EFFECT OF WINDOW OPENINGS ON REINFORCED CONCRETE FRAMES WITH MASONRY INFILL

Transcription

1 EFFECT OF WINDOW OPENINGS ON REINFORCED CONCRETE FRAMES WITH MASONRY INFILL Laura Pavone Home Institution/REU Site: University at Buffalo REU Advisor: Dr. Andreas Stavridis August 28, 214 Abstract Reinforced concrete (RC) frames with masonry infills are commonly found in many structures; yet little is known about their behavior during seismic activity. Thus the analysis of the seismic performance of these buildings is rather difficult. Many of these bays contain window openings which have a rather significant effect on the overall strength and behavior of the structure, the extent to which has not yet been fully understood. However, one of those studies, conducted by Stavridis (29), studied the effect of window openings using a base line model with a weak RC frame and strong infill properties. This paper extends that study using finite element modeling to analyze two additional sets of models (weak frame-weak infill, and strong framestrong infill) in order to better understand the effect the openings have on the behavior of the structure under lateral loads. The results of this study showed a reduction of strength (compared to the respective base model with solid infill) depending on the material properties, window size and location. The goal of this investigation is to further improve the simplified methods of estimating the strength and behavior of RC frames with masonry. It is also hoped that the method of estimating the behavior of these bays may become more efficient and more accurate in the process of designing safer, more earthquake resistant buildings.

2 i Table of Contents Introduction... 1 Literature Review... 1 Methods... 3 Modeling the Reinforced Concrete Frame... 3 Modeling the Masonry Infill... 4 Contributions... 5 Overview of Previous Parametric Study on the CU1 Base Model... 5 CU1M8 Models... 7 CU1S Models... 8 Analysis of Results... 9 Conclusions Contact Information Acknowledgements References Appendix A (CU1)... A-1 Appendix B (CU1M8)... A-5 Appendix C (CU1S)... A-9 Appendix D (All models by Size and Location)... A-13

3 1 Introduction Reinforced concrete (RC) frames with masonry infills are common across the world, including regions of high seismic activity. While some of the older unreinforced masonry infill has been retrofitted, the vast majority of these buildings still remain susceptible to seismic and other damage. Due to the assumption that masonry infill is a non-structural component of the RC frame, there were few standards governing how they were designed, built, or reinforced (Koutromanos et al., 211). The effect of masonry infill on the stability and strength of the frame cannot be reliably predicted due to a combination of factors contributing to the complexity of the structural behavior (e.g. various moduli of each material and the interaction between the different materials). However, in the last half century the research conducted in this field has shown that the masonry infill significantly increases the strength of the structure while also increasing the stiffness. This cannot be ignored in areas of high seismic activity due to the nature of earthquake damage where more ductile structures are desired (Asteris et al., 211). The scope of the National Science Foundation (NSF) funded project is to enhance our knowledge on the behavior of RC frames with masonry infills in the hopes of creating a more efficient and more accurate method in estimating the response of such structures to lateral loads. This paper contributes to the NSF project by investigating a set of RC frames with masonry infill and window openings using finite element models. It is hoped that the patterns observed through this investigation can be applied to the modeling of a series of different multi-bay, multi-story buildings to better predict their actual strength and behavior during seismic activity. This project expands the research conducted by Stavridis (29) regarding the modeling of RC frames with masonry infill with different material properties, four different window opening sizes and five different window locations. Literature Review In previous finite element models of RC frames with masonry infill, the infill was treated as a homogeneous material while the mortar joints were generally ignored (Mehrabi and Shing, 1997). Mehrabi and Shing (1997) proposed a finite element model that implemented both smeared and discrete crack elements to model the infill panel. The use of interface elements to model the mortar joints in the infill highly improved the accuracy of the finite element analysis and its ability to capture the correct lateral resistance of the actual structure. The models accurately captured the experimental tests also performed as part of the research; however, the models were only somewhat successful at demonstrating the different failure mechanisms seen in those experimental results as they did not capture the shear failure of the RC members. A similar finite element approach is discussed in depth by Stavridis (29), in which smeared and discrete crack elements are used to model the mortar joints between the masonry bricks as well as between the infill and the RC frame. He also proposed a way to calibrate the finite

