Journal, V. 110, No. 1, January-February MS No. S reeived Marh 2, 2011, and reviewed under Institute publiation poliies. Copyright 2013, Amerian Conrete Institute. All rights reserved, inluding the making of opies unless permission is obtained from the opyright proprietors. Pertinent disussion inluding author s losure, if any, will be published in the November-Deember 2013 ACI Strutural Journal if the disussion is reeived by July 1, ACI Strutural Journal/January-February

2 Susumu Takahashi is a PhD Student of arhitetural engineering at Nagoya Institute of Tehnology, Nagoya, Japan. Kazuya Yoshida is a Master s Student of arhitetural engineering at Nagoya Institute of Tehnology. ACI member Toshikatsu Ihinose is a Professor of arhitetural engineering at Nagoya Institute of Tehnology. ACI member Yasushi Sanada is an Assoiate Professor of arhiteture and ivil engineering at Toyohashi University of Tehnology, Toyohashi, Japan. Kenki Matsumoto is a Master s Student of arhitetural engineering at Nagoya Institute of Tehnology. ACI member Hiroshi Fukuyama is a Chief Researh Engineer at the Building Researh Institute, Tsukuba, Japan. Haruhiko Suwada is a Researh Engineer at the Building Researh Institute. neutral axis, whose omputation method will be shown in a later setion of the paper. The number of the speimen s name expresses the approximate ratio of /t. For example, the ratio of Speimen PM5 in Fig. 1(g) is 493/100 = 4.9. Although the setions of Speimens NM5 and NM4 are idential, as shown in Fig. 1(a), the loations of the neutral axis are different beause of the differene of axial fores, as shown in a later setion. 4. With or without rosstie in boundary element: Figure 2 shows the detail of the boundary elements of the speimens, exept Speimens NM5, NM4, and NM2. The horizontal bars have a 135-degree hook, as shown in Fig. 2(a). The ap bars have a 90-degree hook at both ends, as shown in Fig. 2(b), and the ap bars vertial spaing is 35 mm (1.4 in.), as shown in Fig. 2(). The rossties have 90- and 135-degree hooks, as shown in Fig. 2(b), and are staggered with a spaing of 70 mm (2.8 in.), as shown in Fig. 2(). The rossties in Speimens NM5 and NM4 are loated at a spaing of 35 mm (1.4 in.), as shown in Fig. 3(a). Speimen NM2 does not have rossties, as shown in Fig. 3(b). The detailing of the wall reinforement for Speimen NM3 is shown in Fig. 4. The spaings of the horizontal and vertial bars are 35 and 100 mm (1.4 and 4.0 in.), respetively. The reinforement details of the wall panels of the other speimens are the same as those in Fig. 4. Beause the wall thikness of eah speimen is different, the lateral and vertial wall reinforement ratios vary from 0.54% to 0.84% and from 0.19% to 0.30%, respetively. The lengths of boundary elements (220 mm [8.7 in.] in Fig. 2(a)) are longer than half the length of the neutral axis in most speimens, as speified by the seismi requirements of ACI In the vertial diretion, rossties are provided from the bottom to one-third of the lear height h, as shown in Fig. 4. This value of h/3 is muh shorter than the requirement of ACI The spaing of the rossties (70 mm [2.8 in.] in most speimens) does not satisfy the requirements of ACI either. The ross-setional areas of the rossties vary from 15 to 31% of ACI The lear heights of Speimens NM4 and NM5 are 1000 mm (3.3 ft), whereas those of the other speimens are 1200 mm (4.0 ft), as shown in Fig. 4. Eight No. 3 (D10) longitudinal bars are provided in the boundary element of all speimens (Fig. 2(a)). Twelve No. 5 (D16) longitudinal bars are provided in the boundary olumn, exept that of Speimen NL2, where eight No. 4 (D13) bars are provided (Fig. 1(e)) so the longitudinal reinforement ratio (2.5%) is similar to that of the other speimens. All speimens are designed to fail in flexure; the shearto-flexural-apaity ratios vary from 1.2 to 2.3, where the flexural and shear apaities are alulated based on the Arhitetural Institute of Japan (AIJ) standards 13 and ACI , 1 respetively. The material properties of the steel bars are indiated in Table 1, where f y is the yield strength, f u is the tensile strength, and E s is the elasti modulus. The material properties of onrete are indiated Fig. 1 Speimen setions. (Note: Dimensions in mm; 1 mm = in.; No. 4 is D13; No. 5 is D16.) 96 ACI Strutural Journal/January-February 2013

