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A 1“." . 11 r it. 1. ilufo‘. .3] )1“ LA LF—d;; fl n Ila—-Eaf‘“ .'.- £3 l*?-' 9 , «h This is to certify that the dissertation entitled MICROCOMPUTER AIDED DESIGN FOR REINFORCED CONCRETE FRAMES SUBJECTED TO SEISMIC LOADS presented by Aecio Freitas Lira has been accepted towards fulfillment of the requirements for Doctor Of PhilosophLdegl-eein Civil Engineering @FM Major professor Date w MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 V-leq —‘j _ _____4 ‘ n.— RETURNING MATERIALS: )V1531_J Place in book drop to remove this checkout from ;::::;::EEL your record. FINES will be charged if book is returned after the date stamped below. “MM“‘W _ Q 7 \p Q ‘ 1%.;‘13579 4"?" k HICROCONPUTER AIDED DESIGN FOR REINFORCED CONCRETE FRAMES SUBJECTED TO SEISMIC LOADS DY AECIO Freitas Lira A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil and Environmental Engineering 1986 ABSTRACT MICROCOMPUTER AIDED DESIGN FOR REINFORCED CONCRETE FRAMES SUBJECTED TO SEISMIC LOADS bY Aecio Freitas Lira A major purpose of the research is to make available. through microcomputers, for the design of "ordinary" R/C structures a highly sophisticated analysis. The latter has been limited to ”special" structures because of economic reasons. The study presents a design procedure for reinforced concrete frames based on nonlinear dynamic analysis. The design procedure consists of four basic steps: 1) preliminary design based on member forces obtained by linear elastic analysis with equivalent static loading as prescribed by design codes. for example, the UBC code; 2) nonlinear dynamic analysis; 3) checking of damage of structure; 4) redesign of the structure if necessary. The establishment of this design procedure required the development of the follow1ng: a) a microcomputer program for the nonlinear dynamic analysis of R/C frames subjected to strong earthquakes; b) design aids, if the redesign of the structure is necessary. The first group of design aids consists of charts for steel reinforcements as functions of curvature ductility. A second group of design aids provides some guidance to choose curvature ductilities of members for selected structural displacement ductility. The software was designed to have: a) file-oriented input data; b) nonlinear dynamic analysis; c) capability of displaying plots of: -undeformed structural geometry; -ground acceleration input; -nodal displacement; -deformed structure; -finite plastic P9810118 and damage ratios. To my Wife, Vania and my son, Lucas. ii ACKNOWLEDGMENTS I would like to acknowledge the support of the many people and agencies who made my Ph.D program and this dissertation possible. I am grateful to Dr. Robert K. Wen , the chairperson of my dissertation committee for his supervision and encouragement; as well to the members. Dr. William Bradley. Dr. Orlando B. Andersland and Dr. Larry J. Segerlind for their professional time dedicated to this research. To the Federal University of Minas Gerais and its Department of Structures. who granted me the leave of absence for my studies abroad. as well as to the Coordenacao de Aperfeicoamento de Pessoal de Hivel Superior (CAPES). which.made these studies possible. I am specially grateful to Jose Duarte Brandao for looking after my interests in Brazil during my studies abroad. Last, but not least . my special gratitude to my family for patience and cooperation. iii CHAPTER 2 CHAPTER 3 TABLE OF CONTENTS INTRODUCTION Object and Scope Background for Seismic Building Analysis 1.2.1 Design Philosophy 1.2.2 Hodels for Nonlinear Dynamic Analysis 1.2.3 DuCtilitY 1.8.4 Damage Factor Notation A DESIGH PROCESS Preliminary Design Nonlinear Dynamic Analysis Redesign of the Structure Selection of Design Earthquake COMPUTER PROGRAM Sub-program.DATA 3.1.1 Control Information 3.1.2 Control Joint Coordinates 3. 1. 3 Node Generation Data iv PAGE 10 12 15 82 22 23 26 26 28 29 31 31 31 CHAPTER PAGE 3.1.4 Boundary Condition Code 3.1.5 Hass Generation Data 3.1.6 Load Control Data 3.1.7 Earthquake Acceleration Control- Damping Factors 3.1.8 Output Control 3.1.9 Beam.E1ement Control 3.1.10 Reinforcing Steel Properties 3.1.11 Concrete Properties 3.1.12 Member Properties Sub-program.HAIH Sub-program PLOT Hardware Requirements DESIGN AIDS Curvature Ductility Diagrams Relationship between Displacement Ductility and Curvature Ductility 4.2.1 Structure Types 4.2.2 Ground Motions 4.2.3 Response Parameters 4.2.4 Presentation of Results 32 32 33 33 34 34 35 35 35 36 37 38 4O 42 43 43 44 45 45 CHAPTER 5 DESIGN EXAMPLE 5.1 Preliminary Design 5. 5. 5. 5. 1. 1. 1. 1. 1 Design Basic Data and Specifications 2 Loads 3 Linear Analysis 4 Design of Beams and Columns 5.2 Nonlinear Dynamic Analysis 5.3 Damage - Redesign of the Frame 5.3.1 Displacement Ductility of the Frame 5.3.2 Curvature DUCtllltY Diagrams CHAPTER 6 SUMMARY AND CONCLUSIONS 5.1 Summary 6.2 Concluding Remarks LIST OF REFERENCES APPENDICES A THE MATHEMATICAL MODEL B EXAMPLE PROGRAM OF DYNAMIC ANALYSIS vi PAGE 77 79 79 80 84 85 86 86 87 88 9O 90 92 95 100 123 TABLE 4. 1 LIST OF TABLES Damage factors for one-bay frames PAGE 75 FIGURE LIST OF FIGURES Flow-chart Design Procedure Bilinear Hysteretic Model Frame—member Model Equivalent Spring MOGOI Bilinear Degrading Hysteretic Model Flow-chart of MC-GUAKE Curvature Ductility versus fc : 5 K81 ; fy = 60 K81 ; Curvature DUCtllltY versus fc = 5 K81 ; fY : 60 ksi ; Curvature Ductility versus fc : 5 K31 ; fY : 60 K81 ; curvature Ductility versus f’ = 5 ksi ; f : 60 ksi ; c Y Curvature Ductility versus fc = 5 K31 ; f : 60 K31 3 Y viii Steel Percentages P/(féhh) : 0.00 Steel Percentages P/(féhh) : 0.10 Steel Percentages P/(féhh) : 0.20 Steel Percentages P/(féhh) : 0.30 Steel Percentages P/(fébh) : 0.40 PAGE 17 18 19 2O 21 39 46 47 48 49 50 FIGURE 4.6 Curvature Ductility versus fc = 5 ksi ; fy = 40 ksi ; Curvature Ductility versus fc : 5 K81 ; fy : 40 K81 ; Curvature Ductility versus f’ = 5 K81 ; f = 40 K81 ; C Y Curvature Ductility versus fc : 5 ksi ; fy : 40 ksi ; Curvature Ductility versus fc : 5 ksi ; fy = 40 ksi ; Curvature Ductility versus fc : 5 ksi ; fY : 50 ksi ; Curvature Ductility versus fc = 3 ksi ; fY : 60 ksi ; Curvature Ductility versus fc : 3 K81 ; fY : 60 K81 ; Curvature Ductility versus fc : 3 K81 ; fY : 6O K81 ; Curvature Ductility versus fc : 3 ksi ; fY : 60 ksi ; Curvature Ductility versus fc : 3 K81 ; fY : 4O K81 ; ix Steel Percentages P/(féhh) : 0.00 Steel Percentages P/(féhh) : 0.10 Steel Percentages P/(féhh) : 0.20 Steel Percentages P/(féhh) : 0.30 Steel Percentages P/(féhh) = 0.40 Steel Percentages P/(fébh) : 0.00 Steel Percentages P/(féhh) : 0.10 Steel Percentages P/(féhh) : 0.20 Steel Percentages P/(fébh) : 0.30 Steel Percentages P/(fébh) : 0.40 Steel Percentages P/(féhh) : 0.00 PAGE 51 52 53 54 55 56 57 58 59 60 61 FIGURE 4.17 Curvature Ductility versus fc = 3 K81 ; fy = 40 K81 ; curvature Ductility versus f’ : 3 K81 ; f : 4O K81 : c Y curvature Ductility versus f’ : 3 ksi ; f : 40 ksi ; c Y curvature Ductility versus fc : 3 K81 ; fy : 4O K81 ; Basic Structure Properties Steel Percentages P/(féhh) : 0.10 Steel Percentages P/(fébh) : 0.20 Steel Percentages P/(fébh) : 0.30 Steel Percentages P/(féhh) : 0.40 Displacement Ductility versus curvature Ductility * Three Stories Frame Displacement Ductility versus Curvature Ductility - Four Stories Frame Displacement Ductility versus curvature Ductility - Five Stories Frame Displacement Ductility versus curvature Ductility - Six Stories Frame Displacement Ductility versus curvature Ductility - seven Stories Frame Displacement Ductility versus Curvature Ductility - Eight Stories Frame Displacement Ductility versus curvature Ductility - Nine Stories Frame Displacement Ductility versus Curvature Ductility - Ten Stories Frame PAGE 62 63 64 65 66 67 68 69 70 71 72 73 74 F I GURE PAGE 5. 1 Computer Program MC-GUAKE - Example 89 xi CHAPTER 1 INTRODUCTION 1.1 Object and Scope The response of reinforced concrete building frames subjected to strong earthquake motion is a complex phenomemon. Its analysis is particularly difficult When it is necessary to consider the nonlinear behavior of materials associated with.hysteretic loops of reinforced concrete behavior under cyclic loading. As will be discussed later. satisfactory models and computer programs such as DRAIN-2D [24] and HACRS-II [28]. are available for the analysis. However these programs were developed to run on large computers and are rarely employed in ordinary building design practice for several reasons. Generally they are too costly to use. The procedure for data input are often rigid and inconvenient. Finally. the design engineer often lacks the background in the specialties of structural dynamics to interpret the results. Therefore.their use generally has been limited to research, and in recent years to special structures such as nuclear 2 power plant structures where sufficient resources are available for use of such specialized programs. For ordinary buildings. which represent thousands and thousands of plane frames. the design has been based on only the so-called equivalent static seismic loading as prescribed by building codes. More realistic dynamic analysis is not carried out for reasons mentioned. Yet. these ”ordinary" buildings are also important because their failure would also spell disaster. During the last earthquake that occurred in Mexico City (1985) [17]. 285 multistory buildings collapsed. 143 of which were made of reinforced concrete. Approximately 10000 people died. It would seem.highly desirable to extend the availability of the special tools for dynamic analysis to ordinary reinforced concrete frames. With.the rapid advances in microcomputer technology this seems a distinct possibility. The main objective of this thesis is to bring the sophisticated method of analysis to the design process of the "everyday structure". This is done in the context of a proposed design procedure for reinforced concrete frames subjected to strong earthquakes. This design procedure is illustrated in a flow-chart. Fig.