4 2 element analysis to ensure accurate modeling of the failure patterns observed in experimental results of RC frames with masonry infill (Stavridis, 29). Such failures include horizontal sliding, diagonal cracking, and panel crushing. Using the aforementioned finite element modeling scheme, Stavridis and Shing (21) were able to accurately model a number of the experiments conducted by Mehrabi and Shing (1997). Stavridis (29) also analyzed the effect that different material parameters had on the strength and stability of the RC frame with infill. By changing the different parameters in the control specimen (CU1), such as aspect ratio and stirrup spacing, the effect the parameters had on the overall strength and stiffness of the structure were analyzed. Based on the analysis he developed a simplified approach to model the backbone curves of RC frames with solid masonry infill. While Stavridis (29) focused on the CU1 base model, Reese (214) expanded the parametric study considering two additional base models with solid infills, CU1M8 and CU1S with material properties seen in Table 1. CU1M8 had the same frame design as the CU1 base model, but with a much weaker infill. CU1S was based on the infill used in CU1 as well as the same frame design, only differing in an increase in shear reinforcement (closer stirrup spacing) (Reese, 214). Base Model CU1 CU1M8 CU1S Table 1. Material Properties of baseline models (Reese, 214) Infill type Blackard et al. (29) Mehrabi et al. (1994) Spec. 8 Blackard et al. (29) Infill Characteristics f' m Infill Aspect Ratio Total Stirrup Area Stirrup Spacing Column Reinforcing Ratio (ksi) (in 2 ) (in) (%) Strong Weak Strong When openings are introduced into the masonry infill, it results in a reduction of strength and stiffness (Mohmmadi and Nikfar, 213). The experimental results surrounding the effects of window openings on the masonry infilled frame are summarized in Mohmmadi and Nikfar (213). Several studies such as those conducted by Fiorato et al. (197) and Mosalam et al. (1997) proved that the reduced load resistance due to window openings is not proportional to the reduction of the infill area. Fiorato et al. (197) showed that a 5% reduction in infill area led to a 2-28% reduction of strength (Shing and Mehrabi, 22). Along with the small reduction in strength, an increase in ductility was observed as well as different cracking patterns. Mosalam et al. (1997) observed cracking in a bay of solid infill started at mid-height and propagated to opposing corners, while infill with windows showed cracks initiating at the window corners followed by propagation toward opposing corners (Shing and Mehrabi, 22). These findings are crucial in terms of understanding the effects window openings have on the overall strength and stability of the RC frames with masonry infill. Investigation into previous research by Mohmmadi and Nikfar (213) shows that the type of bounding frame of infills with

5 3 openings affects the strength reduction factor used in estimating the overall strength of the structures, while the frame type does not affect the initial stiffness reduction factor. However, it was also suggested that few experimental results existed on stiffness of infilled frames with openings. Formulas for calculating the strength and stiffness reduction factors were also purposed by Mohmmadi and Nikfar (213) after an in-depth analysis into previous experimental results. Further investigation by Stavridis (29) correlated the reduction in stiffness and strength and the failure patterns to window size and location. His study kept the material parameters of the base structure (CU1) constant while testing four different window sizes in five different locations. With the results, Stavridis (29) was able to expand his simplified analytical approach to account for openings. While a significant amount of research and experiments have been conducted on RC frames with solid masonry infill, it is the goal of this project to build upon the previous research conducted on masonry infills with window openings. To better understand the effect of window openings and their location on RC frames with masonry infill, it can be useful to combine the research of Stavridis (29) with that of Reese (214). By modeling the same window sizes and locations used by Stavridis (29) on the base structures studied by Reese (214), a more accurate picture of the pattern for overall strength and stiffness of RC frames infilled with masonry with window openings can be predicted. Methods The non-linear finite element method used in this study combines the discrete and smeared crack approaches (further explained in Stavridis and Shing (21)) to model the various failure patterns of both the RC frame and the masonry infill. While the smeared crack approach can accurately model diffused cracks and the compressive failure in the RC frames and the infill, it lacks the ability to model the brittle behavior due to diagonal shear cracks in the frame and the sliding shear failure of the mortar joints in the masonry (Lotfi and Shing, 1994). To account for these failures, zero-thickness interface elements were included to model the shear cracks. However, the location of potential shear cracks must be known beforehand to accurately model the structural behavior. For the masonry infill, this task is reasonable due to the characteristically weak mortar joints and their tendency for shear cracks; however, the same cannot be claimed for the RC frames due to the rather unpredictable and varying cracking patterns. Hence the addition of interface elements in the frame to model its shear behavior was proposed. Modeling the Reinforced Concrete Frame To model complex structures for which laboratory testing is not feasible, Stavridis (29) proposed a modeling scheme that breaks down the typically used rectangular smeared element into a set of triangular smeared crack elements connected with interface elements. Figure 1A shows the usual element set up, while 1B and 1C show the modules proposed by Stavridis (29). It can be seen in Figure 1 that each interior node in the quadrilateral model shown in 1A is replaced by eight nodes in Stavridis model while each exterior node is replaced by four