3 Fig. 3 Boundary element of Speimens NM5, NM4, and NM2. Fig. 2 Boundary element exept for Speimens NM5, NM4, and NM2. (Note: 1 mm = in.; No. 3 is D10.) in Table 2, where f is the ompressive strength, E is the elasti modulus, and f r is the modulus of rupture. Test setup Figure 5 shows the test setup. Lateral fore was applied by a hydrauli jak to a stiff loading steel beam fastened to the speimen. All speimens had stiff RC stubs at both the top and bottom for fixing with the loading frame. No axial fore was applied for Speimen NM4. For the other speimens, two vertial hydrauli jaks were fore-ontrolled so the moment around the enter of the boundary olumn is zero, as shown in Fig. 5. The amount of the axial fore was approximately 20% of the axial apaity of the boundary olumn (f A g ), where A g is the gross ross-setional area of the olumn. The applied axial load was approximately 240 kn (54 kips) for Speimen NL2, 400 kn (90 kips) for NM5, and 540 kn (121 kips) for the other speimens. Horizontal load was applied 2425 mm (8.0 ft) above the bottom of the wall panel for NM5 and NM4 (Fig. 5). The height of the horizontal load was 2525 mm (8.3 ft) for the other speimens. The shearspan ratio of NL2 is 2525/2000 = 1.26, whih is the smallest. The shear span ratio of NS3 is 2525/1020 = 2.48, whih is the largest. OBSERVED DAMAGE AND DEFLECTION COMPONENT Figure 6 shows the lateral load-drift relationship of Speimen NL2. Lateral drift R is defined as the ratio of measured lateral displaement D to speimen height h. The displaement was measured at the top of the lear height in all speimens. During the positive loading (olumn in tension), the maximum strength (530 kn [119 kips]) was observed at a +1.2% drift level. The strength was 1.1 times the analytial flexural strength. Between the drift levels of +2 and +3%, strength dereased rapidly. During the negative loading diretion (olumn in ompression), the maximum strength Fig. 4 Elevation of Speimen NM3. (Note: Dimensions in mm; 1 mm = in.) Table 1 Material properties of reinforing bars Bar f y, MPa f u, MPa E s, GPa D4 411 (351) * 521 (544) * 173 (192) * No. 3 (D10) 391 (376) * 469 (520) * 199 (188) * No. 4 (D13) No. 5 (D16) 389 (387) * 559 (563) * 180 (180) * * Numbers in parentheses indiate material properties for Speimens NM4 and NM5. Notes: 1 MPa = 145 psi; 1 GPa = 145 ksi. Table 2 Material properties of onrete Speimen f, MPa E, GPa f r, MPa NS3 NM3 NM2 NM2 NL2 PL6 PM5 PM3 NM5 NM4 Notes: 1 MPa = 145 psi; 1 GPa = 145 ksi ACI Strutural Journal/January-February

4 Fig. 5 Loading setup. Fig. 6 Load versus drift of Speimen NL2. Fig. 8 Bukling of reinforement. Fig. 9 Instrumentation of speimens. Fig. 7 Speimen NL2 at maximum drift. (280 kn [63 kips]) was observed at a 1.5% drift level. The strength was 1.2 times the analytial flexural strength. Figure 7 shows Speimen NL2 at the end of the experiment at a 5% drift level. The spalling of onrete started at the bottom right orner of the wall panel at a +2% drift level. The spalled zone extended toward the olumn until a +3% drift level. On the other hand, the onrete of the boundary olumn slightly spalled during the negative loading but not during the positive loading, even at a +5% drift level. Figure 8 shows the bukling of the longitudinal bars (eight No. 3 [D10]) in the boundary element at a 3% drift level. The bukled bars fratured in tension between the drift levels of 2 and 3%. Figure 9 shows the linear variable differential transduer (LVDT) used to evaluate the flexural drifts. 7 Figure 10 shows 98 ACI Strutural Journal/January-February 2013

5 Fig. 10 Load versus flexural drift of Speimen NL2. the load-versus-flexural-drift relationship of Speimen NL2. Flexural drift at 80% of maximum strength V max (the blak irle in Fig. 10) is defined as flexural drift apaity in this paper. The hysteresis loops are more spindle-shaped than those in Fig. 6. The strength degradation in Fig. 10 is milder than that in Fig. 6, whih will be disussed in the following. Figure 11 shows the load-versus-shear-drift relationship of Speimen NL2. Shear drift was obtained by subtrating flexural drift from total drift. Shear drift inreased after flexural yielding. The blak triangles in Fig. 10 and 11 show the load step at the onset of strength degradation. The shear drift just before the strength degradation (1.25%) was larger than the orresponding flexural drift (0.75%). Note that the maximum applied shear fore is muh smaller than the shear strength omputed aording to ACI (the top broken line in Fig. 11). The shear drift did