Seismic Behavior of Squat Reinforced Concrete Shear Walls

Transcription

1 Seismic Behavior of Squat Reinforced Concrete Shear Walls Pedro A. Hidalgo, a) Christian A. Ledezma, a) and Rodrigo M. Jordan a) The behavior of reinforced concrete walls that exhibit the shear mode of failure is studied, through the results of an experimental program that included the test of 26 full-scale specimens subjected to cyclic horizontal displacements of increasing amplitude. Test parameters were the aspect ratio of the walls, the amount of vertical and horizontal distributed reinforcement, and the compressive strength of concrete. The results include the cracking shear strength, the maximum shear strength, the drifts associated to these loads and the drift associated to a collapse limit state for each of the specimens tested. Conclusions are drawn concerning the deformation capacity, the energy absorption, the dissipation characteristics and the strength deterioration after maximum strength shown by the walls and the influence of vertical distributed reinforcement on the seismic behavior of walls. [DOI: / ] INTRODUCTION Earthquake-resistant structural systems generally used in reinforced concrete buildings may be one of the following: moment-resisting space frames, shear walls, or a combination of both. The use of shear walls is not predominant in earthquake-prone countries and this fact may explain why moment-resisting space frames have attracted so far the attention of the majority of researchers. However, shear wall systems have shown better performance than the space frame systems, as noted many years ago by Fintel (1974) and evidenced by the behavior of Chilean buildings during the 3 March 1985 earthquake (Wood 1991). When shear walls are used in the lateral force resisting system, it is highly desirable they are designed to exhibit a ductile behavior, as it has been proposed by several researchers (Paulay 1980, Paulay et al. 1982). To achieve this behavior, the designer must provide the shear walls with a shear strength that yields a lateral shear strength higher than that required to develop flexural yielding in the vertical boundary reinforcement of the walls. In such a case, the shear walls would develop a flexural, ductile mode of failure in the event of a severe earthquake. Consequently, the seismic design may be carried out for lateral forces that are significantly smaller than those that would be required if the seismic behavior would remain elastic under such earthquake event. Nevertheless, there are cases where the eventual flexural, ductile behavior of shear walls is not possible to attain, due to the large shear wall cross section area as compared to the floor plan area or the use of spandrel beams or coupling elements between the walls stiff enough to impose a rather small value of M/Vl w on the wall, where M is the bending a) Dept. of Structural and Geotechnical Engineering, Universidad Católica de Chile, Santiago, Chile 287 Earthquake Spectra, Volume 18, No. 2, pages , May 2002; 2002, Earthquake Engineering Research Institute

2 288 P. A. HIDALGO, C. A. LEDEZMA, AND R. M. JORDAN moment at the base of the wall, V the shear force, and l w the length of the wall. Then, the eventual shear mode of failure of the wall may become quite likely, the ability of the structural system to absorb and dissipate energy is reduced, and the seismic design must be carried out for lateral forces larger than those required to design a ductile shear wall. Yet these larger design forces usually do not pose a design limitation since the lateral strength of these systems is larger than that of ductile shear wall systems. The lessons learned from the seismic behavior of Chilean buildings show that detailing of reinforced concrete elements to absorb and dissipate energy through the development of ductile flexural behavior is not the only way to achieve a satisfactory seismic behavior during severe earthquake events. When the total cross section of walls is large enough, that is, 0.02 to 0.04 times the floor plan area in each direction of seismic resistance for buildings up to 25 stories high, flexural yielding of boundary reinforcement of walls is kept at a moderate level in tall buildings and practically does not develop in low-rise buildings. Additionally, shear stresses in the walls are limited to reasonably small values. These facts yield to a satisfactory control of the structural damage, and far more important, to a system where collapse is almost unthinkable. From a conceptual point of a view, development of excessive ductility and structural damage are prevented because of the considerable lateral strength and the stiffness of the shear wall system. This fact is also important to control damage in nonstructural elements. Finally, but not less important, all these benefits may be obtained with methods of design and construction that are much less sophisticated than those required for the development of ductile inelastic behavior in the structural elements under severe earthquake events. Nevertheless, the extrapolation of this successful experience to design and construction of buildings in other earthquake-prone countries may not be easy for a number of reasons. Engineering communities have their particular characteristics concerning architectural layouts, building construction skills and cost of workmanship, soil conditions, etc. As a matter of fact, the authors do not intend to advocate a change in the seismic design philosophy used in countries such as New Zealand or the United States. However, this fact cannot be used to deny significance to the study of the characteristics of seismic behavior of nonductile shear wall systems that have been successfully used in other countries. In the present study, the behavior of walls that exhibit the shear mode of failure is investigated, since many Chilean buildings showed this type of behavior during past severe earthquakes. The need of this study has been originated by the limited knowledge about the seismic behavior of buildings with the nonductile shear wall structural system. Since the Chilean seismic design provisions (Instituto Nacional de Normalización 1996) do not require the buildings to have the amount of walls indicated above, construction practice has shown a tendency to reduce such amount, with consequences that cannot be clearly foreseen. Therefore, the ultimate objective of this research program is to develop a mathematical model that is able to predict the seismic inelastic behavior of this type of buildings, including both the flexural- and the shear-mode of failure of the structural walls under a severe earthquake event. As a first step, 26 full-scale squat shear walls were tested under cyclic lateral deformations as described below.

