MACRO-MODELING FOR SEISMIC SHEAR STREGNTH OF MASONRY INFILLED REINFORCED CONCRETE FRAMES

Transcription

1 10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska MACRO-MODELING FOR SEISMIC SHEAR STREGNTH OF MASONRY INFILLED REINFORCED CONCRETE FRAMES Shady Gergis 1 and Wael Hassan 2 ABSTRACT Modeling the complex behavior of masonry infilled reinforced concrete frames under seismic excitation has received much attention over the last decade. Many researchers resorted to micro fiber-based finite element modeling. Although many nonlinear micro models are able to a great extent to model the behavior, the required computational effort offsets the advantage of using these models. In addition, many practicing engineers will refrain from using a detailed fiberbased micro-model due to the involved complexity in modeling and due to its high computing demands. This motivated many researchers to suggest simplified macro-models that rely on a single or multi-elements. However, most of the available models attempted to capture the global behavior of a single series of tests without giving due attention to the primary mode of failure. A few researchers attempted to develop global macro-models that are claimed to capture many modes of failure; however, experimental verification of these models is still uncertain. It is apparent that using a generalized macro-model that can detect all modes of failure and hence properly estimate the seismic capacity of the infill frame for each corresponding failure mode is a very challenging task. The present study presents the first phase of a comprehensive program that aims at assessing the applicability/accuracy of existing nonlinear macro-models in estimating the seismic capacity of masonry infilled RC frames. In this first phase, which is focused on stiff frame condition, the key strength influential parameters will be assessed the accuracy of one strength model for infilled frames will be evaluated against a database of tests. Upon assessment of the available models, recommendations will be made regarding the need for a new failure mode-based strength expression instead of the available generalized models. 1 Research Assistant, American University in Cairo, New Cairo, Egypt 2 Assistant Professor, American University in Cairo, New Cairo, Egypt Gergis SN, Hassan WM. Macro-Modeling for Seismic Shear Strength of Masonry Infilled Reinforced Concrete Frames. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

2 10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska Macro-Modeling for Seismic Shear Strength of Masonry Infilled Reinforced Concrete Frames Shady Gergis 1 and Wael Hassan 2 ABSTRACT Modeling the complex behavior of masonry infilled reinforced concrete frames under seismic excitation has received much attention over the last decade. Many researchers resorted to micro fiber-based finite element modeling. Although many nonlinear micro models are able to a great extent to model the behavior, the required computational effort offsets the advantage of using these models. In addition, many practicing engineers will refrain from using a detailed fiber-based micro-model due to the involved complexity in modeling and due to its high computing demands. This motivated many researchers to suggest simplified macro-models that rely on a single or multi-elements. However, most of the available models attempted to capture the global behavior of a single series of tests without giving due attention to the primary mode of failure. A few researchers attempted to develop global macro-models that are claimed to capture many modes of failure; however, experimental verification of these models is still uncertain. It is apparent that using a generalized macro-model that can detect all modes of failure and hence properly estimate the seismic capacity of the infill frame for each corresponding failure mode is a very challenging task. The present study presents the first phase of a comprehensive program that aims at assessing the applicability/accuracy of existing nonlinear macro-models in estimating the seismic capacity of masonry infilled RC frames. In this first phase, which is focused on stiff frame condition, the key strength influential parameters will be assessed the accuracy of one strength model for infilled frames will be evaluated against a database of tests. Upon assessment of the available models, recommendations will be made regarding the need for a new failure mode-based strength expression instead of the available generalized models. Introduction Infilling steel or reinforced concrete frames with unreinforced masonry is one of the most common types of construction in different parts of the world, especially the Middle East. In the common practice, structural engineers usually overlook the effect of masonry infills on stiffness and strength on the frames they design. In non-seismic areas of the world, this overlooking is accepted due to few reasons. A main reason is the probable change of the arrangement of partitioning masonry wall during the lifespan of the structure, which could not be accounted for during the design process. In addition, engineers should not depend on masonry infills carrying capacity for gravity loads. Otherwise, skeletal structures would be classified as wall-bearing 1 Research Assistant, American University in Cairo, New Cairo, Egypt 2 Assistant Professor, American University in Cairo, New Cairo, Egypt Gergis SN, Hassan WM. Macro-Modeling for Seismic Shear Strength of Masonry Infilled Reinforced Concrete Frames. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

