Updating the ASCE 41 Provisions for Infilled RC Frames

Transcription

1 2017 SEAOC CONENTION PROCEEDINGS Updating the ASCE 41 Provisions for Infilled RC Frames Andreas Stavridis, Assistant Professor University at Buffalo Buffalo, New York Jimena Martin Tempestti, Graduate Student University at Buffalo Buffalo, New York Supratik Bose, Graduate Student University at Buffalo Buffalo, New York Abstract This paper discusses the development and validation of the simplified analytical framework for the seismic assessment of illed RC frames which will be included in ASCE The proposed methodology is based on an extensive parametric study using a detailed finite element model. The methodology initially classifies the illed frames based on the relative strength and stiffness of the ill and the bounding frame as these dictate the anticipated load-transfer mechanism and failure pattern. This allows the estimation of the peak strength, apparent yield point, and residual strength, as well as the lateral drifts at which these strengths are reached. This procedure has been implemented to predict the response of a large-scale three-story two-bay illed RC frame tested on the shake table. The comparison with the experimentally obtained response indicates that the proposed methodology can predict the main features of the load-vs.-displacement curve with sufficient accuracy and offers a significant improvement over previously followed guidelines. Introduction Masonry-illed RC frames have suffered catastrophic failures due to earthquakes across the world (EERI, 1996 and 2000, and Brando et al., 2016). Understanding and predicting their performance is a necessity, as well as a major challenge for practicing engineers who are often tasked with the assessment of their strength and deciding on their need for retrofit. However, there is a lack of reliable, yet efficient, methods that can be used to accurately predict their performance due to the highly nonlinear behaviors of the masonry panel and the bounding RC frame which interact under seismic forces. The assessment guidelines in ASCE (2006) and (2013) are not satisfactory in terms of completeness and reliability, nor fully validated with experimental results. Moreover, they focus on the actions on individual members and do not provide ormation on the global strength and post-peak behavior of these structures. This paper discusses the development of a simplified, yet accurate methodology for the seismic assessment of masonryilled RC frames, developed to replace the widely used ASCE (2006) methodology and the incomplete ASCE guidelines. The proposed framework limited to frames with an ill aspect ratio h /L, less than 1 here, is based on the results of an extensive parametric study on the performance of RC frames with solid masonry ills. The goal of this study, conducted using a validated detailed FE modeling scheme (Stavridis and Shing, 2010), is to assess the luence of a number of parameters on the response of illed frames to inplane lateral loads. Hence, the study considers the effects of the frame geometry, design details, as well as the material properties. The results of the parametric study indicate that two indices are sufficient to classify an illed frame based on the anticipated failure mechanism. The relative stiffness of the ill with respect to the surrounding frame can be used to classify the ill as strong or weak. Moreover, the ratio of the shear to the flexural capacity of the columns governs the ability of the frame to behave in a ductile or non-ductile manner. Consequently, the illed frames can be classified in four categories, each of which is associated with a distinct failure mechanism. The classification based on the anticipated failure mechanism allows the estimation of the force distribution when the peak, residual, and apparent yield strengths are reached. These strengths together with the estimated associated drifts define a quadrilinear backbone curve that 1

2 2017 SEAOC CONENTION PROCEEDINGS describes the force-vs.