3 SEISMIC BEHAVIOR OF SQUAT REINFORCED CONCRETE SHEAR WALLS 289 Most of the limited amount of research published in the past on the seismic behavior of reinforced concrete shear walls has addressed two topics: the ultimate shear strength and the criteria to design the walls against shear. The ultimate shear strength has been studied from two different approaches: the derivation of empirical expressions from test results (Kokusho and Ogura 1970, Cardenas and Magura 1973, Barda et al. 1977, Vallenas et al. 1979, Aktan and Bertero 1985, Wood 1989, Wood 1990, Tan et al. 1995), and the development of rational models based on the basic concepts of structural mechanics (Collins and Mitchell 1986, Aoyama 1991, Pérez and Pantazopoulou 1996). Among these models the strut-and-tie models for shear behavior deserve special attention (Yañez et al. 1989, Siao 1993). Most of the seismic design provisions found in codes to estimate the ultimate shear strength of walls follow the first of these approaches. Among them, the ACI provisions (Cardenas et al. 1973, ACI Committee ), which have been in effect since 1971, are perhaps the most widely used in earthquake-prone countries. The other topic found in the literature is the study of the design criteria for walls against shear. It is a well-known fact that the energy absorption and dissipation capacities found in the shear mode of failure are considerably less than those in the flexural mode of failure. In the moment-resisting space frame system it is possible to prevent the shear mode of failure and to develop the flexural failure in the so-called plastic hinges, but this is not always feasible in the shear wall system. In 1965, Muto (1965) proposed to slit the walls vertically in order to transform them into a series of columns. Later, Paulay et al. (1971, 1980, 1982) made significant contributions to postpone or control the shear failure in coupling beams and shear walls. The same design philosophy has been followed by Japanese researchers (Hirosawa et al. 1988). Aktan and Bertero (1985) emphasized the deficiencies of seismic design codes to correctly estimate the maximum shear force that can be developed in shear walls during an earthquake. Then they proposed changes in the maximum nominal shear stress that can be used in walls in order to ensure the development of the flexural mode of failure. A few years ago, Hsu and Mo (1985), Mau and Hsu (1986), and Mo (1988) developed expressions to predict the seismic behavior of squat shear walls and proposed design procedures to select the desired mode of failure. EXPERIMENTAL PROGRAM The wall specimens were tested in the test setup shown in Figure 1, which was designed to prevent the rotation of both top and bottom ends of the specimen while the horizontal cyclic load was applied at mid-height of the walls. Reinforced concrete blocks were used to attach the test frame to top and bottom to anchor the specimen. A discussion on the amount of rotation allowed by the test setup at the top section of specimens is included in this paper. Though the test setup has the capability of imposing an axial compressive force on the specimens, all the tests reported here included zero axial compression on the walls except for the own weight of the wall and of the test setup. In the structural systems of buildings the gravitational axial force on the shear walls may increase or decrease due to the seismic action. On the other hand, the shear strength of walls increases with increasing compressive stresses and decreases as the compressive force is reduced or changes into a tensile force. Consequently, the ACI provisions to es-