not inrease during the degradation. This is the reason why the strength degradation in Fig. 10 is milder than that in Fig. 6. Figure 12 shows the horizontal slip along one of the flexural raks near the enter of the wall when the shear drift was 1.25% or the shear deformation was 15 mm (0.59 in.) (the blak triangle in Fig. 11). The observed slip was 8.5 mm (0.33 in.), whih was more than one half of the total shear deformation (15 mm [0.59 in.]). The damage and overall behavior of the other speimens were similar to Speimen NL2, exept that the slips along the flexural raks were smaller than those in NL2. To disuss the ause of the slip, the ompressive fore of onrete C is defined in Eq. (1). Fig. 11 Load versus shear drift (deformation) of Speimen NL2. (Note: 1 mm = in.) Fig. 12 Slip along flexural rak of Speimen NL2. (Note: 1 mm = in.) C = N + A f A f (1) st y s y where N is applied axial load; A st is the gross setional area of longitudinal bars in tension; A s is the gross setional area of longitudinal bars in ompression; and f y is the yield strength of the longitudinal bar. The variable V max in the horizontal axis of Fig. 13 indiates the maximum applied shear fore. The vertial axis of Fig. 13 shows the slip drift angle, whih is defined as the sum of the observed slips (Ss) just before the strength degradation (the blak triangle in Fig. 11) divided by the lear height h. Slip was larger in the speimens with larger V max /C ratios. Fig. 13 Lateral slip drift Ss/h versus V max /C. Suh a orrelation is not obtained between the slip and the average shear stress (V max /A g, where A g is the gross setional area of the speimen). Beause the slip is not the fous of this study, only flexural drift is disussed in the following. The load-versus-flexural-drift relationships of Speimens NM3 and PM3 are shown in Fig. 14(a) and 15(a) to inves- ACI Strutural Journal/January-February

6 Fig. 16 Elasti and plasti deformations. Fig. 14 Load and strain versus flexural drift of Speimen NM3. ompressive dutility of this wall was very limited at the ultimate drift. Therefore, the ontribution of the perpendiular wall should be ignored in evaluating the drift apaity. The vertial axes of Fig. 14(b) and 15(b) show the average strain at the ompression edge (strain between Points E and F). The plasti hinge lengths of these two speimens, whih will be evaluated later as 2.5 times the wall thikness (300 mm [11.81 in.]), are similar to the length between Points E and F (400 mm [1.3 ft]). The strains at the ultimate drifts (the blak irles in the figures) were approximately 0.008, whih agrees with the ultimate strain of onrete e u omputed in the following onsidering the onfinement effet. FLEXURAL DRIFT CAPACITY Simplifiation of plasti deformation In this paper, flexural drift apaity is deomposed into elasti and plasti omponents (R u = R y + R p ), as shown in Fig. 16(a). The urvature at yielding f y is omputed based on the yield strain of longitudinal reinforement (Fig. 16(b)). y f y = (2) d e where e y is yield strain of reinforement; d is effetive depth, defined as the distane between the ompression edge and the enter of the boundary olumn; and is the neutral axis depth omputed from Eq. (3). = C b ft (3) Fig. 15 Load and strain versus flexural drift of Speimen PM3. tigate the effet of a perpendiular wall on flexural drift apaity. The differene between these two speimens is the existene of a perpendiular wall. The drift apaities of NM3 (0.57%) and PM3 (0.61%) were similar. The ompressive failure of the perpendiular wall of PM3 ourred before the lateral strength degradation started. Beause the perpendiular wall is provided with no onfinement (Fig. 1), the where C is the ompressive fore of onrete omputed from Eq. (1); b 1 is the redution fator to determine the neutral axis; f is the ompressive strength of onrete; and t is wall thikness. Theoretially, Eq. (3) is effetive at the ultimate state and ineffetive at yielding; however, this differene may be negligible beause the amount of the wall reinforements is muh smaller than that in the boundary olumn. In this study, linear distribution was used for elasti urvature (Fig. 16(a)). Therefore, the elasti drift R y is omputed from Eq. (4). 2 D fy h h Ry = = y h f 2 6a (4) 100 ACI Strutural Journal/January-February 2013