6 4 nodes. Each diagonal interface element is double noded and all nodes corresponding to the single node in 1A have the same coordinates (thus the zero-thickness). The module used in this project allows for crack propagation in a combination of orientations due to the horizontal, vertical and diagonal interface elements. Interface Concrete Element Smeared-Crack Concrete Element Node A B C Figure 1. (A) Usual quadrilateral modeling scheme (B), (C) Stavridis smeared crack and interface modeling scheme (Adapted from Stavridis, 29) Each physical piece of rebar is divided equally between the eight intersecting nodes to form eight truss members that when combined, model one steel reinforcement. With this scheme (presented in Figure 2) each triangular smeared-crack element is connected to the steel at two of its nodes. The shear reinforcement shown in Figure 2, is divided equally between two members in an X shape between modules. This formation is used to resist horizontal shearing along the interface of modules. In reality the horizontal sliding mechanism is prevented by the dowel action of the longitudinal rebar (Stavridis, 29). Figure 2. Reinforcements (Adapted from Stavridis, 29) Modeling the Masonry Infill The relative strength between the bricks and the mortar that form the masonry infill plays a large role in the infill modeling scheme. Normally, the mortar is much weaker than the brick. The combination of the brick and mortar can result in a variety of failure patterns including the

7 5 fracture of the mortar joints, the crushing and tensile failure of the bricks, as well as the tensile or shear failure of the interface between the bricks and the mortar (Stavridis, 29). Due to the nature of the mortar-brick interaction when the infill is under compression, the masonry units have a tendency to fail due to out-of-plane tensile Brick and Mortar Assembly Finite Element Masonry Infill Assembly Adjustment of Masonry Unit Size Figure 3. Modeling the Masonry Infill Half Brick-Half Brick Interface Half Brick Elements Mortar Interface fracture. To model this, the proposed brick elements each represent a half brick, with a zerothickness interface element between them as shown in Figure 3. To simplify the model, a cohesive, zero-thickness interface element can be used to model the mortar (Lotfi and Shing, 1994). As a result of neglecting the actual thickness of the mortar, the dimensions of the masonry elements must be adjusted to make up for the size difference between the physical wall and the analytical wall. Due to the assumptions used in this scheme, some material properties must be adjusted in order to account for the assumptions made as discussed by Stavridis (29) in his calibration approach. Contributions Overview of Previous Parametric Study on the CU1 Base Model The study done by Stavridis (29) considered four different sized windows; small (SW), regular (RW), large (LW), and extra-large (xlw), in five different locations; 1, 2, 1R, 2R and M as shown in Table 2. In order to change the window size, only the width of the windows was altered while the height remained unchanged because most commonly the vertical location and height of windows in real structures remain constant. The conclusions drawn from the models are described in greater depth in Stavridis (29); however, some of the main ideas are summarized here. Openings of the same size but different location result in different failure patterns as well as different peak loads while they share a similar initial stiffness. Openings of different sizes result in different initial responses as well as different maximum strengths. The opening location results in changes in failure pattern, maximum strengths as well as initial stiffness. In locations where the shorter infill pier is closer to the leeward column (1R, 2R), the reduction of strength was highest while the smallest reduction in strength occurred in the central location (M). Finally, openings of different sizes in the same location resulted in similar failure patterns (Stavridis, 29).