4 290 P. A. HIDALGO, C. A. LEDEZMA, AND R. M. JORDAN Figure 1. Test setup. timate the shear strength of walls neglect the effect of compressive stresses in increasing the shear strength, and this is the reason to have designed the tests with no axial force on the specimens. The characteristics of wall specimens are shown in the first ten columns of Table 1. Specimens numbered 17 through 20 were not part of this study since their tests had other objectives. All of them were squat walls having aspect ratios M/Vl w between 0.35 and 1.00, where M is the bending moment at the base of the wall assuming that rotation is zero at both ends of the specimen, V the shear force and l w the length of the wall. All the walls were designed with enough boundary vertical reinforcement A sb to prevent the flexural failure (A sb is the vertical reinforcement area at each of the vertical sides of the wall). Other test parameters were the amount of vertical and horizontal distributed reinforcement the minimum amount according to ACI 318 (ACI Committee ), half of minimum and none and the compressive strength of concrete. Yield strengths of reinforcement, f y, and the cylindrical strength of concrete determined on the same day of the test are also shown in Table 1. Due to the reduced thickness t w of walls, the distributed vertical and horizontal reinforcement were placed in one layer only. Specimens 3 and 5 have not been included because they were tested under axial compression. In Table 1, h w denotes the height of the specimen and v and h are the distributed vertical and horizontal reinforcement ratios, respectively. Instrumentation of specimens included the measurement of the top horizontal displacement of the wall, the rotation of its top section, and the relative rotation between horizontal sections, as shown in Figure 2. In most of the specimens, strain gauges were attached to both the vertical and horizontal reinforcement, one strain gauge for each bar,

5 SEISMIC BEHAVIOR OF SQUAT REINFORCED CONCRETE SHEAR WALLS 291 Table 1. Characteristics of wall specimens and test results SPECIMEN t w (cm) l w (cm) h w (cm) M V l w h (%) v (%) f y (MPa) f c (MPa) A sb (cm 2 ) V cr (kn) cr (%) V u (kn) u (%) (*) (*) (*) (*) (*) (*) (*) (*) (*) No data registered 1 kfg/cm MPa 14.8 psi; 1 kn kip 102 kgf; 1 cm 10 mm in along the diagonals that joined opposite corners of the walls. The horizontal load was measured by the load cell located at the end of the horizontal actuator (Figure 1). The loading sequence of each test consisted of sets of two displacement cycles at a specified displacement amplitude, as shown in Figure 3. The specified amplitude was gradually increased and followed a sequence that varied according to the aspect ratio, as shown in Figure 3. The duration of each cycle was approximately 10 minutes. The test was displacement controlled and monitored by a computer that also acquired the data; it could be stopped at any time to record the appearance and propagation of cracks, verify instrumentation, etc. All tests were finished when lateral strength of the specimen had dropped to 75% of the maximum value, approximately. The simulated seismic loading test procedures that have been used in other countries have considered three or more cycles at each specified displacement amplitude. However, these tests have also shown

6 292 P. A. HIDALGO, C. A. LEDEZMA, AND R. M. JORDAN Figure 2. Instrumentation of specimens (LVDT s only). that no significant change is observed between the second and subsequent cycles at the same amplitude, before maximum shear strength is attained. Consequently, only two cycles at each amplitude were used in this test program. TEST RESULTS The last four columns of Table 1 show the main results obtained from the test. The cracking load V cr is defined as the load at which a change in the slope of the envelope of the load-displacement relationship is observed; the new value of the stiffness of the specimens is about 60% of the initial stiffness. The cracking load is generally very close to the load that produced the first diagonal crack from corner to corner of the specimen. The value of V cr indicated in Table 1 is the average value of the cracking loads for both Figure 3. Displacement sequence.