7 Fig. 18 Simplified model for plasti deformation. Fig. 17 Measured strain distribution of Speimen NM4. (Note: NA is neutral axis.) where D fy is flexural displaement at yielding; a is shear span length; and h is the speimen s lear height. The ultimate urvature f u is omputed based on the ultimate strain of onrete (Fig. 16()), where e u is the ultimate ompressive strain of onrete defined in a later setion e u f u = (5) The plasti drift is omputed using plasti hinge length L p. R ( ) = L f f (6) p p u y Substituting Eq. (2) and (5) into Eq. (6) leads to the equation to ompute the plasti drift. R L d p p = eu ey Figure 17 shows the strain distribution measured using LVDTs in Fig. 9 along the lear height of Speimen NM4 when the lateral fore dereased to 80% of the maximum strength. On the ompressive side (the right edge), the strain loalized between Points E and F, whereas the strain between Points F and G or G and H was quite small. On the tensile side (the left edge), even the strain between Points C and D exeeded the yield strain ( > e y = 0.002). It is onluded that, for plasti deformation, the ompressed area is limited near the bottom of the wall, as indiated by the shaded retangle (ompressed area) in Fig. 17 and 18, whereas the area in tension is trapezoidal. The hathed area in Fig. 18 is assumed as rigid. The strain at the ompressed edge in Fig. 18 is assumed to be uniformly e p, whih equals the term inside the parentheses of Eq. (7) e =e d e p u y (7) (8) Fig. 19 Assumed stress-strain model for onrete of Speimen NS3. where the seond term is the strain aused by the elasti deformation. In this paper, e p is alled the plasti omponent of ultimate strain. Note that the rigid area in Fig. 18 rotates R L p p = e (9) p around the neutral axis. Therefore, the height of the ompressed area in Fig. 18 an be regarded as the plasti hinge length L p. The deformation shown in Fig. 18 agrees with the observed rak patterns and is similar to that proposed by Hiraishi. 14 There are two unknown parameters L p and e p in Eq. (9). In the following setions, these parameters are examined using the tested speimens. Speimens tested by Wallae and Orakal 2 and Tabata et al. 5 are used beause flexural deformations of speimens are reported. Plasti omponent of ultimate strain The broken lines in Fig. 19 show the stress-strain relationships of onfined and unonfined onrete in Speimen NS3 evaluated by the Saatioglu and Razvi 15 model, whih is appliable to retangular setions. Figure 20(a) shows the boundary element of NS3, where the shaded zone is assumed to be onfined. The onfining pressure on the shaded zone in the x-diretion is omputed assuming that the horizontal bars are 100% effetive. The onfining pressure in the y-diretion is omputed assuming that the ACI Strutural Journal/January-February

8 The ultimate onrete strain e u is defined as the strain when the average stress of onrete dereases to 80% of the maximum strength. The ultimate strain of Speimen NM2 without rossties is , while the ultimate strains of the other speimens are between and The ultimate strains of the speimens of Wallae and Orakal 2 are approximately 0.008, exept for Speimen TW2, whih had a strain of Figure 20() shows the boundary elements of Speimens No. 2 and 3 of Tabata et al. 5 ; although the onfinement ratio is higher than that of Fig. 20(a), its ultimate strain is beause its onrete strength was high (70 MPa [10.15 ksi]). The strain at the ompressive edge when tensile reinforement bars yield shown in Fig. 16(b) (the seond term in Eq. (8)) is approximately in most speimens. Therefore, e p in Eq. (8) is approximately = for all speimens exept NM2 and TW2. Fig. 20 Assumed onfined regions. (Note: 1 mm = in.) Fig. 21 Relationship between R p and l w /. rossties are 100% effetive, while the ap bars at the wall end with 90-degree hooks are 50% effetive beause the observed strain of the ap bars was approximately one-half of the yield strain. Figure 20(b) shows the boundary element of Speimen NM2. Although only ap bars are provided in NM2, the shaded area is again assumed to be onfined. The onfining pressure in the y-diretion is omputed assuming that the ap bars are 50% effetive. The solid line in Fig. 19 shows the average stress-strain relationship of the boundary element alulated as the weighted average of onfined and unonfined onrete. t t t s=s +su (10) t where s is the stress of onfined onrete; t is the enter-to enter distane between the horizontal wall bars (Fig. 20(a)); and s u is the stress of unonfined onrete. t Plasti hinge length As disussed in the Introdution, Wallae