(1.1). It essentially introduces a "proof test” or damage assessment process in the design iteration loop. In order to discuss the design process there is a need to consider the background for seismic design which is presented in the next section. 3 The design procedure itself is described in detail in Chapter 2 and illustrated by a.numwrical example in Chapter 5. In Chapter 3. a microcomputer program for the nonlinear dynamic analysis of reinforced concrete frames subject to strong earthquakes is presented. The software was designed to have: a) file-oriented input data; b) nonlinear dynamic analysis; c) capability of plotting two dimensional Views displaying any of the following ; -undeformed structural geometry; -ground acceleration input; -nodal displacement; -deformed structure; -finite plastic regions. The main portion of the software ((b) nonlinear dynamic analysis) is essentially a translation of the mainframe computer program.RACRS-II [28] to run on microcomputers. The mathematical model for the nonlinear analysis of plane reinforced concrete members is given in Appendix A. Some features have been added for design use. The most important are the interactive data input mode and plotting capability. Damage factor and ductility ratio have been incorporated in the output and plotting options. They are to be used in the decision whether a redesign of the structure is necessary. An example 0f the use Of the program is given in Appendix B. 4 The translation from a program.for mainframe computers to one for microcomputers requires the execution of the following two tasks: a) Re-compilation of the source program. RACES-II. b) Re-design of the core of the program.to be compatible with.the interactive mode of input data and the plot programs. The translation is a challenging task. in the sense that it requires a sufficient background on the subject of earthquake engineering in order to analyze all the subroutines that are parts of the program but also familiarity with the software and.hardware of mainframe computers and microcomputers (FORTRAN compilers for mainframe computers are different from.FORTRAN compilers for microcomputers). Because of the complexity of the topic and the size of the program these tasks were very time consuming . In order to facilitate the redesign process. certain graphs are presented in Chapter 4 as design aids. As alluded to previously. a numerical example of the design procedure is presented in Chapter 5. Chapter 6. presents a summary and conclusions Of this study. 6 1.2 Background for Seismic Building Design 1.2.1 Design Philosophy During an earthquake structures are set into a complex motion in response to the ground motion. In structural engineering terms. the structure may be regarded as being subjected to inertia loads Which.vary with time. For economical reasons. both in cost of computing and of training of personnel. the equivalent load (in lieu of dynamic load) approach has been adopted by building codes. For structural modeling. the assumptions of linear elastic behavior is usually made. Regarding the representation of earthquake ground motions. seismic design of buildings is generally based on inputs reflecting a range of possible earthquake ground motions. The response spectrum method is the most widely used approach for representing earthquake excitations in dynamic analysis. The generation of a response spectrum curve can be carried out by subjecting a series of damped single degree-of-freedom.mass-spring systems with.varying natural periods to a given ground excitation. It is appropriate to consider a number of response spectra in order to arrive at a design spectrum. Many design spectra are presented at a i-g level. Once a design spectra has been chosen. several factors must be considered in determining 6 the level of earthquake excitation that a structure is to be designed to resist. Generally. the objectives of earthquake-resistant design are as follows: a) to insure that no significant structural damage would result from a moderate earthquake having a reasonable likehood of not being exceeded during the life of the structure; b) to insure against collapse or major structural failure for a severe earthquake. with even lower probability of occurrence. The severe earthquake is often called ”maximum credible earthquake" and the moderate level motion is referred to as "maximum probable earthquake". The maximum credible earthquake spectrum reflects an envelope of response values that have a 85-95 x probability of not being exceeded during the lifetime of the structure. The maximum1probable earthquake spectrum1has a 50-50 2 probability of not being exceeded. Design codes for buildings aim to incorporate the above two-level design philosophy in their provisions. The first design objective can be met by sizing the structural members such.that their yield strengths will not be exceeded in a moderate earthquake. At this design level the behavior is essentially elastic. The building should be proportioned to resist this intensity of ground motion without discernible or measurable damage to the basic structure. 7 In meeting the second design objective.because this level of earthquake is unlikely to occur within the life of the structure. the designer is justified in permitting it to cause structural damage; however. collapse and loss of life must be avoided. Thus. the inelastic deformation capacity of the structure need be considered. At this design level. adequate energy absorption in the form of ductility must be provided for. Such information may be obtained only through a nonlinear dynamic analysis. 1.2.2 Models for Nonlinear Dynamic Analysis A considerable amount of work has been carried out on the development of analytical models and numerical methods for the analysis of the behavior of buildings during strong earthquakes. The review in this section is limited to those works which are related to nonlinear dynamic analysis with special emphasis on the inelastic analysis of plane reinforced concrete frame structures subject to earthquake motions. The studies will be cited in two sections; simple models and complex models. Among the earlier work was the shear beam representation of structures (simple models). The stiffness of each story was assigned to a shear spring which included nonlinear deformations. A212 [6] used this shear-beam model in the study of a ten—story frame. A modified shear-beam model was introduced by Aoyama [i] for reinforced concrete Structures. 8 Tansikirikongkol and Pecknold [40] used a bilinear shear model for approximate modal analysis of structures. While the basic element of the simple shear beam model is a story of a frame. the basic element of a complex model is a frame member. that is. a column or a beam. In a complex model the choice of the model to represent a structural member is a crucial one in terms of computational effort and ease of formulating stiffness changes. A number of empirical models have been proposed in the past to represent the hysteretic behavior of reinforced concrete members: Simple bilinear formulations models. Fig.(1.2) were the first ones employed by researchers. Heidebrecht. et al (1963,1964) [20] developed a numerical method to analyze plane frame structures with.elasto-plastic members under dynamic excitations. During the Third World Conference of Earthquake Engineering in New Zealand. two mathematical models were presented for the inelastic analysis of frame structures. In the first model by Wen and Janssen (1965) [41]. a frame member was divided into short segments along its length. A bilinear moment~curvature relationship was assigned to each short segment. (Fig.(1.3)). The application of this model was limited to simple structures because a large size computer memory was required for the analysis. In the second model by Clough. Benuska and Wilson (1965) [12]. a frame member was divided into two imaginary parallel elements: an elasto-plastic element to represent a Yielding 9 characteristic. and fully elastic element to represent strain hardening behavior. An equivalent spring model was proposed by Giberson (1967) [18]; the model consisted of a linearly elastic member with two equivalent nonlinear springs at the member ends (Fig.(1.4)). Due to its relative simplicity. this model attracted considerable attention. It was realized that the behaVior of a reinforced concrete member under cyclic loading is mere complicated than the above described bilinear models. The concept of a degrading bilinear model was introduced by Clough [13] and represents an improvement over the simple bilinear formulations. Fig. (1.5). Takeda [39] examined the experimental results for cyclic loading of a series of reinforced concrete members. and proposed a general trilinear model. which.was in substantial agreement with the test results. This model is known as the "Takeda Model" and has been adopted by a number of investigators. The degrading stiffness model and the Takeda models have been included in the general inelastic dynamic analysis programs DRAIN-2Dt24] and BAKE [31]. The original Takeda model did not include the so-called "pinching effects", which.represents the effect of shear stress on the hysteresis behavior. Meyer and Roufaiel [28] used a modified Takeda-type model (see Fig.A.5 of Appendix A) that includes this consideration. Furthermore. none 0f the above models considered the effect 0f the finite 10 size of the plastic regions. All of them were based on the spring model. In the model proposed by Meyer and Roufaiel the finite size of the plastic regions is taken into account (see Fig.A.7 of Appendix A). The accuracy of the model was demonstrated in [28] by analyzing numerous members and structures for which test results are available in the literature. leading to the conclusion that the model is effective in predicting the nonlinear behavior of reinforced concrete members in plane frames. Based on this mathematical model. the computer program.MACRS-II was developed using a modification of the member stiffness portion of the general-purpose nonlinear analysis computer program. DRAIN-2D. This study has. in turn. adopted MACRS-II for the analysis part of the computer software. 