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STUDY OF MACRO MODELS UNDER SEISMIC PERFORMANCE OF MASONRY INFILLED RC FRAMES
Manoj, S.B, Post-Graduate Scholar, S.J.C.E., Mysore, E-mail: [email protected] Raghavendra Prasad, Research Scholar, S.J.C.E., Mysore, Email :[email protected] Chandradhara, G.P, Professor, S.J.C.E., Mysore, E-mail:[email protected]
ABSTRACT Reinforce concrete frames are infilled by brick or concrete-block masonry walls. For decades now, these infill walls were not taken into account when designing the bearing structures. However, extensive experimental and analytical investigations have shown that there is a strong interaction between the infill masonry wall and the surrounding frame, leading to considerable increase of the overall stiffness. It is well known that the presence of infill walls in reinforced concrete structures can decisively influence the structural behavior to seismic loads. The influence of infill on frame members is studied by several authors and developed various models to understand the behavior and they are grouped in to two main categories: macro-models, based on the equivalent strut method, and micro-models, based on the finite element method. The primary objective of this paper is to present a general review of the different macro models used for the analysis of infilled frames and based on the results a simplified model shall be proposed from the Indian perspective. Also, the present study aims at providing a contribution for the simplified analysis and design procedure for the infilled frames, based on the numerical parametric study. For this purpose, ETABS, a finite element software has been used and the comparison between the performances of masonry infill frames is made using different macro models. Axial force in column and beam, the roof displacement are obtained to identify the seismic performances of infilled frames. The study also focuses on the effects of number of storeys on the overall performance of masonry infill frames against earthquake force. It was inferred that the effect of provision of infill is to strengthen the frames against lateral dynamic load and the effects are more pronounced in taller structures.
Key words: Infilled frames; Masonry; Macro models; ETABS; 2D RC frame; seismic strengthening
1.0 INTRODUCTION A large number of Reinforced concrete buildings containing unreinforced masonry infill walls are commonly used in structural system around the world. Masonry infills are often used to fill the void between the vertical and horizontal resisting elements of the building frames with the assumption that these infills will not take part in resisting any kind of load either axial or lateral load, hence its significance in the analysis of frame is generally neglected. Many buildings of this type have performed poorly during earthquakes. The presence of infill changes the lateral load transfer mechanism of the framed structure from predominant frame action to predominant truss actions as shown in fig.1. This presence of infill changes the behavior of the frame and is responsible for huge reduction in bending moments and slight increase in axial forces in the frame members. The presence of infill also increases damping of the structures due to the propagation of cracks with increasing lateral drift. However, behavior of masonry infill is difficult to predict because of significant variations in material properties and failure modes that are brittle in nature. If not judiciously placed, during seismic excitation, the infills also have some adverse effects. This is due to absence of infill wall in a particular storey. The absence of infill in some portion of an irregularly planned building will induce torsion moment. Also, the partially infilled wall, if not properly placed may induce short column effect or captive column effect creating localized stress concentration.
Fig 1 Change in lateral-load transfer mechanism due to masonry infills (Murty and Jain - 2000)
Moreover in seismic areas, ignoring the frame-infill panel interaction is not always safe, because under lateral loads the infill walls dramatically increase the stiffness by acting as a diagonal strut, resulting in a possible change of the seismic demand because of significant reduction in the natural period of the composite structural system. Non availability of realistic and simple analytical models of infill becomes another hurdle for its consideration in analysis. In fact it has been recognized that frames with infill have more strength and rigidity in comparison to the
bared frames and their ignorance has become the cause of failure of many the multi storied buildings. The recent example in this category is report that RC frames with unreinforced masonry infill are currently being built in India in violation of the building codes, and that they performed poorly during the 2001 January, 26 Bhuj earthquake. The main reason of the failure is the stiffening effect of infilled frame that changes the basic behavior of buildings during earthquake and creates new failure mechanism. The 2008 earthquake in Wenchuan, China, provides numerous examples of frame wall interaction (Li et al. 2008); see Figs. 1.1.