8 6 Stavridis (29) noted that the failure patterns seen in this study could be influenced by the material parameters and the strength of the materials. He suggested that further investigation on specimens with the same frame configurations but with different reinforcing specifications and/or material strengths could result in different specimen failure mechanisms and behavior (Stavridis, 29). To improve our understanding of whether the above observations are general to all window configurations, in this study the models of CU1M8 and the CU1S were added and the analysis and results are shown in the following sections. Table 2. Window Size and Location Specimen Vertical load Infill aspect ratio (L/H) Total Stirrup area l a l b l c Small Windows Regular Windows Large Windows Extra Large Windows kips - in 2 in in in CU1 -SW CU1 -SW-1R CU1 -SW CU1 -SW-2R CU1 -SW-M CU1 -RW CU1 -RW-1R CU1 -RW CU1 -RW-2R CU1 -RW-M CU1 -LW CU1 -LW-1R CU1 -LW CU1 -LW-2R CU1 -LW-M CU1 -xlw CU1 -xlw-1r CU1 -xlw CU1-xLW-2R CU1 -xlw-m

9 7 CU1M8 Models The introduction of a weaker infill drastically reduces the maximum lateral loads the frames can withstand. The average strength for the CU1M8 models was only around 58 Kips while the CU1 models averaged around 114 Kips. When windows of different sizes but same location were compared, it can be seen that the location largely impacted the maximum strength as well as the intial stiffness, both seen in Figure 4. The CU1M8 models showed a reduction of strength between 9 and 25 percent with the smallest reduction of strength resulting from a small window centrally located (M) and the largest reduction of strength from an extra-large window in location 1. For all window sizes, the central location showed the least reduction in strength, while the lowest reduction in initial stiffness occured in location 1R. From Figure 4, it can be seen that windows located with the shorter infill pier closest to the leeward column resulted in the lowest reduction in initial stiffness, while those with the shorter pier closest to the windward column resulted in the highest reduction in initial stiffness (more so in location 1R). Window openings of different sizes in the same location resulted in both different initial stiffness and maximum strength. There seems to be no apparent trend in the reduction of stiffness except that to say that for the CU1M8 models in general, the larger the window the lower the maximum strength. Reduction of Strength (%) Reduction of Stiffness (%) R 1 2 2R 3 M 4 Window Location Small Window Large Window 1 1R R 3 M 4 Regular Window xlarge Window Figure 4. CU1M8 Windows Reduction of Strength and Reduction of Stiffness For CU1M8, openings of the same size resulted in relatively similar failure patterns which is different than the observations made by Stavridis (29), seen in the previous section. All the CU1M8 models failed in shear of the leeward column by the base and/or by crushing of the infill. While the strut patterns were different regarding location of the opening, the general failure pattern remained the same. This may be due to the large difference in strength between the infill and the RC frame. The lateral force-drift curves for models of the same opening size showed similar initial stiffness regardless of location (a difference in stiffness of only 8 to 1% depending on size) as well as similar responses to the lateral loads.