1.2.3 Ductility It is commonly accepted that it would be economically unrealistic to design a structure with.sufficient strength to remain elastic during strong earthquakes. and inelastic behavior should be allowed to occur. To avoid collapse during a major earthquake. members must be ductile enough to absorb and dissipate energy by post-elastic deformations. A key parameter in the characterization of inelastic behavior is ”ductility ratio". The "response ductility" of a member is the ratio of the maximum.deformation to the deformation 11 at first yield of the response history of a structure. The "design ductility" is the ductility attainable by the structure designed. The definition of ductility ratio may be applied at three levels: a) structure or displacement ductility; b) curvature ductility; c) member or rotation ductility. The displacement response ductility factor. up. is defined as the ratio ofAm. the lateral displacement at the top of the structure at the end of the post-elastic range. to A? . the lateral deflection at the same elevation when yield is first reached. The Commentary on the SEAOC code [38] indicates that the displacement ductility response factor required in design would range from 2 to 5. Since ductility in this range is associated with plastic deformations. permanent structural damage is expected. The ductility of reinforced concrete sections. u can ’1 be expressed DY the curvature ductility ratio. flx/fly. where fix is the curvature at the end 0f the post-elastic range and fly is the curvature at first yield. For given section properties this curvature relationship can be derived using conventional reinforced concrete theory [33]. Data for such relationship are presented in Chapter 4 for some usual combinations of material properties. 12 The member or rotation ductility is defined as the ratio of the maximum.end rotation to the end rotation at first yield. Since this ductility is associated with the spring models. it will not be used in this study. In nonlinear response of multistory structures. the relationship between curvature ductility of the members and displacement ductility response of the structure is very complex. In Chapter 4. this relationship is calculated for one-bay frames from 3 to 10 stories. for a particular ground acceleration input. The data is intended to be used as a reference guide for redesign. 1.2.4 Damage Factor In the context of design that allows inelastic response. the degree of "damage" needs to be defined. In past studies. it has generally been treated subjectively. Damage can be looked at from an economical viewpoint. using a scale from zero for no damage to a maximum of unity, representing total failure of the member. Wiggins and Moran [42] have proposed to grade existing buildings on a scale from.0 to 180 points to measure its structural reliability. Culver et a1 [14] have proposed another field evaluation method but its use has been limited because of the subjective nature of the judgement required. Shibata and Sozen [17] have introduced a damage parameter. to be used for design. as the ratio between the initial 13 stiffness and the reduced secant stiffness at maximum deformation. This damage ratio can be easily computed when the moment-curvature relationship is determined. But as damage indicator this factor is of limited use because "failure" is not defined. Meyer and Roufaiel [28] introduced a modified damage factor described in Appendix A. This damage factor represents the ratio between the secant stiffness at the onset failure and the minimum.secant stiffness during the response. The value of zero. indicates no damage. The value of 1.0 indicates a total failure of the member. This damage factor is defined as (see also Fig.A.8 of Appendix A): damage factor : for Mx > M Y n O damage factor for H! < H Y where My is the yield moment of the section of the member and Mx is the maximum moment that has been attained at the section; and Mm is the ultimate moment capacity of the section as described in Chapter 4. According to a recommendation from [28]. the damage factor may be used to classify damage as follows: Damage Factor Damage Class 0.00 to 0.25 low damage; 0.25 to 0.50 moderate damage; 0. 50 or greater high damage( redesign the member )3 14 This classification Will be used herein to decide whether the damage level Of a member is acceptable when responding to a presumed maximum credible earthquake motion. 15 Notation The following notation was used in this work: section Width 0f the member. section depth 0f the member. uniaxial strength of plain(unconfined) concrete. steel yield stress. f . Y ultimate moment capacity of the section. maximum moment that has been attained at the section. yield moment of the section. lateral displacement at the top 0f the Structure at end 0f the post—elastic range. lateral deflection at the same elevation when yield is first reached. strain at fé. concrete crushing strain. displacement response ductility factor. ductility 0f reinforced concrete sections. longitudinal steel percentage. confinement steel percentage. ultimate curvature 0f the section. curvature at the end 0f the post-elastic range. 16 fly = curvature at first yield. l7 'PRELIMINARY DESIGN - STATIC ANALYSIS based on earthquake loading prescribed by codes m + c: NONLINEAR DYNAMIC ANALYSIS E u: > microcom uter design pro ram & _] as will e described in hapter 3 4 a I Z < (J x lw 1 m m i w REDESICN OF THE STRUCTURE F 3; relationship between curvature {E E ductility for members an H (J disPIacement ductility o a a structure g diagrams of curvature ductility U V/ ~< NEH INPUT DATA Fig.(1.l) - Flow-chart - Design Procedure 18 moment > curvature Fig.(I.2)-Bilinear Hysteretic Model l9 Inelastic Spring £F—- Element Model .. . It . .._- A B Section of Uniform Stiffness Sec}¥on Stl nees Di tribution Fig.(1.3) - Frame Member Hodel 20 Nonlinear Rotational Springs / \ l— ———————— Hal—- [Elastic Zone(L) l‘ L ’l Fig.<1.4>- Equivalent Spring Model 21 Moment Jkl Jk3 *> Curvature k3 < k1 F Fig,(1.5)- Bilinear Degrading Hysteretic Model CHAPTER 2 A DESIGN PROCEDURE The objective of this chapter is to present a design procedure for reinforced concrete frames subjected to seismic loads. As illustrated in Fig.(l.1). the procedure consists of four basic steps: a) preliminary design based on member forces obtained by a linear elastic analysis for equivalent static loading as prescribed by design codes, such as the UBC[21]; b) nonlinear dynamic analysis. using the microcomputer program presented in Chapter 3; c) checking of damage of the structure; d) redesign of the structure if necessary. The complete design procedure is illustrated by a numerical example in Chapter 5. 2.1 Preliminary Design The dBSIID seismic loading recommended DY building COdBS. for example the UBC COGO 18 in the form Of statically 22 23 applied loading. It is presumed that these static loadingswould be equivalent in their effects on the structure to the earthquake motions. However. dynamic analysis of structureshave shown that the response inertia loads may be much greater than the static lateral loads recommended by such codes. It is well known that structures designed based on loads prescribed by such codes have survived substantial earthquakes. This has been attributed to the ability of ductile structures to dissipate energy by post-elastic deformations, damping. and soil-structure interation. In recent years, special detailing practices for seismic loads( see for example. Appendix A of A01 Building Code 318-83) have been codified to enhance the performance of the structure. Therefore, the first phase of the proposed design procedure is to use the usual design process a current practice such as the UBC code. It is also presumed that minimum detailing requirements for seismic design in the ACI Code are also followed. 2. 2 Nonlinear Dynamic Analysis This phase essentially represents a "proof test" of the structure obtained in the first phase. A dynamic analysis would be carried out by use of the microcomputer program MC- GUAKE to be described in Chapter 3. A major decision for this phase is the choice of earthquake (recorded or 24 artificially generated) to be applied to the structure. General considerations for this choice are briefly presented in Section 2.4. For the purpose of this study. it is presumed a choice has been made. It may be. for example, the E-w component of the 1940 El Centro earthquake with the amplitudes amplified by a factor of 1.2. The analysis consists of three phases a) input data. b) computations . 0) output of the results. The initial sizing of structural members determined in the preliminary design described before is used in.the first run of the analysis. The consideration of inelastic behavior requires input of additional parameters over those needed for regular linear elastic analysis. The input data include: a) material properties: a. 1) concrete: concrete strength. fé. strain at maximum stress, 6 confinement ratio. (D ” (see 0. Equation A.3); Although.the confinement ratio f)". as precisely defined in Equation A.3, is a function of the confinement steel. it affects the stress-strain relationship of concrete. Therefore. it is considered a concrete parameter. a.2) steel: modulus of elasticity. Es' strain hardening ratio. PS, yield stress. fY' and ultimate strain. 