Fig-1.1 Damages of masonry infilled RC frames after the Wenchuan earthquake (Bixiong, Li et al.(2008)
2.0 MODELING OF INFILL FRAME Model development of any structures is crucial to achieve accurate output results. However, it is difficult to model the as-built structures due to numerous constraints with as it is difficult to incorporate all physical parameters associated with the behavior of an infilled frame structure. Even if all the physical parameters, such as contact coefficient between the frame and infill, separation and slipping between the two components and the orthotropic of material properties are considered, there is no guarantee that the real structure behaves similar to the model as they also the structural behavior could also depend on the quality of material and construction techniques. However, to simulate the structural behavior of infilled frames, two methods have been developed such as Micro model and Macro model. The Micro model method is a Finite Element Method (FEM) where the frames elements, masonry work, contact surface, slipping and separation are modeled to achieve the results.
This method has seems to be generating the better results but it has not gained popularity due to its cumbersome nature of analysis and computation cost. The Macro models which is also called a Simplified model or Equivalent diagonal strut method was developed to study the global response of the infilled frames. This method uses one or more struts to represent the infill wall. The drawback of it is to the lack of its capability to consider the opening precisely as found in the infill wall. 2.1 MICRO –MODELS Micro models are represented by using Finite Element Method (FEM). The finite element method is the most popular analysis tool for complex structural engineering problems. Since the pioneer work of Mallick and Severn (1967), several difficulties were evident from the simulations, namely the issues of modeling the separation between frame and panel, of the bond strength and friction of the connection between frame and panel, and of the mechanical constitutive behavior of masonry itself. Riddington and Stafford-Smith (1977) found that the critical stresses for the masonry panel are located in the centre and are mostly associated with tensile and shear failure. In this case, the frame-panel interaction was modeled by using double nodes and normal springs at the interfaces, with contact/separation modeled in a simplified way. King and Pandey (1978) further extended the numerical representation by adding interface elements capable of taking into account contact and friction for the frame-panel interaction. This work was further extended with non-linear behavior of the panel and frame, by Liauw and Kwan (1982) and Dhanasekar and Page (1986) in the framework of continuum modeling, and by Mehrabi and Shing (1997) in the framework of discontinuous modeling. The benefit of using finite element approach is to study in detail all possible modes of failure but its use is limited due to the greater computational effort and time required in analysis & modelling.
2.2 MACRO-MODELS In order to overcome the complexity and computational requirement using micro-models, research has been done to simplify the modelling of infill panel with a single element. The main idea has been to study the global effects of infill panel on structures under lateral loads. Since first attempts from Polyakov (1956), analytical and experimental tests have shown that a diagonal strut with appropriate mechanical properties can provide a solution to the problem.
Several authors have modified the characteristics of single strut model with multi strut configuration to better understand the effect of micro-cracking in the corner of the infill panel due to tensile stresses and higher shear strength of the infill panel relative to the frame. A brief review of few models has been presented. Based on elastic studies Polyakov (1956) conducted one of the first analytical studies on infilled frames. He considered the effect of infill in each panel as equivalent to diagonal bracing. Holmes (1961) took the idea and suggested that infill panel can be replaced by an equivalent pin-jointed diagonal strut. He proposed that the diagonal strut to have the same material and thickness as the infill panel. The width of strut was taken equal to one third of the strut length (2.1) Stafford (1966) performed a series of test on square steel infilled frames. He observed that contact length between the wall and frame is related to the width of the strut. From the experimental result he proposed the following relation for finding the contact length between the wall and infill frame. √ (2.2) .
(2.3) Where is the non dimensional parameter known as relative stiffness between the reinforced and are the elastic modulus and thickness of the and α represents the
concrete frame and the infill wall. masonry wall and and
are the elastic modulus and moment of inertia of the bounding
concrete frame members. Height of the masonry infill is represented by contact length.