-displacement relation for RC frames with solid ill panels. The proposed methodology is validated with data from shaketable tests of a large scale two-bay three-story specimen. The considered test structure presents significant challenges due to its size and geometry. The comparison of the experimental data and analytical predictions indicates that the proposed simplified methodology is a significant improvement over the previously used framework found in ASCE (2006) as it can capture with reasonable accuracy the main features of the nonlinear behavior. Numerical Parametric Study A parametric study is conducted using the finite element modeling scheme proposed by Stavridis and Shing (2010) to investigate the luence of a number of parameters on the structural response. Specimen M8 tested by Mehrabi et al. (1994) and specimen CU1 that had solid ill (Stavridis, 2009) are used as references for the geometry, reorcement detailing, vertical load, and material properties in the parametric study. The specimens are selected, due to the distinct designs and failure patterns, as Specimen CU1 represented 1920s construction in California and had a strong ill that developed a dominant shear crack which propagated through the column leading to a brittle, shear dominated failure of the RC columns. Specimen M8 incorporated a weak ill that developed significant sliding and crushing leading to a flexure-dominated ductile failure of the RC columns. The modeling methodology used to numerically simulate the response of the two specimens combines the smeared- and discrete crack approaches (Stavridis and Shing, 2008) and can accurately capture the force-vs.-displacement curves, as well as the failure mechanisms of the two specimens (Stavridis, 2009). Three frames are considered as reference structures in the parametric study discussed here. The reference frames are based on the validated models for Specimens CU1 and M8: the first reference structure, identified as M1, is the model of Specimen CU1; the second reference frame, M2, is obtained by replacing the ill wall of CU1 by an ill with the material and geometric properties of the masonry panel in Specimen M8 to represent a weak ill built with hollow units; and the third reference structure, M3, has ductile reorcing details as it is obtained from CU1 by reducing the stirrup spacing to 7 cm (2.75 in.) compared to 28 cm (11 in.) in CU1, which quadruples the amount of shear reorcement. All three reference models, have the same geometry and concrete material properties to limit the variables between the different models. Additional ormation on the three models can be found in Reese (2014). Figure 1 summarizes the performance of the three reference structures in terms of the force-vs.-drift relations and the deformed meshes at the instant of the peak lateral resistance. As shown in the figure, the first base model exhibits a very brittle behavior due to the strong ill and weak frame which develop dominant shear cracks leading to a significant loss of strength at 0.27% drift. In the case of M2, the crushing of the weak ill, shown in Figure 1b, limits the compressive strut forces carried by the ill. This also limits the strength of the structure to almost 50% of that in M1. The compressive failure of the masonry also limits the strut forces carried by the ill and, therefore, the demand on the RC columns. Hence, the columns behave in a ductile manner forming plastic hinges before the development of shear cracks. The ductile behavior is indicated by the deformed mesh, as well as the force-vs.- displacement curve. The only difference between M1 and M3 is only the increased amount of the shear reorcement in M3. This does not increase the peak resistance, but increases the ductility of the frame. Eventually, the frame develops a shear crack whose effect on the force-vs-displacement curve is rather limited due to the considerable amount of shear reorcement as indicated by the plateau around the peak strength and the rather mild strength degradation. (a) Model of M1. (b) Model of M2. (c) Model of M3. Figure 1. Failure patterns and force displacement curves of the baseline models. 2

3 2017 SEAOC CONENTION PROCEEDINGS Using as reference the models M1, M2, and M3 models for 60 illed frames are created by varying one design or geometric parameter for each of the reference models at a time. A summary of the cases considered is provided in Table 1. More ormation on these models can be found in Martin Tempestti and Stavridis (2017). Table 1. Parameters considered in the parametric study. Parameter changed Parametric study set Frame design and material properties Failure Mechanisms Masonry compressive strength RC Column Dimensions ertical load Aspect ratio Stirrup area Longitudinal steel Stirrup spacing Column size M1 CU1 CU1 CU1 X X X X X M2 CU1 M8 CU1 X X X X X M3 CU1 CU1 CU1S X X X X X In all cases considered, the first indication of damage is the separation between the frame and the ill as cracks form at the interface. These cracks are consistent with test observations (Mehrabi et al., 1994, and Stavridis et al ) and they occur at relatively small lateral drifts, i.e. below 0.25%. As the lateral drift increases, cracking and in some cases crushing initiate within the ill before the damage eventually propagates into the RC columns. Based on the results of the parametric study, two damage patterns are commonly observed in the ill. In the first case, a dominant shear-sliding crack develops. This crack typically initiates near the top of the windward column and propagates through the ill to the bottom of the leeward column. This damage pattern is the result of a relatively strong ill. In the case of a weak ill, shear sliding is observed along a number of joints throughout the ill, while crushing can be also observed near the columns. The RC frame can exhibit shear- or flexure-dominated behavior. In the case of a strong ill, the dominant shear crack imposes large shear demands on the columns which can also fail in shear at the top of the windward column initially and the bottom of the leeward column if they are not adequately reorced for shear. In the case of columns with adequate shear resistance, the development of a shear crack can be delayed and in that case the behavior can be dominated by flexure until large values of interstory drifts. When the ill is weak and does not resist the deformation of the frame due to the sliding and crushing, a larger portion along the height of the columns can accommodate the interstory drift. Hence, the shear demand is reduced and a flexural failure is more likely to develop. A poorly reorced column can still fail in shear; however, this is not likely in the case of a weak ill. It should be noted that at large drifts, shear cracks can develop in the RC columns in all cases. However, if these develop at drifts larger than 1.5% they are not considered dominant as at that drift the damage due to in-plane loads eliminates the arching action and the out-of-plane forces can lead to the entire or partial collapse of the ill in an actual earthquake. Table 2. Classification criteria for illed RC frames (Martin Tempestti and Stavridis, 2017a). Infill Weak Strong Frame Ductile Non-Ductile c n p c n p c n p c n p Based on the observed failure mechanisms the illed RC frames can be grouped according to their failure patterns in four cases which are summarized in Figure 2. As shown in the figure, they consist of strong ill and non-ductile frame which develop the most brittle failure, strong ill and ductile frame which tend to be strong and behave satisfactorily, weak ill and non-ductile frame which are the most challenging to predict, and weak ill and ductile frame which are the most ductile of all cases considered. Additional ormation on the behavior of the four types of ill can be found in Martin Tempestti and Stavridis (2017a). Classification of Infilled Frames The post processing of the results of the parametric study with a focus on the failure patterns and force-vs.-displacement curves of the considered illed frames allows the development of criteria that can be used to predict the behavior of any illed frame (Martin Tempestti and Stavridis, 2017a). These classification criteria use the ratio of stiffnesses between the ill and the bounding columns, to determine whether the ill is strong or weak. Once the ill is classified, the frame 3

4 2017 SEAOC CONENTION PROCEEDINGS is then characterized as ductile or non-ductile based on the ratio of the resistance to the development of a shear crack, to the shear force required to develop two plastic hinges in the column. The two ratios can be calculated using the equation in Table 2. Ductile Frame Weak Infill Strong Infill Backbone Curve Based on these results and the careful processing, an analytical backbone curve for ills with aspect ratios, h /L, smaller than 1.0, has been proposed. The proposed backbone curve is an improvement over a previously proposed curve (Shing and Stavridis, 2014) which was limited to strong ills with a nonductile frame. In both cases a quadrilinear is adopted, as shown in Figure 3. The three points needed to define the curve are the peak strength, max, the apparent yield point, y, and the point at which the residual strength is used, d, and the associated drifts. In this section the equations are presented here. Non-ductile Frame Figure 2. Infilled frame classification and associated types of observed failure patterns. The strength terms p and n, correspond to the column shear force required to develop plastic hinges at a distance h p, and a diagonal shear crack respectively. The stiffness terms in Table 2 can be estimated using the following relations: 1, and 1 1 A G f s 3E I, _h m m s f 3 h h 3E I c (1) h c c 3 where _f is the ill flexural stiffness, _s is the ill shear stiffness, c is the column flexural stiffness, A _h is the horizontal cross-sectional area of an ill panel, L is the length of the ill panel, t is the thickness of ill panel, E c is the modulus of elasticity of concrete, E m is the modulus of elasticity of masonry, G m is the shear modulus of masonry, h is the height of the ill panel, I is the moment of inertia of ill panel, I c is the moment of inertia of a column, M p is the moment required for the development of a plastic hinge in the RC column. All these quantities can be calculated if the geometry and basic material properties of the reorced concrete and masonry are known. For the distance between the plastic hinges, h p, it can be assumed to be equal to ill height divided by 2 for weak ill or 2.5 for strong ill when the aspect ratio, h /L, is smaller than 1.0. The derivations of these criteria based on the detailed results of the parametric study are discussed in greater detail in Martin Tempestti and Stavridis (2017b). Figure 3. Quadrilinear backbone curve. Peak strength The peak strength of an illed frame with an aspect ratio h /L, smaller than 1, can be reached at very small drifts just before sliding along ill joints occurs. At this stage the column shear forces are relatively small and their contribution to the lateral resistance can be ignored. Hence, the lateral resistance can be estimated by Equation 2. max1 = P grav μ + A C (2) grav where, P is the gravity load carried by ill initially, μ is the friction coefficient along the mortar joints prior to sliding which can be taken between 0,9 and 1, and C is the cohesion along the mortar joints. After sliding along the ill joints is observed, the ill loses cohesion; however this does not necessarily mean a reduction in ill frame capacity because the vertical load in the ill increases; hence, its frictional resistance increases as well. Moreover, the sliding of the ill activates larger shear resistance in the columns. The columns and ill shear forces vary along the high. For simplicity, only a section at a distance equal to half of the depth of the column from the bottom of the ill is studied here. There, the leeward column reaches its shear strength and fails, 4

5 2017 SEAOC CONENTION PROCEEDINGS while the windward column shows a negligible shear resistance. Hence, the illed frame with an aspect ratio smaller than 1 develops a shear strength before the leeward column fails is obtained by Equation 3. max2 = P max max μ + lc (3) where, lc max is the maximum shear force of the leeward column governed by the column s shear or flexural capacity. The shear capacity of the ill is given by the maximum value between max1 and max2. The analysis of the results obtained from the parametric study indicates that the drift at peak strength depend mainly on the aspect ratio. Hence, the drift at peak strength can be estimated using Table 3. Table 3. Drift at peak strength. Infill Strong Frame Non-Ductile Ductile Yield point For AR 0.50 peak =0.15 For 0.50 < AR 1.0 peak = AR Weak peak =0.35 For AR 0.77 peak =0.30 For 0.77 < AR 1.0 peak = AR The stiffness of an illed RC frame changes when hairline cracks develop in the interface between the ill and the bounding frame. This first sign of minor damage often occurs at a lateral force equal to 2/3 of the peak strength. Hence, the force at yield can be estimated as y = 2 3 max, while the corresponding displacement can be obtained from Equation 4. y = y i h (4) where, i is the initial stiffness of the illed frame. This can be estimated analytically if the illed frame is considered as a composite beam and its flexural and shear stiffnesses are accounted for (Stavridis, 2009). Residual strength As the drift increases, the ill and the columns reach their residual strengths. For the ill the residual strength is provided by friction, while for the columns it is provided by the shear resistance of the stirrups, s for non-ductile frames For ductile frames, it is equal to the force needed for two plastic hinges to develop, p. At a section close to the bottom of the ill, the windward column cannot carry shear force, therefore, it can be neglected. Hence, the residual strength of the illed frame can be estimated from Equation 4. res = P res res μ res + lc Where lc res is the leeward column residual capacity which can be estimated according to the frame classification. The drift at which the residual strength is reached can be estimated using Table 4. Table 4. Drift at residual drift. Infill Strong Frame Non-Ductile res = 1.6 peak Weak (4) res = 0.55 Ductile res = 1.0 alidation The proposed methodology is implemented here to simulate the response of a three-story two-bay masonry-illed RC frame buildings tested on a shake table at the University of California, San Diego (UCSD). The test-structure, shown in Figure 4, represented the construction practice in California in 1920s. It included an illed non-ductile RC frame designed with the allowable stress method considering gravity loads only. The RC frame was illed with solid unreorced masonry