63; 25 b) member properties: magnitude of axial load, P, longitudinal reinforcement./0 . and transversal reinforcement . The following assumptions are made for the nonlinear dynamic analysis: a) b) C) d) e) f) 8) h) The analysis is limited to plane framed structures. Every member in the structure may be treated as a massless line member, that is. the conventional beam theory applies. All mass at a floor level including rotary inertia is concentrated at the Joints. The structure is fixed to an infinitely rigid foundation. The inelastic deformation of each constituent member follows the modified Takeda’s hysteresis model. The ground motion takes place in the plane of the structure and in the horizontal direction only. The deformations are small and the geometry of the structure retains the initial configuration. However. the effects of gravity loads ( the P- A effects) are considered. Axial load remains constant and equal to the gravity load effect present at the beginning of the ground motion. The output results include the following: a) maximum horizontal displacement at the top Of the frame: 26 b) displacement ductility factor ”D; and for each end of every member: 0) finite size of the plastic regions; d) damage factor; e) maximum moment. 2.3 Redesigning of the Structure The structure will be modified or redesigned if the damage factor of one or both ends of one or more members attains a certain prescribed level. for example, 0.5. The new design may be guided by the design aids presented in Chapter 4 in a manner described therein. 2.4 Selection of Design Earthquake In order to establish the ground motion characteristics of the maximum probable earthquake for any given building site. it is necessary first to study the earthquake history of the region. It may be necessary to analyze seismological parameters, such as length of faults. fault distance from the site. etc, in order to estimate the intensity of the earthquake expected at the site. Such study could provide estimates for the maximum.acceleration expected at the site concerned, predominant period for maximum.acceleration and duration Of shaking. 27 One approach to obtaining an appropriate ground motion record has been to modify and distort an actual earthquake record so that it represents an event of different magnitude and distance. The intensity of it may be adjusted by a amplitude-scaling factor. the frequency content may be modified by a change of time scale. and the duration of the earthquake may be changed by truncating or duplicating portions of the record. It is more desirable to have a statistically significant sample of earthquake motions appropriate to the given magnitude and distance, rather than one. It is also quite feasible to derive artificial earthquake motions which represent the desired design earthquake. These ground motions are generated by random process that may be repeated to prov1de the samples needed for the desirable input motion. It is noted again, however, that for the purpose of this study. the designer is presumed to have been provided with this input ground record. CHAPTER 3 COMPUTER PROGRAM A computer program (code name : HC-QUAKE) for the nonlinear dynamic analysis of plane reinforced concrete frames subject to strong motion earthquakes is presented. The program is written using FORTRAN 77 and.has been developed to run on microcomputers. In order to make the computer program more convenient to use the input and output data were handled in a file- oriented format, as illustrated in the flow-chart , Fig. (3.1). HC-GUAIE is composed of three sub-programs: a) Sub-program.DATA - for input data; b) Sub—Program.HAIK - the main program; c) Sub-Program PLOT - for plotting input data and output results A complete example illustrating the use of HC-GUAKE is presented in Appendix B. 28 29 3.1 Sub-program DATA Even for a relatively small structure. a nonlinear dynamic analysis requires a set of data of almost a hundred itemm. In order to handle these large data sets. DATA was designed to be a file-oriented program. in the sense that data can be created. saved. retrieved, edited and listed. DATA creates the input data file for subsequent use in Sub-program HAIR. The input is carried out in an interactive mode with.the user responding to prompts. When one selects DATA (by typing "DATA") the following sub-system menu appears as prompts: O : HEW DATA 1 : CORRECT DATA 2 : LIST DATA 3 : END) The system waits for a number corresponding to the desired option. For example. if one wishes to enter new data, respond with 0, etc. a) HEW DATA -— before data can be entered into the system. a data file must be opened to accept data. When a data file is opened for the first time. the user specifies the name of the data file. When.the data file is first opened. all data values are initially equal to zero. The system.automatically prompts for the information needed. 30 b) CORRECT DATA -- to change data values from existing input data files. select the CORRECT DATA option of the DATA menu. Once this option is selected. the user specifies the variable to be corrected, followed by the new data value. c) LIST -- the data file may be displayed on the screen and/or have them printed out as a hard copy. The input data for the analysis of a structure can be grouped into the following sets; 1) Control Information; 2) Control Joint Coordinates; 3) Node Generation Data; 4) Boundary Condition Code; 5) Mass Generation Data; 6) Load Control Data; 7) Earthquake Acceleration Control-Damping Factors; 8) Output Control; 9) Beam Element Control; 10) Reinforcement Steel Properties; 11) Concrete Properties; 12) Member Properties. A set of data within each group is needed for the overall analysis. 31 3.1.1 Control Information To supply the "control information". responses to the following prompts are needed. - number of nodal points; - number of control nodes for x and y coordinates generation (number of nodes to be used as input data); - number of sets of nodes to be generated ; - number of sets of boundary condition code to be generated; - number of sets of mass data to be generated; - data checking or run; 0 : run 1 2 check only. 3.1.2 Control Joint Coordinates The prompts are: node number; x-coordinate; y-coordinate. 3.1.3 Node Generation Data The prompts are: - fIPSt node number; - last node number; 38 - number Of nodes to be generated; - difference between two successive nodes. 3.1.4 Boundary Condition code 1 : for fixed D.O.F. o : for free D.O.F. first node in the group; code for x-displacement; code for y-displacement; code for rotation; last node in the group; difference between two successive nodes. - For example. if first node : 1. last node : 6 and difference between two successive nodes : 1. all nodes 1. 2. 3. 4 .5 and 6 Will have the same boundary conditions. 3.1.5 Hass Generation Data - first node number in the group; - x-mass; - y-mass; - rotary mass; - last node number in the group; - difference between two successive nodes. 33 3.1.5 Load Control Data - gravity acceleration (consistent With the basic units chosen); - number Of integration steps for dynamic analysis; - integration time step size; - amplification factor. c1.to be applied to the amplitudes Of ground acceleration ; - scaling factor. c to be applied to the time coordinate 2’ Of the ground motion record; - absolute value of maximum permissible displacement. AF" Factors 01 and c2 are used to modify and distort the earthquake record used so that it may represent an event of different magnitude and distance. as described in Section 2. 4. The quantity A 1.8 used to end the computation F when the horizontal displacement at the top of the frame becomes too large (signifying failure). It is taken as 0.06 H. where H is the total building height. 3.1.7 Earthquake Acceleration Control-Damping Factors - number Of time-ground acceleration pairs defining the ground motion input; - code for printing acceleration input; 0 2 do not print acceleration record; 34 1 : print acceleration record; - number of steps between printing; - title to identify record; 1 : 1940 El Centro HS; 2 : Caltec A-1[23]; 3 : Caltec A-Z; 4 : Caltec 8-1; 5 : Caltec B-2; 6 : Caltec C-1; 7 : Taft; 8 : San Fernando 1941; 9 : Other; - mass proportional damping factor. a; - tangent stiffness proportional damping factor. B. 3.1.8 Output Control - number of nodes for x-displacement; - list of nodes for x-displacement. 3.1.9 Beam.Element Control - number Of members in the Structure; - number Of reinforcing steel property types; - number Of concrete property types. 35 .1.10 Reinforcing Steel Properties modulus of elasticity. Es; strain hardening ratio. ps; yield stress. fy; ultimate stress. 68 .1.11 Concrete Properties concrete strength. fé; Strain at mmximum.stress. Go: confinement steel ratio.f ”. .1.12_Hember Properties member number (negative value for symmetric section so that the last three items of the following data list need not be input); node number at end of the member. node I; node number at the other end. node J; steel type number ( if zero. all the information except node number will be the same as the preceding element and' the following parameters could be omitted); concrete type number; magnitude Of axial load due to gravity; 36 - height of the section; - width of the section at the bottom; - cover of the section at the bottom; - reinforcement at the bottom; - width.at the top; — cover at the top; - reinforcement at the top. 3. 