Paulay & Priestley (1992) took a conservatively high value for the width of equivalent strut. According to them, a high value of them is as follows: will result in a stiffer structure. The relation given by
(2.4)
Mainstone (1971) relates the width w of equivalent strut to parameter h, given by equation (2.2) and diagonal length d as shown in the equation (2.5). (2.5) The proposed macro models and respective equivalent diagonal strut width equations for masonry infill by various researchers is tabulated in table 2.1
Table.2.1 Equations for strut width value for full infill by various researchers Researchers Strut width(w) Remark
Holmes[4]
0.333 dm 0.175 D ( 1 H)- 0.4 0.95 hm Cos θ/√( hm)
dm is the length of diagonal 1 H = H[EmtSin2θ/4 Ec Ic
Mainstone[6
hm]1/4 = Em t Sin 2 θ/ 4 Ec Ic
Liauw and Kwan[7]
hm]1/4
Paulay and Priestley[8]
0.25 dm 0.5[αh + αL]1/2
dm is the length of diagonal αh = π/2[EcIchm/2 Emtsin2θ]1/4 and αL = π[EcIbL/ 2 Emtsin2θ]1/4 = Emt Sin 2 θ/ 4 EcIchm]1/4 is the length of diagonal
Hendry[9]
Decanini & Fantin (1986)
Durrani & Luo (1994)
√
3.0 METHODOLOGY In the present study reinforced concrete members and masonry infill members are modelled using ETABS 9.6 software. It is powerful finite element software developed by Computers & Structures Inc., which can greatly enhance a designer’s analysis & design capabilities for structures. etabs
4.0 MODEL DESCRIPTION Three models have been selected and compare the results with different proposed macro models. Experiments are very important to observe the behavior of complex structures. Many a times, analytical models have been developed on the basis of experimental results, and sometimes, experimental studies have been carried out to verify the analytically developed model. The proposed analytical model is initially compared with the experimental results of Chiou, Y. J., et al., (1999). They have conducted a full scale test to study the behavior of one bay one storey framed masonry walls. The infill panel size of the specimen tested is 2.4m x 2.3m. The cross sections of the beam and column elements are 0.35m x 0.40m and 0.3m x 0.35m respectively. The thickness of the masonry wall is 0.2m and the elastic modulus of concrete & masonry are 2.4247 x 107 kN/m2 and 2.087 x 106 kN/m2 respectively. The monotonic loading is adopted in this study (Fig.4.1).
The main output of the experimental investigation was a load versus displacement curve for solid frame. The results from the experimental investigation are used to compare the results of finite element model. Fig.4.2 presents lateral force and the corresponding lateral displacement at the top of the leeward column for the proposed macro models. A good agreement is observed especially at lower loads. Considering this fact, a finite element method is chosen for the present work in order to understand the behavior of infilled frames.
Fig 4.1 Analytical model
Fig 4.2 Macro model using ETABS
The proposed analytical model is initially compared with the analytical results of P. G.
Asteris, M.ASCE1.They have conducted a analytical model (fig 4.3) to study the behavior of
one bay one storey framed masonry walls. The infill panel size of the specimen tested is 3.6m x 3.8m. The cross sections of the beam and column elements are 0.40m x 0.40m and 0.3m x 0.40m respectively. The thickness of the masonry wall is 0.1m and the elastic modulus of concrete & masonry are 2.9 x 107 kN/m2 and 4.5 x 106 kN/m2 respectively. The proposed macro models at 1,2 nd 3 stories are represented in fig(4.4,4.5,4.6).
Fig 4.3 Analytical model
Fig 4.4 Macro model at one story using ETABS
Fig 4.5 Macro model at Two story using ETABS
Fig 4.6 Macro model at Three story using ETABS
The proposed analytical model is initially compared with the analytical results of P. G. Asteris, M.ASCE1.They have conducted a analytical model to study the behavior of one bay one storey framed masonry walls. The infill panel size of the specimen tested is 4.0 x 4.0m. The cross sections of the beam and column elements are 0.30m x 0.30m and 0.3m x 0.30m respectively.
The thickness of the masonry wall is 0.1m and the elastic modulus of concrete & masonry are 2.2 x 107 kN/m2 and 7.5 x 106 kN/m2 respectively. The proposed macro model is shown in fig 4.7.