3 structures, too. In seismic-prone regions, neglecting the lateral resisting capacity of masonry infills is quite detrimental (Asteris et al., 2011). For the past five or six decades, researchers tried different approaches to define the strength and the stiffness of unreinforced masonry infilled frames under lateral loads, including Finite Element (FE) fiber-modeling, macro-modeling, empirical equation formulation, and analytical expression formulation. The use of a single strut to model the contribution of the infill to the strength and stiffness of the frame was widely investigated since the 1970 s until early 2000 s. In recent years, developing finite element fibermodels is adopted mostly for its accuracy. Developing empirical expressions is still common to define peak strength or cracking strength of infilled frames. This paper is a part of a more comprehensive research program aiming at developing a better understanding of failure modes and the effect of the influential parameters on strength and ductility of stiff masonry infilled RC frames. It is intended to evaluate the accuracy of the available strength models assessing strength of infilled RC frames. Developing a shear strength expression is pending the findings of evaluating existing models. Failure Modes Five failure modes are identified based on the experimental work (Liauw and Kwan 1985; Mehrabi and Shing, 1997, Al-Chaar et al., 2002) as well as analytical results (Wood 1978). 1. Corner Crushing (CC): It is described as crushing of masonry at one or more of the corners of the infill. The crushing may take place at other parts of the infill other than the corners (Flanagan and Bennett, 2001). It is observed in infilled frames that has weak masonry units (Asteris et al., 2011) It is followed by plasticization at the joints or the members of the frame (Liauw and Kwan 1985) 2. Diagonal Compression (DC): It is described as crushing of masonry due to excessive compression in a form of out-of-plane buckling of the infill. This mode is mostly observed in slender infills. 3. Sliding Shear (SS): It is described as a shear failure in the masonry bed joint connections. It is usually observed as a horizontal slip across bed joints. It observed in infills with weak mortar joints. It is common in RC frames more than in steel frames (Flanagan and Bennett, 2001) 4. Diagonal Cracking (DK): It is described as a crack a cross the compressed part of the infill in form of a stepladder across the bed joints of the infill. It is considered as another form of Sliding Shear failure due to the concurrency of (SS) failure mode initiation with it. Flanagan and Bennett (2001) considers it as a serviceability limit state as the infills continues to carry more loads if the Diagonal Cracking (DK) strength is greater than the Corner Crushing (CC) strength. 5. Frame Failure (FF): It is described as forming of plastic hinges in columns or frame connections. It is related to a weak frame in general. The classification of the occurrence of the different failure modes based on the relative lateral load carrying capacities of the frame and the infill is quite inaccurate. A modern wellengineered frame can be considered as a strong/stiff frame, regardless of being designed for seismic loads or not. In general, the maximum load carrying capacity is achieved as cracks develop only in the infill panel while the bounding frame is still intact. This assumption eliminates the fifth failure mode (FF) which is not a part of this research program. It is mainly a