10 8 Openings of the same size did however result in different peak strengths, although the range of peak strengths was far smaller than that of the CU1 models. The peak strengths for the CU1 models of the same window size differed between locations by 1 to 19% while the same ranges for the CU1M8 models differed from 5 to 12%. Hence, as exemplified by the comparison of extra-large windows in Figure 5, the window location had a greater effect on strength for models of stronger infill (CU1 and CU1S) than those of a weaker infill (CU1M8). CU1S Models Reduction in Strength (%) CU1 xlarge Windows CU1M8 xlarge Windows CU1S xlarge Windows 1 1R 1 2 2R 3 M 4 Window Location Figure 5. Extra-Large Windows v. Location The CU1S models share very similar properties to those of CU1 however they have an increase in the horizontal reinforcement in the columns. The average strength of the CU1S models is only slightly lower than the average of the CU1 models (114Kips) at around 111Kips. Exemplified by the comparison of regular windows in Figure 6, the trend in stiffness of the CU1S models are very similar to that of the CU1 models. Reduction in Stiffness (%) CU1 Regular Windows CU1M8 Regular Windows CU1S Regular Windows 1 1R 1 2 2R 3 M 4 Window Location Figure 6. Regular Windows v. Location Figure 7 shows the patterns for the reduction of strength and reduction of stiffness for the CU1S models. As seen in the figures, the lowest reduction of strength occurred in the large window centrally located (M) while the highest reduction of strength resulted from an extralarge window in location 1R. The overall reduction in strength of the CU1S models range from 7 to 31% while the CU1 models range from 3 to 25%. As seen in the CU1 models, openings of the same size for the CU1S models resulted in different failure patterns based on location. Models in locations which have a shorter windward pier (1 and 2) resulted in similar failure patterns. The RC frame had a major diagonal shear failure in 7 of these 8 cases; in the eighth model the failure was still present but on a smaller scale. For models with the shorter leeward pier (locations 1R and 2R) in 6 of the 8 models failure of the RC frame occurred in bending while in the remaining two models failure occurred as horizontal

11 9 shearing of the windward column-beam interface. For the location central to the infill, in 2 of the 4 cases failure occurs in bending of the windward column, and in the fourth failure occured as the crushing of the brick infill near the windward column-beam interface and on the leeward side of the lintel beam. Reduction of Strength (%) R 1 2 2R 3 M 4 1 1R 2 2R M Window Location Small Window Large Window Reduction of Stiffness (%) Regular Window xlarge Window Figure 7. CU1S Windows Reduction of Strength and Reduction of Stiffness Window Location Analysis of Results In the results of the CU1M8 models, it was noted that openings of different sizes in the same location failed in similar patterns. However, this was not necessarily true for the CU1 and CU1S models. For example, the windows in location M of the CU1M8 models all had crack propagation like that shown in Figure 8A. However, only small A and regular windows of the CU1 and CU1S models showed crack propagation like that in Figure 8A, while extra-large windows in this location showed propagation like that in Figure 8B (the large window for CU1 failed like that of 8A while the CU1S model failed as a combination of the two). B Figure 8. While failure in CU1M8 tended to be in crushing of the infill and/or Crack Propagation horizontal shearing of the leeward column, the CU1 models tended to have diagonal shear failure of the RC frame while the CU1S models tended to have bending failure in the RC frame (most evident in the windward column). The different failure patterns observed between the models may account for the large difference in strengths. The original simplified analytical method of predicting the force-drift curves for the structures with windows proposed the formula:

12 1 K ini solid = 1 α i R A (1) K ini where K ini is the initial stiffness of the bay, K sol ini is the initial stiffness of the frame with solid infill, R A is the ratio of the area of the opening to the area of the solid infill, A op /A tot, and previously, α i has a constant value of 2 for window openings. To further prove that location is more influential on initial stiffness than size, an investigation of the results showed that the value of α is better estimated dependent on window location instead of window size. The difference between the individual α values for each model and the average α for each window size and base structure showed a standard deviation between 1.3 and 6.7%. When the value of α was calculated for each location regardless of window size, the difference between the individual values and the average showed a standard deviation of between 1.1 and 4.%, that is a 46% more accurate range. However, for the sake of simplicity in the analytical method a value 2.2 for α was calculated regardless of base structure, opening size or location. Shown in Figure 9, this value (used to calculate the reduction in stiffness show by the dotted lines) is a conservative assumption regardless of base model (the range of differences between the average value of α of each base model and the average α of all base models being only 1.1 to 2.7%). Reduction of Stiffness (%) CU1 Windows M8 Windows 1 1R 1 2 2R 3 M 4 1 1R 1 2 2R 3 M 4 1 1R R 3 M 4 Window Location Window Location CU1s Windows Window Location Small Window Regular Window SW Large Window xlarge Window LW Figure 9. Prediction of Initial Stiffness RW xlw The simplified method also uses the following formula for estimating the maximum strength of the bay with a reduction factor of.8: solid V max = γv max (2) where V max is the peak strength of the bay with opening, V solid max is the peak strength of the bay with solid infill and γ is the strength reduction factor of.8. Investigation into this reduction factor, seen in Figure 1, showed that for the CU1 models, 9% of the maximum strengths were conservatively estimated with a reduction factor of.8. If the standard is to remain 9%, a different value for the reduction factor needs to be considered for different base models. For CU1M8, a reduction factor of.76 provides the 9% while for the CU1S models, a factor of.73