7 SEISMIC BEHAVIOR OF SQUAT REINFORCED CONCRETE SHEAR WALLS 293 actuator directions. Likewise, the value of V u corresponds to the average value of the maximum shear loads attained during the test in both directions, and cr and u are the drift ratios associated to the average values of the horizontal displacements at the top section at V cr and V u, respectively. In all cases, the values that were averaged were quite similar and corresponded to the same or consecutive cycles of the test sequence. The discussion related to the cracking strength V cr, the maximum strength V u, the contribution of concrete and of reinforcement to shear strength, and the influence of other parameters of this experimental program on the shear strength of walls will be the subject of a subsequent paper. Figures 4a through 4n show the load vs. top displacement hysteresis curves for specimens 1 through 16, while Figures 5a through 5l show the hysteresis curves and cracking patterns for specimens 21 through 32. The behavior shown in all cases is clearly controlled by the shear mode of failure; initial behavior is practically linearelastic but pinching of hysteresis curves appears as soon as diagonal cracking develops, reflecting the transition between closing of cracks in one direction and opening in the opposite direction. Although cracking patterns of specimens are not significantly different, the beneficial effects of using horizontal reinforcement to yield a more ductile behavior of the wall are clearly shown. This was particularly true for specimens with aspect ratios equal to or larger than 0.50 (see Figures 5c for specimen 23 and 5g for specimen 27), but was not the case for the specimen 31 that had an aspect ratio of 0.35 (Figure 5k). Another result that may be drawn from the comparison of Figures 5a, c, and d (aspect ratio of 0.69), and of 5e, g, and h (aspect ratio of 0.50), is the lack of importance of the distributed vertical reinforcement in the strength and energy absorption characteristics of shear walls as compared to that of the horizontal reinforcement. This fact becomes less evident for aspect ratio of 0.35 (see Figures 5i, k, and l). These examples confirm the findings obtained from the test of specimens 1 through 16 and will be discussed later in this paper. The tests of walls with no distributed reinforcement at all (Figures 5a, b, e, f, i, and j) show rather poor seismic behavior after the first major diagonal crack is developed. Nevertheless, the positive effect of compressive strength of concrete in increasing the shear strength was clearly observed in the specimens with aspect ratios of 0.50 and Maximum drift that can be achieved without a significant loss of strength is also affected by the amount of horizontal distributed reinforcement and by the aspect ratio of the wall. When there was no such reinforcement or when the aspect ratio was too small (0.35), the test setup was not able to control the lateral deformation during the step when the maximum shear strength was attained; this is shown in all of the parts of Figure 5, with the exception of Figures 5c and g. This fact produced straight lines in the hysteresis loops; they would have become curved loops if smaller steps had been used in the controlled displacement amplitude. It is not easy to directly evaluate the behavior of shear walls from the test results obtained in the present program by comparing them with the relevant existing experimental data described above. The tests reported herein were designed to study the shear mode of failure. On the other hand, the experimental program carried out by Cardenas and Magura (1973) had the goal of evaluating the provisions of ACI to predict the shear strength of walls from the point of view of developing the flexural strength of

8 294 P. A. HIDALGO, C. A. LEDEZMA, AND R. M. JORDAN Figure 4. Hysteresis curves for specimens as follows: (a) specimen 1, (b) specimen 2, (c) specimen 4, and (d) specimen 6. Hysteresis curves for specimens as follows: (e) specimen 7, (f) specimen 8, (g) specimen 9, and (h) specimen 10. Hysteresis curves for specimens as follows: (i) specimen 11, (j) specimen 12, (k) specimen 13, and (l) specimen 14. Hysteresis curves for specimens as follows: (m) specimen 15, and (n) specimen 16.