4 problem of existing structures, which may need to be retrofitted, not modern structures that are still in the design process (Asteris et al., 2011). The fourth failure mode (DK) is hard to distinguish from the third failure mode (SS) considering that they usually occur together. They can allow us to consider both due to shear failure mechanism of the mortar joints, which should be quantified by one strength expression. Based on the experimental work done by Mehrabi et al. (1996), the diagonal/sliding shear failure actually caused the infilled frames to lose their load carrying capacity even before crushing took place. The diagonal/sliding shear crack corresponded to the maximum lateral loads while crushing took place later during the strength degradation stage of the specimen. The second failure mode (DC) is not important due to the low possibility of having a slender infill (El-Dakhakhni et al., 2003) It is worth mentioning that the in-plane out-of-plane interaction in cases of loading in both directions is important to consider and it requires complicated strut and tie (SAT) models. Eliminating two failure modes and combining another two leaves two important failure modes: Corner Crushing (CC) and Diagonal/Sliding Shear (SS) Analytical and Empirical Equations Existing Analytical Models The early approaches of developing an understanding of the failure modes were based on the plastic theory of unreinforced shear panels subjected to lateral loads. Wood (1978) managed to formulate an equation that takes into account the relative strength of the infill and the bounding frame by calculating the parameter m as follows where M p is the smaller of the plastic moment capacity of the column or the beam of one joint, f m ' is the prism compressive strength of the masonry infill, t w is the thickness of the infill, and L w is the length of the infill panel. If m is less than unity, failure modes 1, 2, 4, 5 are expected to occur while if m is greater than unity, failure mode 3 is expected to occur (Ghosh and Amde, 2002). Based on the previous discussion on failure modes, possibilities of parameter m are reduced to two: corner crushing (CC) failure mode for m less than one, and sliding shear (SS) failure mode for m greater than one. Most of the analytical equations developed to calculate the infill s peak strength are based on the plastic collapse theory or a single strut analogy are mostly developed for the corner crushing (CC) failure mode (Flanagan and Bennett, 1999). Some of the analytical expressions consider the relative strength parameter m from Eq. 1 as one of the influential parameters. Most if not all of existing empirical equations are mainly developed to predict the (CC) failure mode strength. An important expression was used a part of FEMA 273 (FEMA 1997). It considered the bed joint shear strength not the prism strength of the infill. The net collapse load of the infill was defined as (1)

5 (2) ( ) (3), where A n is the bed joint net area of the infill panel, f ve is the expected shear strength of the infill panel, v te is the average bed joint shear strength, and P CE is the vertical compressive force on the wall. Finite Element Fiber-Models The deficiency of the small spectrum of applicability of analytical equations to other failure modes rather than (CC) failure mode led researchers to develop micro-fiber finite element models to include all of the influential parameters in one model to verify analytical and empirical equations (Gosh and Amde, 2002). These models cannot be used in the everyday engineering practice by structural engineers because of their high computational cost and the modeling complexity. Finite Element Macro-Models Macro models developed to simulate the stiffness and the strength of infilled frames varied from single strut models, with width w given by empirical and semi-empirical equations, to multi-strut models (Asteris et al., 2011). Single strut models fail to capture the effect of the panel on the bending moment and shear force profile of the bounding frame (Crisafulli and Carr, 2007). Crisaulli (1997) developed a model with two struts and a shear spring that takes the shear behavior of the infill into account. The two struts are connected to the corners and to the columns, so they simulate the behavior effect of the infill panel on the joints as well as the columns as in Fig. 1. Figure 1. Two Strut Model with a Shear Spring (Crisafulli, 2007). El-Dakhakhni (2002) proposed a three-strut model to simulate the (CC) failure mode in which the outer struts are spaced from the joints along the axes of the beam and the column at distances α b l and α c h, respectively as in Fig. 2. α b l and α c h were originally defined as contact lengths of the panel with beam and the column, respectively (Saneinejad and Hobbs, 1995). It is worth mentioning that most of the developed macro-models simulate only the (CC) failure mode with an acceptable accuracy.

6 Criteria for selection: Figure 2. Three Strut Model (El-Dkhakhni, 2002). Experimental Database The Experimental work investigated in this research included specimens with many variations considering frame materials (steel and RC), masonry unit materials (common clay bricks, vitrified ceramic bricks, autoclaved aerated concrete blocks, and concrete blocks), and brick types (solid and hollow). It also considered the infill panel type (with and without openings), loading protocol (monotonic, cyclic, pseudo-dynamic, and dynamic), loading direction (in plane only, and in both direction), and condition (virgin, and repaired). The investigated programs are more than 15 test campaigns. It was necessary to develop criteria to choose a coherent set of specimens that have a narrower range of influential parameters to guarantee the accuracy of evaluating the models. Therefore, all of the specimens used in this study can be described as stiff virgin RC frames infilled with no openings and tested quasi-statically. The specimen used are from the test programs done by Mehrabi et al. (1996), Kakaletsis and Karayannis (2008), and Zovkic et al. (2012). Main design parameters are summarized in Table 1. Geometric Parameters are calculated as in Fig. 3. Main results of the test specimens are presented in Table 2. Figure 3. Geometric Parameters (Asteris et al., 2011)