13 11 is necessary. Furthermore, if the average γ value for all the base models (γ=.84) is used to predict the maximum strengths, only 55% of the models are conservatively predicted. 35 Reduction of Strength (%) CU1 Windows M8 Windows CU1S Windows 1 1R 2 2R M 1 1R R 3 M 4 1 1R 2 2R M Window Location Window Location Window Location Small Window Regular Window Large Window xlarge Window Reduction Factor =.84 Reduction Factor =.8 Reduction Factor =.76 Reduction Factor =.73 Figure 1. Prediction of Maximum Strength Conclusions This study shows that a decrease in stiffness and maximum lateral resisting strength is evident when a window opening is included in the infill regardless of design and material parameters. There seems to be no distinct trend between reduction of infill area and reduction of strength except to say that as the opening area increases the reduction in strength increases as well as the range for the amount of strength reduction. According to the results, the strength of the infill not only decreases the strength of the bay but also reduces its stiffness, as is evident in the initial slope of the force-drift curves. The location of the opening is related to the initial stiffness. Windows located with the shorter pier located on the leeward side of the opening, show greater stiffness than their mirrored locations while the centrally located openings have an initial stiffness between the eccentric locations. In the central location, the models seem to show greater maximum resistance and/or the maximum strength occurs at a higher drift; the latter is especially evident in the CU1M8 models. From these results, the simplified method of estimating the strength and behavior of RC frames with masonry infill can be further improved. The results show that the method in which the initial stiffness is predicted seems correct; however some changes can to be made to the method in which the maximum strength is predicted. With this, the method of estimating the

14 12 behavior of these structures may become more accurate and provide a tool to assist in the process of assessing the seismic resistance of infilled RC frames. Contact Information For further information regarding this paper specifically, please contact Laura Pavone. For further information on the continuation of this project, please contact Andreas Stavridis: Acknowledgements Laura Pavone Undergraduate University at Buffalo laurapav@buffalo.edu Andreas Stavridis Assistant Professor University at Buffalo astavrid@buffalo.edu Xuan Gao Graduate Student University at Buffalo xuangao@buffalo.edu I would first like to thank Dr. Stavridis for giving me this opportunity to be involved in the academic research world which most undergraduates are not fortunate enough to experience. I would also like to thank him as well as Xuan Gao, a PhD student at the University at Buffalo, for their expertise and guidance through my often confusing questions. Of course without the National Science Foundation and their contribution to the George E. Brown, Jr. Network for Earthquake Engineering Simulation Consortium (NEES) (Award Number CMMI ) and their grant to the University at Buffalo (Pre/Post Earthquake Damage Assessment for Infilled RC Frame Buildings: Award Number 14318), this paper would not have been possible. Furthermore I would like to thank the NEES REU program (grant number EEC ), which helped me not only throughout my project and on my final paper, but also helped to prepare me for the next steps in my academic career.