9 SEISMIC BEHAVIOR OF SQUAT REINFORCED CONCRETE SHEAR WALLS 295 Figure 4. (Continued) walls. The tests performed by Barda et al. (1977) considered specimens with boundary elements, but significant conclusions were drawn concerning the influence of distributed vertical reinforcement in the shear strength of squat shear walls. The main conclusions from the tests carried out by Aktan and Bertero (1985) have been stated before. Consequently, the most direct comparison of the results obtained in the present program with the existing experimental data is through the shear strength of reinforced concrete shear walls. However, this subject and the evaluation of different models that have been proposed to predict the shear strength of walls will be the subject of a subsequent paper. Therefore, the following discussion of other characteristics of the behavior associated to the shear mode of failure only includes the comparison with previous experimental results when they are available.

10 296 P. A. HIDALGO, C. A. LEDEZMA, AND R. M. JORDAN Figure 5. Hysteresis curves for specimens as follows: (a) specimen 21, (b) specimen 22, (c) specimen 23, and (d) specimen 24. Hysteresis curves for specimens as follows: (e) specimen 25, (f) specimen 26, (g) specimen 27, and (h) specimen 28. Hysteresis curves for specimens as follows: (i) specimen 29, (j) specimen 30, (k) specimen 31, and (l) specimen 32.

11 SEISMIC BEHAVIOR OF SQUAT REINFORCED CONCRETE SHEAR WALLS 297 Figure 5. (Continued) DEFORMATION CAPACITY OF TEST SPECIMENS From the load-deformation hysteresis curves, the drift ratio of the shear wall is obtained as the ratio of the lateral deformation and the wall height. Three significant situations have been chosen to characterize the behavior of specimens during each test. They are, namely, (1) at cracking load V cr ( cr ), (2) at the maximum shear strength V u ( u ), and (3) when the strength had dropped to about 80% of the maximum shear strength ( ult ). The value of cr may be considered as a serviceability limit of the structural element, while ult may be associated with the ultimate condition under which the element may still be considered as an effective part of the resisting mechanism of the structure. The values of drift ratios cr and u are shown in Table 1, and have been plotted in Figures 6 and 7, respectively, as a function of the aspect ratio and of the amount of the horizontal and vertical distributed reinforcement. The estimation of ult is not reliable when there is a sudden failure associated with the development of the maximum shear strength, as shown in all of the parts of Figure 5 with the exception of Figures 5c and g. In such cases, the value of ult was estimated using either the positive or the negative branch of the load-deformation relationship only, whenever this was possible. The values of the drift ratio ult are obtained from the lateral displacement values ult shown in Table 2 and the graphical representation is shown in Figure 8. The experimental values indicated in Figures 6, 7, and 8 show that, in general, deformation capacity of specimens get smaller as the aspect ratio M/Vl w decreases, due to the increase in their lateral stiffness. As expected, there is practically no influence of the amount of distributed reinforcement on drift cr, while modest influence on drift u and a more pronounced influence on drift ult are observed. Values of drift cr are about

12 298 P. A. HIDALGO, C. A. LEDEZMA, AND R. M. JORDAN Figure 6. Drift at first diagonal cracking. 0.1%, while drift u values vary between 0.2% and 0.8%; values of drift ult vary between 0.3% and 1.3%. This information may be useful to correlate deformation demands during a severe earthquake event with the degree of damage exhibited by shear walls having aspect ratios M/Vl w less than unity. ENERGY DISSIPATION OF SHEAR WALLS It is interesting to examine the energy absorption and dissipation characteristics of reinforced concrete walls that exhibit a shear mode of failure. To do this, the normalized dissipated energy (NDE) was defined for a particular hysteresis loop or cycle as shown in Figure 9. The average value of the normalized dissipated energy was obtained by summing the energy dissipated in each cycle and dividing the result by the number of cycles. For specimens 9 through 16, all the cycles between the cracking load V cr and the cycle for which the strength had dropped to about 80% of the maximum shear strength V u were considered. For the same reasons given above, the evaluation of the average NDE for specimens 21 through 32 only included the cycles between the cracking load V cr and the maximum shear strength V u. No computation of energy dissipation was available for specimens 1 through 8. Numerical values are given in Table 3. The graphical representation of the average values of NDE as a function of the aspect ratio and of the amount of the horizontal and vertical distributed reinforcement are shown in Figures 10a and b. The most significant conclusion that may be drawn from these figures is that