7 Table 1. Experimental Database: Specimen Main Design Parameters Investigator Specimen H w (mm) L w (mm) Aspect Ratio (H w /L w ) Infill Material fm' (MPa) fc' (MPa) Column Dimensions (mm X mm) Beam Dimensions (mm X mm) Infill Thickness, t w (mm) A net / A gross A net /m (mm 2 /m) Zovkic et al., 2012 Kakaletsis and Karayannis, 2008 Mehrabi et al., 1996 MODEL Perforated Clay Blocks X X MODEL Perforated Clay Blocks X X MODEL Bare Frame X X S Common Clay Bricks X X IS Vitrified Ceramic Bricks X X B Bare Frame X X Concrete Hollow Units X X Concrete Solid Units X X Concrete Hollow Units X X Concrete Solid Units X X Concrete Hollow Units X X Concrete Solid Units X X Bare Frame X X

8 It is worth mentioning that net area of masonry is calculated by excluding the area of holes/cores of masonry units. If the A net /A gross ratio is greater than 0.75, A net is used equal to A gross. While if the A net /A gross ratio is less than 0.75, A net is used as it is. This classification complies with the suggestion made by Aryana (2006). Table 2. Experimental Database: Key results summary. Investigator Zovkic et al., 2012 Kakaletsis and Karayannis, 2008 Mehrabi et al., 1996 Test Type V peak (kn) Drift (%) Primary Mode of Failure of Infill Panel Relative Strength Parameter (m) Cyclic % Diagonal/Sliding Shear 0.45 Cyclic % Diagonal/Sliding Shear 0.20 Cyclic % N/A N/A Cyclic % Diagonal/Sliding Shear 0.38 Cyclic % Diagonal/Sliding Shear 0.10 Cyclic % N/A N/A Cyclic % Diagonal/Sliding Shear 0.15 Cyclic % Diagonal/Sliding Shear 0.04 Cyclic % Diagonal/Sliding Shear 0.15 Cyclic % Diagonal/Sliding Shear 0.04 Cyclic % Diagonal/Sliding Shear 0.08 Cyclic % Diagonal/Sliding Shear 0.02 Monotonic % N/A N/A Frame Stiffness Effect on Sliding Shear Strength The observed trend of specimens of the same test or under the effect of a certain parameter suggests that the sliding shear strength of masonry infilled RC frames is inversely proportional to the corresponding drifts. In other words, stiffer frames achieve higher strength at lower drifts while flexible frames achieve lower strength at lower drifts. The same applies when comparing identical frames with different strengths of masonry panels; the frame with stronger masonry achieves higher strengths at lower drifts. These results are particularly clear in the test series of Mehrabi et al. [2] Effect of Infill Panel Aspect Ratio The effect of panel aspect ratio on the sliding shear strength of infilled frames can be deduced from observing the triangular symbols of Mehrabi et al. s [2] specimen in Fig. 4. The small triangle represents a specimen of aspect ratio 0.48, and the large triangle represents a specimens. When comparing two specimens (No. 4 and No. 10) of the same masonry unit type (green), it is found that squatter specimens achieve higher strength at higher drifts. This observation could be reasoned for higher capacity of the strut due to the shallow inclination angle. The orange colored squares specimens (No. 5 and No. 11) (Solid Units) should have had the same trend the green ones had except that shear cracks developed at one of the columns before reaching maximum

