SOFT STORY DESIGN IN REINFORCED CONCRETE STRUCTURE AND EFFECT OF MASONRY INFILL WALL

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1 Six th International Conference of Seismology and Earthquake Engineering May 2011 Tehran, Iran SOFT STORY DESIGN IN REINFORCED CONCRETE STRUCTURE AND EFFECT OF MASONRY INFILL WALL S. M. Hosseini-Gelekolai 1, M. R. Tabeshpour 2 1 Department of Civil Engineering, Sharif University, Tehran, Iran, hosseinigelekolai@gmail.com 2 Engineering Faculty, Sabzevar Tarbiat Moallem University, Sabzevar, Iran, tabesh_mreza@yahoo.com 3 Department of Civil Engineering, Sharif University, Tehran, Iran, golafshani@sharif.edu ABSTRACT In past few decades researchers and engineers have researched extensively on the effects of masonry infill walls in structural frames and the effects of masonry infill walls on the structural response was a concern for them. One of the sections in Iranian Codes that existence of masonry infill walls in buildings affects it, is the section 2-10 of 2800 Code that accordance to this section, in order to prevent soft story failure when there is a discontinuity in bracing or shear walls in a certain story, columns of that story must be designed for factored loads. Even though in the contest of 2800 Code there is no notification to necessity of increasing the design loads in existence of discontinuity of masonry infill walls, based on experiences of structural response in past earthquakes even in the case of existence of discontinuity of masonry infill walls the columns of the story must be designed for factored loads. The question is that in this case how much the factor is? The main goal of this research is to investigate the appearance of soft story failure in first story in reinforced concrete structures with moment frame system and different arrangements of masonry infill walls in upper stories (in different bays and different thickness) and also suggesting a factor to strengthen the first story columns in order to prevent the soft story failure. We call this factor, the overstrength factor which is the 2.8 factor in section 2-10 of 2800 Code but here the masonry infill walls discontinued in the first story and in that section, braces or shear walls discontinued. The overstrength factor is equal to 2.8 for all cases while it should be calculated exactly so that not results in overdesigning or under designing of structures. If column of soft story be designed basis of this factor the existence capacity will be used optimally and also we will not have terrible events like soft story failures in future earthquakes. Keywords: Design of Soft Story, Masonry Infill Wall, Reinforced Concrete Structure, Equivalent Compressive Brace, Overstrength Factor of Column 1. INTRODUCTION Masonry infill walls exist in several buildings but their role in the rehabilitation and retrofitting of the structures is neglected by most of the structural engineers. Researches on the behavior of frames with masonry infill walls have been started from 1950s. Several lateral loading tests have been done on the full scale and prototype models including masonry infill walls. There are two general methods for considering the effects of masonry infill walls in structural frames in seismic design of structures [1]; i) Modeling the infill separately and neglecting the interaction of masonry infill walls in the SEE6 / 1 / IIEES

2 structural response ii) Coupled modeling of masonry infill walls and structural frames considering the interaction of infill and structural frame In Iran, buildings are usually designed without considering effects of infill on the seismic behavior of the structure. But it has been observed that the infill increase the strength and stiffness of the frames and consequently leading to change in the seismic behavior of the frames. Considering the importance of the topic it is necessary to study the changes of the seismic behavior of the structures in addition to investigating the impact of the infill on the behavior of frames. The main negative effects of the infill walls in the structures are the followings [2]; i) Story failure (height irregularity) ii) Torsion (plan irregularity) iii) Short column (reinforced concrete structures) 1.1. Modeling Review From a technical point of view modeling are categorized into; i) Detailed modeling (micro) ii) Simple modeling (macro) First category is based on the definition of finite element model of infill wall and is solved by formal plasticity and elasticity methods. In the second category a general behavior of infill wall is important and in this case one or several elements are used to model the behavior of infill wall. i) Detailed Modeling (Micro) All models in the first category are based on finite element method and generally three kinds of elements are used to model infill wall, frame and interaction between them. Mallick D.V. (1967) modelled interaction between infill and wall, using elastic linear rectangular element with two degree of freedom (DOF) for each node as shown in the Figure 1. Friction and slip between infill wall and frame was considered too [3]. Figure 1. Finite element modeling of masonry infill wall Goodman R.E. (1968) developed an element for modeling of interaction between frame and wall. A rectangular plane-strain four nodes element with 2 DOF in each node was enhanced to consider contacts conditions. The shear stress of elements is dependent on cohesion and friction. Mallick D.V. (1971) modeled stud between frame and wall, Rectangular plane-strain elements for wall modeling have been used [3]. ii) Simple Modeling (Macro) The idea of using a single element to model infill wall was always an interesting idea because of having many advantages in the analyzing procedure. It is obvious that diagonal strut with proper mechanical behavior can be a good alternative for modeling of infill walls (Figure 2). Klinger R.E. (1976) modeled masonry infill wall with two equivalent struts considering stiffness degradation effects. Polyakov (1956) investigated normal and shear stress at the middle of infill wall using calculus of variation and introduced an analytical method to predict the force that causes diagonal cracks in the wall by using experimental results. An equation for diagonal strut SEE6 / 2 / IIEES

3 was introduced first time by Holmes (1961), base on assumption that width of equivalent strut equals one third of the diameter length. Based on contact length of wall and frame some other methods for determining width of equivalent diagonal strut were proposed by Mainstone (1971) nad Kadir (1974) [3] Soft Story Failure Figure 2. Simple modeling of masonry infill wall One of the most common failure modes of structures in earthquakes is soft story failure which causes by discontinuity of lateral force resisting elements like braces, shear walls or infill walls in the first story. In this case columns are imposed to large deformation and plastic hinges are formed at top and bottom of the columns. This case is named as story mechanism (severe drift of the story). In most of this case building collapsed or going to collapse. In the following, performance of two buildings in the Wenchuan-China earthquake (2008) is compared (Figure 3). Building 1 is a six story RC structure with parking in the first story, there is no infill wall in the parking story as shown in Figure 4 and building 2 is a five story RC structure with some infill walls in the first story as shown in Figure 5. The first building (1) has localized deformation in the first story and the columns of this story undergone large deformation (200 mm displacement, 8% drift) and passed collapse limit (4% drift in most codes) but in the second building the stiffness and strength of the first story is almost the same as the upper stories and soft story failure did not occur in this building (Li B. 2008). Building 1 Building 2 Figure 3. Buildings locations Column hinging Figure 4. Building 1 poor performance (6 story with "open" parking in first story) SEE6 / 3 / IIEES

4 First story infill cracking Figure 5. Building 2 good performance (5 story some infill walls in first story) 1.3. Section 2-10 of 2800 Code: Increasing of Design Load in Special Columns Some of the national building codes have requirements for design of the columns of the soft stories. In Iranian code of practice there are not any clear requirements for design of soft story due to removal of masonry infill walls Building Code recommends not discontinuing any lateral load resisting element in the structure but if this criteria is not satisfied the recommendation is to increase the design load of structure to the followings [5]; i) (Dead Load) (Live Load) ± 2.8 (Earthquake Load) ii) 0.85 (Deal Load) ± 2.8 (Earthquake Load) Note that in the case of discontinuity of masonry infill walls the above load combination must be imposed, otherwise the soft story failure will occur. In the combination above, the only change to prevent soft story failure is multiplying the earthquake load by overstrength factor α which will be obtained in this research, instead of 2.8 factor. 2. MODELING PROCEDURE AND CONCEPTS i) Material Modeling In this paper the masonry infill walls is modeled as an equivalent compressive strut. This strut is diagonal and connects the opposite joint of the frames with the length equal to diameter and the width 0.2 times of frame diameter. The thickness of strut is equal to the thickness of the wall (Figure 6) [2]. Equivalent struts Figure 6. Coupled Equivalent compressive strut In order to obtain material properties of masonry strut the Australian code [6] used with consideration of usual mortar and bricks used in Iran. The following stress-strain curve is for two kinds of infill walls (17 cm and 23 cm respectively) obtained from Australian code(table 1). Table-1. Equivalent masonry strut's material properties [7] Thickness Thickness 17 (Cm) 23 (Cm) f mo (MPa) ε mo f mu (MPa) ε mu SEE6 / 4 / IIEES

5 To consider the effect of existing openings, New Zealand code [8] equation was used in which a reduction factor for width of strut was considered as; Lopening λ opening = ( ) (1) L infill In the equation above λ opening is effective width reduction factor and L opening is the length of opening in the horizontal direction and L infill is total length of infill wall in horizontal direction. The reduction factor λ opening equals 0.5 when there is 33% opening in infill wall. ii) Element Modeling OpenSees software is used to implement the static nonlinear analysis (pushover) [9]. Nonlinear beam column elements with fiber section are used to model RC elements; in this case elements are divided to longitudinal fibers. The stress-strain relations for each fiber are determined and force deformation relations for each section are obtained by integration of stress-strain curve of section fibers. This integration is based on the assumption of small planner deflection theory without distortion. By using fiber sections and assigning it to nonlinear beam column elements, distributed plasticity properties would be considered all over the elements' length. Seven integration points is used in the length of elements according to Gauss-Lobatto method with two points in the beginning and end of elements. For concrete properties, Concret01 material was used which is a uniaxial material with considering stiffness degradation linearly in loading and unloading [10]. Effects of concrete confining are considered by Mander et al. researches for elements' core (Table 2). Table-2. Stress-strain curve of concrete fiber section f mo (MPa) ε mo f mu (MPa) ε mu core Cover* *for beams is equal to 4 cm from each edge of section *for columns is equal to 4.5 cm from each edge of section Rebars are modeled with steel02 material which is a uniaxial material with hardening on the basis of Menegotto-Pinto (1973) equations. In this research E 0 equals to 2X1011 (MPa), yielding stress equals to 4X108 (MPa) and b (slope after yielding) equals to 1 %. iii) Case Studies Three types of frames with 3, 5 and 9 stories all with 3 bays have been investigated in this study. Lengths of bays are equal to 5.5 (m) and story heights are 3 (m) except 3.5 (m) for first story. Arrangements of infill walls are categorized in 12 cases in general: middle bay, two side bays and all three bays, each with two types of walls with thickness of 17 (cm) and 23 (cm) and with two cases of existence of 33% opening or without opening (Table 3). Lateral force resisting system is intermediate moment frame and the type of soil considered as II. Dead and live loads of stories were considered 600 (kg/m2) and 200 (kg/m2) respectively. These parameters were considered 550 (kg/m2) and 150 (kg/m2) respectively for roof story. Dead load were considered 100 (kg/m2) and 133 (kg/m2) for 17 (cm) and 23 (cm) thick walls respectively. Since investigating the effects of masonry infill walls was the main goal of this research, the considered frames were designed according to last version of Iranian building codes without considering infill walls (This paper is part of M.Sc. Thesis of Mr.Hosseini) [1]. Table-3. Naming different models of existing of masonry infill walls in 3 story building and wall thickness of 17 (cm) (O: opening, W: without opening) (Hosseini 2010) Model 0 Model 1-O Model 2-O Model 3-O SEE6 / 5 / IIEES

6 Model 1-W Model 2-W Model 3-W 3. DETERMINING OF OVERSTRENGTH FACTOR BY INCREASING DIMENSION OF COLUMNS To determine overstrength factor α for first story column, trial and error method has been used, in this method dimension of first story column in the direction of frame will increase by 2.5 cm increment, in the perpendicular direction the dimension of column remains unchanged and also the rebar percentage remains constant. For example for a rebar percentage equals to 2.9 % in a 45x45 cm section, 12#25 were used and for the final section of this case a 50x45 cm section with 12#26.36 was obtained in which the rebar percentage remains 2.9%. Increment of column dimension is continued till disappearance of soft story mechanism it means when the first story drift reaches 1 % (half of Life-Safety acceptance criteria) upper stories' walls fail and story drift distributed between stories. This leads structure to have more ductile behavior and there is no drift localization in the first story. Reaching final state, the ratio of strength of final column to strength of initial columns is named as overstrength factor α. In order to compare the behavior of the initial structure and final structure, the pushover curves of two cases should be the same, so in the final structure which has a distributed drift in stories, strength of infill walls increased 10 times. Now the compression of maximum base shear in pushover curves of two cases is almost the comparison of the first story columns of them, which is the overstrength factor α. In the figures below obtaining α factor for model No.3-O in 3 story frame is shown [1] Pushover Curve for (3 Story+Strut 17 cm,1/3 Opening,3 Bays) 5.0 Story Drift for (3 Story without Strut) Base Shear (kn) bare frame without strut bare frame+strut designed frame+strut designed frame+10*strut Drfit Ratio % story 1 story 2 story Displacement(m) Figure 7. Pushover curves for 3 story frame model No.3-O Displacement(m) Figure 8. Story drift for 3 story frame model No.0 (bare frame) As shown in Figure 7 adding infill walls lead to stiffen the structure and the slope at the pushover curves will increase and also the maximum strength will increase. Since infill walls are brittle material and have a high stiffness, in the distribution of forces between elements, these walls bear a large amount of lateral load till they fail. After failure of infill walls, a drop of stiffness (slope) and strength of pushover curves occurs. As it can be seen in Figure 7 after failure of the infill walls the slope of the pushover curve will be the same as model No. 0 (bare frame). Now to obtain α factor the maximum strength in pushover curves for two cases should be compared. First case is bare frame with masonry struts (masonry infill walls) in upper stories model No.3-O (bare frame + strut with openings) and the second one is bare frame with masonry strut in upper stories, stronger first story columns and stronger infill walls (designed frame + 10xstrut with openings) [1]. V α = = = (2) V SEE6 / 6 / IIEES

7 8.0 Story Drift for (3 Story+Strut 17 cm,1/3 Opening,3 Bays) 7.0 Story Drift for (3 Story New Design+Strut 17 cm,1/3 Opening,3 Bays) Drfit Ratio % story 1 story 2 story 3 Drfit Ratio % story 1 story 2 story Displacement(m) Figure 9. Story drift for 3 story frame model No.3.O Displacement(m) Figure 10. Story drift for 3 story frame model No. 3-O and designed for soft story 4. PUSHOVER ANALYSES RESULT The results obtained from analyzing the models are shown in tables below. These results help us to find a reasonable trend in the overstrength factor α in different models. Table-4. Overstrength factor α for 3 story structure Infill 17,(L/3)opening 17,wo opening 23,(L/3)opening 23,wo opening Model Number 1-O 2-O 3-O 1-W 2-W 3-W 1-O 2-O 3-O 1-W 2-W 3-W α Table-5. Overstrength factor α for 5 story structure Infill 17,(L/3)opening 17,wo opening 23,(L/3)opening 23,wo opening Model Number 1-O 2-O 3-O 1-W 2-W 3-W 1-O 2-O 3-O 1-W 2-W 3-W α Table-6. Overstrength factor α for 9 story structure Infill 17,(L/3)opening 17, wo opening 23,(L/3)opening 23, wo opening Model Number 1-O 2-O 3-O 1-W 2-W 3-W 1-O 2-O 3-O 1-W 2-W 3-W α alfa y = x R 2 = y = x R 2 = y = x R 2 = masonry area % Figure 13. Overstrength factor α for 3,5,9 story structures 3 story 5 story 9 story alfa y = x R 2 = area modified Figure 14. Overstrength factor α in general As shown in the pushover curves with considering infill walls, stiffness and strength of buildings increased compared to a building without considering infill walls. It s a valuable phenomenon and has engineering advantages, but because of discontinuity of infill walls in the first story stiffness and strength of this story is less than upper story causing localizations of drift and deformations in this story, as shown in Figure 9. First story drift increases rapidly and plastic hinges form in the first story's columns. If the first story is designed by overstrength factor α as shown in Figure 10 there will be no deformation localization in the first story and all story drifts are increasing uniformly. The results show that by increasing the ratio and thickness of infill walls, this factor (α) increases; also by increasing number of stories (increasing column's dimension) the effects of infill wall decreases and the overstrength factor α for 9 story SEE6 / 7 / IIEES

8 frame is greater than one in just three cases as shown in Table 6. It is remarkable that obtained values for α factor for different buildings are related to each other as shown in Figure 14 if we modify the masonry strut area ratio (masonry strut area divided by plan area multiply by number of stories minus one, divided by square of number of stories) all the points in Figure 13 could be illustrated in Figure 14 and according to this figure for each number of stories between 3 to 9 in the case of probability of soft story failure, the α factor would be obtained from eq.3 on the basis of masonry area; N Ainfills α ( ) A N + (3) = plan In this formula A infills is the cross sectional area of equivalent masonry struts, A plan is the total area of building's plan and N is the number of stories of building. 5. CONCLUSIONS 1. Overstrength factor for several states was obtained and a good and reasonable trend was observed. Pushover curves show the importance of infill walls effects on the structures behavior and localization of stress and drift. 2. Low strength or thin infill walls have overstrength factor of unit, it means there is no need to overstrengthening the first story columns. 3. In the design procedure by calculating infill walls ratio using architectural plans and number of stories the overstrength factor α could be determined and applied in designing by formulae represented in eq.3 inorder to prevent soft story failure. 4. For strengthening existing buildings, building masonry infill walls in the first story bays or using friction dampers is recommended. 5. REFERENCES 1. Hosseini Gelekolai, S. M. (2010). "Design of Soft Story in Reinforced Concrete Structure due to Removal of Masonry Infill Wall", Master of Science Thesis, Department of Civil Engineering, Sharif University of Technology, Tehran, Iran 2. Tabeshpour, M. R., Golafshani, A. A., Hosseini Gelekolai, S. M. (2010). "The Overstrength Factor in Soft Story Design due to Removal of Masonry Infill Walls", In Proceedings of 1st National Conferences on Structure Earthquake Geotechnics, Babolsar, Mazandaran, Iran. 3. Tabeshpour, M.R. (2009). "Handbook series, No.18, Masonry Infill Walls in Structural Frames", Fadak Isatis Publishing Co, (in Farsi). 4. Li, B., Wang, Z., Mosalam, K.M. and Xie, H. (2008). "Wenchua earthquake field reconnaissance on reinforced concrete framed buildings with and without masonry infill walls", Bul. Soc. Mex. Ing. Sismol., Vol. 2(1). 5. BHRC-IR (2005). "Seismic Design of Buildings-2800 Code", Build. And Housing Research Center of Iran (BHRC-IR), 3th edition, (in Farsi). 6. Australian Standard, AS 3700, (2001). "Masonry Structures", Prepared by Committee BD Hashemi, A., Mosalam, K.M. (2007). "Seismic Evaluation of Reinforced Concrete Buildings Including Effects of Masonry Infill Walls", Report No.PEER 2007/100, University of California, Berkeley. 8. New Zealand assessment code (2002). "Assessment and Improvement of the Structural Performance of Buildings in Earthquake", Prepared for the Building Industry Authority. 9. Pacific Earthquake Eng. Research Center(PEER.) (2010). "Open system for earthquake engineering simulation (OpenSees)", Version , Univ. of California, Mazzoni, S., McKenna, F., Scott, M.H., Fenves, G.L. & Jeremic, B. (2006). "OpenSees Command Language Manual", Univ. of California, SEE6 / 8 / IIEES