13 SEISMIC BEHAVIOR OF SQUAT REINFORCED CONCRETE SHEAR WALLS 299 Figure 7. Drift at maximum strength. the average value of NDE seems to be independent of the variation of aspect ratio and of the variation of both horizontal and vertical distributed reinforcement, at a value of about 23%. STRENGTH DETERIORATION AFTER MAXIMUM SHEAR STRENGTH One of the relevant characteristics of the behavior after maximum shear strength has been attained is the strength deterioration that is apparent from the hysteresis loops. To quantify this deterioration the definition shown in Figure 11 was used. The straight line that could best fit the descending portion of the load-deformation curve was used to define the parameter m. The numerical values obtained from this definition are shown in Table 2. Although the values of u to define the strength deterioration m were the same as those used to define drift u, the values of ult were somewhat different than those used to determine ult, as indicated in Note 2 of Table 2. The graphical representation of the strength deterioration m as a function of the aspect ratio and of the amount of the horizontal and vertical distributed reinforcement is shown in Figures 12a and b. As it can be observed, strength deterioration increases with decreasing values of the aspect ratio and of both horizontal and vertical reinforcement. As the aspect ratio goes from 1.0 to 0.35, and reinforcement ratios decrease from 0.25% to none, typical strength deterioration shows a maximum rate of 20 kn per millimeter of the lateral wall displacement.

14 300 P. A. HIDALGO, C. A. LEDEZMA, AND R. M. JORDAN Table 2. Ultimate displacement and strength deterioration after maximum shear strength SPECIMEN M/(V l w ) h (%) v (%) ult (mm) ult (mm) m (kn/mm) m (kn/mm) ult (mm) m (kn/mm) (1) 1.31 (1) (2) (2) (2) 20.0 (2) (2) 20.0 (2) (2) 21.2 (2) (2) (2) (3) (3) (3) (3) (3) (3) (3) (3) 5.0 (2) (3) (3) 5.0 (3) (3) 4.2 (2) (3) (3) 4.2 (3) (2) (3) (3) (3) 7.1 (3) (3) 6.7 (2) (3) (3) 6.7 (3) (2) 12.7 (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) 6.0 (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (1) No strength deterioration was observed ( very ductile type of failure). (2) Maximum displacement registered during test, not necessarily associated to the eighty percent of the maximum strength. These were tests where brittle or ductile type of failure was observed. (3) No reliable data was available. ANALYSIS OF ROTATION OF TOP SECTION OF SHEAR WALLS The most significant parameter of wall specimens tested in this program is their aspect ratio. It can be expressed as the ratio M/Vl w, where V is the shear force, l w is the length, and M is the bending moment at the base of the wall assuming zero rotation at both top and bottom cross sections of the specimen. The assumption of zero rotation at the top section is examined in the following. As shown in Figure 1, rotation of the top beam of the test setup is prevented through its linking to the upper steel beam. Therefore, the following relationships hold for the fixed-end bending moments M and the shear force V: 2M Vh w (1)

15 SEISMIC BEHAVIOR OF SQUAT REINFORCED CONCRETE SHEAR WALLS 301 Figure 8. Drift at ultimate. M/ Vl w h w / 2l w (2) Nevertheless, as the wall develops cracks that are not symmetric with respect to the mid-height section and the behavior ceases to be linear-elastic, Equations 1 and 2 do not exactly represent the distribution of internal forces in the specimen. As the top section Figure 9. Definition of normalized dissipated energy NDE.