walls in one bay and walls with eccentric opening on the other. The dimensions and reorcement details are presented in Figure 5. The test structure was subjected to a sequence of 44 dynamic tests, including recordings of ambient vibration, white noise and 14 scaled earthquake ground motions of increasing intensity obtained by scaling the acceleration time histories recorded along the N-S direction at the Gilroy 3 station during the 1989 Loma-Prieta earthquake, and in El Centro during the 1940 Imperial alley earthquake. The specimen was tested until its stability was severely compromised because of the induced damage. More ormation on the test structure and its performance can be found in Stavridis et al. (2012). Following the proposed methodology, the force-vs.- displacement curve for the solid panel in the first story is first estimated once the ill is classified as strong and the frame is classified as non-ductile. Then, the curve for the panel with the window is obtained following the adjustments outlined in Stavridis (2009). The two curves can be seen in the Figure 6. 5

6 2017 SEAOC CONENTION PROCEEDINGS Combining the two curves, one can obtain the base shear force curve for the structure, which is illustrated in Figure 7. As shown in the figure the proposed methodology can accurately capture the initial stiffness and the peak strength of the test specimen. The analytically derived curve conservatively underestimates the post peak strength of the test-structure; however, this can be expected considering its simplicity. Comparison with ASCE The guidelines for illed RC frames found in ASCE (2006) are considered here to simulate the response of the three-story shake-table test-structure. The gravity loads considered are determined based on actual masses of the specimen during the tests. Initially a static analysis is performed to compare the capacity and demand of the various structural components, i.e. the diagonal masonry struts and the reorced concrete beams and columns shown in Figure 8. The results, summarized in Table 5, indicate that all the RC members would fail in shear and only the upper story beams have the required flexural strength. This can be expected for a frame with non-ductile detailing designed according the construction practice in California in 1920s. However, this is not consistent with the test observations that indicate that the structure was able to withstand five earthquakes with intensities equal or higher than the design level earthquake for a site of soil class D in San Diego, California. Figure 4: Test structure. Figure 6: Estimated force-vs.-displacement for all bays. Figure 5: Reorcement detailing. Figure 7: Estimated base shear-vs.-1 st story drift. 6

7 2017 SEAOC CONENTION PROCEEDINGS orientation, with the one to the left considered positive, following the convention established for the test structure. The results for these analyses are presented in Figure 7. As it can be seen from the figure, the model with the struts connected to the joints provides the highest strength, which can be expected as it is the loads is shared by the beams and columns in this case. However, the behavior of all three models is far from that of the specimen as they largely underestimate the stiffness and the strength of the test structure. On the contrary, the methodology proposed here; yet less complex, yields significantly better results. Figure 8: Identification of the different members. Table 5: Results of the linear static procedure. Strut Beam Column ID Axial ID Shear Moment ID Shear Moment S1 fails B1 fails fails C1 fails fails S2 fails B2 fails fails C2 fails fails S3 fails B3 fails fails C3 fails fails S4 fails B4 fails fails C4 fails fails S5 fails B5 fails C5 fails fails S6 fails B6 fails C6 fails fails S7 fails C7 fails fails S8 fails C8 fails fails S9 fails C9 fails fails S10 S11 S12 S13 S14 S15 In addition to the linear static analysis, nonlinear static analysis according to the ASCE (2006) provisions was also performed using PERFORM3D software. The aforementioned guidelines are not clear as to the location of the struts, so three options have been considered as shown in Figures 9 to 11. In Model 1, the struts are connected to the RC frame at the beamcolumn joints; in Model 2, the struts are connected to the columns at the offset specified in ASCE 41-06, and in Model 3, the struts are connected to the RC beams. All three models have been subjected to pushover analysis. Given the existence of the windows at the one bay in every floor, two pushover analyses are considered for each model; one on each Figure 9: Model 1-Struts connect at beam-column joints. Figure 10: Model 2-Struts connect at RC columns. Conclusions This paper discusses a simplified analytical tool to predict the seismic response of reorced concrete frames with masonry ills using strut models. The proposed methodology is based on a parametric study conducted using a detailed finite element model validated with experimental data. The first step of the proposed tool involves the classification of the frame and ill in every bay of the structure. Then, one can estimate the profile of the lateral resistance of every bay and combining those on the same floor can obtain the backbone story shear force as a function of the drift of that story. 7

8 2017 SEAOC CONENTION PROCEEDINGS Brando G., Rapone D., Spacone E., Barbosa A., Olsen M., Gillins D., Soti R., arum H., Arede A., ila-pouca N., Furtado A., Oliveira J., Rodrigues H., Stavridis A., Bose S., Fagella M., Gigliotti R., Wood R., 2015, Reconnaissance report on the 2015 Gorkha Earthquake effects in Nepal. Proc. XI Convegno Anidis, L Aquila, Italy. EERI, 1996, 1994 Northridge earthquake Reconnaissance Report, Earthquake Spectra, ol. 12, Issues S1 and S2. Figure 11: Model 3-Strut connect at RC beams. The proposed methodology is applied to simulate the response of a three-story illed frame tested in the outdoor shake table in the University of California, San Diego. The comparison of the analytical and experimental responses indicates that the newly developed framework, yet not complex, can predict accurately the strength and stiffness of the test structure. On the contrary, the method outlined in ASCE besides being vague, has major disadvantages in predicting the behavior of the same test structure. The comparison between the two methods indicates that the proposed simplified procedure is a major improvement in terms of simplicity, as well as accuracy over the ASCE guidelines. Additional detailed ormation on the proposed method, its derivation and validation can be found in Martin Tempestti and Stavridis (2017b). Acknowledgments The study presented here is supported by the National Science Foundation (Award No and ). The second and third authors of the paper are grateful for the financial support provided by University at Buffalo during their graduate studies, while the second author is also the recipient of the BEC.AR Argentine Presidential Fellowship in Science & Technology. The assistance of Martin Ramirez, Austin Reese, and Laura Pavone is also acknowledged. The authors would also like to thank the ASCE 41 committee for the feedback provided in the development of the assessment guidelines proposed in this study, which have been adopted in the ASCE document. However, the opinions expressed in this paper are those of the authors and do not necessarily represent those of the sponsors or the collaborators. References ASCE/SEI 41-06, 2006, Seismic rehabilitation of existing buildings, American Society of Civil Enineers, Reston, A. ASCE/SEI 41-13, 2013, Seismic rehabilitation and retrofit of existing buildings, American Society of Civil Enineers, Reston, A. EERI, 2000, 1999 ocaeli, Turkey earthquake reconnaissance report, Earthquake Spectra, ol. 16, Issue S1. Martin Tempestti J.Y., Stavridis A., 2017a, Simplified method to assess lateral resistance of illed reorced concrete frames. Proc. 16th World Conference in Earthquake Engineering, Santiago Chile. Martin Tempestti, J.Y., Stavridis A., 2017b, Simplified Method to Assess the In-Plane Lateral Resistance of Infilled RC Frames, Bulletin of Earthquake Engineering, (under review). Mehrabi, A.B., Shing, P.B., Schuller, M.P., and. Noland, J.L, 1994, Performance of masonry-illed R/C frames under inplane lateral loads. Report No. CU/SR-94/6, University of Colorado at Boulder. Reese, A., 2014, "Development of Simplified Analytical Method of Estimate the Seismic Responce fo Reorced Concrete Frames with Solid Masonry Infills," Master s Thesis, Univerity of Texas Arlington, Arlington, TX. Shing, B., Stavridis A., 2014, Analysis of masonry-illed RC frames through collapse,aci Special Publication. 297: 1:20. Stavridis, A., 2009, Analytical and Experimental Study of Seismic Performance of Reorced Concrete Frames Infilled with Masonry Walls, Ph.D. Dissertation, University of California at San Diego, La Jolla, CA. Stavridis A. and Shing P.B, 2008, Calibration of a numerical model for masonry-illed RC frames. Proc. of 14th World Conference on Earthquake Engineering. Beijing, China. Stavridis, A. and Shing, P.B., 2010, "Finite-Element Modeling of Nonlinear Behavior of Masonry-Infilled RC Frames," Journal of Structural Engineering, 136, No.3, pp Stavridis, A., outromanos, I., and Shing, P.B., 2012, "Shaketable tests of a three story reorced concrete frame with masonry ill walls," Earthquake Engineering & Structural Dynamics, vol. 41, no. 6, pp