Fig 4.7 Macro model using ETABS 5.0 RESULTS AND DISCUSSION Comparison of lateral displacement of various macro models with the experimental and analytical micro models is shown in table 5.1
Table 5.1: Comparision of Lateral displacement
Technical papers Load kN EXPT Micro model Analytical Micro model M1
ASTERIES (1990) YAW-JENG CHOW (1999) ASTERIES (2003)
At one story
Lateral displacement of Macro Models (mm)
M2
0.828 (1.88) 1.08
M3
2.24 (0.56) 1.915
M4
1.04 (1.41) 1.3
M5
1.22 (1.16) 1.40
M6
0.496 (3.815) 0.624
M7
1.262 (1.12) 0.769
1.71 85 0.7 (0.78) 1.137 100 1.8 (1.03)
(1.08)
(0.39)
(0.83)
(0.73)
(2.44)
(1.83)
(1.21)
(1.74)
(0.55)
(1.31)
(1.29)
(4.84)
(1.28)
30
At Two story
-
0.5
0.481
0.364
0.835
0.453
0.164
0.164
0.46
30
At Three story
-
1.28
1.16
0.91
1.97
1.10
1.11
0.494
1.12
30
-
2.3
2.127
1.736
3.4
2.03
2.05
1.099
2.059
NOTE:-The equivalent width of the diagonal strut for various macro models is shown in the bracket (-). The proposed macro models by various researchers and load Vs displacement curves is shown below-
Hendry[9] Holmes[4] Mainstone[6] Paulay and Priestley[8] Liauw and Kwan[7] Decanini & Fantin (1986) Durrani & Luo (1994)
M1 M2 M3 M4 M5 M6 M7
90 80 70 60
load (Kn)
M2 MIC M1 M3 M4 M7 M6 M5
50 40 30 20 10 0 0 1 2
displacement (mm)
Fig.5.1:comparision of lateral deflection of macro models and analytical model for solid infill
M3 EXPT M1 M2 M4 M5 M6 M7
700
600
500
load (Kn)
400
300
200
100 0 2 4 6 8 10 12 14 16 18 20
displacement (mm)
Fig.5.2:comparision of lateral deflection of macro models and experimental model for solid infill
3.0
2.5
2.0
@3 story @2 story @1 story Analytical
story
1.5
1.0
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
displacement (mm)
Fig.5.3:comparision of lateral deflection of macro models and analytical model at various stories
6.0. CONCLUSIONS
The primary objective of this paper is to present a general review of the different macro models used for the analysis of infilled frames. The macro models that can be used in everyday engineering are of practical importance. The simpler ones are the equivalent-strut models, which represent infills with a diagonal strut element. The basic parameter of these struts is their equivalent width, which affects their stiffness and strength. Several formulas have been proposed by researchers to calculate this equivalent width. In all the cases, there are considerable differences among the values obtained. The comparative study of different expressions for calculating the diagonal strut width reveals the Paulay and Priestley equation as the most suitable choice, due to its simplicity and because it gives an approximate average value (among those studied). In the analysis involving analytical models for masonry infills in a single-storey, single-bay reinforced concrete frame, the singlestrut model was found to be predicting the global behavior of the system with reasonable accuracy.