16 302 P. A. HIDALGO, C. A. LEDEZMA, AND R. M. JORDAN Table 3. Average normalized dissipated energy SPECIMEN M/(V*l w ) h (%) v (%) Ē norm. Vu (%) rotates (angle of rotation in Figure 13a), the bending moment at the base becomes larger than the moment at the top section leading to an upward shift e of the inflection point (Figure 13). The angle actually developed during the tests was small in most cases. For specimens 1 through 26, the influence of this rotation on the magnitude of top moment, as well as on the location of the inflection point, was less than 1%. However, for specimens 27 through 32, the influence of this rotation on top moment and location of point of inflection was as large as 10%. INFLUENCE OF DISTRIBUTED REINFORCEMENT It is widely recognized that horizontal distributed reinforcement is essential in the contribution of reinforcement to the shear strength of the wall and in providing strength to the wall after diagonal cracks in the concrete have developed. Moreover, it improves redistribution of cracks and the post-cracking inelastic behavior. All these facts are also supported by the results obtained in this experimental program. On the other hand, the results obtained here indicate that vertical distributed reinforcement used in the test specimens has little or no influence on the maximum shear strength developed by the walls, as can be observed from the values of V u shown in Table 1. Likewise, there is a small influence of the vertical reinforcement on the energy

17 SEISMIC BEHAVIOR OF SQUAT REINFORCED CONCRETE SHEAR WALLS 303 Figure 10. Average normalized dissipated energy. absorption and dissipation characteristics of the specimens, until the maximum shear strength was attained, as shown by Figure 10b and the values of Table 3. The observations above are not in agreement with other experimental results for squat walls, such as those obtained by Barda et al. (1977), who recognized the importance of vertical distributed reinforcement to increase the ultimate strength. They neither agree with the relevance that ACI 318 (1999) attributes to the use of vertical reinforcement when requiring its reinforcement ratio to be not less than the horizontal reinforcement ratio if h w /l w does not exceed 2.0 (provision ). The lack of influence of vertical distributed reinforcement mentioned above does neither support the experimen-

18 304 P. A. HIDALGO, C. A. LEDEZMA, AND R. M. JORDAN Figure 11. Definition of strength deterioration after maximum shear strength. Figure 12. Strength deterioration after maximum shear strength.

19 SEISMIC BEHAVIOR OF SQUAT REINFORCED CONCRETE SHEAR WALLS 305 Figure 13. Rotation of top section. tal observation about the contribution of this reinforcement in controlling the crack width during the post-cracking behavior. In fact, readings from strain gauges attached to the vertical reinforcement showed that majority of reinforcing bars did attain their yielding strains in tests 9 through 32. Figure 14 shows the strain gauge locations in the ver- Figure 14. Strain gauge locations in the vertical distributed reinforcement and ultimate cracking pattern.

20 306 P. A. HIDALGO, C. A. LEDEZMA, AND R. M. JORDAN tical reinforcement for specimens with different aspect ratios, and the relation of these locations with the cracking pattern associated to their shear failure. It is possible that this yielding observed is localized at the cracks and not a part of a trend in which a long portion of the bar elongates, and is perhaps due to a dowel action effect on the vertical bars once the cracks have been developed. What is the explanation for these discrepancies? The authors believe that influence of vertical distributed reinforcement did not arise in the present experimental program due to the type of specimen used. They believe that the strong bases used to anchor the specimen to the test setup and the strong boundary reinforcement used to prevent the flexural mode of failure did not allow the rotation of the end sections of the walls. This does not happen when cantilever specimens are used, because in such a case the top section of the wall specimen is free to rotate and vertical reinforcement contribution to lateral strength may develop. Moreover, a wall specimen in a fixed-fixed test setup does undergo rotation in the sections close to mid-height, but bending moment and cracking in this zone of the specimen are smaller than in top and bottom sections. The question about which type of test setup provides a better representation of the actual behavior of a shear wall segment may be answered once the rotational restraints at the ends of that segment, imposed by the rest of the structural system, are known. Another reason that may explain the lack of importance of vertical distributed reinforcement is its moderate amount when compared with the vertical reinforcement, A sb, used at the boundaries of the specimens. The values from Table 1 show that percentage of distributed vertical reinforcement as compared with total vertical reinforcement used in the specimen walls never exceeded 23%. CONCLUSIONS The main conclusions of this experimental study may be summarized as follows: Deformation capacity of specimens gets smaller as the aspect ratio M/Vl w decreases. Values of drift at cracking are about 0.1%, while drift at maximum strength varies between 0.2% and 0.8%, and values of drift at ultimate varies between 0.3% and 1.3%. Only drift at ultimate is somewhat influenced by the amount of distributed reinforcement in the walls. The energy absorption and dissipation of the walls seems to be independent of the variation of aspect ratio and of the variation of both horizontal and vertical distributed reinforcement. The normalized dissipated energy remains fairly constant at a value of about 23%. The strength deterioration of wall specimens increased with decreasing values of the aspect ratio and of both horizontal and vertical reinforcement. As the aspect ratio goes from 1.0 to 0.35, and reinforcement ratios decrease from 0.25% to none, typical strength deterioration showed a maximum rate of 20 kn per millimeter. Vertical distributed reinforcement used in the test specimens has little or no influence on the maximum shear strength developed by the walls. It is suggested that the test setup has a significant influence on the behavior of the vertically distributed bars.