2 Sub-program HAIR HAIR computes the nonlinear response of reinforced concrete frames subject to dynamic loading following the mathematical model proposed by Meyer and Roufaiel [26] as described in Appendix A. It is a modified version of the program HACRS-II (Nonlinear Analysis of Reinforced Concrete Structures)[26] developed to run in the IBM/370 Computer Systems. The HACRS-II itself is a modified version of the program DRAIN-2D by A.E.Kannan and G.H.Powell[24]. HAIR also prints input and output information. which includes the following: a) input data information; b) nodal displacement envelopes; c) for each frame member of the structure. the inelastic response: 1. curvature ductility provided; 2. plastic length at nodes I and J; d) 6) fl 37 3. damage factor; 4. maximum moment. first yield displacement. AY; maximum horizontal displacement at the top Of the Structure; displacement ductility . UD. 3. 3 Sub-program PLOT PLOT is developed to plot two dimensional Views for: a) b) C) d) e) the undeformed structure : this is prov1ded as a visual aid to confirm.the correctness of input data node coordinates and member incidences; ground acceleration input: plotting this input data is useful to viewing the acceleration record data; displacement at the top of the frame as a function of the time ; the deformed structure: after each time increment the deformed structure could be plotted; the finite plastic regions and the damage factor: this is the most important output in terms of plastic analysis. TWO quantities are presented for each member end the ,length Of the inelastic region and the damage factor. The inelastic length could indicate possible collapse mechanism and the damage factor Will indicate how far or close the 38 member is from.total failure. A damage factor equal 1.0 is considered as total failure. 3.4 Hardware Requirements The following is a list of the minimum hardware requirements for running HC-GUAKE: i. 2. One IBM or IBH compatible microcomputer; 512 kilobytes of random access memory; One 360! floppy disk drive and one 10 megabyte hard disk; A 806? math coprocessor. (Its use greatly reduces run time. to one third or less of the time required without the 8087.) Graphics Card (for the PLOT Sub-program) - the Hercules Graphics Card is required; the program can be easily adapted for running with another graphic card; One dot matrix printer - program output can be printed on any printer which is compatible with the computer. A hard copy of the screen graphics produced by PLOT may be obtained. 39 npu ut data a) In Sub-program b) $1ene erates files For DATA ~lr _ * a) onl near nami Anal sis SUb program] b) one ates QTles Tor 9 >0 H“ 2" MAIN GPLOTr . Sub-program for plotting PLOT END Fig.(3.l) - Flow-chart of MC-OUAKE CHAPTER 4 DESIGN AIDS As explained in Chapter 2. if any member of the structure reaches a level of damage. as defined in Chapter 1. with a-damage factor greater than 0. 5. the structure should be redesigned (although such redesign may involve a modification of only a single member). For- example. one may modify one or more of the basic design parameters (b. d.l0 .f". and so forth) for the columns and/or for the beams and then reanalyze and check the structure again. In general this would be "too loose" (too much freedom). and in consequence. take too many trials in order to arrive at an appropriate design. Design aids are provided herein to give some guidance for the redesign. Instead of dealing with the basic parameters(such as. b. d.lo .and lo".) directly. it is convenient to deal with the maximum curvature ductility factor as an intermediary. First note that there are specific relationships between the basic material parameters and the maximum curvature ductility of a section. The primary moment-curvature relationship of a section can be derived using conventional reinforced concrete theory only. 40 41 Details are given. for example. in Park's book[33]. These primary moment-curvature relationships were used to compute the data presented in Fig.(4.1) to Fig.(4.20) for some practical ranges of the parameters. For a damage factor less than 0.5. the response curvature ductility must be less than the maximum (member section maximum.curvature ductility). Obviously. the maximum curvature ductility needed depends on the structure geometry. such as. number of stories. material properties and the response displacement ductility factor and the ground motion. It is impossible to cover all cases. In order to prov1de a guide. Figures (4.22) to (4.29) present a relationship between the response displacement ductility and the maximum curvature ductility of a section. Note that each point of the graph represents a design with damage factor generally less than 0.5 (or with negligible exceedance). as indicated in Table (4.1). Thus one may begin the modification by first choosing a response ductility factor. in general ranging from.2 to 5. and go to the appropriate graph for the number of stories in order to determine the maximum curvature ductility for the columns and beams. Then. go to the first group of graphs to choose the des ign parameters. 42 4.1 Curvature Ductility Diagrams The yield curvature ”y is defined as the curvature at which.the strain in the steel equals its yield strain. The ultimate curvature ’m is defined as the curvature at which the strain of the concrete cover is equal to em. The ratio pm/py is called the curvature ductilitY. u of the section. ¢n Curves for u are plotted in Figures (4.1) to (4.20) for o a range of practical combinations of fY and fo for normal weight concrete and for 6 = 0.002. AS design aids the 0 diagrams are constructed that give values of curvature ductility as a function of the longitudinal reinforcement percentage and the confinement steel percentage. It may be noted from Fig.(4.1) to Fig.(4.20). that: a) when the longitudinal reinforcement increases. the curvature ductility decreases; b) when the confinement steel increases. the curvature ductility increases; c) when the Steel yield Stress . TY, increases or the uniaxial strength Of the concrete. fc. decreases. the curvature ductility decreases; and d) when the level of axial load on the section increases.the curvature ductility decreases. '5 (I 811. the Sill an: 4-2 The 43 4.2 Relationship between Displacement Ductility and Curvature Ductility Some attempts at relating and u for multistory up ¢ frames have been made. In general they are based on static collapse mechanisms [33] which would involve such simplified assumptions as a) frame reaches yield at all the plastic hinges sections simultaneously; b) bending moment patterns are obtained from the equivalent static lateral loading recommended by code; c) this code static loading corresponds predominantly to the first mode of vibration response. Therefore this static approach can be taken only as a guide. It is the goal here to determine this relationship on the basis of nonlinear dynamic analysis. Framed structures subjected to bOth gravity and seismic loads Will be analyzed. 4.2.1 Structure Types Reinforced concrete frames of one-bay ranging from 3 to 10 stories were selected. The dimensions are shown in Fig.(4.21). a ”typical" one-bay frame. The following additional data are assumed for the analysis: 44 a) concrete properties: fc 3 K81 6o f” b) reinforcement Steel properties: 0.002 1.0 7. for all members f = 60 Ksi Y Es : 29.000 Ksi p8 : 0.01 68 = 0.015 c) dead load per floor : 50 kips 4.2.2 Ground Motions The 1940 El Centro (HS) earthquake is used. From that record a segment of 12 seconds duration with a peak acceleration approximately 0. 33 8 is applied to the frames. 45 4.2.3 Response Parameters The parameters used to characterize the inelastic response were as follows: a) maximum horizontal displacement at the top; D) finite Size Of plastic regions; c) damage factor; d) displacement ductility factor ”D; e) maximum moment Of the member. 4.2.4 Presentation Of Results A series Of dynamic analysis (120 cases). using the software presented in Chapter 3, were carried out to find the relationship between curvature ductility for members and the displacement ductility Of a structure. A review Of the results for these eight frames indicates that the displacement ductility factor ranges from 1.2 to 4.8 as the curvature ductility Of the beam members ranges from.26 to 34 and the column steel percentage ranges from 2% t0 6%. CURVATURE DUCTILITY 46 60 = 0.002 d'/h = 0.10 9 w confinement a 1 A .0 Z V V ’> A confinement - 0.5 9: o confinement =- 0.0 % 0-0 T T r l 0.5 1.0 1.5 2. 2.5 3.0 0 LONGITUDINAL REINF. % (in one face) Fig.(4.1)—Curvature Ductility versus Steel Percentages f' c: 5 ksi fy= 60 ksi P/(f'c bh)= 0.0 CURVATURE DUCTlLlTY 47 90 = 0.002 d'/h = 0.1 30.0 r l T I 20.0- - 10.0- a M C C ,> III confinement = 1.0 X A confinement - 0.5 2 0 0 o confinement - 0.0 Z 0.5 1:0 135 230 215 3.0 LONGITUDINAL REINF. % (in one face) Fig. (4. 2)— Curvature Ductility versus Steel Percuenta es f'c= 5ksi fy= 60 ksi P/(f =0 10 CURVATURE DUCTILITY 48 60 = 0.002 d'/ h = 0.1 15-0 I T r I 10.0- q 5.0% V C C C 4) an confinement =- 1.0 X A confinement - 0.5 X 0 0 o confinement :- 0.0 % ° 0.5 1:0 135 230 2T5 3.0 LONCITUDINAL REINF. % (in one face) Fig.(4.3)-Curvoture Ductility versus . Steel. Percento es f'c= 5 ks. fy= 60 ks. P/(f'c b )= 0.20 C URVATURE DUCTILITY 49 60 = 0.002 d'/h = 0.1 20.0 , h , . , 15.0-5 4 10.0 D 5.0-] - III confinement = 2.0 75 A confinement - 1.5 X 0 0 o confinement :- 1.0 7: 0.5 1:0 1T5 230 215 5.0 LONGITUDINAL REINF. % (in one face) Fig. (4. 4)— Curvature Ductility versus Steel Percenta e)_s f'c= 5 ksi fy= 60 ksi P/( (f'c =0 30 CURVATURE DUCT! LITY 50 80 = 0.002 d'/h = 0.1 20.0 ‘ T l I r 15.0 ‘ -I 10.0 A ‘ . " c - " V 3 a0 5.01 -I III confinement =- 2.5 X A confinement - 2.0 X 0 0 o confinement - 1.5 % ° 0.5 110 135 2f0 235 3.0 LONGITUDINAL REINF. % (in one face) Fig.(4.5)-Curvature Ductility versus Steel Percenta es f'c= 5 kSi fy= 60 ksi P/(f‘c b )= 0.40 CURVATURE DUCTILITY 51 III confinement = 1.0 X A confinement - 0. 5 X o confinement = 0. 0 z 00 I r 0.5 1.0 1.5 2. F 0 LONGITUDINAL REINF. 7.. (in one face) Fig. (4. 6)- Curvature Ductility versus Steel Percfenta es_ f6: 5 ksi fy= 40 ksi P/ =00 CURVATURE DUCTI LITY 40.0 52 e0 = 0.002 d'/h = 0.1 30.0- 20.0- 3 III confinement = 1.0 2 A confinement - 0.5 2 o confinement =- 0.0 X 0.0 0.5 r 1.0 I T I 1 .5 2.0 2.5 3.0 LONGITUDINAL REINF. 75 ( in one face) Fig.(4.7)—Curvature Ductility versus Steel Percenta es PC: 5 ksi fy= 40 ksi P/(f'c b )= 0.10 CURVATURE DUCTlLflY 53 co = 0.002 d'/h = 0.1 30.0 20.0 III confinement = .5 A confinement - 1.0 o confinement = 0.5 NNN 0-0 I I W T 0.5 1.0 1.5 2.0 2.5 3.0 LONGITUDINAL REINF. 75 (in one face) Fig.(4.8)-Curvature Ductility versus Steel Percenta es f’c= 5 ksi fy= 40 ksi P/(f'C b )= 0.20 CURVATURE DUCTILITY e0 = 0.002 d'/h = 0.1 25.0 54 20.0- 15.0‘ C) C) 10.0-4 5.0-5 00 O O '0.5 130 135 LONGITUDINAL REINF. 73 (in one face) I 2.0 I 2.5 fi A O Fig.(4.9)-Curvature Ductility versus Steel Percenta es f'c= 5 ksi f = 40 ksi Y confinement =- 2.0 X confinement - 1.5 X confinement - 1.0 x P/(f'c b )= 0.30 CURVATURE DUCTILITY 55 00 = 0.002 d'/h = 0.1 25.0 20.0 15.0 10.0-1 5.04 00 C) (J (J 4, III confinement - 2.5 75 A confinement - 2.0 X o confinement :- 1.5 75 ' 0.5 I I I I 1.0 1 .5 2.0 2.5 3.0 LONGITUDINAL REINF. 75 (in one face) Fig.(4.10)-Curvature Ductility versus Steel Percenta es f'c= 5 ksi f = 40 ksi P/(f‘c b )= 0.40 Y CURVATURE DUCTI LITY 56 e0 = 0.002 d'/h = 0.1 55.0 r I r T 50.0 - 45.0-I - 40.0- - 35.0- ' - 30.0 .. - 25.0-I . - 20.0-5 - 15.0-* 2 100 III confinement = 1. A 0 X 5-0 V V C 9 A confinement :- 0.5 2 o confinement =- 0.0 % 000 I 0.5 110 135 230 215 530 LONGITUDINAL REINF. 75 (in one face) Fig.(4.11)—Curvature Ductility versus Steel Percenta es f'c= 3 ksi fy= 50 ksi P/(f'c b ) = 0.0 CURVATURE DUCTILITY 57 e0 = 0.002 d'/h = 0.1 25.0 20.0d 15.0 10.0~ - 5.0 d f III confinement = 1.0 A confinement - 0. 75 5 z o confinement - 0.0 X 0-0 r r I I 0.5 1.0 1.5 2.0 2.5 3.0 LONGITUDINAL REINF. 75 (in one face) Fig.(4.12)-Curvature Ductility versus . _ Steel Percenta es fc= 3 kSl fy= 60 kSI P/(fc b )= 0.10 CURVATURE DUCTI LITY 58 e0 = 0.002 (f'/h = 0.1 15°C T I I T 10.0- - I) III confinement s 1.0 X A confinement - 0.5 75 o confinement - 0.0 75 O 0.0 F I I I T 0.5 1.0 1.5 2.0 2.5 3.0 LONGITUDINAL REINF. 7. (in one face) Fig.(4.13)—Curvature Ductility versus ' . Steel Percenta es fc= 3 kSl fy= 60 kSI P/(fc b )= 0.20 CURVATURE DUCTILITY 00 = 0.002 d'/h = 0.1 59 15.0 T . 0.0 , , 0.5 1.0 1.5 LONGITUDINAL REINF. 75 (in one face) Fig.(4.14)-Curvature Ductility versus I 2.0 I 2.5 3.0 . . Steel Percenta es f0: 3 kSI fy= 60 kSI P/(fC b )= 0.30 I A O confinement = 1.5 X confinement - 1 0 Z confinement :- 0.5 75 t_JE.ODQ MKDHdQ/KDO l CURVATURE DUCTILITY 60 e0 = 0.002 d'/h = 0.1 20-0 I I I r 15.0% 10.0% 5.0- - III confinement =- 2.5 X A confinement - 2.0 75 0 0 o confinement :- 1.5 2: ' 0.5 130 135 230 2T5 5.0 LONGITUDINAL REINF. % (in one face) Fig.(4.15)-Curvature Ductility versus ' . Steel Percenta es I0: 3 ks. fy= 60 ks1 P/(fc b )= 0.40 CURVATURE DUCTILITY ' 80.0 61 e0 = 0.002 d'/h = 0.1 70.0‘ 60.0-1 50.0 40.0% 30.0-1 20.0—Kn 10.05 v C C III confinement a 1. X a?) A confinement - 0.5 75 0 0 o confinement = 0.0 75 ' I I l f 0.5 1.0 1.5 2.0 2.5 3.0 LONGITUDINAL REINF. 75 (in one face) Fig.(4.16)-Curvature Ductility versus ' . Steel. Percentages fc= 3 ks. fy= 40 ks. P/(fC b h): 0.0 CURVATURE DUCTI LITY 40.0 so = 0.002 d'/h = 0.1 62 30.0- 20.0- 00 V v I) III confinement =- 1.0 X A confinement - 0.5 75 o confinement - 0.0 75 ' 0.5 F I I f 1.0 1 .5 2.0 2.5 3.0 LONGITUDINAL REINF. 75 (in one face) Fig.(4.17)-Curvature Ductility versus Steel Y Percenta es f'c= 3 ksi f = 40 ksi P/ (f'c b )= 0.10 C URVATURE DUCTILITY 63 co = 0.002 d'/h = 0.10 20.0 15.0- 10.0‘f)'\15\le\fl\fi\1A 5.0- - A) III confinement =3 1.0 X A confinement - 0.5 75 o confinement - 0.0 75 0-0 I I I 0.5 1.0 1 .5 2 2.5 3.0 r .0 LONGITUDINAL REINF. % (in one face) Fig.(4.18)-Curvature Ductility versus ' . Steel Percenta es f0: 3 kSI fy= 40 kSl P/(fc b )= 0.20 CURVATURE DUCTILITY 64 e0 = 0.002 d'/h = 0.10 15.0% 10.04 A '3' A 4A (D C) (D C) 5.0-4 - III confinement = 1.5 Z A confinement - 1.0 Z 0 0 o confinement a 0.5 Z '0.5 15 135 230 235 3.0 LONGITUDINAL REINF. 75 (in one face) Fig.(4.19)-Curvature Ductility versus ' . Steel Percenta es fc= 3 kSI fy= 40 ks1 P/(fC b )= 0.30 CURVATURE DUCTILITY 65 15.0A A z; a . o 10.0« " V C C 40 5.0-1 - III confinement =- 20 Z A confinement - 1.5 Z 0 0 o confinement =- 1.0 Z ' 0.5 130 135 230 235 5.0 LONGITUDINAL REINF. 7. (in one face) Fig.(4.20)-Curvature Ductility versus Steel Percenta es f'c= 3 ksi fy= 40 ksi P/(f'c b )= 0.40 66 10”/30” 10”/30” 10’ 10”/30” #3 to 10 stories we § V 16’ olumns Size: to 10 stories - 1 to 8 stories - 15” and 10 stories - 2 momarw 3R Fig.(4.21) - Basic Structure Properties 3.0 67 I l l r l r I jfi I l U T I I I beam curvature duct.= 28 beam curvature duct.= 30 beam curvature duct.= 34 .o : 2.5— x 2 . '6 3 2.0 a '2 15 - 1 “24 I} LIJ E 1.0- a. 22 ca 0.5- 0.0 . . I"I"II'II'F' 13.5 15.0 16.5 18.0 19.5 21.0 COLUMN CURVATURE DUCTILITY Fig.(4.22)—Displacement Ductilitrtversus I Curvature Ducti y THREE STORIES FRAME 68 300 U I I T r r '7 r I l j a beam curvature duct.= 28 A beam curvature duct.= 30 25‘ III beam curvature duct.= 34 _ 1.5- 24—...{3 . _ 10» 0 1.01 DISPLACEMENT DUCTILITY 0.5- _. 0.0 . . . . , . ,j . 11.5 14.0 16.5 COLUMN CURVATURE DUCTILITY I I Fig.(4.23)—Displacement Ductility versus Curvature Ductilit FOUR STORIES FRA E 69 DISPLACEMENT DUCTILITY 3.0 I I I I r I I I f a beam curvature duct.= 28 A beam curvature duct.= 30 2,5— a! beam curvature duct.= 34 J 2.0~ _ 1.55 — 1.0- - 0.54 d 000 I I I r I I I I I 10.0 12.5 15.0 COLUMN CURVATURE DUCTILITY Fig.(4.24)—Displacement Ductility versus Curvature Ductility FIVE STORIES FRAME 3.0 1 7O I. I I I 1 beam curvature duct.= 28 beam curvature duct.= 30 beam curvature duct.= 34 ; 2.5- I. 2 I.— o D o '_. z LIJ 2 LL] 9:” 1.0« 0. 20 c: 0.5- 0.0 I 9.0 9. I I I r I 510.010.511.011.512.012.5 COLUMN CURVATURE DUCTILITY Fig.(4.25)-Displacement Ductilit Curvature Ducti M, SIX STORIES FRA VGI'SUS t E 71 3-0 r I I I beam curvature duct.= 28 A beam curvature duct.= 30 2.5.. III beam curvature duct.= 34 _ O 2.0- 1.5-l 1.0- — DISPLACEMENT DUCTILITY 0.5-l _ 0.0 I I I I 8.0 8.5 9.0 9.5 10.0 10.5 COLUMN CURVATURE DUCTILITY Fig.(4.26)—Displacement Ductility versus Curvature Ductility SEVEN STORIES FRAME 3.0 72 I 0 A * I I I I beam curvature duct. 1 = 28 beam curvature duct.= 30 beam curvature duct.= 34 : 2.54 ZJ 5 3 2.04 D E Lu 1.54 2 LIJ $5 1.04 O. ‘2 o 0.5- 00 ° 9.0 935 10010511301135123.0125 COLUMN CURVATURE DUCTILITY Fig.(4.27)—Displacement Ductilitltversus I Curvature Ducti EIGTH STORIES FRA E 73 30 I f I I I a beam curvature duct.= 28 A beam curvature duct.= 3O DISPLACEMENT DUCTILITY 2,51 3! beam cu __oture duct.= 34 _ a 2.0-4 - ¢ .. e .3 1.54 A _ ‘ A 1.0— _ 0.5-4 _ 0 0 '80 835 930 935 103.0 10.5 11.0 COLUMN CURVATURE DUCTILITY Fig.(4.28)—Disp|acement Ductility versus Curvature Ductility NINE STORIES FRAME 74 :1 4.0- I g o . D O 3.0“ 5 '— 2 WW “5 LIJ 2.0“ 5 gr: be. A AA 0. £9 1.0~ -I 0 II! beam curv. duct.- 34 A beam curv. duct.=- 30 a beam curv. duct.=- 28 0-0 I I I I 7.5 8.0 8.5 9.0 9.5 10.0 COLUMN CURVATURE DUCTILITY Fig.(4.29)-Displacement Ductilitrtversus I Curvature Ducti TEN STORIES FRA E 75 Damage Factors(*) Number Beam f Values for Columns Used of Curvature - Stories 2% 3x 4x 5% 6x 28 0.470 0.420 0.490 0.43 0.48 3 30 0.460 0.470 0.260 0.41 0.43 34 0.460 0.44 0.42 0.38 0.41 28 0.38 0.48 0.52 0.35 0.50 4 30 0.470 0.44 0.44 0.47 0.49 34 0.460 0.41 0.47 0.52 0.43 28 0.500 0.490 0.49 0.35 0.32 5 30 0.500 0.49 0.50 0.50 0.45 34 0.48 0.44 0.43 0.53 0.45 28 0.500 0.470 0.500 0.52 0.48 6 30 0.44 0.47 0.50 0.45 0.50 34 0.41 0.52 0.51 0.47 0.53 28 0.27 0.45 0.30 0.49 0.53 7 30 '0.32 0.29 0.38 0.52 0.49 34 0.52 0.50 0.36 0.40 0.50 28 0.37 0.52 0.49 0.53 0.49 8 30 0.26 0.36 0.49 0.46 0.50 34 0.50 0.53 0.51 0.41 0.47 28 0.34 0.26 0.24 0.40 0.39 9 30 0.51 0.45 0.51 0.35 0.34 34 0.50 0.50 0.54 0.50 0.40 Table 4.1 Damage Factors for One -bay Frame 8 76 Damage Factorsiil Number Beam. f) Values for Columns Used of Curvature Stories 2% 3x 4x 5% 6x 28 0.35 0.40 0.43 0.50 0.35 10 30 0.46 0.52 0.53 0.51 0.52 34 0.50 0.47 0.50 0.52 0.50 I - Factors listed are for beams unless followed by the letter C. in Which.case. the factor is associated with a column. Table 4.1 Damage Factors for One-bay Frames (continued) 001 de. in CO: 811 SE 111 81 Us 11' la. 311 CHAPTER 5 DESIGN EXAMPLE In Chapter 2. a design procedure was presented involVing an explicit consideration of damage due to seismic loads.The computer software has been described in Chapter 3. Certain design aids to help guide necessary redesign were presented in Chapter 4. In order to illustrate the material presented in the preceding chapters, the design of a three story frame is considered in this chapter. The geometry of the structure is shown in Fig.(5.1). For simplicity. all beams will have the same properties and so will all columns. Since an example on the use of the program for dynamic analysis has already been given in Appendix B, it will not be repeated here. The following basic steps. as described before. will be used to illustrate the design procedure. a) Preliminary design - applying prescribed dead load and live load and earthquake loading in the form of static lateral loading as prescribed by the 030 Code. the initial 8121118 0f structural members and steel reinforcement are 77 78 determined based on a linear elastic analysis and the ACI Building Code. b) Nonlinear dynamic analysis - it is performed on the structure using the NC-QUAKE computer program presented in Chapter 3. c) Check damage - in case of occurrence of high damage to one or more members( according to the damage scale factor,as presented in Chapter 1) the frame should be redesigned. This will be guided by what was presented in Chapter 4 . d) Redesign - using Figures (4.22) to (4.29) in Chapter 4. for a particular number of stories. according to the value of the displacement ductility chosen for the frame, the curvature of the beams and the columns may be selected from design aids such as Figures (4.1) to (4.20). for a particular combination of material properties. and using the curvature ductility chosen for the members, new values for the confinement steel or for the longitudinal reinforcement may be determined. Using these new values, another nonlinear dynamic analysis 18 performed as in b). and 80 on. 79 5.1 Preliminary Design 5.1.1 Design 3381C Data and Specifications The following data are given for the design: a) concrete properties: f0 : 3 K81 60 0.002 b) reinforcement steel properties: f = 60 K81 Y Es - 29.000 K81 ps : 0.01 63 : 0.015 Dimensions of the members have been assmmed as illustrated in Fig.(5.1). In accordance with ACI Code. U = 1.4 D + 1.7 L When wind load w is considered in the design the required strength U provided should also be no less than U = 0.75 ( 1.4 D + 1.7 L + 1.7 w ) If an earthquake load E is to be included. V will be replaced by 1.1 E. Then for the earthquake load one has U = 0.75 (1.4 D + 1.7 L + 1.7-1.1 E ) 3) Le b) The :81 The No. Con: P881 0 80 For seismic loads the UBC Code is adopted. 5.1.2 Loads a) Dead Load + Live Load Let the dead load intensity w and live load intensity w be D L given as: 'D : 0.2 Kips/in wL = 0.2 kips/in(floor) ; wL = 0.04 kips/in(roof) Then. wU s 0.75( 1.4-0.2 + 1.7 0.2) ; wU : 0.465 kips/in(floor) 'U = 0.75( 1.4~O.2 + 1.7-0.04) ; WU : 0.261 kips/in(roof) b) Seismic Loads( in accordance With. the UBC Code ) The structure is designed to resist minimum total lateral seismic forces in accordance with the following formula: V : 2 III CIS w The value of K is not less than that set forth in Table No.23-I of the UBC Code. Considering that the frame will be a ductile moment- resisting frame. I : 0.67 81 The value of C is determined in accordance with.the following formula: .._._1__ 15”? C : The value of 0 need not exceed 0.12. The period T may be determined by the following formula: 0.05 hn T = TD where hn: height in feet above the base to level n. the highest level. D = the dimension of the structure.in feet. in a direction parallel to the applied forces Then. D = 250/12 = 20.83 ft nu: 480/12 = 40 ft T = 22%?32%%22 = 0.44 sec 0 : ———l———— : 0.10 < 0.12 15 {0.44 The value of S I numerical coefficient for site-structure resonance ) will be considered as equal to 1.5 , based on the fact that there is no substantiated geotechnical data for determining the characteristic site period T8. The product of 0-8 need not exceed 0.14. C-S : 0.10-1.50 : 0.15 > 0.14 C'S V111 be considered to be equal to 0.14. It 82 The value of I (occupancy importance factor) is indicated in Table No.23-K(UBC Code). I : 1.25 z numerical coefficient dependent upon the zone as determined by Figures 1, 2 and 3 in the UBC Code (Chapter 23 ). 2 will be considered as equal 1.0 ( Zone 4 ). W the total dead load W 0.2-250 3 : 150 kips Then, the total lateral seismic load is: V : 1.0-1.25-0.67-0.14-150 : 17.59 kips The force V is distributed over the height of the structure in accordance With V : F + B F t 1:1 1 where Ft = lateral concentrated load at the top of the frame; F1 : lateral concentrated load at level ”i“. The concentrated load at the top is determined according to the following formula: Ft : 0.07'T'V (Ft shall not exceed 0.25 V and may be considered as 0 where T is 0.7 sec or less.) The remaining portion of V is distributed over the height of the structure according to the following formula: 83 ( V - Ft)- wx-h x F : x 1g1'1'h1 hx 1: height above the base to the level x or 1. respectively. w1 x: portion of W which is located at level i or x respectively. Then. T : 0.44<0.70 Ft : 0.0 hi: 160 in ha: 320 in DB: 480 in w1:wa:w3: 0.33 17.59 0.33 480 _ F1 ' 0.33-(160+320+460)‘ 8'79 Kips F2 : 5.85 kips F3 : 2.93 kips Corresponding to the load factors for seismic loads the lateral loads at the floor levels are calculated as: FlU : 0.75 1.7 1.1 8.79 : 12.33 kips FZU : 8.23 Kips F : 4.10 Kips 3U 84 5.1.3 Linear Analysis Using the loads as given by Section 5.1.2 the structure is given a linear static analysis. The results needed for the design of the controlling reinforced members are listed below: a) Dead Load + Live Load 148.88 kips : - column 4: ”U 419.22 kips.in; NU VU : 7.81 kips - column 6: NU = 1147.0 kips.in; NU = 90.75 kips VU : 13.86 kips - column 8: NU = 991.36 kips.in; NU : 32.63 kips VU : 12.41 kips in which.HU. VU and NU denote moment. shear and axial force respectively. b) Dead Load + Live Load + Seismic Load - beam 3: NU = 3504.2 kips.in ; vaax = 70.35 kips - column 4: "U = 1646.8 kips.in; NU = 175.87 Kips 85 VU : 20.13 kips - column 6: NU = 1930.9 kips.in; NU : 105.53 kips VU : 24.13 kips 37.38 Kips - column 8: “U : 1383.5 kips.in; NU V U : 18.57 kips 5.1.4 Design Of Beams and Columns Using conventional reinforced concrete theory and following the ACI Code for designing beams and columns subjected to the moments and axial loads given above. the following percentages of steel reinforcement were determined : a) for the beams: - longitudinal reinforcement = 0.80 x - transverse reinforcement(confinement) : 0.80 z b) for the columns: - longitudinal reinforcement in one face : 0.50 x - transverse reinforcement(confinement) : 0.80 z The percentage of transverse reinforcement(confinement) was calculated from.the amount of shear reinforcement needed for the loads defined. 86 5.2 Nonlinear Dynamic Analysis With the steel reinforcements determined. the frame as shown in Fig.(5.1) can now be analyzed. using NC-QUAKE program. Assume that the first 12 seconds of the N-S 1940 El Centro earthquake has been chosen as the maximum credible earthquake( the ground motion for the "proof test" of the structure ).( It has a peak acceleration of approximately 0.3g. as shown in the plot output for ground acceleration record. Appendix B.) The results of the analysis are given in the Appendix B as was first presented in Chapter 3. The inelastic responses are as follows: a) maximum damage factor at member 5 = 0.45; b) first yield displacement : 3.12 in; c) max. displacement at the top = 4.13 in; d) displacement ductility of the frame = 1.33. For this example . only moderate damage has occurred (damage factor : 0.45 < 0.50). The structure designed.has performed well when subjected to the tBSt ground motion Chosen. 5.3 Damage - Redesign of the frame In order to illustrate the redesign process. assume the test ground motion 18 the same as the preceding one except that COIITF are: 020 Sir thl Va Cc 87 that the amplitudes are amplified by a factor of 1.4. The computed inelastic responses obtained by use of HC-GUAKE are: a) maximum damage factor at member 5 = 0.98; b) first yield displacement = 2.93 in; c) max.displacement at the top : 5.76 in; d) displacement ductility : 1.97. The damage factor in member 5 being greater than 0.50 (high damage). the frame needs to be redesigned. In order to simplify the presentation of the example. it is assumed that the steel percentages of the members are the only design variables to be modified. 5. 3. 1 Displacement Ductility 0f the Frame Commentary on the SEAOC Code [38] indicates that the displacement ductility factor required in design should range from.2 to 5. For this example a displacement ductility of the frame equal 2.25 is chosen( the maximmm value ). For a three-story frame the following curvature ductility factors are obtained from Fig.(4.22): for beams : 30. for columns = 13.5. 5.3 For 011 is re in b) (I) 88 5.3.2 curvature Ductility Diagrams 3 ksi and For the combination Of material properties. fé f? = 60 ksi and a) for the beams. P/fébh : 0.0 Fig.(4.11) for a curvature ductility of 30 and a confinement steel of 0.8 x which is the same as before. a new value of the longitudinal reinforcement of 1.0 X (versus 0.8 2 previously) is indicated. b) for the columns P/fébh = 0.10 Fig.(4.12) for a curvature ductility of 13.5 and a confinement steel of 0.8% which is also unchanged. Similarly a new value of the longitudinal reinforcement of 2.25 X (versus 0.5 X prev1ously) is indicated. Using these new values for reinforcement of the members. another nonlinear dynamic analysis is performed with the following results: a) maximum damage factor at member 5 : 0.35; b) first yield displacement : 2.28 in; c) max.displacement at the top : 2.92 in; d) displacement ductility : 1.28. Since the damage is only "moderate" (damage factor : 0.35 < 0.50) under the maximum credible earthquake. the redesign may be regarded as satisfactory. 89 1 1 2 k ‘3 8 9 \0 "‘ 8 2 4 >l< E e 7 \0 “‘ 5 3 e . I S 4 H 7 8 *fl? 250” /77 X X beams: l0”/30” columns: 20”/20” Fig.