15 13 References Asteris, P. G., Chrysostomou, C. Z., Giannopoulos, I. P., and Smyrou, E. (211). Masonry infilled reinforced concrete frames with openings, III ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfu, Greece, Fiorato, A.E., Sozen, M.A., and Gamble, W.L. (197). An investigation of the interaction of reinforced concrete frames with masonry filler walls. Report UILU-ENG-7-1. Civil Engineering Studies SRS- 37, University of Illinois, Urbana-Champaign, IL. Koutromanos, I., Stavridis, A., Shing, P., and William, K. (211). Numerical modeling of masonry-infilled RC frames subjected to seismic loads, Computers & Structures. 89(11-12), Lotfi, H.R., and Shing P.B. (1994). An interface model applied to fracture of masonry structures. J. Struct. Eng., ASCE, 12(1): Mehrabi, A.B. and Shing, P. B. (1997). Finite element modeling of masonry-infilled RC frames. J. Struct. Eng., ASCE, 123(5), Mohmmadi, M., and Nikfar, F. (213). Strength and stiffness of masonry-iniflled frames with central openings based on experimental results. J. Struct. Eng., ASCE, 139: Mosalam, K.M., White, R.N., and Gergely, P. (1997). Static response of infilled frames using quasi-static experimentation. J. Struct. Eng., ASCE, 123(11): Reese, A. (214). Development of a simplified analytical method to estimate the seismic response of reinforced concrete frames with solid masonry infills, M.S. thesis, Civil Engineering Dept., University of Texas, Arlington, TX. Shing, P.B., and Mehrabi, A.B. (22). Behaviour and analysis of masonry-infilled frames, Prog. Struct. Engng Mater. 4(3), Stavridis, A. (29). Analytical and experimental study of seismic performance of reinforced concrete frames infilled with masonry walls, Ph.D. thesis, Structural Engineering Dept., University of California, San Diego, CA Stavridis, A., and Shing, P.B. (21). Finite element modeling of nonlinear behavior of masonry-infilled RC frames. J. Struct. Eng., ASCE. 136(3):

16 A-1 Appendix A (CU1) SW1 SW2 SWM SW1R SW2R Above: Figure 1A Cracking patterns for CU1 Small Windows at 1% drift with Force distribution plots for at 1% drift Below: Figure 1B: Lateral Force v. Drift curves for Small Windows

17 A-2 RW1 RW2 RWM RW1R RW2R Above: Figure 11A Cracking patterns for CU1 Regular Windows at 1% drift with Force distribution plots for at 1% drift Below: Figure 11B: Lateral Force v. Drift curves for Regular Windows

18 A-3 LW1 LW2 LWM LW1R LW2R Above: Figure 12A Cracking patterns for CU1 Large Windows at 1% drift with Force distribution plots for at 1% drift (LW2R force distribution plot is at.89%) Below: Figure 12B: Lateral Force v. Drift curves for Large Windows

19 A-4 xlw1 xlw2 xlw2 xlw1r xlw2r Above: Figure 13A Cracking patterns for CU1 Extra-Large Windows at 1% drift with Force distribution plots for at 1% drift Below: Figure 13B: Lateral Force v. Drift curves for Extra-Large Windows

20 A-5 Appendix B (CU1M8) SW1 SW2 SWM SW1R SW2R Above: Figure 14A Cracking patterns for CU1M8 Small Windows 1% drift with Force distribution plots for at 1% drift Below: Figure 14B: Lateral Force v. Drift curves for Small Windows

21 A-6 RW1 RW2 RWM RW1R RW2R Above: Figure 15A Cracking patterns for CU1M8 Regular Windows 1% drift with Force distribution plots for at 1% drift Below: Figure 15B: Lateral Force v. Drift curves for Regular Windows

22 A-7 LW1 LW2 LWM LW1R LW2R Above: Figure 16A Cracking patterns for CU1M8 Large Windows 1% drift with Force distribution plots for at 1% drift Below: Figure 16B: Lateral Force v. Drift curves for Large Windows

23 A-8 xlw1* xlw2 xlwm xlw1r xlw2r Above: Figure 17A Cracking patterns for CU1M8 Extra-Large Windows at 1% drift with Force distribution plots for at 1% drift (*xlw1 is at.77% drift- model did not run to 1%) Below: Figure 17B: Lateral Force v. Drift curves for Extra-Large Windows

24 A-9 Appendix C (CU1S) SW1 SW2 SWM SW1R SW2R Above: Figure 18A Cracking patterns for CU1S Small Windows 1% drift with Force distribution plots for at 1% drift Below: Figure 18B: Lateral Force v. Drift curves for Small Windows