21 SEISMIC BEHAVIOR OF SQUAT REINFORCED CONCRETE SHEAR WALLS 307 ACKNOWLEDGMENTS The research reported in this paper was funded by the Chilean Council for Technological Development (FONDECYT) through research project Nos. 813/92, , and The testing facility was provided by the Japan International Cooperative Agency (JICA) as part of a joint study project with the Department of Structural and Geotechnical Engineering of the Universidad Católica de Chile. The sponsorship of these institutions is gratefully acknowledged, as well as the valuable contributions of Professor Carl Lüders of the same department, and the work of the former graduate student J. L. Larenas. REFERENCES ACI Committee 318, Building Code Requirements for Reinforced Concrete, American Concrete Institute, Detroit, MI. Aktan, A., and Bertero, V., RC structural walls: Seismic design for shear, J. Struct. Eng. 111 (8), Aoyama, H., Design philosophy for shear in earthquake resistance in Japan, International Workshop on Concrete in Earthquake, University of Houston, Houston, TX. Barda, F., Hanson, J., and Corley, W., Shear strength of low-rise walls with boundary elements, Reinforced Concrete Structures in Seismic Zones, ACI SP 53-8, pp Cardenas, A., Hanson, J., Corley, G., and Hognestad, E., Design provisions for shear walls, ACI J. 70 (23), Cardenas, A., and Magura, D., Strength of high-rise shear walls-rectangular cross sections, Response of Multistory Concrete Structures to Lateral Forces, ACI SP-36, pp Collins, M., and Mitchell, D., A rational approach to shear design: The 1984 Canadian code provisions, ACI J. 83 (80), Fintel, M., Ductile shear walls in earthquake resistant multistory buildings, ACI J. 71 (19), Hirosawa, M., Hiraishi, H., Fujisawa, F., and Yoshimura, M., Seismic performance of reinforced concrete high-rise frame structure with wall columns-part 1: Deformation capacity of critical structural elements such as wall columns, beams and shear walls, 20th Joint Meeting U.S.-Japan Panel on Wind and Seismic Effects, Washington, DC, Proceedings. Hsu, T., and Mo, Y., Softening of concrete in low-rise shearwalls, ACI J. 82 (83), Instituto Nacional de Normalizacion, Seismic Design of Buildings, Chilean Code NCh433Of.96, Santiago, Chile. Kokusho, S., and Ogura, K., Shear strength and load-deflection characteristics of reinforced concrete members, U.S.-Japan Seminar on Earthquake Engineering, Sendai, Japan, Proceedings, pp Mau, S., and Hsu, T., Shear design and analysis of low-rise structural walls, ACI J. 83 (33), Mo, Y., Analysis and design of low-rise structural walls under dynamically applied shear forces, ACI J. 85 (S21), Muto, K., Recent trends in high-rise building design in Japan, Third World Conference on Earthquake Engineering, New Zealand, Proceedings, Vol. 1, pp

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