7.0 REFERENCES 1. Asteris P.G., (2003), “Lateral stiffness of brick masonry infilled plane frames”, Journal of the Structural Engineering, ASCE, pp. 1071-1079 2. Chiou, Y. J., Tzeng, J. C., and Liou, Y. W., (1999), “Experimental and analytical study of masonry infilled frames”, Journal of Structural Engineering, Vol. 125, No. 10, pp. 1109–1117 3. Asteris P.G., (1996), “Analytical investigation of infill wall influence on the aseismic behaviour of plane frame”, diploma thesis(Supervisor C.A Syrmakezis)”, National Technical University of Athens,(in greek) 4. Diana M. Samoilă*1., “Analytical Modelling of Masonry Infills”1 Technical University of Cluj-Napoca, Faculty of Civil Engineering. 15 C Daicoviciu Str., 400020, ClujNapoca, Romania 5. Prachand Man Pradhan., “Equivalent Strut Width for Partial Infilled Frames”, Department of Civil and Geomatics Engineering, Kathmandu University, Dhulikhel, Nepal
Manoj, S.B, Post-Graduate Scholar, S.J.C.E., Mysore, E-mail: [email protected] Raghavendra Prasad, Research Scholar, S.J.C.E., Mysore, Email :[email protected] Chandradhara, G.P, Professor, S.J.C.E., Mysore, E-mail:[email protected]
ABSTRACT Reinforce concrete frames are infilled by brick or concrete-block masonry walls. For decades now, these infill walls were not taken into account when designing the bearing structures. However, extensive experimental and analytical investigations have shown that there is a strong interaction between the infill masonry wall and the surrounding frame, leading to considerable increase of the overall stiffness. It is well known that the presence of infill walls in reinforced concrete structures can decisively influence the structural behavior to seismic loads. The influence of infill on frame members is studied by several authors and developed various models to understand the behavior and they are grouped in to two main categories: macro-models, based on the equivalent strut method, and micro-models, based on the finite element method. The primary objective of this paper is to present a general review of the different macro models used for the analysis of infilled frames and based on the results a simplified model shall be proposed from the Indian perspective. Also, the present study aims at providing a contribution for the simplified analysis and design procedure for the infilled frames, based on the numerical parametric study. For this purpose, ETABS, a finite element software has been used and the comparison between the performances of masonry infill frames is made using different macro models. Axial force in column and beam, the roof displacement are obtained to identify the seismic performances of infilled frames. The study also focuses on the effects of number of storeys on the overall performance of masonry infill frames against earthquake force. It was inferred that the effect of provision of infill is to strengthen the frames against lateral dynamic load and the effects are more pronounced in taller structures.
Key words: Infilled frames; Masonry; Macro models; ETABS; 2D RC frame; seismic strengthening
1.0 INTRODUCTION A large number of Reinforced concrete buildings containing unreinforced masonry infill walls are commonly used in structural system around the world. Masonry infills are often used to fill the void between the vertical and horizontal resisting elements of the building frames with the assumption that these infills will not take part in resisting any kind of load either axial or lateral load, hence its significance in the analysis of frame is generally neglected. Many buildings of this type have performed poorly during earthquakes. The presence of infill changes the lateral load transfer mechanism of the framed structure from predominant frame action to predominant truss actions as shown in fig.1. This presence of infill changes the behavior of the frame and is responsible for huge reduction in bending moments and slight increase in axial forces in the frame members. The presence of infill also increases damping of the structures due to the propagation of cracks with increasing lateral drift. However, behavior of masonry infill is difficult to predict because of significant variations in material properties and failure modes that are brittle in nature. If not judiciously placed, during seismic excitation, the infills also have some adverse effects. This is due to absence of infill wall in a particular storey. The absence of infill in some portion of an irregularly planned building will induce torsion moment. Also, the partially infilled wall, if not properly placed may induce short column effect or captive column effect creating localized stress concentration.
Fig 1 Change in lateral-load transfer mechanism due to masonry infills (Murty and Jain - 2000)
Moreover in seismic areas, ignoring the frame-infill panel interaction is not always safe, because under lateral loads the infill walls dramatically increase the stiffness by acting as a diagonal strut, resulting in a possible change of the seismic demand because of significant reduction in the natural period of the composite structural system. Non availability of realistic and simple analytical models of infill becomes another hurdle for its consideration in analysis. In fact it has been recognized that frames with infill have more strength and rigidity in comparison to the
bared frames and their ignorance has become the cause of failure of many the multi storied buildings. The recent example in this category is report that RC frames with unreinforced masonry infill are currently being built in India in violation of the building codes, and that they performed poorly during the 2001 January, 26 Bhuj earthquake. The main reason of the failure is the stiffening effect of infilled frame that changes the basic behavior of buildings during earthquake and creates new failure mechanism. The 2008 earthquake in Wenchuan, China, provides numerous examples of frame wall interaction (Li et al. 2008); see Figs. 1.1.
