Gravity load designed RC frame under far field earthquake action

GRAVITY LOAD DESIGNED RC FRAME UNDER FAR FIELD EARTHQUAKE ACTION WIRYI ARIPIN (B.ENG., GADJAH MADA UNIVERSITY) A THESIS SUBMITED FOR DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2006 ACKNOWLEDGEMENT Thanks to the LORD for His grace in providing all the strength and comfort during this study. I also would like to take this opportunity to express my profound gratitude to AUN/SEED-Net and JICA for the opportunity to pursue my master degree in NUS, and also my sincere appreciation to my supervisors Associate Professor Tan Kiang Hwee and Professor T. Balendra, for their kind and systematic guidance, and supervision throughout the course of this study. I would also like to thank to the staff members at the Structural Laboratory for their help and advice. Many thanks to Mr. Sit Beng Chiat, Mr. Edgar Lim, Mr. Ow Weng Moon, Mr. Yip Kwok Keong, Mr. Ong Teng Chew, Mr. Semawi Bin Sadi, Mr. Yong Tat Fah, Mr. Wong Kah Wai, and Mr. Martin who help in many ways in the experiment. Special acknowledgment is given to Mr. Choo Peng Kin, Mr. Koh Yian Kheng, Mr. Ishak Bin A Rahman, Ms. Annie Tan, Mr Ang Beng Onn, and Mr. Kamsan Bin Rasman who had assisted, guided and helped me in the experiment. Gratitude is expressed also to my senior Dr. Li Zhijun and my colleague Mr. Samsu Sukaimi Hendra for their help. I am greatly indebted to my family and Selviana who have encouraged me a lot and made many sacrifices during this study. Last but not least, I thank my lecturers, relatives and friends who have supported me in my study in so many ways. i TABLE OF CONTENT Acknowledgment ...................................................................................................................... i Table of Content ....................................................................................................................... ii Abstract ..................................................................................................................................... v List of Figures ........................................................................................................................... vi List of Tables ............................................................................................................................. x List of Symbols .......................................................................................................................... xi Chapter 1 Introduction ............................................................................................................ 1 1.1 General ........................................................................................................................ 1 1.1.1 Tectonic earthquake .............................................................................................. 1 1.1.2 Far field effect in Mexican Earthquake, 1985....................................................... 2 1.1.3 Seismic demand due to far field effects for building in Singapore ........................ 4 1.1.3.1 Earthquake and soil condition ..................................................................... 4 1.1.3.2 Vulnerability of buildings to far field effects of earthquake ........................ 5 1.2 Response of GLD structures to seismic action ............................................................ 7 1.3 Retrofit of GLD structures to resist seismic action...................................................... 10 1.4 Objective and Scope .................................................................................................... 15 Chapter 2 Analytical Model ..................................................................................................... 27 2.1 General......................................................................................................................... 27 2.2 Seismic analysis........................................................................................................... 28 2.3 Non-linear pushover analysis ...................................................................................... 30 2.4 Material properties for modelling ................................................................................ 32 2.4.1 Steel ....................................................................................................................... 32 2.4.2 Concrete ............................................................................................................... 33 2.4.2.1 Unconfined concrete .................................................................................... 33 2.4.2.2 Confined concrete ........................................................................................ 34 2.4.3 Glass fiber reinforced polymer reinforcement ...................................................... 36 2.5 Nonlinear reinforced concrete beam-column element................................................. 38 2.5.1 Plastic hinge length ............................................................................................... 39 2.5.2 Moment-curvature relation ................................................................................... 41 2.5.3 Moment at the first crack....................................................................................... 42 2.5.4 Shear strength........................................................................................................ 43 ii 2.6 Analytical model of un-retrofitted concrete frame ...................................................... 46 2.6.1 Material properties................................................................................................ 46 2.6.2 Loadings ................................................................................................................ 47 2.6.3 Moment at first crack............................................................................................. 47 2.6.4 Analytical result .................................................................................................... 48 2.7 Analytical model of RC frame using FRP system....................................................... 48 2.7.1 Material properties................................................................................................ 49 2.7.2 Loadings ................................................................................................................ 49 2.7.3 Moment at first cracking ....................................................................................... 49 2.7.4 Analytical result .................................................................................................... 50 2.75 P-delta effect........................................................................................................... 50 2.8 Summary...................................................................................................................... 51 Chapter 3 Experimental Investigation .................................................................................... 74 3.1 General......................................................................................................................... 74 3.2 Design test frame ......................................................................................................... 74 3.2.1 Reinforced concrete frame .................................................................................... 74 3.2.2.Model scaling similitude........................................................................................ 75 3.2.3.Material properties ............................................................................................... 75 3.2.4 Loading.................................................................................................................. 77 3.3 Construction method of specimen ............................................................................... 77 3.3.1 Preparation of test frame....................................................................................... 77 3.3.2 Test setup............................................................................................................... 78 3.3.3 Installation of glass FRP system ........................................................................... 80 3.4 Instrumentation ............................................................................................................ 81 3.4.1 Strain gauges......................................................................................................... 81 3.4.2 Displacement transducers ..................................................................................... 81 3.5 Test result and discussion ............................................................................................ 82 3.5.1 Crack patterns ....................................................................................................... 82 3.5.1.a Unretrofitted frame ...................................................................................... 82 3.5.1.b Retrofitted frame .......................................................................................... 83 3.5.2 Joint Response ....................................................................................................... 84 3.5.3 Moment-curvature curves...................................................................................... 85 3.5.4 Strain development ................................................................................................ 86 3.5.5 Pushover capacity curve........................................................................................ 87 iii 3.5.5.1 Comparison between unretrofitted and retrofitted frames........................... 87 3.5.5.2 Verification of analytical model with experimental result........................... 88 3.6 Summary...................................................................................................................... 90 Chapter 4 Case Study on Retrofit of Four-Storey Concrete Frame ..................................... 109 4.1 General......................................................................................................................... 109 4.2 Overview of the frame ................................................................................................. 109 4.3 Analytical model of the unretrofitted frame ............................................................... 110 4.3.1 Material properties................................................................................................ 110 4.3.2 Moment at first crack............................................................................................. 111 4.3.3 Analytical result .................................................................................................... 111 4.4 Analytical model of the RC frame with FRP system................................................... 111 4.5 Summary...................................................................................................................... 113 Chapter 5 Conclusion................................................................................................................ 125 References .................................................................................................................................. 127 iv ABSTRACT In recent years, there has been an increased emphasis on the far-field effect of earthquake on buildings sited on soft soil due to the large amplifying effect on long distance earthquake waves by the soil. This problem is especially pertinent in countries like Singapore where buildings are designed according to non-seismic codes. It is necessary therefore, to examine the vulnerability of such gravity load designed (GLD) buildings to far-field earthquake action. In this study, the response of a GLD reinforced concrete frame found in typical lowrise buildings to lateral action was investigated analytically and experimentally. The analytical study provided a reasonable prediction of the response of the frame under pushover load. Using a glass FRP retrofit system, the strength and the ductility of the frame were increased by 29% and 75% respectively. It was also observed that the system delayed the formation and widening of the cracks in the frame member. A strong column-weak beam failure mechanism was observed both analytically and experimentally for the unretrofitted and retrofitted frame. v LIST OF FIGURES Figure 1.1 Configuration of tectonic plates of the world ..................................................... 17 Figure 1.2 Basic categories of fault movement ................................................................... 17 Figure 1.3 Tectonic map of Mexico ..................................................................................... 18 Figure 1.4 Percentage of observed buildings damages versus number of storey of different construction types .............................................................................................. 18 Figure 1.5 Records of Mexican earthquake 1985 ................................................................ 19 Figure 1.6 Location Sudanese Trench and Sumatran Fault ................................................. 19 Figure 1.7 Singapore soil formations ................................................................................... 20 Figure 1.8 Typical details of old GLD buildings in western US ......................................... 20 Figure 1.9 Global structural response at performance point against design earthquake at site condition of (a) SB (b) SC (c) SD ................................................................................................ 21 Figure 1.10 Typical infill wall technique using reinforced concrete wall. .......................... 22 Figure 1.11 Seismic resistanct bracing techniques .............................................................. 23 Figure 1.12 Reinforced concrete jacketing technique .......................................................... 24 Figure 1.13 Steel jacketing technique .................................................................................. 25 Figure 1.14 Column jacket with gap .................................................................................... 25 Figure 1.15 Glass FRP-strengthened specimens tested by (a) Ghobarah and Said, and ElAmoury and Ghobarah. .................................................................................... 26 Figure 1.16 Rehabilitation of exterior columns and joints: (a) column wrapping (b) joint strengthening (c) U-wrapping on the beam ...................................................... 26 Figure 2.1 Prototype Structure (a) plan view of the whole building (b) selected critical frame (c) a one- and half-bay and two-storey frame chosen for the test frame ........... 54 Figure 2.2 (a) Layout of the frame (b) Cross-section of the member .................................. 55 Figure 2.3 Bilinear stress-strain relation for steel reinforcement ........................................ 56 Figure 2.4 Stress-Strain Relationship of Unconfined and Confined Concrete Model.......... 56 Figure 2.5 Stress-strain relation of unconfined concrete ..................................................... 57 Figure 2.6 Confinement effect of transverse reinforcement on the rectangular reinforced concrete cross-section ........................................................................................ 57 vi Figure 2.7 Stress-strain relationship of Mander Confined Concrete Model ........................ 58 Figure 2.8 The stress-strain relation of FRP ........................................................................ 58 Figure 2.9 Confinement effect of FRP-wrapped on rectangular cross-section .................... 58 Figure 2.10 Stress-strain model of FRP-wrapped rectangular cross-section ....................... 59 Figure 2.11 Location of Fiber Beam-Column Element, Rigid Zone Length and Nonlinear Hinge ................................................................................................................ 59 Figure 2.12 The Lateral Load-Displacement Relationship of the structure deflected to ..... the same ∆u on (a) Elastic System (b) Elastic-Plastic System ......................... 60 Figure 2.13 Curvature distribution along beam at ultimate moment (a) Beam (b) Bending moment diagram (c) Curvature diagram .......................................................... 61 Figure 2.14 Empirical equation of the plastic hinge length (lp) for z = 0.5 ......................... 62 Figure 2.15 Material models for un-retrofitted and FRP-retrofitted members .................... 62 Figure 2.16 Moment-curvature analysis from Xtract and its simplified bilinear curve........ 63 ............................................................................................................................. Figure 2.17 Typical wrapping schemes for shear strengthening using FRP laminates ....... 65 Figure 2.18 Illustration of the dimensional variables used in shear strengthening .............. 66 Figure 2.19 Frame layouts with element’s and nonlinear hinge node’s name...................... 66 Figure 2.20 Bilinear stress-strain curve of steel reinforcement ........................................... 67 Figure 2.21 Stress-strain curves for concrete........................................................................ 68 Figure 2.22 Pushover curve .................................................................................................. 69 Figure 2.23 Final deformation of the unretrofitted frame at failure ..................................... 69 Figure 2.24 Lateral load-Roof drift ratio curve of unretrofitted frame................................. 70 Figure 2.25 Location of Glass-FRP strengthening with amount of the layer ....................... 70 Figure 2.26 Stress-strain curve of glass FRP-retrofitted member......................................... 71 Figure 2.27 Deformation shape of the retrofitted frame at the failure.................................. 71 Figure 2.28 Lateral load-Roof drift ratio curve of G-FRP-retrofitted frame ........................ 72 Figure 2.29 Comparison of analytically Pushover curve for RC frame with and without P delta effect ..................................................................................................... 73 Figure 3.1 (a) Layout of the frame (b) Cross-section of the member ................................... 93 Figure 3.2 3D view of the specimen ..................................................................................... 94 vii Figure 3.3 3D view of the set-up of the test specimens ........................................................ 95 Figure 3.4 Side view of the set up of the test specimen ....................................................... 96 Figure 3.5 Steel arrangement of concrete block before casting............................................ 96 Figure 3.6 Side view of the lateral support system ............................................................... 97 Figure 3.7 3D view of the glass FRP retrofitted frame system............................................. 97 Figure 3.8 Glass FRP system at beam and column............................................................... 98 Figure 3.9 Location of strain gauges on the reinforcing bars ............................................... 98 Figure 3.10 Location of strain gauges on compression side of concrete member ................ 99 Figure 3.11 Location of strain gauges on glass FRP laminates ............................................ 99 Figure 3.12 Location of displacement transducers on the frame .......................................... 100 Figure 3.13 Cracking characteristics..................................................................................... 101 Figure 3.14 Configuration of the LVDT on the joint panel.................................................. 103 Figure 3.15 Joint Rotation histories ...................................................................................... 104 Figure 3.16 Comparison of moment-curvature curve of critical member ............................ 105 Figure 3.17 Strain development............................................................................................ 106 Figure 3.18 Lateral load vs drift ratio curve of un-retrofitted (S1) and retrofitted frame (S2) ............................................................................................................................. 107 Figure 3.19 Load-drift ratio curves: comparison with analytical prediction ........................ 108 Figure 4.1 Details of the frame ............................................................................................. 117 Figure 4.2 Factored-gravity loading on the frame ................................................................ 118 Figure 4.3 Inverted-triangular lateral-pushover load ............................................................ 118 Figure 4.4 Location of the nonlinear hinge........................................................................... 119 Figure 4.5 Stress-strain curves for concrete.......................................................................... 119 Figure 4.6 Bilinear stress-strain curve of reinforcement bar ................................................ 120 Figure 4.7 Lateral load-Roof drift ratio curve of unretrofitted frame................................... 120 Figure 4.8 Stress-strain curve of glass FRP-retrofitted member........................................... 121 Figure 4.9 Lateral load-Roof drift ratio curve of frame retrofitted for 1st two stories.......... 122 Figure 4.10 Location of Glass-FRP strengthening with amount of the layers...................... 123 Figure 4.11 Deformation shape of the retrofitted frame at the failure.................................. 123 viii Figure 4.12 Lateral load-Roof drift ratio curve of bare frame .............................................. 124 Figure 4.13 Load-drift ratio curves: comparison between un-retrofitted and retrofitted frames ............................................................................................................................. 124 ix LIST OF TABLES Table 2.1 Comparison of the analytical model to simulate seismic loading ........................ 52 Table 2.2 Parameter for bilinear moment-curvature curve of plastic hinge nodes ............... 52 Table 2.3 Shear strength of elements .................................................................................... 52 Table 2.4 Moment and curvature at the first cracking of the concrete ................................. 52 Table 2.5 Parameter for bilinear moment-curvature curve of plastic hinge nodes ............... 53 Table 2.6 Shear strength of elements .................................................................................... 53 Table 3.1 The tensile properties of reinforcement bars ........................................................ 92 Table 3.2 Properties of FRP fabrics...................................................................................... 92 Table 4.1 Parameter for bilinear moment-curvature curve of plastic hinge nodes of unretrofitted frame ................................................................................................ 114 Table 4.2 Shear strength of elements of unretrofitted frame ................................................ 114 Table 4.3 Moment and curvature at the first cracking of the concrete ................................. 115 Table 4.4 Parameter for bilinear moment-curvature curve of plastic hinge nodes of retrofitted frame ..................................................................................................................... 115 Table 4.5 Shear strength of elements of retrofitted frame .................................................... 116 x LIST OF SYMBOLS Ae/Ac= effective confinement ratio Afv = area of FRP reinforcement (mm2) Ag = gross area of the concrete section (mm ) As = area for one reinforcement rebar (mm2) Av = area of transverse reinforcement (mm2) b = width of the web (mm) d = distance of the extreme compression fiber to the outer tensile reinforcement (mm) D = equivalent circular column ratio Ec = Young’s Modulus of concrete (MPa) 2 Efrp = Young’s Modulus of FRP reinforcement (MPa) Esec = secant modulus Esl = Young’s Modulus of steel reinforcement (MPa) E2 = slope of the straight line second portion. fc’ = uniaxial compression strength of unconfined concrete (MPa) fcc’ = confined concrete strength ffe = strength of FRP reinforcement (N) fl = confining pressure fr = modulus of rupture of concrete (MPa) fvy = yield strength of transverse reinforcement rebar (MPa) fy = yield strength of reinforcement (MPa) h = height of the members (mm) Igross = moment inertia of the gross concrete section (mm4) κv = bond reduction coefficient Le = active bond length lp = plastic hinge length (mm) Mcrack= moment at the first cracking of the concrete (kN.m) Mu = ultimate bending moment (kN.m) Nu = compression axial load (in N) n = number of FRP reinforcement layers xi Rc = radius of the corner (mm) S = scale factor (=2) s = spacing of the link (mm) tf = thickness of FRP reinforcement (mm) Vc = shear capacity contributed by concrete (N) Vfrp = shear capacity contributed by additional FRP reinforcement (N) Vs = shear capacity contributed by transverse reinforcement (N) Vu = shear demand (N) w = width of FRP reinforcement (mm) ytension= distance from the extreme tension fiber of concrete to the centroid of the section (mm) z = distance of critical section to point of contra-flexure (mm) εc = concrete strain εcc = concrete strain at peak stress εcu = ultimate concrete strain εfe = effective strain of FRP reinforcement εfu = ultimate strain of the fiber εh,rup = rupture strain of the FRP reinforcement εsp = spalling strain εt = axial strain at the transition point εu = maximum strain εy = yield strain κv = bond reduction coefficient µ = ductility ratio φcrack = curvature at the first cracking of the concrete φu = ultimate curvature φy = yield curvature Ф = capacity reduction factor θp = plastic rotation ρsc = cross-sectional area ratio of the longitudinal steel reinforcement σc = concrete stress (MPa) xii σu = ultimate strength (MPa) σy = yield strength (MPa) xiii CHAPTER 1 INTRODUCTION 1.1 General 1.1.1 Tectonic earthquake The earth's crust is not a single plate but is broken into seven large and many small moving plates (Figure 1.1). These thick plates move relative to one another an average of a few centimeters a year. Figure 1.2 shows four types of movement at the boundaries of plates which are recognized as the basic categories of fault movement: strike slip fault, normal fault, reverse slip, and oblique movement. These fault movements are the major causes of earthquake, called tectonic earthquake. In 1911, H.F. Reid formulated the elastic rebound theory to explain the tectonic earthquake. According to the theory, an earthquake occurs when the accumulated strain in the rock masses reach the point where the accumulated stresses due to the friction of the two plates exceed the strength of the rock, causing sudden fracture. In general, the area within a short distance (up to 200 km) from the location of the rupture, called the epicenter, significant damages to buildings and infrastructures can be expected. This is due to the fault movement and high peak ground acceleration of earthquake, as well as its resulting effects. This near-field effect has yielded the worst damages, notably in Chile (1960, 9.5 Richter), San Francisco (1906, 8.3 Richter), Tokyo (1923, 8.3 Richter), China (1976, 7.2 Richter), Armenia (1988, 6.9 Richter), San Francisco (1989, 7.1 Richter), Kobe (1995, 7.2 Richter), and Sumatra (2004, 9.0 Richter). 1 On the other hand, the earthquake engineering community has derived numerous new lessons on far-field effect of earthquakes from the Mexico earthquake in 1985 with a magnitude of 8.1. 1.1.2 Far field effect in Mexico Earthquake, 1985 Although Mexico City is located on the stable part of the North American plate, it experienced many shocks originating from the nearest subduction zone near the SouthWest of Mexico. The subduction zone stretches over 1500 km, where the Cocos plate is subducted under the North American plate at the rate of 75 mm/year (Figure 1.3). In September 1985, an earthquake occurred at this subduction zone, near the Southern coast of Mexico, as shown in Figure 1.3. This earthquake caused substantial damages to hundreds of buildings and infrastructures, as well as the loss of thousands of lives in Lake Zone, Mexico City. What is unusual about this earthquake is the fact that major damages occurred at a distance of about 400 kilometres from the epicenter. Investigators pointed to the large amplification of seismic wave on local soil as the cause of the damages being located so far away from the epicenter. This phenomenon has come to be known as the far field effect of earthquake. The buildings in Lake Zone, Mexico City in 1985, were dominated by the medium to high rise reinforced concrete (RC) building without shear wall, which were designed with low or intermediate levels of ductility according to the 1977 Mexico City Code. These buildings were also identified by the Earthquake Engineering Field Investigation Team (EEFIT, 1986) as the most damaged buildings. 2 Figure 1.4 illustrates that the percentage of buildings depends on the construction type. For buildings of one- to five-storey in high, the RC frame structure was most vulnerable to ground acceleration, while the stone masonry structure experienced the least damage. The vulnerability of buildings to ground acceleration was also influenced by the building height, of which a high percentage of 6- to 20- storey buildings was found to have been damaged. The worst damage was observed to have occurred in RC frame buildings of 9-to-11- storey (Figure 1.4). The Mexico earthquake has taught a valuable lesson that an earthquake can affect buildings at distant fields due to the long period of shear waves (s-waves) that propagate through the soil medium. The local soil condition also plays a significant role in the far field effect since it can alter the frequency or the acceleration of the s-waves. Figure 1.5 illustrates the amplification of the ground acceleration of the Mexico earthquake in 1985 through the soft soil compared to the ground acceleration recorded in the hard ground. An amplification factor of 6 is observed in the peak ground acceleration through 40 m depth of soft superficial soil with a shear wave velocity of 75 m/s. Another major factor that needs consideration is the resonance of the natural frequency of both soil and building (Kramer, 1996), which also played a part in the Mexico earthquake, 1985. The local soil filtered the frequency of ground motion to predominantly between 0.25 and 0.5Hz, which corresponded to the natural frequency of medium to high rise buildings. Because of this resonance effect and the amplification of ground motion, the buildings suffered greatest damage, resulting collapse. Other buildings with different vibration characteristics and heights, however, were found either slightly damaged or completely unaffected. 3 1.1.3 Seismic demand due to far field effects for buildings in Singapore 1.1.3.1 Earthquake and soil condition In Singapore, which is located far away from the seismic fault zone, there has been concern on the far field effect of earthquake on buildings and infrastructures. According to Balendra et al. (2002), there are two possible sources of major earthquakes near Singapore (Figure 1.6). The nearest fault is the Sumateran fault, located at a distance of about 400 km from Singapore. It is a 1500-km long strike slip fault with the maximum energy release estimated at 7.6 on the Richter scale. The next fault is the subduction fault in the Hindia Ocean, along the Sudanese trench, where the nearest point is approximately 600 km from Singapore. This fault, where the Indian Australian Plate subducts under the Eurasian Plate, moves at about 67 mm a year. It was along this subduction zone that several major earthquakes, with magnitude greater than 7.0 on the Richter scale, have been recorded, with the earthquake occurred on the Boxing Day of 2004 with the magnitude of 9.3 being the greatest in recent years. In terms of soil condition, main island of Singapore can be classified into three regions, as shown in Figure 1.7. The western tracts, known as Jurong Formation, consist of a group of sedimentary rocks, and in the central tract lies igneous rocks of granite or similar composition, known as Bukit Timah Granite. The last formation, known as Kallang Formation, generally consists of recent sediments, and old alluvium, covers a large proportion of the total surface of the island, including virtually a whole of eastern part of the island. The reclaimed lands in the south-eastern region of Singapore, namely Marina, Marine Parade and Changi, are all reclaimed using marine clay, taken from Kallang Formation (Kog and Balendra, 1995). This marine clay consists of unconsolidated 4 soft clay with a recorded thickness as high as 42 m and shear wave velocity of 60 to 80 m/s. The fundamental period of vibration of the soil strata vibrating in shear (Ts) can be approximated using: Ts = 4H V (1.1) where H is the thickness of soil strata and Vs is the shear wave velocity of the soil. According to this equation, the fundamental period of the soil strata (Ts) is about 2 seconds for both the soft clay in the Mexico City and Marine Clay in Singapore. Pan (1995) suggested that the seismic environment of the marine clay deposits in Singapore is uncomfortably similar to the soft clay in the Mexico City. Both soils may have the capacity to amplify low frequency components of the ground motion resulting from the long distance earthquake. 1.1.3.2 Vulnerability of buildings to far field effects of earthquake Since Singapore's Independence in 1965, numerous public housing programmes were launched by the by the Housing Development Board (HDB). Many medium to high rise reinforced concrete building were being developed rapidly all over Singapore (Kog and Balendra, 1995). All the buildings in Singapore can be referred to as gravity load design (GLD) buildings because they have been designed primarily to resist gravity load according to the British Standards and its predecessors, which do not have any provision for seismic design. The only lateral load that has to be considered in the design that due to wind gusts of up to 35 m/s or a notional load of 1.5% of the dead weight, whichever governs. These buildings may be inadequate in terms of detailing to resist seismic actions. Hence, they may not have enough inelastic deformation to dissipate the energy caused by 5 earthquake, causing brittle failure of the structure. It is also worth noting that such buildings suffered the worst damage during the Mexico Earthquake in 1985. Since the 1970s, there have been a number of reports in the local press about the panic caused by tremors felt in some buildings within the Central Business District (CBD) due to earthquake occurring in Sumatra (Kog and Balendra, 1995). There was a reported case of a collapse of warehouse roof in 1986, causing injuries to three women. Pan (1995) reported that the Liwa earthquake in Sumatra on 16 February 1994, with a magnitude of 7.0 on the Richter scale and epicentral distance of more than 750 km, caused an alarm system on the 15th floor of 17-storey building, founded on marina clay soil, to ring repeatedly. It was reported also that the acceleration response on the 15th floor reached at least 0.02 g and the base shear coefficient was not less than 1.0%, which was comparable to the 1.5% of the dead weight taken as the notional horizontal load requirement in the British Standards. Balendra et al. (1990) reported that due to soil amplification, the earthquake with an epicentral distance of 400 km can affect a building in Singapore with spectral values corresponding to a base shear larger than 1.5 % of the characteristic dead weight of the structure. Based on the above study, even though Singapore is located on the stable plate and experiences no seismic record, it is still prudent to investigate further seismic performance and behavior of the GLD reinforced concrete buildings in Singapore due to the far field effect of large earthquake and to propose a seismic retrofitting scheme as needed. 6 1.2 Response of GLD structures to seismic action Besides the British Standards which has no seismic design provisions, other older codes in European countries and United States also did not consider seismic actions in design. For example, the codes in the United States and in Europe prior to 1950 and 1960 respectively provided no formal seismic design provisions and even in the earthquake zone, the lateral resistance of the structure was only designed according to wind load. Moreover, the seismic provision for the design and detailing of the members and structures were only included in the mid-1970s in US codes and in the mid-1980s in the European national codes (Fardis, 1998). This means that besides buildings in Singapore, other old buildings in the Europe countries and the US are also GLD buildings. Although designed according to different codes, GLD frames share some common features such as (Aycardi et al, 1994; Lee and Woo, 2002a; Lee and Woo, 2002b; and Moehle, 2000): (a) discontinuity of longitudinal reinforcement in beams, (b) minimal or no shear reinforcement in the beam-column joints, (c) hoops with 90-degree bends, (d) minimal transverse reinforcement in columns for confinement and shear resistance, (e) relatively wide spacing and of the transverse reinforcement in column or beam, and (f) lap splices located in potential plastic hinge zones at the bottom base of columns or near to the end of the beam. Figure 1.8 illustrates the typical frame details of old GLD buildings in the US. Since GLD frames were designed with no seismic detailing, they have been vulnerable to 7 seismic actions. Therefore, some researchers have been trying to investigate the performance and behaviour of gravity load frame against seismic actions. It has been observed that GLD frames when subjected to seismic actions might demonstrate behaviours such as large side-sway deformation, significant stiffness degradation and premature soft storey failure mechanism with weak column-strong beam characteristics (Aycardi et al., 1994; Bracci et al, 1995a, Bracci et al, 1995b ; El-Attar et al., 1997), and premature joint shear failure (Dhakal et al., 2005). However, the strong column-weak beam characteristics of GLD frame was observed in the study conducted by Quek et al. (2002). The overstrength and ductility of GLD structures against seismic actions were observed by Balendra et al. (1999), Lee and Woo (2002b) and Han et al. (2004). Bracci et al. (1995a) constructed a 1/3-scale, 3-storey frame and El-Attar et al. (1997) constructed a 1/6-scale 2-storey and a 1/8-scale 3-storey office building with strength and reinforcing details following non-seismic provision of ACI Code (1989). A shake table was used in these studies to simulate seismic load in the low to moderate seismic zone. The investigators concluded that the inherent lateral strength and flexibility of GLD frames are adequate to resist minor earthquake without major damage. However, for moderate to severe earthquakes, the frames may register substantial side-sway deformations that can exceed recommended limits. These large side-sway deformations resulted from the significant stiffness degradation of the member due to wide cracking and pullout of some reinforcing bars. The GLD frames were observed to be dominated by weak column-strong beam behavior and might suffer from soft-storey collapse mechanism due to inadequate ductility in columns under ultimate load and lack of sufficient strength 8 in the columns as compared to beams. They also concluded that the strength capacity of GLD structures could be predicted using plastic analysis and pushover analysis. Recently, Han et al. (2004) evaluated the seismic performance of a 1/3 scale, 3storey ordinary moment-resisting concrete frame (OMRCF), designed primarily to resist vertical loads according to ACI Code (2002). The frame was constructed and tested under quasi-static reversed cyclic lateral loading. In the study, the OMRCF was observed to be quite stable with no immediate strength degradation and response dominated by flexural behavior. Capacity spectra method was carried out to evaluate the seismic performance of the frame. Figure 1.9 shows the global structural response against design earthquake at several soil conditions. The frame can resist design seismic loads of all seismic zones for soil type SA and SB; for soil type SC only at zones 1, 2A, 2B and 3; and for soil type SD only at zones 1 and 2A. The seismic zones and soil conditions were determined according to UBC Code (1997). Other researchers have also investigated GLD structures which were constructed according to the British Standards. They also observed that the gravity load design structures had over strength and ductility due to the distribution of internal forces under seismic load. Balendra et al. (1999) highlighted that three-bay multi-storey RC frames designed to resist gravity loads and wind loads/notional loads according to BS 8110 had an overstrength factor of 7.5, 5.6 and 2.2 times the design lateral loads for three-,six- and ten-storey frame respectively and a ductility factor of about 2. Lee and Woo (2002b) studied the performance of 1/5 scale 3-storey GLD RC frame constructed according to Korean practice with non-seismic detailing against seismic action. The experimental result showed that the drift of the frame was approximately 9 within the tolerance value. The overall displacement ductility ratio and the over strength value was approximately 2.4 and 8.7 respectively. 1.3 Retrofit of GLD structures to resist seismic action As explained above, even though GLD buildings were found to possess overstrength and ductility, they are vulnerable to damage and even collapse due to seismic action. Therefore, additional studies are required for these particular buildings. Due to economic costs of demolishing and rebuilding, it is essential to find a more rational method for seismic enhancement of existing buildings. This has led to an increased interest in the retrofitting system on existing reinforced concrete buildings. Some of the traditional seismic retrofitting techniques are adding infill wall, steel bracing, and jacketing frame using steel plate. These methods can increase the lateral force carrying capacity and stiffness of the structures to reach the target of the retrofitting work. Infill walls are generally applicable for one to three-storey RC frame buildings (Wyllie, 1996). The infill material can be reinforced concrete, shortcrete, masonry or precast element. Adding infill wall is the one of the most cost-effective technique to increase the lateral load-carrying capacity and lateral stiffness of the existing members and thus to reduce deformation demands on existing members (Wyllie, 1996; Fardis, 1998). However, it should be remembered, that due to their large cross sectional dimensions, they will introduce additional mass to the existing footings (Wyllie, 1996). Figure 1.10 illustrates the typical infill wall technique using reinforced concrete walls. The addition of steel bracings is also a very effective technique for global strengthening (Fardis,1998). They are usually placed near the facade of the buildings for convenience. Kong (2003) conducted several tests of seismic retrofitting technique using 10 knee bracing system. Two GLD RC frames retrofitted using knee bracing system and one unretrofitted GLD RC frame were tested against pushover loading. This novel technique effectively increases the stiffness, strength and ductility of the retrofitted frame as compared to the unretrofitted frame by confining most of the inelastic responses and energy dissipation to the knee element, which is not a primary member of structure. Another advantage of this technique is that it does not introduce large additional mass to the foundation. However, Lombard et al. (1999) found that adding steel bracings may alter the magnitude and distribution of the seismic loads and may lead to unexpected local failure. Figure 1.11 shows the typical seismic resistant steel bracing technique. Another seismic retrofitting technique is the jacketing of several columns, beams and joints. Until the early 1990s, the jacketing technique uses materials such as steel plates and reinforced concrete (see Figure 1.12 and 1.13). The minimum thickness for reinforced concrete jacket should be 10 cm (Davidovici, 1993). The jacketing technique can effectively increase the shear capacity of the existing member. For shear strengthening purpose only, the jacketing element is intentionally discontinued at the end of the member to avoid increasing flexural strength and corresponding shear demand (see Figure 1.14). Steel jacketing technique can also be effectively used to correct the short lap-splices in column by confining inadequate lap-splices (Aboutaha et al., 1996). However, jacketing technique using steel and reinforced concrete is characterized by disadvantages related to constructability issues, durability issues, labour intensiveness, loss of space, difficulty of ensuring the perfect bond between new and old parts, and, in the case of RC jacketing, the generation of significant additional mass to the foundation (Teng et al., 2002; Prota et al., 2005). 11 In recent years, the retrofitting technique using FRP composites has been used widely to replace the jacketing using traditional material (Teng et al., 2002). The advantages of FRP composites are that they are lightweight, non-corrosive and require less maintenance, possess high tensile strength, relatively easy to install on the site and the application does not imply a loss of space. Laboratory studies confirmed the potential of FRP techniques for enhancing the flexural capacity and shear capacity of the RC column and beam as well as the confinement of the column (ACI 440, 2002). Triantafillou and Antonopoulos (2000) concluded that the performance of the FRP to shear capacity is typically controlled by either the maximum effective strain or the debonding strain. The use of proper anchoring (e.g. full wrapping) will significantly increase the shear capacity by delaying the debonding mechanism (Triantafillou and Antonopoulos, 2000). Figure 1.15 shows the glass FRP retrofitted scheme proposed by (a) Ghobarah and Said, and (b) El-Amoury and Ghobarah. In the application field, one of the successful examples of FRP seismic retrofitting application was the retrofitting of a seven-storey building in Los Angeles (Elhassan and Hart, 1995). As a result of the Landers earthquake with magnitude 7.5 on 28 June 1992, the columns of this hotel had significant diagonal cracks. Glass Fiber Reinforced Polymer was used to improve the seismic resistance by wrapping the FRP reinforcement around the columns. This retrofitting work was completed a few weeks before the Northridge Earthquake in 1994. Observation of this building confirmed that there was no damage due to this earthquake. Recently, some researches have been conducted on FRP retrofitting technique for GLD structures ( Harajli and Rteil, 2004; Kong, 2004, Harajli, 2005; Balsamo et al., 2005; Li, 2006). Kong (2004) and Li (2006) studied the seismic enhancement of glass FRP 12 retrofitted RC shear walls. Harajli and Rteil (2004), Memon and Sheikh (2005) and Harajli (2005) studied the improvement in seismic performance of GLD RC columns retrofitted using FRP system. They reported that the retrofitted columns under seismic loading possessed higher energy dissipation, ductility, shear and moment capacity as compared to the unretrofitted columns. Balsamo et al. (2005) concluded that seismic rehabilitation of a full scale three-storey GLD RC structure using glass FRP laminates increased the strength and maximum displacement without altering the torsional behavior as compared to the unretrofitted frame. Kong et al (2003) investigated the retrofitting technique of two 1/5 scaled 25-storey shear walls designed to BS 8110 using glass FRP under pushover load. One specimen was a control specimen, while the other was a retrofitted wall. The experimental result showed that the glass FRP retrofitting enhanced the seismic performance by increasing the ultimate load and lateral displacement of the wall by 1.45 times and 1.66 times respectively of the unretrofitted wall. Li (2006) tested a similar shear wall, but against cyclic loading. The comparative result between cyclic and pushover loading tests shows that the pushover test gives a backbone representation of the cyclic behaviour of the GLD shear wall structures. Harajli and Rteil (2004) tested twelve specimens consisting of 150 x 300 x 1000 mm-long GLD RC columns externally confined with carbon FRP sheets. Most of the specimens experienced significant slip of the column reinforcement and widening of a single crack at the base of the column. It was reported that carbon FRP wrapping reduced the bond deterioration, and enhanced the energy absorption and dissipation capabilities of the columns, resulting in significantly improved seismic performance. 13 Memon and Sheikh (2005) reported that the performance of Glass-FRP external confinement of columns exceeded the performance of similar columns designed according to the seismic provision of the current North American codes. Based on experimental results of eight-column specimens representing columns of building and bridges constructed prior to 1971, the GFRP confinement significantly increased the ductility, energy dissipation ability, and shear and moment capacity of the columns. Harajli (2005) evaluated analytically the effect of externally wrapped FRP reinforcement on the rectangular GLD RC columns. Bond strength degradation due to the spliced longitudinal reinforcement at the column base and effect of the FRP confinement were considered to evaluate the strength and ductility of the columns. It was shown that the analytical results agreed with limited experimental data well. Balsamo et al. (2005) conducted a seismic rehabilitation of a full scale three-storey GLD RC structure using Glass-FRP laminates. Figure 1.16 illustrates the FRP rehabilitation scheme of the frame. This RC frame was tested bi-directionally using pseudodynamic test to investigate the seismic enhancement of GFRP retrofitting technique. The experimental result showed that the GFRP retrofitted frame can withstand the higher level of excitation (0.3g PGA) as compared to unretrofitted frame (0.2g PGA) without any significant damages. The GFRP retrofitting technique increased the maximum displacement of retrofitted frame by roughly 50% under higher level of excitation (0.3 PGA) as compared to the maximum values reached during 0.2 PGA test for the unretrofitted frame. It was also observed that the GFRP intervention did not alter the torsional behaviour of the structure. It is noted that only a small number of studies focused on FRP retrofitted GLD RC frame. Also, most of the studies focused on the FRP retrofitting technique by wrapping the 14 existing members of structure without any longitudinal layer for flexural strengthening. Therefore it is of interest to examine the FRP retrofitted GLD RC frame under seismic load. This research will study a 1970s-built public housing building in Singapore which was designed according to the British Standards. The FRP retrofitting technique used is a system with transversal and longitudinal layers of FRP reinforcement. As mentioned earlier, even though Singapore is located on the stable plate and records no seismic activity, it is still prudent to investigate seismic performance and behavior of the GLD reinforced concrete buildings in Singapore against seismic actions. Even though GLD buildings possessed the overstrength and ductility, researches have shown them to be vulnerable to damage and even collapse due to seismic action. Therefore, it becomes important to find and propose seismic retrofitting scheme of existing GLD buildings. In recent years, the retrofitting technique using FRP composites has been used widely to enhance the seismic performance of existing buildings. However, there have been only a few studies on FRP seismic retrofitting technique of the GLD buildings. Therefore, it is of interest in this study to learn the seismic retrofitting technique of GLD RC frame using FRP system. 1.4 Objective and Scope The objective of this thesis is to observe the behaviour and performance of RC frame, designed primarily for gravity loads, when subjected to far field earthquakes; and to propose a seismic retrofitting method using FRP system. 15 For this purpose, a GLD RC frame with 1½-bay width of total 3100 mm and 2storey height totaling 2825 mm, designed according to British Standards Code, was modeled and analyzed using software CAPP-2D against pushover load. The frame was retrofitted using glass FRP reinforcement, consisting of transverse layers and longitudinal layers on the tension side of frame members, to improve the global seismic performance. The experimental work verified the result of the analytical modelling. The enhancement of stiffness, strength and ductility of the retrofitted structure over the unretrofitted frame was evaluated. 16 Figure 1.1 Configuration of tectonic plates of the world (Kramer, 1996) Figure 1.2 Basic categories of fault movement (Paulay and Priestley, 1992) 17 ±400 km Figure 1.3 Tectonic map of Mexico (EEFIT, 1986) 80 70 60 50 40 30 20 Concrete frame 10 Brick load bearing wall Stone masonry 0 Up to 2 3 to 5 6 to 8 9 to 11 12 to 14 15 to 17 18 to 20 > 20 Figure 1.4 Percentage of observed buildings damages versus number of storey of different construction types (EEFIT, 1986) 18 Figure 1.5 Records of Mexico earthquake 1985 (a) hard ground (b) soft ground (Pan, 1995) ±600 km ±400 km Figure 1.6 Location Sudanese Trench and Sumateran Fault 19 Figure 1.7 Singapore soil formations (Kog and Balendra, 1995) Figure 1.8 Typical details of old GLD buildings in western US (Moehle, 2000) 20 Figure 1.9 Global structural response at performance point against design earthquake at site condition of (a) SB (b) SC (c) SD (Han et al., 2004) 21 new shear infill wall existing column shear connector (a) Position of added infill wall and existing column Figure 1.10 Typical infill wall technique using reinforced concrete wall (Davidovici, 1993). 22 existing beam added infill wall (b)Position of added infill wall and existing beam existing shear wall added infill wall (c) Position of existing and added shear walls Figure 1.10 Typical infill wall technique using reinforced concrete wall (cont’d). Figure 1.11 Seismic resistant bracing techniques 23 existing member steel connector (a) column jackets (b) beam jackets (c) joint jackets Figure 1.12 Reinforced concrete jacketing technique (Davidovici, 1993) 24 Figure 1.13 Steel jacketing technique (Aboutaha et al, 1996) gap jacket existing column Figure 1.14 Column jacket with gap 25 Figure 1.15 Glass FRP-strengthened specimens tested by (a) Ghobarah and Said, and (c) El-Amoury and Ghobarah. (Engindeniz et al., 2003) Figure 1.16 Rehabilitation of exterior columns and joints: (a) column wrapping (b) joint strengthening (c) U-wrapping on the beam (Balsamo et al., 2005) 26 CHAPTER 2 ANALYTICAL MODEL 2.1 General This chapter describes the analytical study of a 4-storey public building in Singapore, built in 1970s, under pushover loading using a commercial software CAPP-2D Pushover (www.imbsen.com/CAPP). The reinforced concrete building was designed according to the British Standards, using a low concrete strength of 20 MPa. Figure 2.1 shows the plan view of the whole building and the critical frame having the weakest lateral capacity (Li, 2006). It has been observed that considerable inelastic deformations and hysteretic energy dissipation occurred on the first and second stories of a 3-storey 1:3 scale GLD frame under seismic loading by Bracci et al. (1995a). Also, ElAttar et al. (1997) found that the most of the deformation, damage, and energy dissipation of the two-storey and threestorey GLD RC frames occurred in the first-storey column. Lee and Woo (2002b) reported that the plastic hinges and cracks occurred mainly at the lower two stories, followed by the soft-storey collapse mechanism at the first storey. Since the lower two stories are the critical part of the GLD frame, it is reasonable to choose only the lower two stories of the 4-storey building for the purpose of this study. The analytical model is a ½ scale, one- and half-bay, and two-storey frame, representing the lower two stories of this 4-storey building as shown in Figure 2.1. For simplicity and on the conservative side, slabs and infill walls were not incorporated in the experimental study. Figure 2.2 shows the layout of the reinforced concrete test frame and the cross-section properties of its members. 27 2.2 Seismic analysis There are four analytical methods which are commonly used to model the seismic loadings on a building structure (Naeim, 2001). They are: (a) Linear Static Analysis (LSA) LSA is only permitted for buildings with a “regular” structural configuration and in which higher mode effects are not significant. This is generally true for low rise and regular buildings with no torsional irregularities. A regular configuration is defined by means of a parameter called “demand capacity ratio” (DCR) and of geometrical requirements. DCR is defined as the ratio between the force acting on a member due to gravity and earthquake loads and its expected strength. This parameter is intended to roughly evaluate the magnitude and distribution of the inelastic demand on the building and to determine the structural regularity. Linear elastic properties of materials are adopted in this analysis. (b) Linear Dynamic Analysis (LDA) In LDA, the building is modelled as a multi-degree-of-freedom (MDOF) system with a linear elastic stiffness matrix and an equivalent viscous damping matrix. The seismic input is modelled using either modal spectral analysis or time history analysis but in both cases, the corresponding internal forces and displacements are determined using linear elastic analysis. The advantage of LDA over LSA is that the former considers higher modes. However, since they are based on linear elastic response, the applicability decreases with increasing nonlinear behavior. 28 (c) Nonlinear Static Analysis (NSA) In general, linear analysis is applicable when the structure is expected to remain nearly elastic for the level of ground motion. If the performance objective of the structure implies greater inelastic demands, the uncertainty with linear procedures increases to a point that requires a high level of conservatism in demand assumptions and acceptability criteria to avoid unintended performance. Therefore, procedures incorporating nonlinear analysis are used to reduce the uncertainty and conservatism. In NSA, nonlinear properties of materials are used. But as in other static analysis, NSA is only permitted for buildings in which higher mode effects are not significant. The seismic load is simulated as a pushover loading. That is an increasing lateral load is applied to the building until a target displacement is reached at the control node. This loading can be monotonic or cyclic loads. Non-linear properties of materials are used in this analysis. (d) Nonlinear Dynamic Analysis (NDA) NDA utilizes the combination of ground motion records with a detailed structural model. Therefore, it is capable of producing results with relatively low uncertainty. In nonlinear dynamic analysis, the detailed structural model subjected to a ground-motion record produces estimates of component deformations for each degree of freedom in the model and the modal responses are combined using schemes such as the square-root-sumof-squares. NDA can be used to analyze all types of buildings with no limitation and restriction. Seismic loads are taken from the data recorded in the previous earthquake; this method is also known as time history analysis. Table 2.1 shows the advantages and disadvantages of the above method. 29 2.3 Non-linear pushover analysis In recent years, nonlinear static analysis or pushover analysis has gained significant popularity and become widely used in seismic design field. Some codes recommend pushover analysis as the method to design a new building and evaluate the old building under seismic load. For example, Federal Emergency Management Agency (FEMA) 273/274 guideline (FEMA, 1997) recommends pushover analysis as one of the three analysis techniques for seismic design. In Applied Technology Council (ATC) 40 guideline (ATC, 1996), pushover analysis is a main component of the Spectrum Capacity Analysis Method. FEMA 273/274 recommends pushover analysis as a method to evaluate and rehabilitate the all types of buildings. ATC 40 also recommends pushover analysis as a approach to evaluate the respond of rehabilitated reinforced concrete buildings. This is because pushover analysis provides information on the response characteristic of the structure that cannot be obtained using other analysis methods (Krawinkler and Seneviratna, 1998). They include: (a) realistic force/moment demands of every structural element; (b) inelastic deformation of structural element to dissipate the seismic energy; (c) consequences of the strength degradation of structural elements; (d) identification of critical parts of a structure that need attention in detailing; (e) inter-storey drift or roof storey drift of a structure to control the damage; and (f) completeness and adequacy of load path of the structural system. In static pushover analysis, the structure under seismic base excitation is assumed to respond in a way that is similar to an equivalent single-degree-of-freedom (SDOF). The response is assumed to be dominated by a single mode (Krawinkler and Seneviratna, 30 1998). This assumption is supported by numerous investigations, while reported that the pushover analysis with these assumptions can provide a good prediction of the seismic response of the single mode domination of multi degree of freedom (MDOF) structures (Krawinkler and Seneviratna, 1998; Saiidi and Sozen, 1981; Fadjfar and Fischinger, 1988). With the rapid advancement in computer technology, numerous of nonlinear finite element softwares have become available for pushover calculation. They include Etabs and SAP developed by CSI (www.csiberkeley.com), Drain2DX and Drain3DX developed by University of California, Berkeley http://nisee.berkeley.edu, Ruaumoko developed by Canterbury University (www.civil.canterbury.ac.nz), and Capacity Analysis Pushover Program (CAPP) -2D Pushover developed by Imbsen & Associates Inc. (www.imbsen.com). This study uses the CAPP-2D Pushover software to analyze the reinforced concrete frame with and without retrofitting against pushover loading. The CAPP-2D Pushover program is suitable for the nonlinear analysis of buildings and bridges. The important features in this software include (Chadwell, Imbsen & Associates, 2002): (a) piecewise nonlinear hinge elements to model connection and/or plastic behavior including strain hardening, strain softening, asymmetric rotation response and rigidplastic capabilities; (b) moment-axial force interaction hinges to capture effects of axial load on moment yielding; (c) multi-linear nonlinear axial spring elements to capture behavior of nonlinear foundations, unbounded brace behavior, buckling braces, and nonlinear trusses; (d) P – delta effects; 31 (e) fully functional beam elements with offsets, releases, and moment rotation hinges; (f) pile elements with varying effects through the depth and plastic hinges that form within the elements as yield moments are exceeded; and (g) full pushover capabilities with any user-defined load pattern and user-defined limit state. 2.4 Material properties for modelling The properties of constituent materials play an important part in the analysis. The behavior and strength of reinforced concrete (RC) are dependent on the stress-strain relations of the concrete and the reinforcement (Macgregor and Wight, 2005). The stressstrain relations including a maximum strain and a maximum stress of the materials are used to create a moment-curvature relation for each RC structural element. Since this study uses monotonic pushover analysis, the monotonic stress-strain relations are used to define the nonlinear behavior of the element. 2.4.1 Steel Under monotonic loading, the maximum strain of the steel reinforcement has a significant effect on the ductility of reinforced concrete since it becomes a failure criterion for the structural element (Priestley. et al., 1996). In this study, the stress-strain relation is simplified as bilinear elastic-plastic with isotropic hardening in both compression and tension. Figure 2.3 illustrates the bilinear stress-strain curve of steel reinforcement. The modulus of elasticity of the steel (Es1) is given by the slope of the linear elastic portion of the curve. 32 There are two significant points in this curve: the yield point and the ultimate point. The yield point is the point when the stress of steel reinforcement reaches its yield strength (σy), corresponding to the yield strain (εy). The ultimate point corresponds to the fracture of the bar, when the steel reinforcement reaches its ultimate stress (σu) with the maximum strain (εu). The yield point and the ultimate point can be obtained from tensile test. 2.4.2 Concrete In this study, the uniaxial compressive strength of concrete is required. The tension strength of the concrete is neglected. The behavior of the plain concrete is less ductile. But in the practice, reinforced concrete member is confined by transverse reinforcement; thus the ductility of the concrete can be increased significantly (Figure 2.4). In this study, both unconfined and confined concrete are used to more accurately assess the strength and ductility of the structural member. 2.4.2.1 Unconfined concrete model This model is used for the cover concrete which is not confined by the transverse reinforcement. The Mander Model (Mander et al., 1988) is used in this present study. Figure 2.5 shows the stress-strain relationship of the model, which is given by: ⎡ where, x = εc ε cc xr ⎤ σ c = fc ' ⎢ r ⎣ r − 1 + x ⎥⎦ for εc < εsp (2.1) σ c = 0.2 f c ' for εc ≥ εsp (2.2) (2.3) 33 r = Ec E c − E sec Esec = fc ' ε cc (2.4) (2.5) in which, σc = concrete stress; εc = concrete strain; fc’ = uniaxial compression concrete strength; Ec = elastic modulus; Esec = secant modulus; εcu = ultimate concrete strain; εcc = concrete strain at peak stress (= 0.002); and εsp = spalling strain (=0.006). Kent and Park (Park and Paulay, 1975) suggested that a residual strength, due to friction along failure surfaces, of 0.2 fc’ be assumed for large strains. 2.4.2.2 Confined concrete model The stress-strain relation of confined concrete when the concrete is loaded under low stress is similar to that of unconfined concrete (Figure 2.4). As the stress level approaches the uniaxial compression strength, the confinement of the transverse reinforcement works due to the higher strain of the transverse reinforcement rebar and thus, the concrete performs as a confined concrete (Park and Paulay, 1975). To achieve the designed level of ductility of the concrete element, the transverse reinforcement has to be provided sufficiently to confine the compressed concrete within the core region and to prevent the longitudinal reinforcement from buckling. The stressstrain relation for confined concrete has been proposed by many researchers. Based on the investigation using different shapes of the transverse reinforcement, it is concluded that the shape (rectangular or circular) of the transverse reinforcement affects concrete confinement. The circular transverse reinforcement provides a continuous confining pressure but the rectangular transverse reinforcement can only confine near the corners of 34 the hoop (Park and Paulay, 1975). Figure 2.6 shows the confinement effect on the rectangular reinforced concrete’s cross-section. All the concrete elements used in this study are a rectangular in shape; and this will be discussed next. The stress-strain relation of the rectangular confined concrete has been proposed by many researchers (Kent and Park, 1971; Chan, 1955; Blume et al, 1961; Baker and Amarakone, 1964; Roy and Sozen, 1964; Soliman and Yu, 1967; and Mander et al., 1988). In this study, the confined concrete model is based on the model proposed by Mander et al (1988) since it yields only a small loss of accuracy which is not significant in the terms of the natural variability of the material properties (Booth, 1994). This confined model is based on the Mander’s unconfined concrete model with some modifications to account for the transverse reinforcement confining effects. Figure 2.7 shows Manders’s confined concrete model. The stress-strain relation of the confined concrete (Figure 2.7) is defined using the following formula (Mander et al., 1988): ⎡ xr ⎤ σ c = fc ' ⎢ r ⎣ r − 1 + x ⎥⎦ where, x = for εc ≤ εcu εc ε cc (2.7) ⎡ ⎤ εcc = 0.002⎢1 + 5⎛⎜ f cc ' − 1⎞⎟⎥ ⎜ ⎟ ⎢⎣ r = ⎝ fc ' ⎠⎥⎦ Ec E c − E sec Esec = (2.6) fc ' ε cc (2.8) (2.9) (2.10) in which, fcc’ = confined concrete strength and other terms are defined earlier. 35 2.4.3 Glass fiber reinforced polymer reinforcement In the present study, glass fiber reinforced polymer (FRP) reinforcement is used due to its wider application in construction site and relatively lower price compared to other types of FRP reinforcement. It is a composite with strength comparable to steel reinforcement and weight lighter than steel (by about 20%). Typically FRP reinforcement has linear stress-strain relation, as shown in Figure 2.8, in which the Young’s Modulus is denoted by Efrp, rupture strain by εu, and ultimate strength by σu. The confining effect of FRP wrapping is similar to the confining effect by transverse reinforcement. The FRP reinforcement confines the whole concrete including the cover concrete which is not confined by the transverse reinforcement confinement. For rectangular section, the corner is rounded to prevent the tearing of FRP reinforcement under high stresses. In the present study, rounded corners with radius (Rc) of 25 mm were applied. Figure 2.9 shows the confinement effect of FRP reinforcement on rectangular cross-section. There are many researchers who have tried to understand and model the behavior of the FRP-wrapped concrete (Mirmiran et al., 1998; Pessiki et al., 2001; Rochette and Labossiere, 2000; Campione and Miraglia, 2003; and Lam and Teng, 2003). However, most of them have developed the stress-strain model specifically for FRP-wrapped circular cross-section, not for FRP-wrapped rectangular cross-section. In this study, the stress-strain model developed by Lam and Teng (2003) was adopted. This model is based on the assumption that the stress-strain curve can be divided into two portions: a parabolic portion and a straight line portion; the initial slope of the parabola is equal to the modulus 36 elasticity of the unconfined concrete (Figure 2.10). The equation for uniformly confined concrete is given by: σ c = Ec ε c − ( Ec − E2 ) 2 (0 ≤ ε c ≤ ε t ) 4 fc ' σ c = f c '+ E2ε c (2.11) (ε t ≤ ε c ≤ ε cu ) (2.12) where σc and εc are the axial stress and strain of confined concrete respectively, Ec is the young modulus of unconfined concrete, εt is the axial strain at the transition point, and E2 is the slope of the straight line second portion. The value of εt and E2 can be derived from following equations: εt = ε2 = 2 fc ' Ec − E2 (2.13) f cc '− f c ' (2.14) ε cu The ultimate compressive strength of FRP-confined concrete fcc’ is predicted by modifying the compressive strength equation of Saaman et al (1998). The equation is given by: f f cc ' = 1 + k 1 k s1 l fc ' fc ' (2.15) where fc’ is the unconfined concrete compressive strength, k s 1 fl is the effective fc ' confinement ratio, k1 is the coefficients values equalling to 3.3, ks1 is the shape factor, and fl is the confining pressure. The ultimate axial strain of the FRP-confined concrete, εcu, is given by ε cu f ⎛ ε h,rup ⎞ ⎟ = 1.75 + k 2 k s 2 l ⎜⎜ ε co f c ' ⎝ ε co ⎟⎠ 0.45 (2.16) 37 where, εh,rup is the rupture strain of the FRP reinforcement which is taken to be equal to the ultimate strain of the fiber in this study, εco is taken to be 0.002, k2 is the coefficients values equalling to 12, and ks2 is the shape factor. The latter three parameters are given by: α ⎛ b ⎞ Ae k s1 = ⎜ ⎟ ⎝ h ⎠ Ac (2.17) β ⎛ b ⎞ Ae ks2 = ⎜ ⎟ ⎝ h ⎠ Ac fl = 2σ j t D = (2.18) 2 E frp ε j t f (2.19) D where Efrp is the elastic modulus of FRP, b and h are the dimensions of the concrete crosssection, tf is the thickness of the FRP-wrapped, and εj is taken as the ultimate strain of FRP fiber. The effective confinement ratio (Ae/Ac) and the equivalent circular column (D) are given by: Ae 1 − = Ac [(b h )(h − 2R ) + (h b )(b − 2R ) ] (3 A ) − ρ 2 2 c c g sc 1 − ρ sc D = h2 + b2 (2.20) (2.21) where Ag is the gross area of the concrete section, Rc is the radius of the corner, and ρsc is the cross-sectional area ratio of the longitudinal steel reinforcement. 2.5 Non-linear RC beam-column element In the CAPP-2D Pushover program, there are five elements to model the elements of the prototype structure: elastic truss element, elastic beam-column element, axial spring element, rigid element and pile element. The present study used the elastic beam-column element to model the elements of the structure. In the software, the thickness of the beam 38 and the column section are represented as a fiber line which is located in the middle of the section. Rigid zone length feature, provided by CAPP software, was used to account for the rigidity of beam-column joint core (Figure 2.11). To represent the nonlinear behavior of the member, nonlinear hinges were placed at the surface of beam-column joints (Figure 2.11). There are three types of hinges: nonlinear moment-rotation hinge, nonlinear axial-force deformation spring, and momentaxial forces interaction hinge. 2.5.1 Plastic Hinge Length In capacity design, a moment redistribution may occur when the yield force or yield moment of a section is exceeded, forming plastic hinge which leads to a plastic mechanism of the element (McGreggor and Wight, 2005). In seismic design, this concept provides a design of structure with adequate ductility. These plastic mechanisms dissipate the energy of the earthquake; thereby decreasing the force that must be resisted by the structure (Park and Paulay, 1975). From Figure 2.12, it can be seen that for a ductility ratio of µ, the maximum lateral load acting in the elastic-plastic structure would be 1/µ times the lateral load acting in the elastic structure. Figure 2.13 shows a cantilever reinforced concrete element which is loaded at the free end until the ultimate curvature (φu) and bending moment (Mu) at the critical section are reached. Figure 2.13c shows the distribution of the curvature along the element. The element can be idealized into two regions of curvature: the elastic and inelastic curvature region. The inelastic curvature region is the region where the demand curvature (φ) exceeds the yield curvature (φy) of the section. The enhanced rigidity of the member 39 between the cracks causes the fluctuation of the curvature along the beam and the peaks of the curvature line corresponding to the crack position along the member. The shaded area in Figure 2.13 (c) indicates the regime where inelastic rotation of the element occurs. The plastic hinge is defined by lp and the plastic rotation (θp) can be calculated from: θ p = (ϕ u − ϕ y )l p (2.22) Many empirical equations were investigated and proposed by researchers (Baker and Amarokone, 1965; Corley, 1966; Sawyer, 1964; Mattock, 1967). In this study, the empirical equation proposed by Mattock (1967) is used to calculate the plastic length of the member. This equation was modified from the equation proposed by Corley (1966). Based on the research investigation by Mattock (1967), this new equation fits the trend of the data better than the original equation. The new equation is given by: l p = 0 .5 d + 0 .05 z (2.23) where d = the distance from the extreme concrete compression fiber to the outer tensile reinforcement, and z = the distance of critical section to point of contra-flexure. The value of the plastic hinge generally varies from 0.3 to 1.0 of depth of the section. Figure 2.14 shows the investigation by Pannelis and Kappos (1997). They reported that the value of the plastic hinge based on the empirical equation by Sawyer, Corley and Mattock varied between 5 to 10% of the span for common value of the depth of the section to the length of the span. 40 2.5.2 Moment-curvature relation In the present study, the moment-curvature relation of the RC section is calculated using the commercial Microsoft Windows-based software, Xtract (Chadwell and Imbsen, 2004). Xtract provides material models for the stress-strain curve for both Mander’s unconfined and confined concrete and bilinear stress-strain curve for steel reinforcement. The stress-strain curve for FRP reinforcement model is obtained by modifying the bilinear stress-strain curve since there is no default model for FRP reinforcement in Xtract. The linear elastic portion of bilinear stress-strain curve is used to model the stress-strain of the FRP reinforcement, but the strain hardening portion is ignored by equaling the value of ultimate point to the value of the yield point. To accommodate the confining effect of FRP reinforcement external wrapping, Xtract provides a user-defined model. This model can generate a stress-strain curve according to the information on the stress and the corresponding strain, manually input by the user. All of the material models used in this analysis followed the explanation of material model as mentioned earlier. Figure 2.15 defines the material model for part of both un-retrofitted member and FRP-retrofitted members. In calculating the moment-curvature relation of column, the axial load was calculated from the gravity load resisted by a particular column. This axial load was assumed to be a fixed value. For the beam, the axial load was taken to be equal to zero. Then from the result of the moment-curvature curve given by Xtract, a simplified bilinier moment-curvature curve was adopted for the purpose of this study. Figure 2.16 shows the result of the moment-curvature analysis from Xtract and its simplified bilinear curve. 41 2.5.3 Moment at the first crack When the load was initially applied to the member, the member was un-cracked. Since it was un-cracked section, the moment inertia of the gross concrete section was used in the analysis in this stage. The internal stress distribution was essentially linear and the internal strain was very small. The moment curvature curve in this stage was still linear. When the tensile stress demand reached the tensile strength capacity of the concrete, the first cracking occurred in the member. The moment at the first cracking of the concrete (Mcrack) was calculated according to: f r I gross M crack = y tension (2.24) where, fr is the modulus of rupture of concrete (in MPa), Igross is the moment inertia of the gross concrete section (in mm4), and ytension is the distance from the extreme tension fiber of concrete to the centroid of the section (in mm). The curvature at the first cracking of the concrete (φcrack) was calculated by: fr ϕ crack = Ec y tension (2.25) where, Ec is the Young’s Modulus of concrete (in MPa), and other terms are defined earlier. The modulus of rupture in the present study was obtained from the flexural test and calculated using the following equation: fr = 6M bh 2 (2.26) where, M is the moment obtained from the flexural test (kN.m), b is the width of specimen, and h is the overall depth of specimen. 42 2.5.4 Shear Strength When the shear demand of a member during pushover loading exceeds its shear capacity, the shear failure takes place at that member. This shear failure is brittle in nature and causes a sudden failure of the member. The basic design equation of the shear is given by (ACI 440, 2002): ФVn ≥ Vu (2.27) Vn = Vc + Vs +Vfrp (2.28) Where Ф is the capacity reduction factor, Vu is the shear demand, and Vn is the shear capacity. The shear capacity of the member is contributed by concrete (Vc), shear reinforcement (Vs), and additional FRP reinforcement (Vfrp). In this study, the capacity reduction factor is taken to be 1.0. The concrete shear strength, Vc (in N), based on ACI 318 Building Code (2002) is given by: ⎛ Vc = ⎜⎜ ⎝ f 'c + 120 ρ scVu d ⎞ bd ⎟⎟ Mu ⎠ 6 (2.29) where fc’ is the uniaxial compression strength of unconfined concrete (in MPa), b and d are the web width and effective depth of tensile reinforcement respectively (in mm), Mu is the moment demand at the section (in kN.m), Vu is the shear demand at the section (in kN), and ρsc is the cross-sectional area ratio of the longitudinal steel reinforcement (in mm2). The contribution of the compression axial load in the shear strengthening calculation, as in columns, is given by: 43 ⎛ Nu Vc = ⎜ 1 + ⎜ 14 A g ⎝ ⎞ ⎟ ⎟ ⎠ f 'c bd 6 (2.30) where Nu is the compression axial load (in N) and Ag is the gross area of the cross-section (in mm2). The shear strength contributed by transverse reinforcement, Vs (in N) reinforcement using ACI 318 (2002) is given by: Vs = Av f v y d (2.31) s where Av is the area of transverse reinforcement (in mm2), fvy is the yield strength of transverse reinforcement rebar (in MPa), and s is the spacing of the link (in mm). The shear resistance provided by the FRP reinforcement is calculated according to the equation given by ACI 440 (2002). Figure 2.17 shows typical wrapping schemes for shear strengthening using FRP laminates. The shear contribution of the FRP shear reinforcement is given by: V frp = A fv f fe (sin α + cos α ) d f sf (2.32) where the area of FRP reinforcement, Afv, (in mm2) and the strength of FRP reinforcement, ffe, (in N) are calculated according to: A fv = 2 nt f w (2.33) f fe = ε fe E frp (2.34) where n is the number of FRP reinforcement layers, tf is the thickness of FRP reinforcement (in mm), w is the width of FRP reinforcement (in mm), εfe is the effective 44 strain of FRP reinforcement, and Efrp is the young modulus of FRP reinforcement (in MPa). Figure 2.18 shows the illustration of the dimensional variables that used in the equation. The effective strain in FRP laminates (εfe) is given by: ε fe = 0.004 ≤ 0.75ε fu , for completely wrapped member (2.35) ε fe = κ v ε fu ≤ 0.004 , for bonded U-wraps or bonded face plies (2.36) where εfu is the ultimate strain of the fiber and κv is the bond reduction coefficient which is function of the concrete strength, the type of wrapping scheme and the stiffness of the laminates. This bond reduction is given by: κv = k1 k 2 Le ≤ 0.75 11900ε fu (2.37) where Le is the active bond length that is the length where the bond stress is maintained. This length is given by: Le = 23300 (nt f E f ) 0.58 (2.38) The reduction account (k1) to the concrete strength is given by: ⎛ f '⎞ k1 = ⎜ c ⎟ ⎝ 27 ⎠ 2 3 (2.39) and the reduction account (k2) to the type of wrapping scheme is given by: k2 = k2 = d f − Le df , for U-wraps d f − 2 Le df , for two sides bonded (2.40) (2.41) 45 ACI 440 (2002) requires that the total shear reinforcement-contributed by FRP and transverse reinforcement- should be limited to: Vs + V frp = 0.66 f c 'bd (2.42) where all the terms are defined earlier. 2.6 Analytical model of unretrofitted RC frame The dimensions of the unretrofitted frame with the cross-section properties of each member are shown at Figure 2.2. 2.6.1 Material properties In this nonlinear analysis of the unretrofitted concrete frame, the elastic beam column element is used with the nonlinear hinge at the end of the member (Figure 2.19). Figure 2.20 shows the average stress-strain relation of the steel reinforcement bar obtained from the two tensile test coupons of the material. Figure 2.21 shows the unconfined compressive and confined compressive stress-strain curve of concrete, derived from Mander’s Model (see Section 2.4.2). The moment-curvature relation of each member was simplified from those calculated using software Xtract (Figure 2.16). Table 2.2 shows the bilinear moment curvature curve of each nonlinear hinge in the frame. Table 2.3 shows the shear capacity of each member based on Eq. (2.28). 46 2.6.2 Loadings The vertical loads, placed at the top of the 2nd story column (Figure 2.19), were calculated from the dead and live loads based on the tributary area. The pushover load with a proportion of 39% and 61% is placed at the 1st and 2nd-storey beams respectively (Figure 2.19). This proportion followed the load proportion in the experiment. The second order (P-delta) effect was also considered in the pushover analysis. 2.6.3 Moment at first crack CAPP Pushover 2D software adopts the bilinear moment-curvature relation as the input parameters to represent the nonlinear hinge of the member. Therefore, the pushover curve calculated using CAPP software does not provide information of the initial crack of the concrete. To obtain a more accurate pushover curve, some modifications were adopted in the present study. The moment and curvature at the first cracking of the concrete for every member was calculated according to Eq. (2.24) and Eq. (2.25). Table 2.4 shows the moment and curvature at the first cracking of the concrete for the members. These values of moment and curvature were used as input parameters for nonlinear hinges. Then, the frame was analyzed against pushover loading and a pushover curve until the first cracking of the concrete (1st pushover curve) was obtained (see Figure 2.22a). Then, the frame with the input parameter of bilinear moment-curvature curve as shown in Table 2.2 was analyzed against pushover loading. This analysis yields a pushover curve until a failure on the frame occurred (2nd pushover curve). In this pushover curve, a linear line was used by the software to connect the origin point and the first yield of the reinforcement bar in the member (see Figure 2.22b). 47 Two pushover curves were obtained based on the pushover analysis of two similar frames with different parameters of nonlinear hinges of the frame, as explained earlier. Then, these two curves were combined into one modified pushover curve. For the initial part of the combined pushover, the pushover curve until first cracking of the concrete was used. Then, a linear line was adopted to connect the point of first cracking of the concrete and the point of the first yielding of the reinforcement bar in the member. The rest of the combined pushover curve followed the 2nd pushover curve (see Figure 2.22c). 2.6.4 Analytical results The deformation form of the frame at failure and the sequence of the plastic hinge formation against pushover load are shown in Figure 2.23. Judging from the location of the plastic hinges, the frame was seen to develop a collapse mechanism featuring strong column-weak beam characteristics. First yield of the reinforcement bar occurred in at hinge number 2 at the drift ratio of 0.56%. The flexural failure occurred at plastic hinge number 1 when the total ultimate lateral load reached 78 kN and the ultimate drift ratio 2%. The predicted lateral load-displacement curves of the unretrofitted concrete frame can be seen in Figure 2.24. 2.7 Analytical model of RC Frame with FRP system In the present study, glass FRP seismic retrofitting system was used. Studying from analytical result of the unretrofitted frame, it can be concluded that the critical location of the unretrofitted frame under pushover loading are the bottom end of both exterior and interior columns; and both end of the 1st- and 2nd- storey beams. Thus, these 48 critical locations were retrofitted. Figure 2.25 shows the location of the glass FRP and the amount of layers used in each retrofitted member. 2.7.1 Material properties The stress-strain curve of the simplified bilinear stress-strain curve of reinforcement bar; and the unconfined and steel transverse reinforcement confined concrete are shown in Figure 2.20 and 2.21 respectively. The stress-strain curve of glass FRP reinforcement is shown in Figure 2.25. The stress-strain of the glass FRP-wrapped concrete was calculated according to Eq. (2.11) and (2.12). Figure 2.26 shows the stressstrain of the glass FRP-wrapped concrete for various sections. The bilinear moment curvature for unretrofitted members were calculated as previously explained at Section 2.6.1. The bilinear moment-rotation curve for glass FRPretrofitted members were simplified from moment-rotation curve calculated using Xtract (Figure 2.15). Table 2.5 shows the bilinear moment-curvature curve of each nonlinear hinge in the frame. Table 2.6 shows the shear capacity of the members based on Eq. (2.28). 2.7.2 Loadings All loads applied on the frame were exactly the same as the loads on unretrofitted frame. The second order (P-delta) effect was also considered. 2.7.3 Moment at first crack The moment and curvature at first cracking of concrete for every member were calculated according to Eq. (2.24) and Eq. (2.25). 49 2.7.4 Analytical results The deformation form of the frame at ultimate failure and the sequence of the plastic hinge formation against pushover load are shown in Figure 2.27. Judging from the location of the plastic hinges, the frame exhibited a collapse mechanism featuring a strong column-weak beam characteristic. The first yield of reinforcement bar occurred at joint number 1 at a drift ratio of 0.33%. The flexural failure occurred at hinge number 9 when the ultimate lateral load of 103.5 kN and the ultimate drift ratio of 1.77% were reached. The predicted lateral load-displacement curve of the retrofitted RC frame is shown in Figure 2.28. 2.7.5 P-delta effect P-delta effect is a second order effect that occurs in every structure in which elements, subjected to axial load, deflect laterally. This effect is associated with the magnitude of the applied axial load (P) and the displacement (delta). Figure 2.29 shows that the lateral capacity of the frame considering P-delta effect to be about 5% lower than the frame without considering P-delta effect. The difference is not significant because the frame is taken from a low-rise building where the magnitude of the applied axial load is relatively low. On the other hand, for a high-rise building, P-delta effect has to be carefully considered in the design stage because the applied axial load and the lateral displacement are relatively large. 50 2.8 Summary The global performance in terms of the strength, stiffness, ductility of both unretrofitted and retrofitted GLD reinforced concrete frames under pushover loading were numerically obtained using CAPP 2D program. Comparing the pushover capacity curve of the unretrofitted and retrofitted frames, it was shown that the glass FRP system increased the strength and the ductility of the unretrofitted frame by 33% and 50%, respectively. Higher stiffness at higher load was also observed for retrofitted frame compared to the unretrofitted frame. A collapse mechanism featuring strong column-weak beam characteristics was exhibited by for both unretrofitted and retrofitted frames, judging from the location of the plastic hinges. It can be concluded that the FRP system did not alter the failure mechanism of the frames in this study. 51 Table 2.1 Comparison of the analytical model to simulate seismic loading (Naeim, 2001) Analysis Method Linear Static Linear Dynamic Nonlinear Static Nonlinear Dynamic Must nonlinear response be approximately proportional to elastic response? Yes Must structural configuration be regular? Is consideration of higher mode effect limited? Can it really address the nearfault issues? Yes Yes No Yes No No No No No Yes No No No No Yes Table 2.2 Parameter for bilinear moment-curvature curve of plastic hinge nodes Hinge Node 1 2 3 4 5 6 7 8 9-14 Type of element Column Column Column Column Column Column Column Column Beam Yield Moment Curvature (kNm) (10-3 1/m) 52 8 26 9 52 8 26 9 42 6 20 7 42 6 20 7 18 18 Ultimate Moment Curvature (kNm) (10-3 1/m) 57 81 31 122 57 81 31 122 53 37 27 58 53 37 27 58 23 280 Table 2.3 Shear strength of elements No of element 1,3 2,4 5-8 Type of element Column Column Beam Shear Strength (kN) 71 46 31 Table 2.4 Moment and curvature at first cracking of concrete Element Interior Column Exterior Column Beam Mcrack (kN.m) 12.7 5.7 3.9 φcrack (E-3 1/m) 0.9 1.3 1.6 52 Table 2.5 Parameter for bilinear moment-curvature curve of plastic hinge nodes Hinge Node 1 2 3 4 5 6 7 8 9-12 13-14 Type of element Column Column Column Column Column Column Column Column Beam Beam Yield Moment Curvature (kNm) (10-3 1/m) 57 8 29 10 52 8 26 9 42 6 20 7 42 6 20 7 21 18 18 18 Ultimate Moment Curvature (kNm) (10-3 1/m) 74 65 33 94 57 81 31 122 53 37 27 58 53 37 27 58 31 98 23 280 Table 2.6 Shear strength of elements No of element 1 2 3 4 5-6 7-8 Type of element Column Column Column Column Beam Beam Shear Strength (kN) 145 71 103 46 89 31 53 Figure 2.1 Prototype Structure (a) plan view of the whole building (b) selected critical frame (c) a one- and half-bay and two-storey frame chosen for the test frame. (Li, 2006) 54 e e e e 0.61P 1.350 m c c e e e e d d 0.39P 1.475m a a 1.275 m b b 1.825 m (a) Ø6mm-140mm Ø6mm-140mm (Ø8mm-250mm) 100 8Ø8mm 8Ø7mm 450 450 Section a-a Section c-c Ø6mm-140mm 250 Ø6mm-140mm 100 4Ø10mm 6Ø8mm 6Ø7mm 300 300 Section b-b Section d-d 100 Section e-e (b) Figure 2.2 (a) The layout of the frame (b) The cross-section of the member 55 Figure 2.3 Bilinear stress-strain relation for steel reinforcement Figure 2.4 Stress-Strain Relationship of Unconfined and Confined Concrete Model 56 Figure 2.5 Stress-strain relation of unconfined concrete (Mander et al., 1988) Figure 2.6 The confinement effect of transverse reinforcement on the rectangular reinforced concrete cross-section (Penelis and Kappos, 1997) 57 Figure 2.7 Stress-Strain Relationship of Mander Confined Concrete Model Figure 2.8 The stress-strain relation of FRP Figure 2.9 The confinement effect of FRP-wrapped on rectangular cross-section 58 Figure 2.10 The stress-strain model of FRP-wrapped rectangular cross-section (Lam and Teng, 2003) Figure 2.11 Location of Fiber Beam-Column Element, Rigid Zone Length and Nonlinear Hinge 59 Figure 2.12 The Lateral Load-Displacement Relationship of the structure deflected to the same ∆u on (a) Elastic System (b) Elastic-Plastic System 60 Figure 2.13 Curvature distribution along beam at ultimate moment (a) Beam (b) Bending moment diagram (c) Curvature diagram (Park and Paulay, 1975) 61 Figure 2.14 The Empirical equation of the plastic hinge length (lp) for z = 0.5 (Penelis and Kappos, 1997) (a) Un-retrofitted member (b) FRP-retrofitted member Figure 2.15 Material models for un-retrofitted and FRP-retrofitted members 62 (a) Beam (b) Interior column: 1st storey (c) Interior column: 2nd storey Figure 2.16 Moment-curvature analysis from Xtract and its simplified bilinear curve 63 (d) Exterior column: 1st storey (e) Exterior column: 2nd storey (f) FRP-retrofitted Beam Figure 2.16 Moment-curvature analysis from Xtract and its simplified bilinear curve (cont’d) 64 (g) FRP-retrofitted interior column: 1st storey (h) FRP-retrofitted exterior column: 1st storey Figure 2.16 Moment-curvature analysis from Xtract and its simplified bilinear curve (cont’d) Figure 2.17 Typical wrapping schemes for shear strengthening using FRP laminates (ACI 440, 2002) 65 Figure 2.18 Illustration of the dimensional variables used in shear strengthening (ACI 440, 2002) Figure 2.19 Frame layouts with element’s and nonlinear hinge node’s name 66 (a) Steel bar with diameter 7mm (b) Steel bar with diameter 8mm (c) Steel bar with diameter 10mm Figure 2.20 Bilinear stress-strain curve of steel reinforcement 67 (a) Unconfined concrete (b) Confined concrete Figure 2.21 Stress-strain curves for concrete 68 (a) At the first cracking of the concrete (b) Without the first cracking of the concrete (c) Modified pushover curve Figure 2.22 Pushover curve 69 Figure 2.23 The final deformation of the unretrofitted frame at failure Figure 2.24 Lateral load-Roof drift ratio curve of unretrofitted frame 70 Figure 2.25 The location of Glass-FRP strengthening with amount of the layer (a) Exterior Column (b) Interior Column (c) Beam Figure 2.26 Stress-strain curve of glass FRP-retrofitted member 71 Figure 2.27 The deformation shape of the retrofitted frame at the failure Figure 2.28 The Lateral load-Roof drift ratio curve of G-FRP-retrofitted frame 72 (a) Unretrofitted frame (b) FRP retrofitted frame Figure 2.29 Comparison of analytically Pushover curve for RC frame with and without P delta effect 73 CHAPTER 3 EXPERIMENTAL INVESTIGATION 3.1 General This test program was carried out to study the behaviour of reinforced concrete frame retrofitted with glass FRP under pushover loading. The performance in terms of strength and ductility was assessed and used to verify the predictions presented in the Chapter 2. The specimen consisted of a one-and-a-half bay, two-storey frame (see Figure 3.1). It was subjected to pushover lateral loading until one of the following conditions occurred: a collapse mechanism resulting from the formation of sufficient number of plastic hinges; a 20 % reduction of the base shear capacity of the frame; or the maximum top drift ratio has exceeded 2%. 3.2 Design of test frame 3.2.1 Reinforced concrete frame As explained in Chapter 2, the model frame was part of a larger frame in a 4-storey public housing building, built in the 1970s, in Singapore. The building was designed according to the British Standards using concrete strength (fcu) of 20 MPa. 74 3.2.2 Model scaling similitude The geometrical dimensions of the frame were scaled down to half of the original frame with 100mm x 300mm and 100mm x 450mm sections for exterior and interior column respectively in the test frame. Similarly, the beam sections were scaled down to half of the original frame into 100mm x 250mm sections in the test frame. The concrete grade in the original frame and the test frame was maintained at 20MPa. The reinforcement bars for the test frame were determined according to: ( f y As ) prototype = ( f y As ) exp erimental × S 2 (3.1) where fy = yield strength of reinforcement; As = area for one reinforcement rebar; and S = scale factor(=2). 3.2.3 Material properties The concrete mix was designed for a target compressive strength of 20 MPa at 28 days. Cement, sand and coarse aggregate with a maximum size of 10mm, and water were mixed in the ratio of 1:3.2:3.8:0.9 by weight. For the steel reinforcement, three types of rebar were used: deformed rebar, plain mild steel bar and plain high strength bar. Deformed bars with a diameter of 10mm were used as beam longitudinal reinforcement. Plain high strength bars, with diameters of 8mm and 7mm, were used as column longitudinal reinforcement at 1st and 2nd storey, respectively. For transverse reinforcement of both beams and columns, 6mm plain mild steel bars were used. 75 (a) Concrete Along with the frame, concrete cubes with a dimension of 100mm x 100mm x 100mm, concrete prisms with a dimension of 100mm x 100mm x 300mm, and concrete cylinders with a 200 mm height and 100 mm diameter were cast. For each mix, at least 3 concrete cubes, 3 concrete prisms, and 3 concrete cylinders were cast in the oiled steel moulds and compacted using a vibrator table. After 24 hours, the cube, prism and cylinder specimens were removed from the moulds and then cured under wet gunny sacks for 7 days. The cubes and cylinders were tested using the Instron Universal Testing Machine to obtain the compressive strength and the Young’s Modulus of concrete. The average compressive strength and Young’s Modulus of concrete were 20.8 MPa and 18.7 GPa respectively. (b) Steel reinforcement Four different diameters of reinforcement bars were used in this study. They were 6 mm plain mild steel bar, 7 mm plain high strength bar, 8 mm plain high strength bar, and 10 mm deformed bar. For each bar type and size, two specimens were tested using Instron Universal Testing Machine. An extensometer with a gauge length of 50 mm was used to capture the elongation until failure of the specimen. The yield strength of the transverse reinforcement was 260 MPa, and the tensile properties of other reinforcement bars were shown in Table 3.1. 76 (c) Glass FRP system In this study, glass FRP system (type EC-900 from Master Builder Technology) was used as seismic retrofitting system in confining the member and serving as as additional tensile reinforcement. Table 3.2 shows the fiber properties of the glass FRP. 3.2.4 Loading The live load was taken to be 1.5 kN/m2 for public housing building. The dead load consisted of self weight of the frame, partition and finishing of the floor. The self weight was calculated according to the weight of the concrete of 25 kN/m3. The partition and finishes of the floor are assumed to be 1.0 kN/m2 and 1.2 kN/m2 respectively. The combination of loads used in this study followed that given in the British Standard. There are in general two loading cases to be considered in the design of the structural members: the ultimate loading and the common loading. Since this objective of the study is to observe the performance of existing GLD RC frame due to far field earthquake, the common load combination of 1.0 x dead load plus 0.4 x live load is adopted. 3.3 Construction method of specimen 3.3.1 Preparation of test frame This part explains the preparation of the frame from the steel reinforcement until casting the concrete. All the of reinforcement cages, for concrete block and frame were fabricated off site. The cage reinforcement bars for frame were prepared separately for 1st storey and 2nd storey. 77 The concrete blocks were firstly placed on the strong beam, the extension bars were placed in the concrete block as a lap splice bar to the longitudinal bars for column, and the oiled wood mould was installed. After all the preparations were complete, the blocks were cast. After the concrete block cage was completely set, the cage of reinforcement bar of the 1st storey was installed. Each extension bars which were prepared before would be tackwelded corresponding with each reinforcement bar of the first floor column. The 2nd storey reinforcement bar cage was installed on the top of the previous cage; then the frame was adjusted vertically using water levelling tool both for longitudinal direction and transversal direction. The oiled wood mould then prepared and installed into the frame. During the installation, the dimension of the members (columns and beams) was controlled, and the vertical alignment and horizontal alignment were also kept. To prevent the mould from opening up during the casting due to the fresh concrete pressure, the G clamps were used. The casting was divided into two steps due to the limitation of the capacity of concrete batcher. At the first step, the casting was done until the top of the 1st floor beam, followed by the second step until the top of the 2nd floor beam. After one day, the wood moulds were removed and the frame then would be cured 7 days using wet gunny sacks wrapping the concrete frame. 3.3.2 Test setup The specimen was tested in the upright position. Figure 3.2 and 3.3 show the 3D view of the specimen and the set-up respectively. The set up included a vertical steel beam, a 78 pre-stressing system, and a lateral support system. Figure 3.4 shows the side view of the set up. The lateral load was applied from the hydraulic actuator (650 kN) at a slow rate of 0.01 mm/s to push the specimen until its failure. To transfer the load from the actuator to the specimen, a vertical steel beam was designed and fabricated. Pin joint connection was used to connect the vertical steel beam to the beam end. The pin joint of each beam was bolted to the two L angles which were sandwiched by bolting on the side surface of the beam end. These pin joints then were bolted to the vertical steel beam. In this way, the lateral load was transferred from the actuator, through the vertical steel beam and pin joint connections, and finally to the beams (see Figure 3.3b) Two concrete blocks were prepared as the bottom base of the 1st storey column. These blocks were rigidly mounted to a strong beam, which was anchored to the strong floor slab, and assumed to be in a fixed condition. A total of fourteen bolts each with a diameter of 24 mm was used to connect each concrete block to the strong beam. Four lateral supports were used to prevent out-of-plane bending during the testing. These lateral supports were bolted to two reaction steel frames. Figure 3.5 and 3.6 shows the 3D view of the steel arrangement of the concrete block and side view of the lateral support system respectively. To simulate the gravity load, a constant axial load representing the weight of the above stories was applied to the top of the columns using pre-stressing strands. Because of the difficulty in application, the uniform load on the beams were converted to axial load on the column and added to the pre-stressing force in the strands. In the test frame, the particular loads were scaled down from the loads of the original frame by dividing it with S2, 79 where S is the scale factor. A total of four pre-stressing wires each with a diameter of 9 mm was used in this study. Each column had 2 pre-stressing strands with the stress of each strand equal to half of the point load at the respective column. The exterior column and interior column were pre-stressed by loads of 60 kN and 80 kN respectively. To transfer the prestressing load to the respective column, a steel hollow beam was connected to the top of each column. The strands were first anchored at the base of the frame and then stressed to the desired level before anchoring them to the ends of the steel hollow beam. 3.3.3 Installation of glass FRP system The surfaces of the members were first cleaned from dust, moisture, grease, curing compound, waxes and foreign particles. Uneven concrete surface was then patched up using the cement paste and ground smooth. The corners of the section, where the transverse glass FRP fabrics were to be placed, were rounded to a radius of about 25 mm. Next, the primer was applied uniformly using roller to the ground surfaces until non-porous shiny film on the concrete was created. After one day, the saturant was applied using roller to both surfaces of the prepared glass FRP fabric until all surfaces were covered by the saturant. The saturant was also applied at the primered concrete surface. The glass FRP fabric was installed onto the concrete member in the following sequence: longitudinal layer followed by the transverse layer. A hard roller was used to impregnate resin into the glass FRP material, to remove entrapped air. To allow for the epoxy impregnation, a ten-minute delay was taken between the applications of different layers. The curing of glass FRP took 7 days. Figure 3.7 80 and Figure 3.8 show the 3D view of the test frame retrofitted with glass FRP system and the glass FRP retrofitted in beam and column, respectively. 3.4 Instrumentation 3.4.1 Strain Gauges Figure 3.9 shows the location of strain gauges installed on the reinforcing bar. The strain gauges used were of type FLA-5-11, with a gauge length of 5mm and manufactured by TML. Figure 3.10 shows the location of the strain gauges on the surface of the concrete. The strain gauges were of type PFL-30-11 with a gauge length of 30mm. Figure 3.11 shows the location of the strain gauges on the surface of the glass FRP laminates. All the strain gauges were of type PFL-30-11 and were installed in the direction of the fibers. 3.4.2 Displacement transducers In this experiment, TML displacement transducers of 50 mm, 100 mm and 200 mm range were used. In order to obtain accurate readings, the aluminium plates and angles were mounted on the members to receive the tip of the displacement transducer. They were attached on the surface of the concrete or glass FRP system using epoxy adhesive. Figure 3.12 shows the overall location of the displacement transducers. Four TML displacement transducers with a 200mm range (TML 200mm) were used to measure the lateral displacement of the frame. They were placed at the mid-height beam of the 1st and 2nd storey. Nine TML displacement transducers with a 100mm range (TML 100mm) were used to measure the relative lateral displacement of the joint and the 81 displacement of the strong beam at the base of the frame. Another twelve TML displacement transducers with a 50mm range (TML 50mm) were used to measure the vertical displacement of the joint and also vertical displacement of the interior and exterior column at the base. 3.5 Test results and discussion 3.5.1 Crack patterns 3.5.1.a Unretrofitted frame Figure 3.13(a) shows the crack pattern of the unretrofitted frame under pushover loading. The first flexural crack occurred at the bottom of the interior column at location 1, when the total applied lateral force was about 20 kN. When the force reached 29.5 kN, cracks were observed to appear on the beams at locations 2 and 3 while the cracks at location 1 began to propagate in an inclined direction. At location 4, several fine cracks occurred at the bottom of the exterior column. When the force reached about 37.6 kN, new cracks developed in the beams at locations 5, 6, and 7, and more cracks appeared at the bottom of columns above locations 1 and 4. The first flexural cracks at beam-column interface occurred at the 2nd story at locations 8 and 9, when the force was around 49.5 kN. The first diagonal shear crack at the beam-column joint formed at location 12 next to the exterior joint at the 2nd story, when the applied force was about 63.8 kN. The steel reinforcing bars first yielded at the bottom of the interior column at a load of about 65.4 kN. Also, yielding of the tensile reinforcement in the 1st story beam occurred at a load of about 67 kN. At about 70 kN, flexural cracks formed at locations 13 and 14. 82 With further increase in the applied load, cracks at locations 8, 9, 13, and 14 became wider and longer. The applied force reached a maximum value of 79 kN with a 2nd storey drift ratio (∆/H) of about 1.8%. When the storey drift ratio increased to 2%, the base of the columns rotated about the compressive edge, causing the columns to crush under compression, which resulted in a dramatic drop in the applied force. Most of the cracks were concentrated in the beams and at the base of columns. Except for some minor cracks, there was no obvious failure at the joint areas. It can be concluded that the unretrofitted frame behaved as a strong column-weak beam structure. 3.5.1.b Retrofitted frame The cracking characteristics of the FRP retrofitted frame under pushover loading is shown in Figure 3.13(b). Because of the installation of the FRP system, cracks could only be observed at locations outside the retrofitted regions. The first crack was observed at the bottom of the exterior column at location 1 at a load of about 60 kN. When the lateral load was increased to 66 kN, cracks appeared at location 2 at the interior column and at location 3 at the 1st floor beam. At the same time, the flexural crack at location 1 propagated in an inclined direction. Subsequent cracks appeared at locations in the order of the number shown in Figure 3.13(b). Cracks were first observed at the joint at about 80 kN. All cracks extended and widened further with increasing load. Beyond about 99 kN, local failure was concentrated at the base of the interior column (at location 29), exterior end of the exterior beam (at location 30) and top of exterior column (at location 34). The longitudinal FRP sheets were observed to restrict the cracks from widening. The applied 83 load reached a maximum value of 101 kN with a storey drift ratio of 1.48%. When the storey drift ratio reached 1.75%, cracks of 3 to 4 mm width at location 30 caused the tear of the longitudinal FRP sheets, resulting in a 14% decrease in the applied load. Thereafter, the retrofitted frame continued to sustain a lateral load of about 94 kN before failing at a drift ratio of about 2.6% due to the rupture of FRP sheets at locations 30 at the 2nd storey beam and 29 at the interior column. The reinforcing bars first yielded at the bottom of the interior column at about 65 kN. Most of the cracks were concentrated at the beams and the base of the columns. No obvious failure was observed at the joint area and other parts of the column except for some minor cracks. It was thus concluded that the glass FRP retrofitted frame continued to behave as a strong column-weak beam structure. 3.5.2 Joint Response To capture the response of the joint during test, four displacement transducers are used at the four mid-points of each side of the rectangular joint panel (Figure 3.14). Two displacement transducers are placed vertically and two displacement transducers are placed horizontally. The vertical displacement transducers are used to capture the relative horizontal displacement of the joint movement and the horizontal displacement transducers are used to capture the relative vertical displacement of the joint movement. Figure 3.15 shows the joint rotation histories in the pushover test. From the Figure 3.15 (a), it can be seen that the rotation of the joints at the 1st storey are similar. It can be seen from the same figure that the maximum rotation of the joint panel is 0.02 radians (1.2o). Thus, it can be concluded that the 1st storey joints remained rigid without severe damage. This also corresponded with the crack observation during test which 84 showed little cracks at the particular joint panel. Figure 3.15 (b) shows the rotation in each direction of the 2nd storey joint panel. It can be seen that there were some differences between each curve, which indicating some deformations at the 2nd storey joints. This may be caused by the concentration of cracks on the 2nd storey joints. The maximum rotation of the 2nd storey joints was 0.03 radians (1.5o). Since the differences were minimal and the crack observations during testing did not show many cracks, it can be concluded that the 2nd storey joints had minor damage. As shown in figure 3.15(b), the rotation at beam direction (number 5 and 7) was larger than the rotation of column direction (number 6). Thus, the strong column – weak beam mechanism of the structure was confirmed. 3.5.3 Moment - Curvature curves The response of the beam and column are based on the reading of strain gauges which were placed at the compression concrete surfaces and the reinforcing steel bar of the consideration part of section (columns end and beams end). The calculation of the curvature for each section is according to equation as given: ε −ε' D (3.1) where, ε’ is the strain gauges reading at the outermost compression rebar , ε is the strain gauges reading at the outermost tension rebar and D is the distance between the locations of ε and ε’ were measured. Note that the tensile strain is positive and compressive strain is negative. The curvature of every section was calculated according to equation based on Equation 3.1. Based on the strain gauge reading of all reinforcing bars and concrete surfaces 85 at a section, the forces in all reinforcing bars and the height of neutral axis of a section can be calculated, and then the moment can be generated from the forces previously obtained. Figure 3.16 shows the comparison of the moment-curvature curve of critical members for un-retrofitted and glass FRP retrofitted frames. It was observed that the retrofitted member exhibited higher stiffness and higher moment as compared to the unretrofitted member. 3.5.4 Strain development The development of the strain in tensile reinforcement bars, longitudinal FRP reinforcement and concrete for the retrofitted frame are shown in Figure 3.17, at critical locations, i.e. base of columns and ends of the 1st-storey exterior beam. Noting that the value of the yield strain for column bar and beam bar were 0.275% and 0.298% respectively, it was observed in Figure 3.17(a) that the tensile reinforcement bars at interior column yielded first at load of 65 kN, this was followed by yielding of tensile reinforcement bar at the exterior column. In the exterior beam, the tension reinforcement bars yielded at load of 81 kN at the exterior end and 87 kN at the interior end of beam. It could be deduced that all the tensile reinforcement bars at critical sections yielded before the maximum lateral load for the frame was reached. In Figure 3.17(b), it can be observed that the all recorded strains of the concrete at the compression side were low, and less than the ultimate strain of 0.35% (the ultimate strain of the concrete according to the British Standards BS8110). The maximum recorded strain 86 of the compressive fibre of concrete was 2478 x 10-6 mm/mm at the base of the interior column. In Figure 3.17(c), it can be observed that the maximum strain on longitudinal FRP reinforcement was developed at the base of the exterior column. However, the magnitude of the strains on the longitudinal FRP was lower compared to the strain on the tensile reinforcement bar at the same member. This was because the strain gauges on longitudinal FRP reinforcement on the column were located further away from the base of the column compared to the location of the strain gauges on tensile reinforcement bar; and also in the beam, the location of the strain gauges on longitudinal FRP reinforcement were further away from the surface of the column compared to the location of the strain gauges on tensile reinforcement bar. Comparison of strain development in unretrofitted frame (tested by Li, 2006) and the retrofitted frame (tested in this study) was not possible due to unavailability of the test records of the former. 3.5.5 Pushover capacity curve 3.5.5.1 Comparison between un-retrofitted and retrofitted frames Figure 3.18 compares the lateral force versus drift ratio curves of the un-retrofitted frame with that of the glass FRP-retrofitted frame. It is observed that both frames had similar initial stiffness. This was because the thickness of the glass FRP laminates was only 0.353 mm, which is very small compared to dimension of the member. Hence, the glass FRP system did not contribute much to the stiffness of the member and thus the frame. However, 87 the glass FRP system delayed the formation and widening of cracks, resulting in a higher stiffness of the retrofitted frame as compared to the un-retrofitted frame at higher loads beyond the cracking load. During the pushover test, the crack in the concrete of the bare frame was firstly observed at a load of about 20 kN at the bottom of interior column. In retrofitted frame, the cracks that could only be observed at locations outside the retrofitted regions due to the installation of the FRP system. The first crack was observed at the bottom of the exterior column at a load of about 60 kN. At a load of about 65 kN, the reinforcing bars first yielded at the bottom of the interior column for both un-retrofitted and retrofitted frames. The glass FRP-retrofitted frame yielded a higher ultimate strength of 102 kN, compared to the un-retrofitted frame of 79 kN. However, the applied load dropped drastically for retrofitted frame at an ultimate drift ratio of 2.6%, which was lower than the ultimate drift ratio of 2.8%, taken to correspond to a load of 80% of the ultimate load for the un-retrofitted frame. Nevertheless, the retrofitted frame possesses a higher ductility index (defined as the ratio of the ultimate displacement to the displacement at first yield of the steel reinforcement), which was 6.5, compared to 3.7 for the un-retrofitted frame. The tests therefore indicated that by retrofitting with glass FRP system, the ultimate strength and ductility index of the frame were increased by 29% and 75% respectively. 3.5.5.2 Verification of analytical model with experimental result The analytical prediction of un-retrofitted and glass FRP retrofitted frames had been explained in Chapter 2. Figure 3.19(a) and 3.19 (b) show the two curves of analytical models and experiment result of un-retrofitted and glass FRP retrofitted frames respectively. 88 Although the analytical curve for both cases do not exactly match the experimental curve, but the analytical study can provide a reasonably prediction on the pushover capacity curve for both the un-retrofitted and glass FRP strengthened frame under pushover loading until its maximum load. The analytical modelling can reasonably predict the maximum load of un-retrofitted and retrofitted frames with an error of 1.3% and 1.5% respectively. However, the analytical study cannot model the declining part of curve after the maximum load was reached for both frames (see Figure 3.19). This may be due to the limitation of software that simplifies the nonlinear properties of moment curvature of the members to bilinear curve. The analytical study reasonably predicted the load and drift ratio at the first yield of the reinforcement bar with an error of 4.6% and 14% respectively. For the glass FRP retrofitted frame, the analytical study also provide a reasonably prediction of the load and the drift ratio at the first yield of the reinforcement bar with an error of 9% and 13% respectively. In both the analytical and experimental study of retrofitted frame, the first yield of the reinforcement bar occurred at the interior column. The experimental study confirmed the analytical modelling that both of the unretrofitted and glass FRP retrofitted frames against pushover loading exhibited a collapse mechanism featuring a strong column-weak beam characteristic. 89 3.6 Summary Major codes, such as UBC (1997), New Zealand Code (1995) and ACI318 (2002) set ductile behaviour as a condition for building under seismic action. This ductile behaviour is observed in this study for both unretrofitted and FRP retrofitted GLD RC frames. By observing the crack patterns on the frame and beam-column joint response, it can be concluded that the retrofitting method using FRP systems can still ensure a strong-column and weak-beam mechanism. This mechanism is required to avoid a soft-storey failure mechanism, which is brittle in nature. This study also shows that the FRP composite retrofitting system does not significantly affect the initial stiffness of the existing RC member, but improves its stiffness, strength and ductility ratio. This observation is reasonable since the thickness of FRP is too small (0.353 mm per-layer) to have a significant change in the initial stiffness of the members. The same conclusion was also arrived by El-Amoury and Ghobarah (2005) through investigation of the effect of FRP retrofitting system on 9-and 18-storey GLD RC frame. The experimental study of the GLD retrofitted two-storey frame also showed the relatively good seismic performance; that is a ductility index of 6.5 and ultimate drift ratio of 2.6%; and a failure mode which was dominated by flexural behaviour instead of shear failure. As compared to the pushover capacity curve of the un-retrofitted two-storey frame, it can be concluded that the glass FRP seismic retrofitting system could enhance the seismic performance of the half-scale frame by increasing the ultimate strength and ductility index 90 by 29 % and 75% respectively. The glass FRP system also delayed the formation and widening of cracks, resulting in higher stiffness of the frame at higher load. It was observed also that the proposed FEA model using CAPP could reasonably predict the pushover capacity curve of the both un-retrofitted and retrofitted half-scale, twostorey frames. 91 Table 3.1 Tensile properties of reinforcement bars Steel Bar Yield Strain (10-6) Yield Stress (MPa) Ultimate Strain (10-6) Ultimate stress (MPa) 8mm 2745 527 25000 621 Young’s Modulus (GPa) 192 7mm 2870 556 12000 638 193 10mm 2980 500 80000 584 168 Table 3.2 Properties of FRP fabrics Density Thickness Fiber Orientation Young's Modulus Ultimate Strength Ultimate Tensile Strain 915 g/m3 0.353 mm Uni-directional 96.5 GPa 1930 MPa 0.02 92 e e e e 1.350 m c c e e e e d d 1.475m a a 1.275 m b b 1.825 m (a) Ø6mm-140mm Ø6mm-140mm (Ø8mm-250mm) 100 8Ø8mm 8Ø7mm 450 450 Section a-a Section c-c Ø6mm-140mm 250 Ø6mm-140mm 100 4Ø10mm 6Ø8mm 6Ø7mm 300 300 Section b-b Section d-d 100 Section e-e (b) Figure 3.1 (a) Layout of the frame (b) Cross-section of the member 93 Figure 3.2 3D view of the specimen 94 Pre-stressing Lateral support (a) the pre-stressing system and lateral support system (b) the loading system Figure 3.3 3D view of the set-up of the test specimens 95 Figure 3.4 Side view of the set up of the test specimen (Li, 2006) Figure 3.5 Steel arrangement of concrete block before casting 96 Figure 3.6 Side view of the lateral support system Figure 3.7 3D view of the glass FRP retrofitted frame system 97 (a) beam (b) column Figure 3.8 Glass FRP system at beam and column` Figure 3.9 Location of strain gauges on the reinforcing bars 98 Figure 3.10 Location of strain gauges on compression side of concrete member Figure 3.11 Location of strain gauges on glass FRP laminates 99 Figure 3.12 Location of displacement transducers on the frame 100 View A View B View C (a) Unretrofitted frame Figure 3.13 Cracking characteristic 101 Location 29 Location 30 Location 34 (b) Retrofitted frame Figure 3.13 Cracking characteristics (cont’d) 102 Figure 3.14 Configuration of the LVDT on the joint panel 103 (a) 1st Storey Joint (b) 2nd Storey Joint Figure 3.15 Joint Rotation histories 104 Figure 3.16 Comparison of moment-curvature curve of critical member 105 (a) Tensile reinforcement bar (b) Compressive concrete (b) Longitudinal FRP reinforcement Figure 3.17 Strain development 106 Figure 3.18 Lateral load vs drift ratio curve of un-retrofitted (S1) and retrofitted frame (S2) 107 (a) Un-retrofitted frame (b) Retrofitted frame Figure 3.19 Load-drift ratio curves: comparison with analytical prediction 108 CHAPTER 4 CASE STUDY ON RETROFIT OF A FOUR-STOREY RC FRAME 4.1 General The analytical and experimental studies of glass FRP retrofitting system on the halfscale two storey RC frame were conducted in Chapter 2 and 3 respectively. The comparison study in Section 3.5.4.2 showed that the analytical modeling can be used to predict a pushover capacity curve of both unretrofitted and retrofitted frames until its maximum base shear is reached. Thus, in this chapter, a study case of the seismic performance of a full-scale four-storey-and-three-bay RC frame was conducted and the glass FRP system was used to enhance the seismic performance of the frame. 4.2 Overview of the frame Figure 4.1 shows the layout of the details of the RC frame. Built in the 1970s, the frame was designed according to British Standards with a design concrete strength of 20 MPa. The building was designed for a characteristic live load of 1.5 kN/m2. Besides the selfweight of structural members, dead loads included partition walls and floor finishes, were assumed to be 1.0 kN/m2 and 1.2 kN/m2 respectively. A common case loading was considered in the study, in which the vertical load is 1.0 times the dead load plus 0.4 times the live load. Figure 4.2 shows the factored-gravity loading on the frame. The lateral-pushover loading was used to simulate the seismic effect on the frame. Since the frame was classified as a low rise building, the lateral-pushover load was 109 distributed linearly throughout the height of the frame. Figure 4.3 shows the inverted-triangle load distributions on the frame. The second order P-delta effect was also considered in the pushover analysis. 4.3 Analytical model of the unretrofitted RC frame The dimension of the bare frame with the cross-section properties of each member is shown at Figure 4.1. The nonlinear hinges, to represents nonlinear behavior of the member, were located at the end of the member (Figure 4.4). . 4.3.1 Material properties The stress-strain relation of the concrete followed the Mander’s stress-strain relation, as explained in Chapter 2. Figure 4.5 shows the un-confined compressive and confined compressive stress-strain curve of concrete. The yield strength of the reinforcement bars for longitudinal bar and transversal bar were assumed to be 460 MPa and 250 MPa, respectively. Figure 4.6 shows the bilinear stress-strain relation of the steel reinforcement bar. The moment-curvature relation of each member was simplified from the momentcurvature relation calculated using software Xtract. Table 4.1 shows the bilinear momentcurvature relation from each nonlinear hinge in the frame. Table 4.2 shows the shear capacity of each member based on Eq. (2.28). 110 4.3.2 Moment at first crack The moment and curvature at first cracking of concrete for every member were calculated according to Eq. (2.24) and Eq. (2.25), which is shown in Table 4.3. 4.3.3 Analytical Result Shear failure occurred in the unretrofitted frame at beam number 25 (see Figure 4.2) at an ultimate lateral load of 334kN and drift ratio of 0.31%. This shear failure occurred when the reinforcement bar has not yielded yet. The lateral load – drift ratio curves of the unretrofitted RC frame is shown in Figure 4.7. It can be seen that the building was still in the linear response when the failure occurred. 4.4 Analytical model of RC frame with FRP system The glass FRP system was used to enhance the seismic performance of the frame. Both transverse and longitudinal FRP layers were used. The locations of the FRP retrofit system were initially proposed to be at the base of all 1st-storey columns and both ends of all 1st-and 2nd- storey beams since this is the soft storey of the building under earthquake action. The number of FRP layers to be applied was calculated according to Equation (2.16) until the ultimate strain of FRP confined concrete reached a minimum of 1%, that is the usually obtained using transverse links. Based on this retrofit scheme, the retrofit frame was tested under pushover loading. The stress-strain curve of the simplified bilinear stress-strain curve of reinforcement bar and the Mander’s model of un-confined and transverse-reinforcement confined concrete are shown in Figure 4.5 and 4.6 respectively. The stress-strain relation of glass FRP-wrapped 111 concrete was calculated according to Eq. (2.11) and (2.12), as shown in Figure 4.8 (a) to (e). The five stress-strain relations are superimposed as shown in figure 4.8 (f), which indicates that the difference due to different aspect ratio of the member sections is small. The bilinear moment curvature for bare members was calculated as previously explained at Section 2.5.1. The bilinear moment-rotation curve for glass FRP-retrofitted members was simplified from the moment-rotation curve calculated using Xtract. Table 4.4 shows the bilinear moment-curvature curve of each nonlinear hinge in the frame. Table 4.5 shows the shear capacity of the members based on Eq. (2.28). The moment and curvature at first cracking of concrete for every member were calculated according to Eq. (2.24) and Eq. (2.25), which is shown in Table 4.3. Figure 4.9 shows the results of the pushover capacity curve of the frame. The frame failed by shear at the left end of beam 27 on the 3rd-storey (see Figure 4.2) at the ultimate load and drift ratio of 491 kN and 0.38% respectively. To prevent the shear failure at beam 27, shear strengthening using U-wrapping was recommended for the left end of beam 27. The rest of the FRP retrofit scheme remained as previously described. Figure 4.10 shows the revised FRP retrofit scheme of the frame after the addition of shear strengthening at beam 27. The frame was subjected to pushover analysis once again. The locations of the plastic hinge and the deformation shape of the frame are shown in Figure 4.11. The predicted lateral load-displacement curves of the bare concrete frame can be seen in Figure 4.12. The first yield of the reinforcement bars occurred at beam number 26 at the drift ratio of 0.33%. The flexural failure occurred at 2nd storey exterior beam (see 112 Figure 4.11) when the ultimate lateral load was 770 kN and the ultimate drift ratio was 1.52%. 4.5 Summary As compared to the unretrofitted frame, the fully FRP-retrofitted frame had higher ductility and higher strength of 4.6 times and 2.3 times, respectively as shown in Figure 4.13. Glass FRP retrofitting system also enhanced the seismic performance of the unretrofitted frame by changing the failure mode to flexural failure from shear failure. This study showed that the glass FRP system enhanced the seismic performance of the bare frame by increasing its ductility and the strength. 113 Table 4.1 Parameter for bilinear moment-curvature curve of plastic hinge nodes of unretrofitted frame Hinge Node 1 2 3 4 5 6 7 8 9-10, 23-24, 37-38, 51-52 11-12, 25-26, 39-40, 53-54 13-14, 27-28, 41-42, 55-56 15,19 16,20 17,21 18,22 29,33 30,34 31,35 32,36 43,47 44,48 45,49 46,50 Type of element Column Beam Column Yield Moment Curvature (kN.m) (x10-3/m) 202 4.7 404 3.0 555 2.1 534 2.7 202 4.7 404 3.0 555 2.1 534 2.7 130 7.8 130 7.8 130 7.8 143 3.3 284 2.3 200 4.3 380 1.9 129 3.2 262 2.6 137 3.6 349 2.2 113 4.5 230 3.1 118 4.7 310 2.6 Ultimate Moment Curvature (kN.m) (x10-3/m) 202 65 404 41 562 38 534 38 202 65 404 41 562 38 534 38 178 215 178 215 178 215 148 88 298 57 200 66 389 45 139 106 277 67 143 94 162 50 139 124 255 80 130 118 333 59 Table 4.2 Shear strength of elements of unretrofitted frame No of element 1-4,10-12 5-8 9 13-16 17-28 Type of element Column Beam Shear Strength (kN) 176 272 332 302 124 114 Table 4.3 Moment and curvature at the first cracking of the concrete Element Column 200x600 Column 200x900 Column 200x1000 Column 200x1100 Beam Mcrack (kN.m) 46 103 127 153 32 φcrack (x10-3 1/m) 0.7 0.5 0.4 0.4 0.8 Table 4.4 Parameter for bilinear moment-curvature curve of plastic hinge nodes of retrofitted frame Hinge Node 1 2 3 4 5 6 7 8 9-10, 23-24 37-38, 51-52 11-12, 25-26 39-40, 53-54 13-14, 27-28 41-42, 55-56 15,19 16,20 17,21 18,22 29,33 30,34 31,35 32,36 43,47 44,48 45,49 46,50 Type of element Column Beam Column Yield Moment Curvature (kN.m) (x10-3/m) 230 4.0 415 2.1 577 1.6 540 2.0 202 4.7 404 3.0 555 2.1 534 2.7 135 6.5 130 7.8 135 6.5 130 7.8 135 6.5 130 7.8 143 3.3 284 2.3 200 4.3 380 1.9 129 3.2 262 2.6 137 3.6 349 2.2 113 4.5 230 3.1 118 4.7 310 2.6 Ultimate Moment Curvature (kN.m) (x10-3/m) 332 50 597 32 806 25 749 29 202 65 404 41 562 38 534 38 203 47 178 215 203 47 178 215 203 47 178 215 148 88 298 57 200 66 389 45 139 106 277 67 143 94 162 50 139 124 255 80 130 118 333 59 115 Table 4.5 Shear strength of elements of retrofitted frame No of element 1 5 9 13 1-4,10-12 5-8 9 13-16 17-18,2122,25-26 27 19-20,2324,28 Type of element Column Beam Shear Strength (kN) 424 634 704 775 176 272 332 302 249 213 124 116 h h h 2.7 m e f h e h f e h e h g 2.7 m g h h 2.7 m e f h a h h g 3.2 m a b c 4m D 5.2 m 3m (a) Layout Φ6mm-140mm Φ6mm-140mm 200 200 6Φ16mm 6Φ13mm 600 600 Section a-a Section e-e Φ6mm-140mm Φ6mm-140mm 200 Φ8mm250mm 500 4Φ20mm 200 8Φ16mm 8Φ13mm 900 900 Section b-b Section f-f Φ6mm-140mm Φ6mm-140mm 200 Section h-h 200 200 10Φ16mm 250 10Φ13mm 1100 1000 Section c-c Section g-g Φ6mm-140mm 200 10Φ16mm 1000 Section D-D (b) Cross-section properties Figure 4.1 Details of the frame 117 15 kN/m 15 kN/m 15 kN/m 74.2 kN 18 kN/m 18 kN/m 18 kN/m 87.7 kN 18 kN/m 18 kN/m 18 kN/m 18 kN/m 18 kN/m 18 kN/m 18.6 kN 26.7 kN 26.7 kN 26.7 kN 87.7 kN 87.7 kN 4.2 Factored-gravity loading on the frame 0.4P 0.3P 0.2P 0.1P Figure 4.3 Inverted-triangular lateral-pushover load 118 Figure 4.4 Location of the nonlinear hinge (a) Unconfined concrete (b) Confined concrete Figure 4.5 Stress-strain curves for concrete 119 Figure 4.6 Bilinear stress-strain curve of reinforcement bar Figure 4.7 Lateral load-Roof drift ratio curve of unretrofitted frame 120 20 15 15 Stress (MPa) Stress (MPa) 20 10 5 10 5 0 0 0 0.002 0.004 0.006 Strain 0.008 0.01 0 0.012 0.002 (a) Column 200x600 (2T+1L) 0.006 Strain 0.008 0.01 0.012 (b) Column 200x900 (3T+1L) 20 20 15 Stress (MPa) 15 10 10 5 5 0 0 0 0.002 0.004 0.006 Strain 0.008 0.01 0 0.012 (c) Column 200x1000 (3T+1L) 0.002 0.004 0.006 Strain 0.008 0.01 0.012 (d) Column 200x1100 (3T+1L) 20 15 Stress (MPa) Stress (MPa) 0.004 10 5 0 0 0.002 0.004 0.006 Strain 0.008 0.01 0.012 (e) Beam 200x500 (2T+1L) Figure 4.8 Stress-strain curve of glass FRP-retrofitted member 121 (f) All Sections Figure 4.8 Stress-strain curve of glass FRP-retrofitted member (cont’d) Figure 4.9 Lateral load-Roof drift ratio curve of frame retrofitted for 1st two stories only 122 Figure 4.10 The location of Glass-FRP strengthening with amount of the layers Figure 4.11 Deformation shape of the retrofitted frame at the failure 123 Figure 4.12 Lateral load-Roof drift ratio curve of fully retrofitted frame Figure 4.13 Load-drift ratio curves: comparison between unretrofitted and fully retrofitted frames 124 CHAPTER 5 CONCLUSIONS In this study, the performance of reinforced concrete frame designed primarily for gravity load, under far-field earthquake has been investigated. The analytical study of a half-scale, two- storey GLD RC frame was conducted to predict the pushover capacity curve of the frame and the experimental study was carried out to validate the predictions. A seismic retrofitting method using FRP system was proposed; and both analytical and experimental studies of the GFRP retrofitted RC frame was conducted. The performance of the un-retrofitted and retrofitted frames was compared using the pushover capacity curves in terms of strength, stiffness, and ductility. An analytical study of the performance of glass FRP seismic retrofitting system on full-scale, four-storey reinforced concrete frame against pushover load was also conducted in this study. By comparing the pushover capacity curve of un-retrofitted and retrofitted frames, the seismic performance in terms of strength, stiffness and ductility of the retrofitted frame was observed. The principal conclusions from this study were as follows: 1. An experimental study of the half scale GLD retrofitted frame showed the relatively good seismic performance: strong column – weak beam failure mechanism; good ductility with a ductility index of 6.5 and ultimate drift ratio of 2.6%; and a failure mode which was dominated by flexural behaviour instead of shear failure. 2. The proposed FEA model using CAPP could reasonably predict the pushover capacity curve of the both un-retrofitted and retrofitted half-scale, two-storey frames. 125 3. As compared to the pushover capacity curve of the un-retrofitted half-scale, two-storey frame, it can be concluded that the glass FRP seismic retrofitting system could enhance the seismic performance of the half-scale frame by increasing the ultimate strength and ductility index by 29 % and 75% respectively. The glass FRP system also delayed the formation and widening of cracks, resulting in higher stiffness of the frame at higher load. 4. The study of a pushover capacity curve of the full-scale, four-storey GLD RC frame showed that the glass FRP retrofitting system enhanced the seismic performance of the un-retrofitted frame by changing the failure mode to flexural failure from shear failure; and increasing the ultimate strength and ductility index by 2.3 times and 3.4 times, respectively. Higher stiffness at higher load on glass FRP retrofitted frame was also observed. Further studies on this retrofitting technique using FRP system are recommended as below: 1. In this study, the seismic action was only represented using pushover analysis. As a further study, one may carry out experimental and numerical studies under cyclic loading to determine the performance of buildings. 2. Full-scale dynamic tests on FRP retrofitted RC frame are recommended to further check the reliability and effectiveness of this retrofitting technique 126 REFERENCES Aboutaha, R., Engelhardt, M., Jirsa, J., and Kreger, M. 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(1996). “Strengthening strategies for improved seismic performance.” Proceedings of 11th World Conference on Earthquake Engineering, pp. 1424. 132 [...]... that the gravity load design structures had over strength and ductility due to the distribution of internal forces under seismic load Balendra et al (1999) highlighted that three-bay multi-storey RC frames designed to resist gravity loads and wind loads/notional loads according to BS 8110 had an overstrength factor of 7.5, 5.6 and 2.2 times the design lateral loads for three-,six- and ten-storey frame. .. technique of GLD RC frame using FRP system 1.4 Objective and Scope The objective of this thesis is to observe the behaviour and performance of RC frame, designed primarily for gravity loads, when subjected to far field earthquakes; and to propose a seismic retrofitting method using FRP system 15 For this purpose, a GLD RC frame with 1½-bay width of total 3100 mm and 2storey height totaling 2825 mm, designed. .. unaffected 3 1.1.3 Seismic demand due to far field effects for buildings in Singapore 1.1.3.1 Earthquake and soil condition In Singapore, which is located far away from the seismic fault zone, there has been concern on the far field effect of earthquake on buildings and infrastructures According to Balendra et al (2002), there are two possible sources of major earthquakes near Singapore (Figure 1.6)... concrete frame (OMRCF), designed primarily to resist vertical loads according to ACI Code (2002) The frame was constructed and tested under quasi-static reversed cyclic lateral loading In the study, the OMRCF was observed to be quite stable with no immediate strength degradation and response dominated by flexural behavior Capacity spectra method was carried out to evaluate the seismic performance of the frame. .. so far away from the epicenter This phenomenon has come to be known as the far field effect of earthquake The buildings in Lake Zone, Mexico City in 1985, were dominated by the medium to high rise reinforced concrete (RC) building without shear wall, which were designed with low or intermediate levels of ductility according to the 1977 Mexico City Code These buildings were also identified by the Earthquake. .. strengthening Therefore it is of interest to examine the FRP retrofitted GLD RC frame under seismic load This research will study a 1970s-built public housing building in Singapore which was designed according to the British Standards The FRP retrofitting technique used is a system with transversal and longitudinal layers of FRP reinforcement As mentioned earlier, even though Singapore is located on the stable... 7.2 Richter), and Sumatra (2004, 9.0 Richter) 1 On the other hand, the earthquake engineering community has derived numerous new lessons on far- field effect of earthquakes from the Mexico earthquake in 1985 with a magnitude of 8.1 1.1.2 Far field effect in Mexico Earthquake, 1985 Although Mexico City is located on the stable part of the North American plate, it experienced many shocks originating from... of the transverse reinforcement in column or beam, and (f) lap splices located in potential plastic hinge zones at the bottom base of columns or near to the end of the beam Figure 1.8 illustrates the typical frame details of old GLD buildings in the US Since GLD frames were designed with no seismic detailing, they have been vulnerable to 7 seismic actions Therefore, some researchers have been trying... detailing, they have been vulnerable to 7 seismic actions Therefore, some researchers have been trying to investigate the performance and behaviour of gravity load frame against seismic actions It has been observed that GLD frames when subjected to seismic actions might demonstrate behaviours such as large side-sway deformation, significant stiffness degradation and premature soft storey failure mechanism... strength and reinforcing details following non-seismic provision of ACI Code (1989) A shake table was used in these studies to simulate seismic load in the low to moderate seismic zone The investigators concluded that the inherent lateral strength and flexibility of GLD frames are adequate to resist minor earthquake without major damage However, for moderate to severe earthquakes, the frames may register ... distribution of internal forces under seismic load Balendra et al (1999) highlighted that three-bay multi-storey RC frames designed to resist gravity loads and wind loads/notional loads according to... buildings are designed according to non-seismic codes It is necessary therefore, to examine the vulnerability of such gravity load designed (GLD) buildings to far- field earthquake action In this... hand, the earthquake engineering community has derived numerous new lessons on far- field effect of earthquakes from the Mexico earthquake in 1985 with a magnitude of 8.1 1.1.2 Far field effect