9 0.0% 0.2% 0.4% 0.6% 0.8% 1.0% 1.2% 1.4% Normalized Shear Strength (MPa 0.5 ) lateral load on the envelope curve of this specimen (No. 5). Therefore, the highest load and its corresponding drift before frame cracking was considered instead of the maximum load. In summary, increasing the panel aspect ratio decreased its sliding shear/diagonal cracking shear strength. Evaluation of Relative Strength Parameter Expression The relative strength parameter m from Wood (1978) of all specimens in the experimental database is less than unity as in Table. 2. As discussed previously, when m is less than unity, the diagonal cracking (DK) and corner crushing (CC) are expected to occur. The calculated values of m indicate the same as the observed primary modes of failure. However, the diagonal cracking (DK) was followed by a sliding shear failure (SS) in all specimens that was expected to have a value of m greater than unity. This discrepancy can be reasoned for the order of occurrence of failure modes rather than the ultimate or primary failure mode of the panel. In other words, when m is greater than unity, sliding shear (SS) should occur first without a need for occurrence of diagonal cracking (DK) to initiate it. Zovkic et al. Kakaletsis and Karayannis Mehrabi et al.- Hollow Units Mehrabi et al.- Solid Units Drift (%) Figure 4. Experimental Database: Normalized Shear Strength. Evaluation of Analytical Model to Estimate Sliding Shear Strength Flanagan and Bennett (1999) proposed a single strut model to estimate the ultimate strength of masonry infilled steel frames. The extended its application to concrete frames later (Flanagan and Bennett 2001). The model estimates a strut area A as in Eq. 5 based on the strut area modulus l defined by Staffor-Smith and Carter 1969 as in Eq. 4. The model is claimed to

10 Analytical Lateral Load (kn) estimate the strength of any failure by changing empirical factor C that is based on the displacement. (4), where E m is the modulus of elasticity of the infill, EI is the flexural rigidity of the columns, and is the angle of inclination of the diagonal of the panel with the horizontal. (Flanagan and Bennett, 2001). In Fig. 5, it can be observed that all specimens except one indicate that the experimental values of the sliding shear strength of the specimens is higher than the analytically estimated strength. This could be considered as a conservative model. In average, the model estimates the sliding shear strength by about one-half of the experimental value. (5) Zovkic et al. Mehrabi et al. Kakaletsis and Karayannis Experimental Lateral Load (kn) Figure 5. Analytical model evaluation Conclusion The main influential parameters on the seismic shear strength of the strong frame-weak infill scenario were identified. These include infill panel aspect ratio, panel material strength and frame relative stiffness. In the case of strong frame-weak panel, the maximum lateral load that masonry infilled stiff RC frames can resist is governed by the infill panel sliding shear strength/diagonal cracking strength. The aspect ratio of the panel significantly affects the shear strength. A squatter panel achieves higher strength. A stiffer frame or a stronger infill achieves higher strength at lower drift. The infilled RC frame research literature still lacks an accurate relative strength parameter since the available m does not indicate the primary failure mode, but

11 indicates the first failure mode to occur. A single strut model for shear strength estimation was evaluated to underestimate the sliding shear strength of infilled frames by approximately 50% for the case of strong frame-weak infill. This indicates the need for a specific shear strength model for that case that focuses primarily on the SS and DK failure modes rather than the CC failure mode. This model is intended to be developed through the remainder of the current research program. References 1. El-Dakhakhni, W. W. (2002). Experimental and analytical seismic evaluation of concrete masonry-infilled steel frames retrofitted using GFRP laminates. Ph.D. thesis, Drexel Univ., Philadelphia 2. El-Dakhakhni, W. W., Elgaaly, M., and Hamid, A. A. (2003). Three-strut model for concrete masonryinfilled frames. J. Struct. Eng., 129(2), Flanagan, R. D., and Bennett, R. M. (1999). In-plane behavior of structural clay tile infilled frames. J. Struct. Engrg., ASCE, 125(6), Ghosh, A. and Amde, A. (2002). Finite Element Analysis of Infilled Frames. J. Struct. Eng., 128(7), Kakaletsis, D. J. Karayannis C. G. (2008): Influence of Masonry Strength and Openings on Infilled R/C Frames Under Cycling Loading, Journal of Earthquake Engineering, 12:2, Mehrabi, A. B., Shing, P. B., Schuller, M., and Noland, J. (1996). Experimental evaluation of masonryinfilled RC frames. J. Struct. Engrg., ASCE, 122(3), Smith, B. S., and Carter, C. (1969). A method of analysis for infilled frames. ICE Proc., 44(1), Wood, R. H. (1978). Plasticity, composite action and collapse design of unreinforced shear wall panels in frames. Proc., Instn. Civ. Engrs., Part 2, 65, Zovkic, J., Sigmund, V. and Guljas, I. (2013), Cyclic testing of a single bay reinforced concrete frames with various types of masonry infill. Earthquake Engng. Struct. Dyn., 42: