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Nonlinear dynamic analysis of reinforced concrete frames and application to seismic reliability Martìnez, Arturo Ivàn 1998

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NONLINEAR DYNAMIC ANALYSIS OF REINFORCED CONCRETE FRAMES AND APPLICATION TO SEISMIC RELIABILITY by Arturo Ivan Martinez B. Ing. Pontificia Universidad Catolica del Peru A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Applied Science in The Faculty of Graduate Studies Department of Civil Engineering We accept this thesis as conforming to me^ j^ pHe^ l^ andard fj The University of British Columbia October 1998 ©Arturo Martinez, 1998 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Civil Engineering The University of British Columbia 2324 Main Mall Vancouver, Canada V6T 1Z4 ABSTRACT The main objective of this thesis is the development of a procedure for computing the nonlinear dynamic response of reinforced concrete frames subjected to seismic ground accelerations. In computing this response, nonlinear material models for unconfined concrete, reinforcing steel and nonlinear bond stress-slip model were used. These were utilized to develop a reinforced concrete finite element. The approach, which inherently includes the calculation of the hysteretic behavior during the excitation, is then implemented in a computer program to calculate the desired response. The results are used to compute the time history response and to estimate the seismic reliability of a reinforced concrete portal frame. ii T A B L E O F C O N T E N T S ABSTRACT ii T A B L E OF CONTENTS iii LIST OF FIGURES v ACKNOWLEDGMENT vi CHAPTER 1 Introduction 1 CHAPTER 2 Analytical Models of the Constitutive Materials 3 2.1 Compressive Behavior of Concrete 3 2.2 Concrete in Tension 5 2.3 Description of Analytical Concrete Model 6 2.3.1 Stress-Strain Relation for Monotonic Loading 6 2.3.2 Stress-Strain Relation for Cyclic Loading 8 2.4 Description of Analytical Reinforcing Steel Model 10 2.4.1 Monotonic Response 11 2.4.2 Cyclic Response 13 2.5 Description of Bond Stress-Slip Model 14 2.5.1 General Description 16 2.6 Computer Modeling 17 CHAPTER 3 Reinforced Concrete Finite Element 22 3.1 Introduction 22 3.2 General Assumptions 23 3.3 Derivation of the RC Finite Element 24 3.4 Internal Force Vector and Tangent Stiffness Matrix 27 CHAPTER 4 Dynamic Analysis of Reinforced Concrete Frames 31 4.1 Introduction 31 4.2 Equilibrium Equations 32 4.2.1 Mass Matrix 32 4.2.2 Damping Matrix 34 4.2.3 Externally Applied Forces 35 4.3 Solution to the Nonlinear Problem 36 CHAPTER 5 Applications 39 5.1 Time-History Response 39 5.2 Reliability Applications 43 CHAPTER 6 Conclusions 48 iii REFERENCES 50 APPENDIX A User's Guide 52 Example of input file 56 APPENDIX B Listing of NODARC 58 iv L I S T O F F I G U R E S Fig. 2.1: Cyclic response of plain concrete. (Karsan and Jirsa, 1969) 3 Fig. 2.2: Stability limit and common point curves, (from Karsan and Jirsa, 1969) ... 4 Fig. 2.3: Analytical model of plain concrete ™ 7 Fig. 2.4: Monotonic response of reinforcing steel 11 Fig. 2.5: Analytical model of reinforcing steel 13 Fig. 2.6: Bond stress-slip analytical model 15 Fig. 2.7: Comparison of analytical and experimental results 19 for concrete stress-strain relationship. (a) Test by Sinha, Gerstle and Tulin (1964) (b) Computed response Fig. 2.8: Comparison of analytical and experimental results 20 for steel stress-strain relationship. (a) Test by Viwathanatepa, Popov and Bertero (1979) (b) Computed response Fig. 2.9: Comparison of analytical and experimental results 21 for bond stress-strain relationship. (a) Test by Eligehausen et al. (1983) (b) Computed response Fig. 3.1: Cross section and degrees of freedom of RC finite element 23 Fig. 3.2: Deflection of beam 24 Fig. 4.1: Newton-Raphson iterative process 38 Fig. 5.1: Details of reinforced concrete frame 40 Fig. 5.2: El Centra earthquake record 41 Fig. 5.3: Time-history of the displacement at the top 41 Fig. 5.4: Stress-strain curves in concrete layers 42 Fig. 5.5: Variation of bending moment 43 Fig. 5.6: Reliability application 46 v ACKNOWLEDGMENT I would like to express my deep gratitude to my thesis advisor, Dr. Ricardo Foschi, whose advice and expertise made possible the preparation and writing of this thesis. The financial support from the Canadian International Development Agency (CTDA) and the Universidad de Piura is gratefully acknowledged. To my wife Ruth whose patience and support throughout the duration of this research has helped me in successfully finish it. Finally, I would like to thank the professors and staff of the Civil Engineering Department for the knowledge I gained from them, the staff at the Applied Science Cooperative Education Office for their assistance, Felix Yao for his support and help in making computers work properly, and to my friends. vi CHAPTER 1 Introduction One of the most active seismic zones in the world is situated along the west coast of North and South America. The interaction between the Nazca and the Continental Plate along the main part of the Peruvian coast has been the source of many destructive quakes which resulted in many deaths and material damage. Over the past three decades, many improvements in construction and design methods have been incorporated into both the civil engineering codes and practice. Most of this improvement comes from research in North America and Europe. The current reinforced concrete design code of Peru (NTE E-060) is based on the ACI (American Concrete Institute) code and takes from it almost all of the design equations and resistant factors. However, load factors are greater than those incorporated in the ACI Code. As a result, it is clear that the current design code is in need of calibration. An accurate reliability analysis should use mathematical models to closely simulate the different mechanisms governing the analysis and design of reinforced concrete elements. In particular, the seismic dynamics analysis should consider the nonlinear behavior of all components in reinforced concrete elements. The objective of this thesis is to develop a computer program to analytically model the nonlinear behavior of RC frames under seismic ground accelerations, using models for the cyclic behavior of the different materials to calculate the hysteretic response of the structure as a function of time. This differs from traditional approaches where, for 1 CHAPTER 1 Introduction 2 s example, hysteretic damping has been introduced through experimentally-based, empirical relationships between bending moment M and curvature <t>. The analytical models for the three mechanisms used in the development of the reinforced concrete finite element, i.e. concrete, reinforcing steel and bond behavior, are presented in Chapter 2. Chapter 3 describes the steps involved in the derivation of the reinforced concrete finite element based on the principle of virtual work. The kinematic relationships for displacements and strains are used together with the application of the principle to derive the internal force vector and the stiffness matrix of the RC finite element. Chapter 4 is focussed in the developing of the computer program. A Newton-Raphson technique is used to solve the nonlinear dynamic equations at each time step. Chapter 5 is intended to provide some examples of the use of the computer program. It shows results for time-history dynamic analysis and its application to reliability studies. Chapter 6 gives conclusions and recommendations as well as guidelines for further research in the field. Finally, two appendices are included. A user's guide and an example of input file are included in Appendix A. Appendix B contains the listing of NOD ARC. CHAPTER 2 Analytical Models of the Constitutive Materials In this chapter, a brief introduction of various models for the cyclic response for concrete is presented. A description of the monotonic response of concrete under compression and tension is followed by its behavior under cyclic loads. The model for reinforcing steel under monotonic and cyclic loading is described and finally the model for the bond strain-stress cyclic behavior is presented. 2.1 Compressive Behavior of Concrete Many models have been proposed to describe the stress-strain curve of concrete under monotonic and repeated loads. The simplest models are based on the assumption of simplifying the stress tensor to one direction, so that a uniaxial stress field is developed within the element. This restriction, which neglects the effect of shear deformation and removes the Poisson's effect, allows for a better description of the cyclic behavior of concrete. Compression Tension Fig. 2.1: Cyclic response of plain concrete. (Karsan and Jirsa, 1969) 3 CHAPTER 2 Analytical Models of the Constitutive Materials 4 In an early study of the cyclic response of concrete, Karsan and Jirsa (1969) found that the monotonic stress-strain curve is also the cyclic envelope. Fig.2.1 shows one of the experimental curves. It also can be seen that the residual plastic strain is important in the shape of the unloading curve, which starts with high stiffness and decreases to a low stiffness. r They also reported that there is a band of points on the stress-strain plot which influences the degradation of concrete under continued cycles of load as shown in Fig. 2.2. Fig. 2.2: Stability limit and common point curves, (from Karsan and Jirsa, 1969) If the load is cycled below this band, the stress-strain curve forms a closed hysteresis loop. If the load is cycled into or above this band, additional permanent strain would accumulate, provided the peak stress is maintained between cycles. This band has a lower limit, called the stability point limit, and an upper limit, called the common point limit. Yankelevsky and Reinhardt (1987) proposed a model for random cyclic compression. The behavior is determined from a set of focal points that reproduce graphically the unloading/reloading curves as linear branches. CHAPTER 2 Analytical Models of the Constitutive Materials 5 Harajli (1988) in a study of the behavior of partially prestressed concrete joints under cyclic loading adopted a model based on a monotonic curve which post peak response depends on the level of concrete confinement. The hysteretic response is simplified and the common point limit is not present. The effect of transverse confinement in the compressive behavior of concrete shows benefits in strength and ductility. Kent and Park (1971) proposed a monotonic model that neglected the increase in strength but took into account the ductility provided by the transverse confinement. Scott et al (1982) and Park et al (1982) modified the Kent and Park (1971) model to consider the enhancement of both the strength and ductility due to confinement and strain rate. Mander et al (1988) proposed a unified approach applicable to all configuration of circular- and rectangular-shaped transverse reinforcement and included the effects of cyclic loading and strain rate. 2.2 Concrete in tension The simplest model, which is still used in design practice, ignores the post peak resistance of plain concrete and assumes that the stress drops to zero once the tensile strength is reached. Analysis based on this assumption overestimated deflections and it was realized that the additional resistance of RC elements was due to the presence of tension above and between cracks. Hence the term "tension stiffening". CHAPTER 2 Analytical Models of the Constitutive Materials 6 Three basic procedures for representing this effect have been advocated for use with nonlinear analysis based on the smeared crack assumption. These are: a) A strain softening branch for concrete strained beyond cracking strain. b) An increase in steel modulus to account for concrete adhering to the bars. c) An inclusion of a bond linkage element. Cyclic tension was studied by Reinhardt, Cornelissen and Hordijk (1986). They proposed an expression for the post-cracking monotonic response and a set of rules for modeling the loops. Later, Yankelevsky and Reinhardt (1989) redefined the modeling of the loops based on a focal point approach. 2.3 Description of the Analytical Concrete Model The model developed for concrete is one dimensional and accounts for strength degradation, stiffness degradation and hysteretic behavior under load cycles. It also considers the opening and closing of cracks during cyclic tension. The hysteretic response under cyclic loading is inherently considered by the shape of the unloading/reloading cycle. In the following, the model rules are given and are summarized in Fig. 2.3. 2.3.1 Stress-Strain Relation for Monotonic Loading The envelope curve is described by the Smith-Young equation, as it is assumed by Karsan and Jirsa (1969) / 8 —r = k — exp fc £o f e ^ 1 (2.1) CHAPTER 2 Analytical Models ofthe Constitutive Materials 7 where fc is the compressive strength of concrete, eo is the strain at peak stress and k is a factor that depends on the method used to evaluate fc. Afactor k=1.0 is used when fc is obtained from standard cylinders having a diameter of 6 in. and a height of 12 in. Yankelevsky and Reinhardt (1987) correlated test results by Karsan and Jirsa (1969), in which specimens of non-standard geometry were used, with concrete strength in standard cylinders. A factor A=0.85 was found, as it is shown in Fig. 2.2. The initial modulus of elasticity, E 0 is given by the expression E0 =5500yffc Mpa (2.2) Fig. 2.3: Analytical model of plain concrete. CHAPTER 2 Analytical Models of the Constitutive Materials 8 The available ultimate concrete compressive strain, ecu, is based on experimental work on the deformability of compressed concrete which resulted in empirical equations for Ecu . A summary of the results is given in Park and Paulay (1975). In this model e^ , is assumed as 0.0035 for normal concrete. A linear stress-strain relation is considered in tension up to the tensile strength /,. Thus, the tensile stress ft is given by: f=E0e when /< / , (2.3) otherwise / = 0.0 where / , = 033 Jfc MPa 2.3.2 Stress-Strain Relation for Cyclic Loading The hysteretic response shown in Fig. 2.3 has been constructed according to the following method. In this model the band of points limited by the stability and common point limits, see Fig. 2.2, are reduced to a single curve of "locus of common points". This curve is an empirical exponential expression of the form similar to the Smith-Young curve / P e (. e 1 •exp 1 - e0 0.315 + 0.77/3 J (2.4) f'c 0.315 + 0.77/?f0 where P = 0.76 as proposed by Karsan and Jirsa (1969). When unloading from the envelope, point A (eA, ft) in Fig. 2.3, the path is determined by defining the points B, C and D. Point B belongs to the common point curve and is known as the turning point. Point C is the residual strain and it is assumed that the CHAPTER 2 Analytical Models of the Constitutive Materials 9 stiffness is zero at this point. Point D is the reloading point and belongs to the monotonic curve. The relationships among these points were determined by Karsan and Jirsa (1969) and were given as a set of functions as shown below: Sc= 0A45S1 +0.1305^ (2.5.a) Sc= 0.160S2B + 0.133SB (2.5.b) Sc = 0.093^+0.091^ (2.5.C) Where Sc=£c /EO, SX=EA/£O, SB=£B/EO, and SD=£D/EO, are the corresponding normalized strains at those points. In the attempt to find simpler relationships, the above equations were linearized to find Sc, SB and SD as functions of SA- It was found that the following equations fit well with the original ones, especially when considering a reasonable range for the strains to be encountered during an earthquake. Sc = 0.145^+0.1305, (2.6.a) SD = 1.2836^ (2.6.b) SB = 0.95755^  (2.6.c) Unloading from A follows a linear path AB until reaching the common points curve, i.e. point B. The nature of these points will provide high stiffness while in this path.. Further unloading is represented by a parabola BC whose origin is at point C. The parabola represents the degradation of stiffness and will have a zero value at the residual strain C and is defined by the following quadratic expression: CHAPTER 2 Analytical Models of the Constitutive Materials 10 (2.7a) ieB-sc) where fs is the stress at the common point curve and it is calculated by using Eq. 2.4, as: It can be shown that the stiffness at path AB is always greater than the stiffness of the parabola BC when evaluated at B. Further unloading will develop tensile stresses up to the point where a crack is formed. After the crack is formed, the concrete will not be able to sustain any tensile stress in the following cycles, meaning that further unloading reaching point C will just open the crack. If reloading occurs from a strain below point C, the concrete will follow a zero stress line up to the point C, then a straight line connecting points C and B, then another straight line BD until reaching the monotonic curve. Reloading from path AB will follow the same path up to the monotonic curve. Reloading and unloading between C and B will follow a closed loop B2-C1-C2-B1 as shown in Fig. 2.3. The model described above is based on test results from the literature. However, since few tests have been performed at low levels of compressive strains, the model assumes linear loading and unloading with a stiffness equal to the initial modulus of elasticity for concrete strains less than 0.163 e0. A=0.84/c^-exp(l- 0.9f0 ) (2.7b) 2.4 Description of Analytical Reinforcing Steel Model Inelastic deformations of reinforced concrete are mainly due to steel and not to concrete. Concrete is a very brittle material that cracks at low tensile strains. Therefore, t CHAPTER 2 Analytical Models oj the Constitutive Materials 11 the model chosen to represent the behavior of steel bars is very important when modeling reinforced concrete structures since the post-cracking response may be mainly dependent on the reinforcement characteristics. The behavior of reinforcing steel is relatively simple to model. Depending on the carbon content, there are very well defined regions that are easily described by mathematical rules. In the following, the analytical model is described when subjected to monotonic and cyclic loading. 2.4.1 Monotonic Response Fig. 2.4 shows a typical stress-strain curve for reinforcing steel obtained from rebars under monotonic tension. This behavior is typically represented by four regions: (1) The linear elastic region (2) The Liiders strain or yield plateau (3) The strain hardening region (4) The post ultimate stress region UJ o-l . . . . 1 . . 0 2 4 6 8 10 12 14 16 m Engineering Strain |e, | , (%) Fig. 2.4: Monotonic response of reinforcing steel. CHAPTER 2 Analytical Models of the Constitutive Materials 12 The assumed stress-strain relation in the elastic region is linear as follows: f,=EgetZfy (2.8) Where E, is Young's Modulus of Elasticity or elastic modulus and fy is the yield stress. Monotonic curves for normal strength reinforcing bars, i.e. low contents of carbon, show an almost flat post-yielding response. The response in this zone is well represented by a straight line with slope Et until the ultimate strain is reached. Fronteddu (1992) proposed a trilinear monotonic model in order to represent the cyclic behavior of steel under high levels of strains, as those carried out by Aktan et al. (1973). The effect of carbon content is also important in defining the shape of both monotonic and cyclic curves. In a study, Dodd and Restrepo-Posada (1995) developed an analytical model for reinforcing steel fabricated under New Zealand Standards (NZS 3402). They found differences between analytical and experimental curves when compared with results from Atkan et al. (1973) which can be attributed to the carbon content of the steel tested. For high strength bars, a Ramberg-Osgood equation can be used to represent the monotonic curve: 1-A f =Es A + - \c\\/c J Where A, B and c are found from the stress-strain curve of the specific steel, as it is described in Collins and Mitchell (1987). The same curve is assumed for rebars under compressive stresses. CHAPTER 2 Analytical Models ojthe Constitutive Materials 13 2.4.2 Cyclic Response When the steel is cyclically strained below the elastic limit, there is no degradation of stiffness and the material behaves elastically. Cycling beyond the elastic limit reduces the modulus of elasticity making the reinforcing steel to show a nonlinear effect before reaching the yield strength. This behavior, attributable to the carbon content, is known as the Bauschinger effect and is an important factor in modeling the cyclic behavior of reinforcing steel. The model used here is shown in Fig. 2.5, which is basically that used by Menegotto and i fe i < > Fig. 2.5: Analytical model of reinforcing steel. CHAPTER 2 Analytical Models of the Constitutive Materials 14 In it, the cyclic behavior is represented by the following Ramberg-Osgood formulation: / * = (1-^) Where, for the first loading: f* = fy and Ex . - i L o •R\\/R £ (2.10) £ = And, for the curves subsequent to the first load inversion: and e = e.-e. f o - f r sa-er Ei is the modulus of elasticity and E, is the slope of the strain hardening region. The parameter R controls the Bauschinger effect and the sharpness of the curve when it goes from Es to Ej. An expression was suggested by Giuffre and Pinto (1970) which relates R to the strain distance between the previous and the current points of reversal: 4 £ R = R 0 - (2.H) A2+£ where £ is the normalized strain distance between the point of intersection and the previous load reversal and is given as: (2.12) The parameters Ro, Ai, A2 are taken as 20, 18.5 and 0.15 respectively, as suggested by Fillipou et al (1983). 2.5 Description of Bond Stress- Slip Model During a strong earthquake event, most of the critical regions of a structure are subjected to large strains, thus producing cracks in the concrete. The mechanism that CHAPTER 2 Analytical Models of the Constitutive Materials 15 allows the concrete to sustain tensile strains without failure is the bond that exists between a reinforcing bar and its surrounding concrete. A realistic model of the bond stress-slip mechanism during random excitations is required to represent the hysteretical behavior of the reinforced concrete elements. The model presented here is based on a complete experimental investigation by Eligehausen et al. (1983). In that study, the specimens simulated the confinement and loading conditions in interior and exterior joints of reinforced concrete frames. Many other related parameters were studied such as the influence of bar diameter, concrete strength and transverse confining pressure. q Fig. 2.6: Bond stress-slip analytical model. CHAPTER 2 Analytical Models of the Constitutive Materials 16 2.5.1 General Description The model, shown in Fig. 2.6, consists of the following parts: (1) A monotonic envelope, valid for both tension and compression. These envelopes are updated with each slip reversal to account for the accumulated damage originated during consecutive loading and unloading. The monotonic curve has an initial nonlinear relation given by: for u <ui (2.13.a) followed by a constant stress line: <l = <lx fori// <u(2.13.b) then a descending linear branch: ° = +9* q* (M-u2) foru2 <u <u3 (2.13.c) u2-u3 and finally a constant frictional bond resistance: a = a3 fori/ *>Mj (2.13.d) The parameters qj, qs, u2, u3 and a depend on parameters such as bar diameter, distance between lugs of deformed bars and concrete strength among others. In order to keep the model simplicity, the above parameters were assumed to be those corresponding to a bar diameter #8 (25.4 mm. diameter) and the influence of concrete strength was taken into account by multiplying qx and q3 by the factor ^30/ f'c . Therefore: q, (MPa) = 13.5 /^30/ f'c(MPa) (2.14.a) CHAPTER 2 Analytical Models ofthe Constitutive Materials 17 q3 (MPa) = 5.0^30//; (MPa) (2.14.b) and ui = 1.0 mm., u2 = 3.0 mm., u3 = 10.5 mm. and a= 0.40 (2) An unloading path that consists of a steep straight line with slope K = 180.0 N/mm3 until it reaches the frictional bond resistance q/. Then it follows the constant frictional resistance until it reaches the updated monotonic envelope. The bond stress-strain parameters of the reduced monotonic envelope, i.e. q'j and q's, are related to a damage parameter d that depends on the total energy dissipated during the bond-slip process. Similarly, the frictional bond resistance depends on a damage parameter df which depends on the frictional energy dissipated during the bond-slip process. The reduction in stress is then given by: q\=qx*(\-d) (2.15.a) q'3=q3*(l-d) (2.15.b) qf=qf*(\-df) (2.15.C) where d = \-exp[-l.2(ElE0)u] and df =l-exp[-l.2(Ef lE0f)067] E is the total dissipated energy and Eo is the energy dissipated during monotonically increasing slip up to the value u3 and is used as a normalization parameter. Ef is the frictional energy dissipated on the reloading branches and Eo / is the frictional energy absorbed under monotonically increasing slip up to the value u3 and is also used as a normalization parameter. 2.6 Computer modeling All models described in this chapter were implemented into subroutines. CHAPTER 2 Analytical Models of the Constitutive Materials 18 While running, the subroutines ask for peak strains and compute the corresponding stresses. Since these subroutines model the hysteretical behavior, they are capable of keeping track of its previous state so that they output a new state at any given strain. These programs were compared to experimental results obtained from the literature. Fig. 2.7 compares an experimental curve obtained by Sinha, Gerstle and Tulin (1964) with results from the proposed concrete model. They show very good agreement, especially at strain levels of around 1.5eo where maximum strains from a strong earthquake are expected. Fig. 2.8 shows a comparison between experimental results from Viwathanatepa, Popov and Bertero (1979) and an analytical curve obtained from the steel model. Results are very close and in good agreement. Results from the bond stress-slip model were compared to test results from Eligehausen et al. (1983). The test corresponded to four series of five cycles each between the following slip values ±0.44 mm., ±1.65 mm., ±4.57 mm. and ±9.20 mm. Fig. 2.9 compares the results and a very good agreement can be found. CHAPTER 2 Analytical Models of the Constitutive Materials 19 » . c / e. (a) Test by Sinha, Gerstle and Tulin (1964) r/rc (b) Computed response Fig. 2.7: Comparison of analytical and experimental results for concrete stress-strain relationship. drqsuoijBpj UTBJJS-SS3JJS pajs JOJ s;inssj rejuauruadxa pire reoiiXreire jo uosLrediuo3 :8'Z asuodsaj p9jndui03 (q) M n n • • • * o e- »- »- »• oi- a- «- »i-(6Z.6I) ojaLisg pin? Aodoj 'BdsjBuTjqi.BMiA Aq isaj, (B) T 1 1 r—1 1 1 1 00 8-008 [ j U J U i / N ] x> OZ spudivpi 3Aftnttjsuoj aqi fo siapopt jvotutymiy z IHLLdVHD CHAPTER 2 Analytical Models of the Constitutive Materials T ( N / m m 2 ) 16 (a) A F T E R 5 C Y C L E S (b) A F T E R 10 C Y C L E S (c) A F T E R 15 C Y C L E S (d) A F T E R 2 0 C Y C L E S - 8 H -16 (a) Test by Eligehausen et al. (1983) s (mm) (b) Computed response Fig. 2.9: Comparison of analytical and experimental results for bond stress-strain relationship. CHAPTER 3 Reinforced Concrete Finite Element This chapter describes the assumptions and steps in the derivation of a displacement-based reinforced concrete finite element. It details the procedures and the mathematical approach used in the formulation of the internal force vector and the tangential stiffness matrix in direct relation to the constitutive models described in Chapter 2. 3.1 Introduction The behavior of reinforced concrete elements under dynamic excitations depends on the mechanical characteristics of concrete, steel and concrete-steel bond. The stress-strain relations are nonlinear even for small displacement levels, and as loading increases, the development of cracks further contribute to the nonlinear nature of the element. As a result, the appearance of the structure is very different before and after the development of cracks. Such behavior is very complex and difficult to model taking into account the effect of each of the intervening factors. The objective in this work is to capture the main or more important aspects of the behavior, leading to a simplified model. The principle of virtual work is used to develop the nonlinear finite element, and to obtain the tangential stiffness matrix needed for the iterative solution of the nonlinear problem. 22 CHAPTER 3 Reinforced Concrete Finite Element 23 3.2 General Assumptions In order to simplify the analysis, the following assumptions are made: 1. Displacements are assumed small enough so that second order effects are neglected. 2. Plane sections are assumed to remain plane for the concrete cross sections. Slip is allowed between the reinforcing steel and its surrounding concrete. 3. Normal stresses perpendicular to the element length are ignored. All strains and stresses are uniaxial and parallel to the element length. Therefore, Poisson effects are not taken into account. The effect of shear strain is not considered in the formulation of the virtual work equation. 4. The concrete cross section is rectangular and it is divided into a number of layers to represent the stress distribution over the cross section with sufficient accuracy. Each layer has a strain obtained from the distribution indicated above. 5. All reinforcing steel located at the same distance from the center of the beam is considered as a layer with an area equal to the sum of the areas of all the bars and a perimeter equal to the sum of the perimeters of each individual bar. A typical cross section is shown in Fig. 3.1. z Steel layers Concrete layers Fig. 3.1: Cross section and degrees of freedom for the RC finite element CHAPTER 3 Reinforced Concrete Finite Element 24 3.3 Derivation of the RC Finite Element The kinematic relationships used to develop the finite element can be formulated from the deflection in a beam element, as shown in Fig. 3.2. The beam element is composed of a concrete element with two end nodes and N steel layers with three nodes each, with both components internally connected by the bonding mechanism. The degrees of freedom associated with these nodes are shown in Fig. 3.1. ^ Y y- Steel layer y. y \ * \ / «c(x,y)) \ | » >. ! xr-K dw/dx / CG axis *c(x) \ / ^ N H/2 f 1 0 > ' r ' X Fig. 3.2: Deflection of beam Based on the small deformation theory, the displacement uc(x,y) in the x-direction of a concrete layer located at a distance^ from the center of gravity is determined by: «Ax,y)=u-e(x)-y^ (3i) where ue(x) and w are the axial displacement and the deflection of the element centroidal axis. Similarly, the displacement of the steel layer / is: « . ( * . * ) = « : ( * ) (3-2) CHAPTER 3 Reinforced Concrete Finite Element 25 From the displacements defined above, the slip between the steel layer /* and its surrounding concrete is expressed as: K(x,y) = ue(x,y)-uM(x,y) = ue(x)-y^ — -ui,(x) (3.3) ax where yti is the location of steel layer /'. To approximate the displacements uc(x) and w within the concrete element, a set of interpolation functions is used. Displacement uc(x) is defined as a linear interpolation of the axial displacements of the end nodes. Displacement w is defined by cubic Hermitian functions. Thus: uc(x) = M1u1+M4u4 (3.4) w =M2u2 +M3u3 +M5u5 +M6u6 (3.5) Displacement of steel layer /' is approximated by the use of a quadratic function as follows: u',(x) =M7u'ti +Msu',2 +Mgufs3 (3.6) Although the displacement of the steel layer could have been defined by two end nodes, thus resulting in a linear function, it was found that adding another node at mid length and using quadratic interpolation functions, gave better results. The slip is now defined as the difference of two quadratic functions, instead of a difference between a quadratic function on the concrete side and a linear function for the steel layer. The interpolation functions are: M , = l - 7 M2 = 2/73 -3/72 +l M% =(n3-In2 +n)L M4=n M5=-2n3+3n2 M6=(n3-n2)L Mn =2/72 -3/7 + 1 Mt =-4n2 +4/7 M9=2n2-n CHAPTER 3 Reinforced Concrete Finite Element 26 where n = x/L. The displacements of the RC components can now be defined in vectorial form as: ue (x) = {N1)T {a} w = {Nlf {a} and u\ (x) = {/V3}f {a} where: Term ' 0 ' ' 0 1st 0 M2 0 2nd 0 M3 0 3rd M4 0 0 4th 0 M 5 0 5th 0 M6 0 6th 0 0 0 {/V2} = « 6+ith 0 g g 6+Nth 0 0 0 • • M% 6 + N+ith 0 g 0 6 + 2Nth 0 0 0 i • M9 6 + 2N+ith 0 0 0 6 + 3Nth (3.7) and {a} is the nodal displacement of the reinforced concrete finite element in vectorial form: M = {*l U2 « 3 U A « 5 U6 I «il »il I « i 2 — « i 2 — " I s ' *' U* ' ' ' U* J Knowing the displacements uc(x) , w and u[(x), the strains in the concrete and the steel layers and the slip between them can be written as: (d{Nlf ..;d'{N2)T\ . duc(x) d2w dx dx2 dx y dx2 W (38a) CHAPTER 3 Reinforced Concrete Finite Element 27 „ , du\ d{N3}T f x where the derivatives can be easily obtained from the interpolation functions. (3.8.b) (3.8.C) 3.4 Internal Force Vector and Tangent Stiffness Matrix Knowing the slip and the strains in concrete and steel, the Principle of Virtual Work can be applied. A strain vector and its associated nonlinear stress vector are defined as: f f. 1 • = B2 M=MM and {/X (3.9) B3 ifX. where: 6 terms 3N terms x(3N+6) = [A/; -yM\ -yM\ M[ -yM\ -yM\ \ 0 - 0 | 0 - 0 | 0— 0] 3N terms 6 terms < > e x(3AT+6) 0 6 terms Ml Mg N terms N terms >^< > X0N+6) ~ Mx -y«M\ -y„M\ MA -y„M'5 -y„M'6 -Mn -M, CHAPTER 3 Reinforced Concrete Finite Element 28 2N terms - M . - M o - M a - M D N terms and fc,f, and fb are the corresponding stresses from the constitutive material models. The principle of virtual work equation is now to find the internal force vector. Applying a virtual displacement to the system, the external work (dW) and the internal energy (dU) developed by the forces and stresses are defined as: dV = j{Se}T{f)dV (3.10.a) 6W = jfo}T{FpV (3.10.b) Since the change in the internal energy is the same as the change in the external work of the system, both expressions are equal: \ { S a J ^ = \{5s}T{f)dV (3.11) Substituting {&}r = & f [B]T will yield: V V Using Eq. 3.9 into Eq. 3.12: (3.12) (313) Vc VM Ap where Vc and Vs are the concrete and steel volumes respectively, and Ap is the surface area under bond contact. The tangent stiffness matrix is determined by: CHAPTER 3 Reinforced Concrete Finite Element 29 w - W - f e ! - J w S K ( 3 , 4 ) The term determines the nonlinearity of the tangent stiffness matrix and it is evaluated as the slope of the stress-strain relationship of the corresponding material model. Developing the vector of internal forces in Eq. 3.12 and the tangent stiffness matrix given in Eq. 3.14, all the terms of both vector and matrix can be defined. As an example, the internal force at degree of freedom 2 and the matrix term k/2,3) are shown: r^) = \{-y)KfcdVc^\iry.W'JbidAPi (3.15.a) Vc NLS Api *,(2,3) = J(-;y)2M;M;7J^^^ ( 3 1 5 b ) where DFC and DFB are the slope of the concrete stress-strain relationship and the slope of the bond stress-slip curve respectively. It can be seen that adding the bond stress behavior to the analysis of RC elements will contribute to the terms of the stiffness matrix and to the internal forces. Due to the nonlinear nature of equations 3.15.a and 3.15.b a Gaussian integration scheme is used to evaluate the integrals in the longitudinal direction. It is necessary then to use a new variable fc; with values £ = -1 at x = 0, and E, = 1 at x = L. The corresponding transformation is: l = 2 y - l (3.16) 2 And its derivative: d£ =—dx * L CHAPTER 3 Reinforced Concrete Finite Element 3 0 To evaluate the derivatives of volumes and surface areas, the following approximations are made: •dV,=Ajbt = ±AJU* dVt=AJx = ±AmaZ (3.17) dAp = 7tDtdx = —nDid<f; where Aci is the area of the ith. concrete layer, AIt and Dt are the area and the representative diameter of the ith. steel layer respectively. The terms corresponding to rint (2) and k, (2,3) are given in their discrete form: ^ ( 2 ) = V Z ( - : ^ Z M ; ^ *• NLC NGP *- NLS NGP *• NLC NOP *• NLS NOP MltfjWMDFB^j) where NLC = number of concrete layers, NLS = number of steel layers, NGP = number of sampling Gaussian points, = sampling Gaussian point and W(£) = weight factor at sampling point. The concrete strain e j and the slip A j are evaluated at the sampling point £ j by using equation 3.9, and the corresponding concrete stress and bond stress are found from the constitutive relationships. CHAPTER 4 Dynamic Analysis of Reinforced Concrete Frames This Chapter describes the processes involved in the solution of the nonlinear problem. The RC frame is subdivided into finite elements that are interconnected at selected nodes. Since nonlinear relations between the nodal forces and displacements exist, an iterative scheme is required. 4.1 Introduction The nonlinear dynamic analysis of reinforced concrete frames has been traditionally approached in two ways. The first is based on what is called the "qualitative approach". Here, some simplified functions in the form of force-displacement (P-6) or moment-curvature (M-<J)) relationships under dynamic loading are suggested. These relationships, known as hysteretic models, are based on parameters that depend on the test characteristics that were used to develop them. Many models have been used to represent these relationships, from those known as elasto-plastic and bilinear models to more elaborate models presented in Park and Paulay (1975). It is clear that the choice of the hysteretic model determines the final result of the nonlinear dynamic analysis. In that sense, the area limited by the hysteretic curves is especially important because it represents the measure of energy dissipation. Therefore, good results can also be achieved with simple models as long as the shape of the curves is adapted to the characteristics of the element whose behavior is being modeled. This dependency in the element characteristics can be greatly reduced by the use of relationships to simulate the stress strain behavior of the constitutive materials and 31 CHAPTER 4 Dynamic Analysis of Reinforced Concrete Frames 32 mechanisms involved in the nonlinear dynamic response. In that way, the response is dependent on the quality of the models rather than in the shapes or reinforcement ratios of the elements of the frame. As part of this thesis, the displacement-based finite element program NODARC was developed based on the constitutive model relationships discussed in Chapter 2 and in the finite element formulation given in Chapter 3. Knowing the internal force vector {rM} and the tangent stiffness matrix fkj, the nonlinear problem is solved by the use of a direct time integration method and an iterative process within each time step. 4.2 Equilibrium Equations The equations governing the nonlinear dynamic response of a system subjected to ground acceleration is given by: where [M] and [C] are the mass and damping matrix; {Rmt} is the internal load vector and {Ro} is the externally applied gravity load vector; fr) is a selective vector for the degrees of freedom affected by the ground acceleration and ag the ground acceleration magnitude. y} ,y} and {£/} are, respectively, the acceleration, velocity and displacement vectors, all relative to the ground. It is understood that this equation is time dependent and that the system is in equilibrium at time t. 4.2.1 Mass Matrix (4.1) At the element level, the mass matrix is computed from the shape functions, i.e. a CHAPTER 4 Dynamic Analysis of Reinforced Concrete Frames 33 consistent mass matrix, and from the mass of the structural elements such as columns and beams. Any other imposed masses, such as slabs or dead load or live load independent of the structural frame, are considered as lumped to degrees of freedom related to concrete nodes (RC-DOF). The mass of rebars is neglected, thus no masses are considered acting on degrees of freedom related to the reinforcing steel (RS-DOF). The form of the element mass matrix is shown here: ML 420 0 pAL 6 0 0 UpAU 0 54pAL \3pAL2 420 420 420 4pAL3 0 l3pAL2 3pAL3 420 420 420 pAL 0 0 3 l56pAL 420 22pAL2 420 Symmetric 4pAL3 420_ J(3W+6)x(3W+6) where A = area of cross section and p = mass density. After the assembling process, the mass matrix of the system has a size corresponding to the number of degrees of freedom related to concrete (RC-DOF). The vector {r} in Eq. 4.1 is used to select those degrees of freedom affected by ground accelerations, i.e. horizontal degrees of freedom. In this way, the mass assigned to these nodes will be subjected to a horizontal acceleration equal and in an opposite direction to the ground acceleration. CHAPTER 4 Dynamic Analysis of Reinforced Concrete Frames 3 4 4.2.2 Damping Matrix It is practically impossible to find the viscous damping parameters for a finite element system because the amount of damping is due to mechanisms such as hysteresis and slip failures and also because these parameters are frequency dependent. Therefore, a more practical way of formulating the damping matrix is to approximate it by viscous damping in such a way that it relates the mass and stiffness of the complete system to an amount of damping obtained from experimental results or past experience. These observations of the vibratory response of structures are used to assign a fraction of critical damping £ as a function of frequency, or as it is common, to assign a single damping ratio for all the range of frequencies of the structure. This ratio is dependent on materials and stress levels, but for reinforced concrete structures, an approximate range of 2% to 5% is commonly used with good results. When a damping matrix is constructed in this way it is called a "proportional damping matrix" because it is formed from a combination of the mass and stiffness matrices: Parameters a and P are dependent on the critical damping ratio C assigned to a frequency co, where the bounds of <o should be the lowest and the highest frequencies of the structure required to represent well the response. The procedure used to find these lowest and highest frequencies of the structure is described in Bathe (1982). In finding the eigenvalues, the stiffness matrix was condensed to RC-DOF due to compatibility with the mass matrix. [C]=a[K]+B\M] (4.2) — 0) K« Ku\ 0 cc (4.3) CHAPTER 4 Dynamic Analysis ofReinforced Concrete Frames 35 where Kcc and Ka are the stiffness matrix related to RC-DOF and to RS-DOF respectively. The condensed stiffness and mass matrices become: \ K ] = [ K j - [ K A K a r \ K j (4.4.a) ]M]=WJ (4 4 b) r And the maximum and minimum frequencies are found by solving the following eigenproblem: §K]-a>>\M]}{pc}={0} (4.5) In this study, it is assumed that, for the purpose of finding [CJ, matrix [Kcc] corresponds to an uncracked concrete state. 4.2.3 Externally Applied Forces As it is seen iii Eq. 4.1 the external load is treated as the algebraic sum of gravity loads {Ro} and inertial loads [A/]{r)arx produced by the ground acceleration acting on selected degrees of freedom. Even when a finite element formulation is used, vector {R0} is evaluated in a way similar to the inertial loads. Here, a vector {r0} is used to select RC-DOF's affected by gravity, i.e. RC-DOF's in vertical direction, such that the gravity load vector is formulated as: R}=-Mr0k (46) where g = gravity acceleration and the minus sign is added because the global vertical axis is considered positive in the upwards direction. CHAPTER 4 Dynamic Analysis of Reinforced Concrete Frames 3 6 4.3 Solution to the Nonlinear Problem The use of an implicit direct integration method has many advantages, especially when considering the stability of the solution to Eq. 4.1. The Newmark-Beta integration scheme with constant-average acceleration within a time step is widely used because of its unconditional stability and because it has no restriction on the time step other than as required for accuracy. The constant-average acceleration method was used to relate displacements, velocities and accelerations at the beginning and end of each time step, thus: P i ! = - Pi)- Pi <4 7») Ph=-£r(PL,-P).)~Pl-Pi <«*> Combination of Eqs. 4.7.a and 4.7.b with the equilibrium equation Eq. 4.1 yields the following equation: V. At At J where: (4.9) The solution is now reduced to solve Eq. 4.8, in which the right hand side is known from the previous step. Since this is a nonlinear equation, the Newton-Raphson method is then used to solve the equations, through iterations, within each time step. Let us first define a vector {<f>} as a function of the displacement vector {U}: CHAPTER 4 Dynamic Analysis ofReinforced Concrete Frames 37 4 M 2[C] I, At2 At , (4.10) which has to be equal to zero in order to find the solution (U) = {U}„+i. A Taylor series expansion of Eq. 4.10 gives: fy(U + AU)} = fy(u)}+ d&(U)} {AU}+ higher - order terms dp) (4.11) Neglecting the higher order terms and making the right hand side of Eq. 4.11 equal to zero, the increment in the displacements can then be calculated: 1 L m {-Wo) (4.12) It can be seen that the term [^p] in Eq. 4.12 has to be calculated before the Newton-Raphson method is used. Applying the partial derivative of Eq. 4.10 with respect to the vector {U}: afeint} dp} = "4M 2[C] Ar 2 Ar ep) (4.13) The second term of the right hand side of Eq. 4.13 is the tangent stiffness matrix of the system, and is calculated by assembling the element tangent stiffness matrix given in Eq. 3.14 (Sect. 3.4) to the global nodes. An equivalent stiffness matrix [Keff] is defined by: lKeS]=M+m+[Ki] 1 J Ar 2 Ar 1 ' J (4.14) in which matrix [KJ is a function of {U} and updated at each iteration inside the step. The process used to solve the nonlinear problem from step /' to step i+J is shown graphically in Fig. 4.1 and summarized below: (1) Evaluate (<p(Ui)} using Eq. 4.10 and compute ERRORo = 11 {tfUM 11 CHAPTER 4 Dynamic Analysis of Reinforced Concrete Frames (2) Assume {lf,+t} = {U,} (3) Compute [KJ at {ifM} (4) Evaluate [Keff] and [Keffj' by using Eq. 4.14 (5) Find new {ifby using Eq. 4.12 (6) Compute {tfnew if and ERROR = \\{tfnew lfi+j)}\\ (7) If ERROR > TOLER*ERRORo Then: • Take (if = new {if i+J) • Return through all steps from step (3) Else: • Take {U,+1} = new {lfi+i} • Update and j / J M ) by using Eq. 4.7. • Start a new time step At and return to step (1). new {Rext} {Rext}w {Rext}i > {U} Fig. 4.1: Newton-Raphson iterative process CHAPTER 5 Applications This Chapter focuses on two specific applications of the computer program NODARC. The first application is devoted to find the time-history response of a one-level reinforced concrete frame. It also shows another derived applications such as the time variation of a bending moment and the stress-strain hysteretic curves for selected locations in concrete and steel layers. The second application consists of a reliability-based capacity design analysis of a RC frame, that is subjected to a ground acceleration, for a required reliability index p. 5.1 Time-History Response The analyzed structure consists of a concrete slab supported by beams and columns with dimensions and reinforcement as shown in Fig. 5.1. The analysis was performed on a single frame with half the total top mass located at 3 m. from the base. For the purpose of computing the elastic seismic force acting on the frame, the mass was considered as the sum of the dead load plus a 25% of the live load taken as 3.0 kN/m2, as it is stated in NBC-90. The frame was subdivided into 15 elements and each typical cross section was divided in 20 layers. More details are shown in the input data file Appendix A. The ground acceleration considered for this analysis was the El Centra record, which has a peak acceleration of 0.35g as shown in Fig.5.2. 39 CHAPTER 5 Applications 40 B«H»25tte5Q<> Concrete slab e*l50 mm Beam 250x500 5000 mm 1 BEAM CROSS SECTION Top reinf: 3#4 BoL Reinf: 2#4 + l#5 5000 mm COLUMN CROSS SECTION Corner reinf.: 4#5 Rest4#4 Fig. 5.1: Details of Reinforced Concrete Frame The frame was designed according to NBC-90 and A23.3-94. Due to the acting loads and to the dimensions of the frame, no substantial stresses were calculated within the structure, then resulting in minimum reinforcement ratios for beams and columns. The elastic displacement of the frame calculated according to NBC-90 was 0.75 mm with a ductility factor R equal to 4. To compute the time-history displacement at the top, the frame was subjected to the normalized El Centra record with 0.2g as peak acceleration. The variation of the displacement at the top is shown in Fig. 5.3. The maximum displacement is 1.53 mm which is almost twice the elastic displacement. It can also be noticed that the frame has sustained inelastic deformations that resulted in a small permanent set at the top of the frame. This inelastic behavior can be attributable to the cracking .occurred in the column as Fig. 5.4 shown. CHAPTER 5 Applications 41 0.25 Time (sac.) Fig. 5.2: El Centra NS (1940) earthquake record scaled to 0.2g. E E 1 0.5 0 0) E -0.5 S £ -1 -1.5 1 1 il \ 1 I • 11 l 1 10 20 30 T i m e ( s e c . ) 40 50 60 Fig. 5.3: Time-history of the displacement at the top. \ CHAPTER 5 Applications 4 2 During the analysis, two concrete layers located at the outer and inner faces of a cross section near the base of the column were monitored. Their respective stress-strain hysteretic curves are shown in Fig. 5.4. It can be seen that this section has sustained some opening and closing of cracks during cycles that contributed to the overall inelastic response. Tensile strains reached values up to 3x10 , as it is expected due to the stresses developed by the dynamic loads in this region. Also, from the curve corresponding to the outer layer, it is seen that the concrete is going through elastic unloading without reaching much stress. These results are reasonable because the low axial load in the columns produce low compressive stresses which, added to the stresses from the dynamic loading, can be easily increased or reversed. From these results it can be concluded that the concrete has remained almost elastic when subjected to compression and that most of the inelastic behavior can be attributed to the initial formation of cracks and to their opening and closing during de cycles. 3 2 1 ^ 0 I"1 ~ -2 -3 -4 -5 -6 -7 k 1 1 // Outer layer -4.5 -2.5 -0.5 1.5 S t r a i n x 1 0 - 4 ( m m / m m ) 3.5 -3 -2 - 1 0 1 2 S t r a i n x 1 0 - 4 ( m m / m m ) Fig. 5.4 Stress-strain curves in concrete layers CHAPTER 5 Applications 4 3 Fig. 5.5 shows the time history response of the internal bending moment in the beam at its connection with the column. It can be seen that it varies around 10 kN.m, which corresponds to the bending moment produced by gravity loads at that section. The maximum bending moment reached during the shake is about 14.6 kN.m, far less than the ultimate moment capacity of the beam calculated as 41 kN.m. The ultimate moment in the positive direction is 72 kN.m. 4 . 2 : —• 0 \ 1 1 , 1 1 0 10 20 30 40 50 60 T i m e (sec . ) Fig. 5.5 Variation of bending moment. 5.2 Reliability Applications Program NODARC can also be used to perform reliability analyses when used in combination with reliability software like RELAN or HAELAN (Foschi, 1988) for, respectively, forward or inverse reliability problems. CHAPTER 5 Applications 44 The same frame used in Sec. S.l with a constant slab thickness of 5 in. is used again, but this time the mass at the top is changed. This variation of the mass is considered as a percentage of the design live load taken from NBC-90 as 3 kN/m2. In this study, the range of variation is limited from 25% to 300% of the design live load. The objective is to find the live load percentage that corresponds to a given probability of exceeding a given relative top displacement. This probability can also be expressed as a reliability index J3. Here we will assume that only the peak ground acceleration is a random variable and that all other variables are fixed to their mean value. The earthquake record used to perform the dynamic analysis was the El Centro NS (1940) record after being scaled to the required peak acceleration. As it is stated in NBC-90, the design peak acceleration has been obtained for a 10% probability of being exceeded in a period of 50 years, which in turn, corresponds to an annual exceedence probability of 1/475. In this study the design peak acceleration aD for the annual exceedence risk mentioned above is taken as 0.25g and it is used for the computation of the mean value of peak ground acceleration for two arrival rates. The peak acceleration follows a lognormal distribution as: aG=-fi^=eR"'^r) (5.1) where OG is the peak acceleration, a^ is the mean value of aD, V is the coefficient of variation, usually taken from attenuation equations as 0.6. RN is a standard normal variable that depends on the level of reliability to achieve. CHAPTER 5 Applications 45 The first analysis considers earthquakes occurring, on average, once in 20 years. Thus, the probability of exceeding the design acceleration aD during an earthquake is obtained from the assumption that these arrive according to a Poisson process in which: P.=l-e-"' (5.2) where PA is the annual exceedence probability, //. is the arrival rate and PE is the probability of exceeding the design acceleration during the arrival time. Then, PB =PE^G ><*D) = — — InO——) = 0.0421 (5.3) B D F 1/20 v 475 Thus, since the acceleration aG is assumed to follow a lognormal distribution (Eq. 5.1): P « fa>« a ) = l - / » « ( ^ (5.4) Vln(l+F2) Taken PE {fla > dto) = 0.0421 from Eq. 5.3 and replacing into Eq. 5.4 gives RN as: /?A r=0)- ,(l-P i r) = <D-,(l-0.0421) = 1.73 (5.5) The mean peak acceleration, OM, is obtained by replacing RN in Eq. 5.1, with aG= oto. Thus aM is found to be 0.1 lg. The second analysis considers a reliability level of (3=3.4, i.e. RN = 3.4. The corresponding peak ground acceleration is, from Eq. 5.1: a = 0-"g e MVSa?) = Q 6 2 g ( 5 6 ) Vl + 0.62 with a exceedance probability of: P j r=l-«D(3.4) = 1 -0.999663 = 0.34xl0-3 (5.7) The frame was subjected to El Centra ground accelerations with peaks of 0.25g and 0.62g for the entire range of live load variation. The results are plotted in Fig. 5.6. CHAPTER 5 Applications 46 As stated, these accelerations correspond, respectively, to exceedance probabilities of 0.0421 (P=1.73) and 0.34xl0"3 (0=3.4) during an earthquake event. In this work, the collapse of the frame is defined as the event in which a sufficient number of concrete layers exceed the ultimate compression strain, leading to the complete failure of concrete sections and numerical singularity. The lower curve in Fig. 5.6 corresponds to a reliability level of 1.73. It shows that at a live load percentage of about 260% there is a 4.21% 0=1.73) probability of exceeding a displacement of 8 mm. However, as shown, the frame will collapse. 2 . : : : 0 I i i i i i i 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 P e r c e n t a g e o f L i v e L o a d (%) Fig. 5.6: Reliability application On the other hand, the upper curve obtained for a reliability level of ($=3.4, shows that a 55% live load percentage can ensure that a deflection of 10 mm will not be exceeded with CHAPTER 5 Applications 47 a corresponding probability of 0.34xl0'3. Also, the frame will collapse, with this probability, at live load levels of around 120%. Fig. S.6 shows the collapse cases at the maximum displacement achieved up to the collapse. This maximum normally occurred at a time just after the peak acceleration but before the collapse. This application then shows a very useful application of NOD ARC to assessing the seismic reliability of existing structures. We may want to know how much load a frame can sustain for a given reliability level and also how it is going to perform without collapsing. CHAPTER 6 Conclusions Hysteretic models for concrete, steel and bond have been used to develop a displacement-based finite element program for reinforced concrete frames. The models have shown to be accurate in predicting results that agree with experimental results from the literature. Results from the program can be applied to time-history analyses of RC frames or any other applications where results from a dynamic analysis are needed. NOD ARC predicts the location and time in which the failure of a frame starts by indicating the concrete layer that reaches the ultimate compressive strain. This situation usually leads to the subsequent failure of other concrete layers around the first crushed layer up to the point where numerical singularity stops the program. The program has also the option to monitor the global displacements at given nodes and to keep track of the internal actions, i.e. internal forces and local displacements, for selected elements. When it is used as a subroutine, NOD ARC can be useful in performing reliability analyses of reinforced concrete frames. In this case, the performance function can consider different limit states involving, for example, structural responses such as bending moments, cracks of a given width, crushing of concrete, maximum displacements, etc. The application mentioned in this work only considered the peak ground acceleration as a random variable. However, any other design variable such as concrete strength fc, yield stress Jy, or member dimensions can be selected as random variables and entered as arguments of the subroutine. 48 CHAPTER 6 Conclusions 49 It is clear that better results can be obtained when more refined models are used. Since NOD ARC calls the subroutines of the corresponding materials, any other model can be used as long as it provides the parameters that NOD ARC requires. Further research on this matter should also consider the use of a confined concrete model, the use of bi-dimensional or tri-dimensional stress-strain material models, the addition of nonlinear shear stresses in the derivation of the finite element and the implementation of the RC finite element into a computer program to perform push over analysis. R E F E R E N C E S Aktan, A. E. , Karlsson, B. I., Sozen, M. A., (1973). Stress-strain relationships of reinforcing bars subjected to large strain reversals. Struct. Res. Ser. No. 397, Univ. of Illinois at Urbana-Champaign, 111. Bathe, K. J., (1982). Finite element procedures in engineering analysis. Prentice-Hall, New Yersey. Collins, M. P., Mitchell, D., (1987). Prestressed concrete basics, 1st. Edition, Published byCPCI. Dodd, L. L., Restrepo-Posada, J. I., (1995), "Model for predicting cyclic behavior of reinforcing steel", J. Struct. Div., ASCE, Vol. 121, No. 3, pp. 433-445. Eligehausen, F.C., Popov, E.P., Bertero, V.V., (1983). Local bond stress-slip relationships of deformed bars under generalized excitations. Earthquake Engineering Research Center, Report No. UCG7EERC-82/23, University of California, Berkeley, 169 pp. Fronteddu, L.F., (1992), "Response of reinforced concrete to reverse cyclic loading", M. A. Sc. Thesis, University of British Columbia, 118 pp. Filippou, F.C., Popov, E.P., Bertero, V.V., (1983). Effects of bond deterioration on hysteretic behavior of reinforced concrete joints. Earthquake Engineering Research Center, Report No. UCG/EERC-82/19, University of California, Berkeley, 175 pp. Foschi, R O. (1988), User's Manual: RELAN (RELiability ANalysis). Civil Engineering Department, University of British Columbia, Vancouver. Giuffre, A., Pinto, P.E., (1970), "II comportamento del cemento armatoper sollecitazioni cicliche di forte intensiia (Reinforced concrete behavior under strong repeated loadings) ", Giomale del Genio Civile, No. 5, Maggio, (May). Harajli, M. H., (1988), "Behavior of partially prestressed concrete joints under cyclic loading", J. Struct. Div., ASCE, Vol. 114, No. 11, pp. 2525-2532. Karsan, I. D., Jirsa, J. O., (1969), "Behavior of concrete under compressive loading", J. Struct. Div., ASCE, Vol. 95, No. ST12, pp. 2543-2563. Kent, D. C , Park, R., (1971), "Flexural members with confined concrete", J. Struct. Div., ASCE, Vol. 97, No. 7, pp. 1969-1990. Mander, J. B., Priestley, M. J. N., Park, R , (1988), "Theoretical stress-strain model for confined concrete", J. Struct. Div., ASCE, Vol. 114, No. 8, pp. 1804-1825. 50 References 51 Menegotto, M., Pinto, P.E., (1973), "Method of analysis for cyclically loaded reinforcement concrete plane frames including changes in geometry and nonelastic behavior of elements under combined normal force and bending", Proceedings, IABSE Symposium on the resistance and ultimate deformability of structures acted on by well-defined repeated loads, Lisbon. Park, R, Paulay, T., (1975). Reinforced concrete structures. Jhon Wiley and Sons, New York, N. Y. Reinhardt, H.W., Cornelissen, H.A.V., Hordijk, D A , (1986), "Tensile test and failure analysis of concrete", J. Struct. Div., ASCE, Vol. 112, No. 11, pp. 2462-2477. Scott, R.H., Gill, P.AT., (1987). "Short term distributions of strain and bond stress along tension reinforcement", The Structural Engineer, J. of the Institution of Structural Engineers, Vol. 65B, No.2, June, pp. 39-48. Sinha, B. P., Gerstle, K. H., Tulin, L. G., (1964), "Stress strain relation for concrete under cyclic loading", J. of the American Concrete Institute, Vol. 61, No. 2, pp. 195-211. Viwathanatepa, S., Popov, E. P., Bertero, B. B., (1979). Effects of generalized loadings on bond of reinforcement bars embedded in confined concrete blocks. Report No. EERC 79-22 Earthquake Research Center, Univ. of California, Berkeley. Yankelewsky, D. Z., Reinhardt, H. W., (1987), "Modelfor cyclic compressive behavior of concrete ", J. Struct. Div., ASCE, Vol. 113, No. 2, pp. 228-240. Yankelewsky, D. Z., Reinhardt, H. W., (1989), "Uniaxial behavior of concrete in cyclic tension", J. Struct. Div., ASCE, Vol. 115, No. 1, pp. 166-181. APPENDIX A USER'S GUIDE NAME: NODARC LANGUAGE: MS FORTRAN POWERSTATION 4.0 DATE: OCTOBER 1998 Introduction: This user's guide provides the necessary steps to write the input data file for the use of NODARC. Since some of the input lines are formatted, it is recommended that the input data file be first prepared by running NODARC and entering the data through the keyboard. Once it is stored, it can be used as a model for other frames or edited to change the data. BLOCK 1: GENERAL INFORMATION, Enter ONE line of data with the following information: T I T L E Title of the problem up to a maximum of 80 characters. Enter ONE line of data with the following information: Format: 2E15.6 FC Concrete cylinder strength at 28 days. (MPa) DC Unit weight of concrete, (kg/m3) Enter ONE line of data with the following information: Format: 5E15.6 < ' ESS Young's modulus of elasticity. (MPa) DS Unit weight of steel, (kg/m3) FY Yield stress of reinforcing steel. (MPa) FSU Ultimate stress of reinforcing steel. (MPa) ESU . Ultimate strain of reinforcing steel, (mm/mm) BLOCK 2: TYPICAL CROSS SECTIONS Enter ONE line of data with the following information: Format: 15 NST Number of typical cross sections. Enter NST blocks of data containing the following information: a) ONE line containing the following: Format: 2E15.6,2I5 HTYP Depth of cross section, (mm) BTYP Base of cross section, (mm) NLTYP Number of layers in which the section is going to be 52 APPENDIX A: User's guide divided. NSTYP Number of steel layers in this cross section. b) NS lines, each containing the following: Format: 3el5.6 DIATYP Diameter of layer ith. (mm) ASTYP Area of layer ith. (mm) ZSTYP Location from center of cross section, (mm) BLOCK 3: CONNECTIVITY OF NODES Enter ONE line of data with the following information: Format: 315 NEL Number of reinforced concrete elements. NOD Number of reinforced concrete nodes. NRS Number of reinforcing steel nodes. Enter NEL blocks of data containing the following information: a) ONE line containing the following: b) NSTYP lines, each containing the following data: Format: 415 NBAR Steel layer number of the corresponding typical cross section. NODSI Node number at end i of steel layer NBAR. This node corresponds to node i of the RC element. NODSJ Node number at end j of steel layer NBAR. This node is located at mid-length of the layer. NODSK Node number at end k of steel layer NBAR. This node corresponds to node j of the RC element. BLOCK 4: COORDINATES AND LUMPED MASSES Enter NOD lines of data, each with the following information: Format: I5,3E15.6 NODE Node number. X Global x-coordinate of node NODE, (m) Format: 415 NTYP Identification number of the corresponding typical cross section. Node number at end i. Node number at end j. Identification code for connectivity between elements. Enter 1: If node i is connected to a joint. Enter 2: If node j is connected to a joint. Enter 0: If both ends are connected to another elements. NODCI NODCJ NODM APPENDIX A: User's guide 54 Y Global y-coordinate of node NODE, (m) MASS Lumped mass at node NODE, (kg) BLOCK 5: RESTRAINTS a) Enter ONE line of data with the following information: Format: 15 NRES Number of nodes with restrained displacements. b) Enter NRES lines of data, each with the following information: Format: 415 NODRES Number of restrained node. TDC1 Enter 1 if displacement of NODRES is restrained in the global X-direction. Otherwise, enter 0. IDC2 Enter 1 if displacement of NODRES is restrained in the global Y-direction. Otherwise, enter 0. IDC3 Enter 1 if rotation of NODRES is restrained in the global Z-direction. Otherwise, enter 0. BLOCK 6: GAUSS SAMPLING POINTS Enter ONE line of data with the following information: Format: 15 NGPX Number of Gaussian points to be used in the numerical integration. BLOCK 7: DAMPING PARAMETERS Enter ONE line of data with the following information: Format: 2E15.6 DAMP1 Damping ratio corresponding to the lowest frequency. (%) DAMP2 Damping ratio corresponding to the highest frequency. (%) BLOCK 8: DISPLACEMENTS AT SELECTED NODES a) Enter ONE line of data with the following information: Format: 15 NTAR Number of RC nodes whose global displacements are going to be stored in an external file. Enter 0 if none. b) If NTAR is not 0 then enter NTAR lines of data, each with the following information: Format: 15 RCNOD Node number where global displacements are sought. APPENDIX A: User's guide 55 c) If NTAR is not 0 then enter NTAR lines of data, each with the following information: FILE1 Name of output file where displacements are stored. Maximum 12 characters. BLOCK 9: INTERNAL ACTIONS IN SELECTED ELEMENTS a) Enter ONE line of data with the following information: Format: 15 NSTAR Number of elements whose internal forces at the element degrees of freedom are going to be stored in an external file. Enter 0 if none. b) If NSTAR is not 0 then enter NSTAR lines of data, each with the following information: Format: 15 NT1F Element number where internal forces are sought. c) If NSTAR is not 0 then enter NSTAR lines of data, each with the following information: FTLE2 Name of output file where internal actions are stored. Maximum 12 characters. APPENDIX A: User's guide 56 EXAMPLE OF INPUT DATA FILE The following shows the input data file used by NOD ARC to compute the time history response of the two applications mentioned in Chapter 5. RC FRAME 04 (AGO. • .300000E+02 • .200000E+06 .400000E+00 • 2 • • .250000E+03 .381000E+02 .254000E+02 .381000E+02 •500000E+03 •381000E+02 •445000E+02 15,1998) .240000E+04 .765000E+04 .250000E+03 .387000E+03 .258000E+03 .387000E+03 .250000E+03 .387000E+03 •529000E+03 .400000E+03 20 ' 3 .750000E+02 .000000E+00 -.750000E+02 20 2 .200000E+03 -.200000E+03 •600000E+03 15 16 88 1 1 2 1 1 1 4 7 2 2 5 8 3 3 6 9 1 2 3 0 1 7 10 13 2 8 11 14 3 9 12 15 1 3 4 0 1 13 16 19 2 14 17 20 3 15 18 21 1 4 5 0 1 19 22 25 2 20 23 26 3 21 24 27 1 5 6 2 1 25 28 31 2 26 29 32 3 27 30 33 2 6 7 1 1 34 36 38 2 35 37 39 2 7 8 0 1 38 40 42 2 39 41 43 2 8 9 0 1 42 44 46 2 43 45 47 APPENDIX A: User's guide 57 2 9 10 0 1 46 48 50 2 47 49 51 2 10 11 2 1 50 52 54 2 51 53 55 1 11 12 1 1 56 59 62 2 57 60 63 3 58 61 64 1 12 13 0 1 62 65 68 2 63 66 69 3 64 67 70 1 13 14 0 1 68 71 74 2 69 72 75 3 70 73 76 • 1 14 15 0 1 74 77 80 2 75 78 81 3 76 79 82 1 15 16 2 1 80 83 86 2 81 84 87 3 82 85 88 1 a 000000E+00 •000000E+00 •000000E+00 2 000000E+00 •300000E+00 .000000E+00 3 a 000000E+00 .900000E+00 •000000E+00 4 000000E+00 .210000E+01 •000000E+00 5 000000E+00 •270000E+01 .000000E+00 6 000000E+00 •300000E+01 .245000E+00 7 500000E+00 •300000E+01 .734000E+00 8 • 150000E+01 .300000E+01 .146900E+01 9 350000E+01 .300000E+01 .146900E+01 10 450000E+01 .300000E+01 .734000E+00 11 500000E+01 •300000E+01 .245000E+00 12 500000E+01 .270000E+01 .000000E+00 13 500000E+01 .210000E+01 .000000E+00 14 500000E+01 .900000E+00 .000000E+00 15 500000E+01 •300000E+00 .000000E+00 16 O 500000E+01 .000000E+00 .000000E+00 £. 1 1 1 1 16 5 1 1 1 .500000E+01 .500000E+01 0 2 5 11 forces APPENDIX B 58 £ tn CO o Q CM «-» o — c z w u * Q M Eu O •» _ a. 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S H H „ SC O 1 • •• „ » CM rt •» VO " U — — » — re td co ".3 f § • X z u z z X O Q H U O c Z 2 S 88 I 1 X M Cd 2 » « 2 Cd _ M Cu 2 X » « Cd I-l . < « Cu TJ CO H H S I tu CO — < 4J Q 2 U O h u CO Cu O H M t-t < Q c-» 2 Cu O co 61 H H a a 2 Q 2 I Cd Q Cd I 2 TJ 2 Cd B Cd X 0 X n x> H JC — X ~ x ~ » l-J « TJ •3 — i-j e — < — o Cu co Q ja M • 2 td td Q X CM CO CD CO I • • • I < Cd X 2 CO H td W g Cu CO X r CO tu < < CO CO 2 Z co m Cu tu a a o o CO CQ I b 13 f-4 — — 2 2 M X X * CO CO t-t Cu CM CO co M D a H n < 4 <: • K n O H Cd CO CO O CO td < td td a tu x td td • 2 t u O O c o < < 4J U H H — CJ CJ Cd 4-1 Q Q 2 Q 2 Cu Cd O Cd H + CM * PO co co X TJ c M — 2 0 •. x u ja rj _ . I M M H - X Cu X . X -a w EH -fc 1-3 — a — *! £ •* . 4J H n •3 CC* Cd . z : u fc i x i • < < I EH H CO CO '. * " t " m CD : cu cu • o a i -z z o o CQ CQ < < EH H CO CO Z Z — CQ CQ Cu Cu x a a — *3 i .1-3 I — — x » Cu X -CO t-1 H CO • < • O H 4 J O CO rf EH fc- 4J rf M . CO *-> TJ 3^ — C • — a o < 2 J3 O fc CJ I M O I I fc • < 1-3 X Z CO EH ] — CO O Cu CO : • ' — CQ Q Z t-H X CU * •3 H H — fc EH < rj Cu co — S cu *t; • X H CO. 4H 1*4 ; — EH • t I Z Z fc . M H O • XX — • CO CO cu CO o 2 — A CO -fc M XXX EH » I t-H = ^ 1 X Cu rf5 0. U US X Z fc fc U M IH fc > fc X - 1 3 b fc X IH fc z z -H H H O IH I iC J< fc Cu TJ •3 a • — < 4-1 I Q EH 4-1 > CM a. u Cu z rf rf aa u CJ CM CO I a D EH EH — H EH * CO CO M rf rf hi* a a J t u u » > 1 O CO M rf < Q rf EH 2 < (0 Cu Cd CJ 2 CO rf Cd CO — CU CO M D rf H CO < • O EH Cd O CO rf rH tu X tu O O CO 1 IH H — I n n 2 Q 2 Cu Cd S Cd M < -3 O 0 EH 2 XI CO O Hfc CO • CO X Cd • a • • < X Z 03 EH CO O Cu CO — CQ Q Z •3 Cu . £ £ ; — D r3 CO CO I Cu ICC —fc fc— « » I £ EH 4J CU X X ! Cd 4-1 Cd CO CO I H I I D —. — > rH CM CO • X U Cd Z D S - » oi Cd EH EH . - M H 1 . 2 < < ! X fc fc Cd M H H fc t-3 T-i Q Cu CO CO I . Cu TJ rf rf rf rf ' fc2§iaaaa; U Q r i J J U U U U I CO z T Cd TJ X B EH O X . — M — X X I •H x r> M as? 3 Q O EH Z J CO O <v cn s s EH H CO CO z z CO CQ Cu Cu Q Q •3 >3 a . Z CQ EH 1 O Cu CO rf rf . a a t» HU WJ «*, n , H4 0 Q Z U U U H CO O C4 U H Q 2 U in —* Cu CO M EH Cd CO rf a Z Cu Cd IH X X CO 1 CO 1 X X M M 1-3 •3 CU cu I H I H rf rf CO CO z 41 Cd * z TJ TJ Cd E CO EH B X O Cu O EH a a . £> X z X X i o 1 X <3 I H X X I H X •3 • H CO M •3 * < f3 TJ 2 •3 TJ z B z 2 B IH Q O o Q O £ Z XI £ EH Z XI CO O Jfc to a CO o J< CO X Cd CQ X EH • as • ai O 1 • rf I • < •J < X z CQ EH •3 H X z CQ CO o Cu CO < CO Cu CO o Cu ca a z Cd u z I H CQ Q CO a Cu rf z Cu I H Cd Cd Cd I H a 1-3 —. cu X -. £ fc 4-1 Cd IH 4J H > 4J Cu l-J » D — — 4J < < M 4J H CO -t ~ < — * O CO M -r-iCu I > — cd a -H W EH Z fc © Z IH Tt B M Cu — « TJ I rf rf ii 4J a a 4J 4J CJ CJ 4J tu X X I JJ Cd CO CO EH -fc > rH CM l*> I fc 2 Cd EH EH — -4 Cu z < «S X fc Cd IH H EH . T i Q Cu CO CO IH ^ f c t u T J r f r f r f J J ^ —-siaaaa^tu U u r l 4 J U U U U « H co a rf z Cd U < < EH EH CO CO z z CQ 03 Cu Cu o a z z o o CQ CO * to H O Cd 2 tc u 2 2 Cd Cd X X FH tH ~ ^ PO CM CO CO cd CO CO CM CJ Cd Cd. CO •d >d o fH M < < CO rt 1-3 < 1 d a ET M fH AN AN CQ x X fH \ rt »H rt CO CM CM fH CO CO a J O O O O 00 (H 1 fH fH CM 1 cn 2 ca- O Q Q • i d CO rt •d CO CO < tH CM ~ W W < I I m • H N <n w H CO CO CO I o o • Q (0 O < X H * CO ~ CQ ro — X TJ CO * — < I f-i CQ CO -(i CO o — Q Q, O 2 2 O O ££ o o U CJ rt CM PO ^- Cu Cu X X X X tH H O • CO CO PO fH I ( ( - H C g f c l - H N r l h O l H W P l T t u X l f l I K « H - X X X H — . X X X X IH — H Cd Q Q Q CO D 2 Cu Cd M Q 2 Cu Cd rH O. 2 Cu Cd M I I >H 2 Cu cs 2 uu PO PO rt CC 3 CQ rt rt Q Cd rt fi • d / 2 2 Cd 2 Cd Cd tC Cd Cd CO 2 — Cd * X TJ EH B 2 o cd — a X — AC EH X X X Cu - X — a CU < X EH Cd Cu rt rt O EH EH CD CO CO < 2 2 H - * » CQ CQ Cu Cu x ca Q rt 2 2 » o o ID CO CQ CC — — Cd X X 2 « . 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CO cn •> M i « * m CO O JQ _ x ? tn •» z Q <TJ «. o * 0 * 0 — O CM • — o —» t~i — CM — CM — Q M » rH — bi < «— — O * r-, EH c. D ffl • X . rH • D < 5 — 60 rH < H < — 1 0 H * rH 1 C* nj ~ < rH t> O O + J HH H T J cn + Q rH CD 3 "s. + cn * < O T J £ i g « < T J * i n 4J it! H C m «. 1 r l CBS, —• * CO o <• o O tn M CQ X) O CM Q * a> & ja * J-! CM — o O A E n ^ o K — Cu Q — 0> T J — • «H O rH o a 4-» • Cu rH • * — +J 3 ~ J * < < 1 -H < a EH H 1 T J O c • EH X 1 1 + rH iH — — CD >v T J T J V) XI to T J • n i n C — * -U X» + Q « O a T3 n ro rH 03 - -Q X c — T J CO 3 \ tH tH ^ CP 0 VI ra * X T J XI X) 1 1 r3 t-J M CO • o — 1 1 T J rH CM CM *H rH ro a 4J 1 w H H CP 4J •H P P £ n T J p < < a> -H 4J *M rH G 0 EH EH +J n V) -H (D CD T-* O O • — a H Q i Cu Cd Z I M 2 B rt • z n H Z < O Cu CO Cu 2 — m Q z t-t a O H O Cu z ca z M u a: u — cn — o rH O « O o Z - l U TJ X * H < S N o l CO o " 5 co of, 2 M H (H rH 5 <-> O tH OX ^ CQ (u D X CO M ro « . Cd CO — C el «- cn U CM fc u In co i n U * M rH O fc CO CM 1<z M H 3 » Cd rt X CO fH H N i n J Q Q Z CD CO •> o • xi o AC CM X a re O TJ I i TJ 4J * O re a •p — — a a E e x a OJ a> 4J re TJ — 4J * * Oi TJ TJ T j O r - . e e . c —i o o o : o TJ n a xt • Si — • . * X AC a o> x x X X rH I I a • c a I TJ 4J 0 < H U cu o I M e OJ co a • x u « -•3 TJ fn • * \ • — u — rH CO o a — •) < CD • fn ja 4J CO cn I TJ z CO X a H • — o - H Q fn a o • rt. • fH fH O O fH 4J Vi -rH I rH « § C u C u - ^ O C u C u — C O Q M — a Q H Cu Z tu z M CO rH CO CS CQ CO * CM — CO z = 1 u ce; rn a rt co EH CO — X v . o o OS co i rt > « m fnSS | 2 g z Cd X _ fH — P «S rH id — I tH — O • in td m CM O I • O • s rH o >H CS a: Cd z CO CO i c o C u ~ ~ i m c u c o i col [ n H - In H " Cu I rt Q a < Q Q rtoi Z Cu Z tu Cd M td M I a to =8 cn Sci O Cu o CO 5 ? Cd ~~ — Cd CO CO Q T) — S » r rt X M rH rH — I • CO •• „ • I rt •> - < o w • Q — • rt — re i l M h r i .q : Q CD * Cd O B i Z « 9C CO I M J \ \ Cu rt ^ rH O y 111 H N H rH I fd Q t3 ' Z CO Z C I cd ce z H fH fH H 5 o O w ce td a CU a x CO cn O —' tn r-H ro T J O o * * CM O — Q rH Cu rH H • 1 «: rH O CM EH — Q EH a o + .< • cn 0 CM 2 o Tj ~ CO Q tn * \ X rH O — EH • o Q rH O CM CM H . — + • 1 ro Cu TH O ro CO o I a w \ — o * Cu < a • O * X rH o o Q» — tn Q T J + . CD 1 O _ o • O Q CQ — rH Q O — S888 e z i i o o o u XI re •o H " • t^ E t g o z ro rf| fci M J h u i n H . f i c u a co Q io a H Q id Z — rt Cd z Cd Cd Q H ce Cd rt eg « tJ » N a >H I O • o xi X -AC — x x i « rt rt n T J co — re c J J3 0 Q CO 6 Si Cd Oi rH x z e i H h \ N fH H — a cj e i z o M o >* 2 ce td g a O O E I H D a x o _ cd z « H o rt ce td tu o Cd « Cu — H CTI td - CO i n -o cn CM -— i n Q -S ° O CM CO — - td ~ CO cn % i n cn co — . td CO CO n TJ i td » o 5 e n t u - *H _ cn cn i n tn CJ CM O X CO — £ XI —- » CJ » O Z. AC rtXt-Ht-trHr-. X O O W I * CO •• n » CM CM Cu * Cd td os u ce z M tH fH M 3 u O rH ce p CO cu a x CO 1-1 »  •• ~  •» . CD ™ H » rt — re H U H • .g t U CJ E X CO x ce rt Cd X z CO Cd i i i 8 o o CJ o I 13 rf f-t M rH X ' rj (-7 M I Z X Cu" 1-3 ! W S 3 — - £ £ rt rf i CO CO EH CO ' I I (0 * ja — I H H A i C I H EH TJ -rf i —. —. H- -! CO C- *3 I • • OJ — • oi a fc i u u i a \~~~$ I X X X — * . « to IH M t-H Xi fc fc fc ro •3 1-3 1-3 TJ CQ CQ Cu -r EH EH £ CO CO Cd CQ Z Z EH QC* I Cd Cu Cu 2 CM IH M Cd EH O K . . — rf IH — — -fc CO fc CU pcC —- ft. CO E-« X it CQ CM H — M I O W O » — W 5E M H X »-? t* IH — O -• J H b W T3 -—' * CM * O O — Q D X r - < fc VD fH t-i . * » o —. •"3 — CM — Q. H Cu X I D CD O < *TJ Q H * O CM CU H M D* CQ —' CO t< * 0) —-Q H oi O r-l CM — rQ CM —' ro • i rH + T J rH rH I I I EH O fc Q M O fc . M tx. a> « » * T J M M l * fc fc O M M •"3 Q ~ fc — O CM t"3 Cu • X — Cd rH Cd Cu SK H x 2 I I r U U D P H H O rH CM < tu Cu Z H E-t H Cd Ot. Cd CM fc CM —-. M at »H «. CO tn fc — c o o*i — CM Cu —• m o Q -» cd Z o fc O CM —- c o -i n cn © i n X Cd H Cu Cd CM cn Q i n —. a-, o »»>. fc CN * i n — ^ rQ — — ro • *— CO T J — 31 g E C CQ CO I £ IH ~ — CO X CM O 2 fc EH Cd * IH -f \ — fc — CM CC 1-3 3: M « E-< i . C M M M — . < X — I o-S a a co 2 * Cd Cu 2 IH EH EH M 3 " O M OS rf CQ CU 3 X CO IH - Cd CO ' CJ CM >H CO . U -55 s — ro o TJ O rH 0 X on cn tn tn i n _ - . O CN S CM — EH — Cu Q D 3 < H C7\ tTl EH « « fc « — m m — cn « •rn « o o fc i n CM CM i n — — M x • 1-3 M » IH — fc O Z M X £ — CO CO rH D I I < m 1-3 , 33 . E-< CO -* —- I — * ; M -- < fc M O M * fc < —' (0 M H Z M ,Q »cd S a lU co z "*fc. >fc **fc, M O M CM rH M M J Q Q J rH Z CQ CQ Z G "s. -v. *«fc. -v. -fc. § § § § § o o o o o o u u u o CMS g -J* CO IH — t-J C X Oi CO Cd I CM ~ „ — Cu EH EH rf o CC tu p p Cd p < «e 2 < EH EH Cd EH a cu • < 5 —, -fc. IH fc EH X X rf rH — I ro — EH a x • fc CO EH to 01 fc fc >H o o o cc CO CO Cd EH EH 2 CO CO Cd 2 2 I >H ro O TJ CC O . -a M o • 1-3 • s X M y '—' tA m co •" a— -+ tn c — -Q : C i <B . < EH T J E I * Z -O O Cd ( Q Q X • O CO H C M H « 5 *>fc + ^ E — — H ro —. — EH X n l I fc rQ O M fQ . 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