Fig-1.1 Damages of masonry infilled RC frames after the Wenchuan earthquake (Bixiong, Li et al.(2008)
2.0 MODELING OF INFILL FRAME Model development of any structures is crucial to achieve accurate output results. However, it is difficult to model the as-built structures due to numerous constraints with as it is difficult to incorporate all physical parameters associated with the behavior of an infilled frame structure. Even if all the physical parameters, such as contact coefficient between the frame and infill, separation and slipping between the two components and the orthotropic of material properties are considered, there is no guarantee that the real structure behaves similar to the model as they also the structural behavior could also depend on the quality of material and construction techniques. However, to simulate the structural behavior of infilled frames, two methods have been developed such as Micro model and Macro model. The Micro model method is a Finite Element Method (FEM) where the frames elements, masonry work, contact surface, slipping and separation are modeled to achieve the results.
This method has seems to be generating the better results but it has not gained popularity due to its cumbersome nature of analysis and computation cost. The Macro models which is also called a Simplified model or Equivalent diagonal strut method was developed to study the global response of the infilled frames. This method uses one or more struts to represent the infill wall. The drawback of it is to the lack of its capability to consider the opening precisely as found in the infill wall. 2.1 MICRO –MODELS Micro models are represented by using Finite Element Method (FEM). The finite element method is the most popular analysis tool for complex structural engineering problems. Since the pioneer work of Mallick and Severn (1967), several difficulties were evident from the simulations, namely the issues of modeling the separation between frame and panel, of the bond strength and friction of the connection between frame and panel, and of the mechanical constitutive behavior of masonry itself. Riddington and Stafford-Smith (1977) found that the critical stresses for the masonry panel are located in the centre and are mostly associated with tensile and shear failure. In this case, the frame-panel interaction was modeled by using double nodes and normal springs at the interfaces, with contact/separation modeled in a simplified way. King and Pandey (1978) further extended the numerical representation by adding interface elements capable of taking into account contact and friction for the frame-panel interaction. This work was further extended with non-linear behavior of the panel and frame, by Liauw and Kwan (1982) and Dhanasekar and Page (1986) in the framework of continuum modeling, and by Mehrabi and Shing (1997) in the framework of discontinuous modeling. The benefit of using finite element approach is to study in detail all possible modes of failure but its use is limited due to the greater computational effort and time required in analysis & modelling.
2.2 MACRO-MODELS In order to overcome the complexity and computational requirement using micro-models, research has been done to simplify the modelling of infill panel with a single element. The main idea has been to study the global effects of infill panel on structures under lateral loads. Since first attempts from Polyakov (1956), analytical and experimental tests have shown that a diagonal strut with appropriate mechanical properties can provide a solution to the problem.
Several authors have modified the characteristics of single strut model with multi strut configuration to better understand the effect of micro-cracking in the corner of the infill panel due to tensile stresses and higher shear strength of the infill panel relative to the frame. A brief review of few models has been presented. Based on elastic studies Polyakov (1956) conducted one of the first analytical studies on infilled frames. He considered the effect of infill in each panel as equivalent to diagonal bracing. Holmes (1961) took the idea and suggested that infill panel can be replaced by an equivalent pin-jointed diagonal strut. He proposed that the diagonal strut to have the same material and thickness as the infill panel. The width of strut was taken equal to one third of the strut length (2.1) Stafford (1966) performed a series of test on square steel infilled frames. He observed that contact length between the wall and frame is related to the width of the strut. From the experimental result he proposed the following relation for finding the contact length between the wall and infill frame. √ (2.2) .
(2.3) Where is the non dimensional parameter known as relative stiffness between the reinforced and are the elastic modulus and thickness of the and α represents the
concrete frame and the infill wall. masonry wall and and
are the elastic modulus and moment of inertia of the bounding
concrete frame members. Height of the masonry infill is represented by contact length.
Paulay & Priestley (1992) took a conservatively high value for the width of equivalent strut. According to them, a high value of them is as follows: will result in a stiffer structure. The relation given by
(2.4)
Mainstone (1971) relates the width w of equivalent strut to parameter h, given by equation (2.2) and diagonal length d as shown in the equation (2.5). (2.5) The proposed macro models and respective equivalent diagonal strut width equations for masonry infill by various researchers is tabulated in table 2.1
Table.2.1 Equations for strut width value for full infill by various researchers Researchers Strut width(w) Remark
Holmes[4]
0.333 dm 0.175 D ( 1 H)- 0.4 0.95 hm Cos θ/√( hm)
dm is the length of diagonal 1 H = H[EmtSin2θ/4 Ec Ic
Mainstone[6
hm]1/4 = Em t Sin 2 θ/ 4 Ec Ic
Liauw and Kwan[7]
hm]1/4
Paulay and Priestley[8]
0.25 dm 0.5[αh + αL]1/2
dm is the length of diagonal αh = π/2[EcIchm/2 Emtsin2θ]1/4 and αL = π[EcIbL/ 2 Emtsin2θ]1/4 = Emt Sin 2 θ/ 4 EcIchm]1/4 is the length of diagonal
Hendry[9]
Decanini & Fantin (1986)
Durrani & Luo (1994)
√
3.0 METHODOLOGY In the present study reinforced concrete members and masonry infill members are modelled using ETABS 9.6 software. It is powerful finite element software developed by Computers & Structures Inc., which can greatly enhance a designer’s analysis & design capabilities for structures. etabs
4.0 MODEL DESCRIPTION Three models have been selected and compare the results with different proposed macro models. Experiments are very important to observe the behavior of complex structures. Many a times, analytical models have been developed on the basis of experimental results, and sometimes, experimental studies have been carried out to verify the analytically developed model. The proposed analytical model is initially compared with the experimental results of Chiou, Y. J., et al., (1999). They have conducted a full scale test to study the behavior of one bay one storey framed masonry walls. The infill panel size of the specimen tested is 2.4m x 2.3m. The cross sections of the beam and column elements are 0.35m x 0.40m and 0.3m x 0.35m respectively. The thickness of the masonry wall is 0.2m and the elastic modulus of concrete & masonry are 2.4247 x 107 kN/m2 and 2.087 x 106 kN/m2 respectively. The monotonic loading is adopted in this study (Fig.4.1).
The main output of the experimental investigation was a load versus displacement curve for solid frame. The results from the experimental investigation are used to compare the results of finite element model. Fig.4.2 presents lateral force and the corresponding lateral displacement at the top of the leeward column for the proposed macro models. A good agreement is observed especially at lower loads. Considering this fact, a finite element method is chosen for the present work in order to understand the behavior of infilled frames.
Fig 4.1 Analytical model
Fig 4.2 Macro model using ETABS
The proposed analytical model is initially compared with the analytical results of P. G.
Asteris, M.ASCE1.They have conducted a analytical model (fig 4.3) to study the behavior of
one bay one storey framed masonry walls. The infill panel size of the specimen tested is 3.6m x 3.8m. The cross sections of the beam and column elements are 0.40m x 0.40m and 0.3m x 0.40m respectively. The thickness of the masonry wall is 0.1m and the elastic modulus of concrete & masonry are 2.9 x 107 kN/m2 and 4.5 x 106 kN/m2 respectively. The proposed macro models at 1,2 nd 3 stories are represented in fig(4.4,4.5,4.6).
Fig 4.3 Analytical model
Fig 4.4 Macro model at one story using ETABS
Fig 4.5 Macro model at Two story using ETABS
Fig 4.6 Macro model at Three story using ETABS
The proposed analytical model is initially compared with the analytical results of P. G. Asteris, M.ASCE1.They have conducted a analytical model to study the behavior of one bay one storey framed masonry walls. The infill panel size of the specimen tested is 4.0 x 4.0m. The cross sections of the beam and column elements are 0.30m x 0.30m and 0.3m x 0.30m respectively.
The thickness of the masonry wall is 0.1m and the elastic modulus of concrete & masonry are 2.2 x 107 kN/m2 and 7.5 x 106 kN/m2 respectively. The proposed macro model is shown in fig 4.7.