and Orakal 2 and Tabata et al. 5 assumed that L p is equal to 0.5l w and 0.3l w, respetively, where l w is wall length. If L p is proportional to l w, based on Eq. (9), R p must be proportional to l w / beause e p is similar for most speimens. The relationship between R p and l w / is examined in Fig. 21. The variable R p is the plasti drift, whih is the flexural drift minus the elasti drift R y omputed by Eq. (4). The broken line in Fig. 21 is the regression line, whih is imposed to pass the origin. The orrelation oeffiient is 0.70, where the results of Speimens TW2 and NM2 are negleted beause the e p values of these speimens are very different from those of the other speimens. The solid lines show the assumptions of L p = 0.5l w and 0.3l w with e p = They do not agree with the regression line. The irles in Fig. 21 show two of the data, whih have different trends from the other speimens. Speimen NS3, whose l w /t ratio is the smallest (=8.5), exhibited a drift apaity twie that expeted by the regression line. On the other hand, Speimen NL2, whose l w /t ratio is the largest (=20), exhibited a drift apaity 60% of that expeted by the regression line. Similarly, speimens with small or large l w /t ratios are loated above or below the regression line, respetively. This tendeny indiates that hinge length is not simply proportional to wall length. ACI requires that the speial boundary region shall be longer than a/4, where a is shear span length. This requirement implies that L p in Fig. 18 equals a/4. To investigate whether the hinge length is related to shear span length a, the relationship between R p and the a/ ratio is shown in Fig. 22. The solid line shows the assumption of L p = a/4 with e p = 0.007, whih does not agree with the regression line (the broken line). The orrelation oeffiient is 0.84 and is better than that in Fig. 21. However, it is noted that the results of Speimens No. 2 and 3 of Referene 5, whose a/t ratios (=50) are muh larger than those of the other speimens (=18 to 28), are loated quite lower than the regression line. This tendeny again indiates that hinge length is not simply proportional to shear span length. Markeset and Hillerborg 16 onduted uniaxial ompression tests of plain onrete prisms with various lengths and setional dimensions. They observed that ompressive failure is quite limited within a ertain length. They onluded that the failure length was 2.5 times the shorter side length of the ompressed setion (Fig. 23). In this study, wall thikness t is shorter than neutral axis depth in all speimens. Figure 24 shows the damage of Speimen NS3 at a 2% drift 102 ACI Strutural Journal/January-February 2013

9 Fig. 24 Observed failure of Speimen NS3 at 2% drift. Fig. 22 Relationship between R p and a/. Fig. 23 Compression loalization. 16 Fig. 25 Relationship between R p and t/. level (right after the strength degradation). The damage length seems to be almost 2.5 times the wall thikness. Therefore, 2.5t is used for plasti hinge length L p in this study. It should also be noted that even in Speimen NM2 with the largest thikness (t = 140 mm [5.5 in.]), the damage of onrete was limited within the height of onfinement (400 mm [1.3 ft]). Therefore, it is onluded that the height of onfinement may be limited to 3t if the expeted ompressive strain is not greater than Figure 25 shows the relation between R p and t/. The orrelation oeffiient is 0.94 and larger than the orrelation oeffiients in Fig. 21 and 22 (0.70 and 0.84). The broken line in Fig. 25 shows the regression line. The solid line shows R p estimated from L p = 2.5t and e p = The solid line reasonably agrees with the regression line, whih implies that the assumption of L p = 2.5t is appropriate. Figure 26 ompares the observed and estimated flexural drift apaities (R u = R y + R p ). All test data exept Speimen TW2 are within 30% from the estimated drift apaities. The observed drift of TW2 is muh larger than the estimated value. The observed ompressive failure zone of TW2 was also muh wider than L p = 2.5t. Similar Fig. 26 Comparison between estimated and observed flexural drift apaities. ACI Strutural Journal/January-February