25 A-1 RW1 RW2 RWM RW1R RW2R Above: Figure 19A Cracking patterns for CU1S Regular Windows 1% drift with Force distribution plots for at 1% drift Below: Figure 19B: Lateral Force v. Drift curves for Regular Windows

26 A-11 LW1 LW2 LWM LW1R LW2R Above: Figure 2A Cracking patterns for CU1S Large Windows 1% drift with Force distribution plots for at 1% drift Below: Figure 2B: Lateral Force v. Drift curves for Large Windows

27 A-12 xlw1 xlw2 xlwm xlw1r xlw2r Above: Figure 21A Cracking patterns for CU1S Extra-Large Windows 1% drift with Force distribution plots for at 1% drift Below: Figure 21B: Lateral Force v. Drift curves for Extra-Large Windows

28 A-13 Appendix D (All models by Size and Location) 6 5 All Small Windows Force (kn) Force (Kips) CU1-SW-1 CU1-SW-1R CU1-SW-2 CU1-SW-2R CU1-SW-M CU1s-SW-1 CU1s-SW-1R CU1s-SW-2 CU1s-SW-2R CU1s-SW-M M8-SW-1 M8-SW-1R M8-SW-2 M8-SW-2R M8-SW-M Drift (%) All Regular Windows Force (kn) Force (Kips) 2 1 CU1s-RW-1 CU1s-RW-1R CU1s-RW-2 CU1s-RW-2R CU1s-RW-M M8-RW-1 M8-RW-1R M8-RW-2 M8-RW-2R M8-RW-M CU1-RW-1 CU1-RW-1R CU1-RW-2 CU1-RW-2R CU1-RW-M Drift (%) 4 2

29 A All Large Windows 12 1 Force (kn) Force (Kips) CU1s-LW-1 CU1s-LW-1R CU1s-LW-2 CU1s-LW-2R CU1s-LW-M M8-LW-1 M8-LW-1R M8-LW-2 M8-LW-2R M8-LW-M CU1-LW-1 CU1-LW-1R CU1-LW-2 CU1-LW-2R CU1-LW-M Drift (%) All xlarge Windows Force (kn) Force (Kips) CU1-xLW-1 CU1-xLW-1R CU1-xLW-2 CU1-xLW-2R CU1-xLW-M CU1s-xLW-1 CU1s-xLW-1R CU1s-xLW-2 CU1s-xLW-2R CU1s-xLW-M M8-xLW-1 M8-xLW-1R M8-xLW-2 M8-xLW-2R M8-xLW-M Drift (%) 2

30 A Location Force (kn) Force (Kips) M8-SW-1 M8-RW-1 M8-LW-1 M8-xLW-1 CU1-SW-1 CU1-RW-1 CU1-LW-1 CU1-xLW-1 CU1s-SW-1 CU1s-RW-1 CU1s-LW-1 CU1s-xLW Drift (%) Location 1R Force (kn) Force (Kips) 1 CU1s-SW-1R CU1s-RW-1R CU1s-LW-1R CU1s-xLW-1R CU1-SW-1R CU1-RW-1R CU1-LW-1R CU1-xLW-1R M8-SW-1R M8-RW-1R M8-LW-1R M8-xLW-1R Drift (%) 2

31 A Location Force (kn) Force (Kips) 1 CU1s-SW-2 CU1s-RW-2 CU1s-LW-2 CU1s-xLW-2 M8-SW-2 M8-RW-2 M8-LW-2 M8-xLW-2* CU1-SW Drift (%) Location 2R Force (kn) Force (Kips) M8-SW-2R M8-RW-2R M8-LW-2R M8-xLW-2R CU1-SW-2R CU1-RW-2R CU1-LW-2R CU1-xLW-2R CU1s-SW-2R Drift (%) 2

32 A Location M Force (kn) Force (Kips) 1 M8-SW-M M8-RW-M M8-LW-M M8-xLW-M CU1-SW-M CU1-RW-M CU1-LW-M CU1-xLW-M CU1s-SW-M Drift (%) 2