Fig 4.7 Macro model using ETABS 5.0 RESULTS AND DISCUSSION Comparison of lateral displacement of various macro models with the experimental and analytical micro models is shown in table 5.1
Table 5.1: Comparision of Lateral displacement
Technical papers Load kN EXPT Micro model Analytical Micro model M1
ASTERIES (1990) YAW-JENG CHOW (1999) ASTERIES (2003)
At one story
Lateral displacement of Macro Models (mm)
M2
0.828 (1.88) 1.08
M3
2.24 (0.56) 1.915
M4
1.04 (1.41) 1.3
M5
1.22 (1.16) 1.40
M6
0.496 (3.815) 0.624
M7
1.262 (1.12) 0.769
1.71 85 0.7 (0.78) 1.137 100 1.8 (1.03)
(1.08)
(0.39)
(0.83)
(0.73)
(2.44)
(1.83)
(1.21)
(1.74)
(0.55)
(1.31)
(1.29)
(4.84)
(1.28)
30
At Two story
-
0.5
0.481
0.364
0.835
0.453
0.164
0.164
0.46
30
At Three story
-
1.28
1.16
0.91
1.97
1.10
1.11
0.494
1.12
30
-
2.3
2.127
1.736
3.4
2.03
2.05
1.099
2.059
NOTE:-The equivalent width of the diagonal strut for various macro models is shown in the bracket (-). The proposed macro models by various researchers and load Vs displacement curves is shown below-
Hendry[9] Holmes[4] Mainstone[6] Paulay and Priestley[8] Liauw and Kwan[7] Decanini & Fantin (1986) Durrani & Luo (1994)
M1 M2 M3 M4 M5 M6 M7
90 80 70 60
load (Kn)
M2 MIC M1 M3 M4 M7 M6 M5
50 40 30 20 10 0 0 1 2
displacement (mm)
Fig.5.1:comparision of lateral deflection of macro models and analytical model for solid infill
M3 EXPT M1 M2 M4 M5 M6 M7
700
600
500
load (Kn)
400
300
200
100 0 2 4 6 8 10 12 14 16 18 20
displacement (mm)
Fig.5.2:comparision of lateral deflection of macro models and experimental model for solid infill
3.0
2.5
2.0
@3 story @2 story @1 story Analytical
story
1.5
1.0
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
displacement (mm)
Fig.5.3:comparision of lateral deflection of macro models and analytical model at various stories
6.0. CONCLUSIONS
The primary objective of this paper is to present a general review of the different macro models used for the analysis of infilled frames. The macro models that can be used in everyday engineering are of practical importance. The simpler ones are the equivalent-strut models, which represent infills with a diagonal strut element. The basic parameter of these struts is their equivalent width, which affects their stiffness and strength. Several formulas have been proposed by researchers to calculate this equivalent width. In all the cases, there are considerable differences among the values obtained. The comparative study of different expressions for calculating the diagonal strut width reveals the Paulay and Priestley equation as the most suitable choice, due to its simplicity and because it gives an approximate average value (among those studied). In the analysis involving analytical models for masonry infills in a single-storey, single-bay reinforced concrete frame, the singlestrut model was found to be predicting the global behavior of the system with reasonable accuracy.
7.0 REFERENCES 1. Asteris P.G., (2003), “Lateral stiffness of brick masonry infilled plane frames”, Journal of the Structural Engineering, ASCE, pp. 1071-1079 2. Chiou, Y. J., Tzeng, J. C., and Liou, Y. W., (1999), “Experimental and analytical study of masonry infilled frames”, Journal of Structural Engineering, Vol. 125, No. 10, pp. 1109–1117 3. Asteris P.G., (1996), “Analytical investigation of infill wall influence on the aseismic behaviour of plane frame”, diploma thesis(Supervisor C.A Syrmakezis)”, National Technical University of Athens,(in greek) 4. Diana M. Samoilă*1., “Analytical Modelling of Masonry Infills”1 Technical University of Cluj-Napoca, Faculty of Civil Engineering. 15 C Daicoviciu Str., 400020, ClujNapoca, Romania 5. Prachand Man Pradhan., “Equivalent Strut Width for Partial Infilled Frames”, Department of Civil and Geomatics Engineering, Kathmandu University, Dhulikhel, Nepal