10 tendenies are observed for the test results of Paulay and Priestley, 8 whih are not plotted in Fig. 26 beause their flexural drift apaities are not reported. These disrepanies may be attributable to the differene of onfinement. Reall that the strain loalization depited in Fig. 23 is observed in plain onrete. In the ase of well-onfined onrete olumns subjeted to uniaxial ompression, large plasti strain shall be distributed uniformly over its entire length until strength degradation starts (e max in Fig. 19). If the onrete olumn is long enough, bukling ours 17 before the strain reahes e max. The strain at bukling depends on the length of the olumn and the tangential stiffness at the strain. 17 The boundary elements of Speimen TW2 and the speimens of Paulay and Priestley 8 almost satisfied the requirements of ACI If suh a wall would be subjeted to pure bending, uniform urvature orresponding to e max or less would be observed in its lear height when out-of-plane bukling would our. Therefore, for suh a wall, e u in Eq. (7) should be replaed with the strain at bukling and L p should be a funtion of shear span length, whih would be muh longer than 2.5t. On the other hand, the ross-setional areas of the horizontal bars and the rossties of the speimens tested by the authors are 40% to 52% and 6% to 31% of those required by ACI , 1 respetively. The ross-setional areas of the onfining bars of Speimens No. 2 and 3 tested by Tabata et al. 5 and Speimens RW1 and RW2 tested by Wallae and Orakal 2 are 24 to 63% of those required by ACI It is onluded that L p = 2.5t is valid if the onfinement of the boundary element is less than half of that required by the seismi provisions of ACI Otherwise, the equation tends to underestimate the apaity. CONCLUSIONS The test results of 10 RC walls are desribed in this study. Based on the experimental results and analytial work presented in this paper, the following onlusions are obtained: 1. All tested RC walls with limited onfinement in the boundary element failed in ompression after flexural yielding. The observed flexural drift apaity was between 0.4 and 1.2%. 2. Shear drift aused by lateral slip along the flexural rak may be large if the ratio of the maximum shear fore to the ompressive fore of onrete is large (Fig. 13). 3. Plasti omponents of flexural drift an be modeled as shown in Fig. 18, where the length of the ompression zone L p is 2.5 times the wall thikness (L p = 2.5t) if the depth of the neutral axis is longer than the wall thikness and the onfinement of the boundary element is half of that required by the seismi provisions of ACI Ultimate flexural drift is defined as the drift when the lateral fore dereases to 80% of maximum lateral strength. Ultimate flexural drift an be omputed as the sum of Eq. (4) and (7), where e u shall be determined as shown in Fig. 19 onsidering the onfinement effet. 5. The detailing of the boundary element shown in Fig. 2() with the height of the onfined area 3t is suffiient to obtain an ultimate strain of e u = The effet of a perpendiular wall on ultimate drift is negligible if the wall is not onfined. ACKNOWLEDGMENTS This study was finanially supported by the Ministry of Land and Transportation. The authors thank J. Wallae of the University of California, Los Angeles (UCLA), who independently oneived the idea that hinge length may be proportional to wall thikness, for valuable disussions. Data provided by T. Tabata, H. Nishihara, and H. Suzuki of Ando Corporation are greatly appreiated. The authors also thank H. Sezen of The Ohio State University for ritially reading the manusript. REFERENCES 1. ACI Committee 318, Building Code Requirements for Strutural Conrete (ACI ) and Commentary, Amerian Conrete Institute, Farmington Hills, MI, 2008, 473 pp. 2. Wallae, J. W., and Orakal, K., ACI Provisions for Seismi Design of Strutural Walls, ACI Strutural Journal, V. 99, No. 4, July-Aug. 2002, pp Thomsen, J. H. IV, and Wallae, J. W., Displaement-Based Design of Slender Reinfored Conrete Strutural Walls Experimental Verifiation, Journal of Strutural Engineering, ASCE, V. 130, No. 4, 2004, pp Design Guidelines for High-Rise RC Frame-Wall Strutures, National Institute for Land and Infrastruture Management, Kaibundo, Tokyo, Japan, 2003, pp Tabata, T.; Nishihara, H.; and Suzuki, H., Dutility of Reinfored Conrete Shear Walls without Column Shape, Proeedings of the Japan Conrete Institute, V. 25, No. 2, 2003, pp (in Japanese) 6. Kabeyasawa, T.; Shiohara, H.; Otani, S.; and Aoyama, H., Analysis of the Full-Sale Seven-Story Reinfored Conrete Test Struture, Journal of the Faulty of Engineering, V. 37, No. 2, 1983, pp Orakal, K., and Wallae, J. 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