(5.1) - Example CHAPTER 6 SUMMARY AND CONCLUSION 5.1 Summary The behavior Of reinforced concrete frames during earthquakes is complex and influenced by a variety Of material and structural parameters. in addition to the ground motion characteristics. Considerations 0f economics require the composite material be used beyond their linearly elastic ranges. Thus a reasonably accurate analysis needs to consider the nonlinear behavior 0f the structure. Although nonlinear analysis computer programs are available. they are rarely used for design 0f ordinary buildings because they are too costly to run. The purpose Of this study was to present a design procedure for reinforced concrete frames subjected to strong earthquakes based on a microcomputer program for nonlinear dynamic analysis. The design procedure consisted 0f four basic steps: a) preliminary design based on member forces Obtained by a linear elastic analysis for equivalent static 9O 91 loading as prescribed by design codes. e.g., the UBC Code [21]; b) nonlinear dynamic analysis; c) checking of structural damage; d) if necessary. redesign of the structure and repeat of the design cycle. The design procedure was described in Chapter 2 and illustrated by a numerical example in Chapter 5. The establishment of this design procedure required development of the following: a) a microcomputer program for the nonlinear dynamic analysis of reinforced concrete frames subject to strong earthquakes. as presented in Chapter 3; b) design aids to be used in the redesign of the structure if it reached a damage factor. as defined in Chapter 1. greater than 0.5. The microcomputer program ( code name: NC-QUAKE ) is composed of three sub-programs: a) Sub-program.DATA - for input data; b) Sub-program.HAIN - for nonlinear dynamic analysis; c) Sub-program PLOT - for plotting input and output results. Sub-program.MAIN is an adaptation of Program.NACRS-II [28] prepared for use on mainframe computers. The design aids provided herein are to give guidance for redesign Of the structure in order to avoid taking too many 92 trials in order to arrive at an appropriate design. In the first group. Figures (4.1) to (4.20). diagrams are constructed that give values of curvature ductility of a section as a function of the longitudinal reinforcement percentage and.the confinement steel percentage. In the second group. Figures (4.22) to (4.29). the relationship between the displacement ductility of a structure . and ”DI curvature ductility of a section. was determined for U¢I reinforced concrete frames Of one-bay ranging from 3 to 10 stories subjected to the 1940 El Centro (NS) earthquake. O. 2 Concluding Remarks This study has demonstrated that microcomputers can make available to the designer of "ordinary" reinforced concrete structures highly sophisticated tools of analysis that has heretofore been limited. because of economic reasons. to “special” structures. This study has also attempted to extend the use of the analytical tool for the design procedure by introducing a "proof test" step in the process. A key point in the design procedure is the choice of the "proof test" ground motion. Several questions may be raised such as: what type of motion (El Centro . Taft. or generated artificial earthquakes). what amplification factor if different than 1.0. What duration of the ground motion. Of course. such questions are also faced now by designers Of 93 "special“ structures. The kinds of considerations that may be needed for choice of test ground motion have been pointed out in Section 2.5 - Selection of Design Earthquake. Obviously some standardization at the local or regional level (microzonation) would be highly desirable. This is perhaps the most important "link" that needs to be strengthened in the proposed design procedure. Studies of this type need a synthesis of expertise from seismology. geology. geotechnical and structural engineering. The first group of design aids are based on material properties and structural mechanics. and therefore are "exact". Their usefulness as design aids are direct in limdting the choices of variations of parameters in the design procedure. As regards the second group. they were based on only one-bay frames and one ground motion(1940 El Centro NS). Their usefulness is limited to providing a reference or a rough guide for choosing the curvature ductilities. Of course the ”soundness" of a design will always be checked by the analysis. FromIthe structural engineering point of View, further studies may include: a) shear walls - many realistic reinforced concrete buildings contain shear walls in addition to a ductile moment frame. It is not appropriate to model such.structural walls using the mathematical model presented in Appendix A. Therefore. it would be very b) C) 94 useful if a reinforced concrete shear wall element. which could accurately simulate the behavior under seismic loads. be developed and included in the uncrocomputer program. variation of axial force - in the present analysis. member axial forces were considered to remain constant throughout the response. leading to a constant geometric stiffness matrix to approximate the P- A effect. A more realistic analysis that considers the effects of variable axial forces would enable the analysis to include the possibly important effects of vertical ground motion. the structures considered.herein were limited to plane frames. Although.they have a wide range of applicability. there are circumstances for example. asymmetric structural framing. for which the three dimensional space behavior beyond the linear range of the members needs to be considered. This would be a most challenging task for further research. LIST OF REFERENCES 95 LIST OF REFERENCES Aoyama. H.. Simple Nonlinear Models for the Seismic Response of Reinforced Concrete Buildings. U.S.- Japan Cooperative Research Program in Earthquake Engineering with Emphasis on the Safety of School Buildings, August 1975. pp. 291-309. Applied Technology Council. Tentative Provisions for the Development of Seismic Regulations for Buildings. National Science Foundation Publication 78-8. NBS Special Publication 510. U.S.Dept. of Commerce. Washington. D.C.. June. 1978. Aranda H.G.R.. Ductility Demands for Reinforced Concrete Frames Irregular in Elevation.Proceedings.Eighth World Conference of Earthquake Engineering. San Francisco. California. U.S.A.. Section 6.3, Vol.IV. 1984, pp. 559- 566. Arnold.P.. Adams.P.F. and Lu.L.W.. Strength and Behavior of an Inelastic Hybrid Frame. Journal of the Structural Division. ASCE. Vol.94, No. 8T1. January. 1968. pp. 243- 266. Atalay.M.B. and Penzien.J.. The Seismic BehaVior of Critical Regions of Reinforced Concrete Components as Influenced by Moment. Shear and Axial Force. Earthquake Engineering Research Center. Report No.EERC 75-19. University of California. Berkeley. December, 1975. A212. T.S.. Inelastic Dynamic of Building Frames. Publication No. R76-37. Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge. August 1976. Bertero.V.V..State of the Art and Practice in Seismic Resistant Design of Reinforced Concrete Frame-Wall Structural Systemm.Proceedings, Eighth World Conference of Earthquake Engineering. San Francisco. California. U.S.A.. Section 7.2. Vol.V. 1984. pp. 613-620. Bertero. V.V.. Herrera, R.A.. and Mahin. S.A.. Establishment of Design Earthquakes - Evaluation of Present Methods. Proceedings International Symposium.on Earthquake Structural Engineering, August 1976. pp. 551- 580. 10. 11. 12. 13. 14. 15. 16. 17. 18. 96 Bertero,V.V. and Nahin,S.A.. Prediction of Nonlinear Seismic Building Behavior. Journal of the Technical Councils. ASCE. Vol.104, November, 1978. pp. 21-37. Blume .J.A..Redundancy and Relative Earthquake Resistance of Tall Buildings. Proceedings, Eighth.World Conference of Earthquake Engineering. San Francisco. California, U.S.A.. Section 7.1. Vol.V, 1984. pp. 403- 409. Boukamp.J.G..Neuss.C.F. and Maison.B.F.. A Study of Computer Modeling Formulation and Special Analytical Procedures for Earthquake Response of Multistory Building. Technical Report to the National Science Foundation, Berkeley. January. 1983. Clough. R.. I.L. Benuska, and E.L. Wilson, Inelastic Earthquake Response of Tall Buildings. Proceedings. Third World Conference on Earthquake Engineering. New Zealand. 1965. Vol. II, Session II. PP. 68-89. Clough. R.W., and Johnston. S.B.. Effect of Stiffness Degradation on Earthquake Ductility Requirements. Proceedings of Japan Earthquake Engineering Symposium. October 1966. Culver. 0.0.. Lew. H.S.. Hart. 0.0. and Pinkman C.W., Natural Hazards Evaluation of Existing Buildings. National Bureau of Standards, Building Science Series 61. January 1975. Driscoll,G.C.. Lehigh.Conference on Plastic Design of Multistory Frames - A Summary. Engineering Journal. A180. 3. No.2. April. 1966. Filippou.F.C. and Popov.E.P.. Hysteretic Behavior of Reinforced Concrete Beams and Joints. Proceedings, Eighth.World Conference of Earthquake Engineering. San Francisco, California, U.S.A.. Section 7.4, Vol.V, 1984, pp. 821-828. Fintel. Mark. Lessons Learned from Past Earthquakes Concerning Multistory Reinforced Concrete Buildings Presented by Concrete Reinforcing Steel Institute. Southfield. Michigan. May 1986. Giberson. M.F.. The Response of Nonlinear Multi-Story Structures Subjected to Earthquake Excitation. thesis submitted to the California Institute of Technology at Pasadena in partial fulfillment of the requirements of the degree of Doctor of Philosophy. 1967. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 97 Goel.S.C. . P-A and Axial Column Deformation in Aseismic Frames. Journal of the Structural Division. ASCE. Vol.95, No.ST8. August. 1969. pp. 1693-1717. Heidebrecht. A.C.. S.L. Lee. and J.F. Fleming. Dynamic Analysis of Elasto-Plastic Frames. Journal of the Structural Division. ASCE. Vol. 90. No. 8T2. April 1964. pp. 315-343. International Conference of Building Officials. Uniform Building Code. 1982. Jagmohan.H.. Seismic Response of Reinforced Concrete Frames. Journal of the Structural Division . ASCE. Vol.107. No.7. July. 1981. pp. 1215-1232. Jennings.P.C.. Housner.G.W.. and Tsai.N.C.. Simulated Earthquake Motions. Report to the National Science Foundation. California Institute of Technology. April 1968. Kanaan.A.E. and Powell.G.H. DRAIN-2D - A General Purpose Computer Program.for Dynamic Analysis of Inelastic Plane Structures. Report No. EERC 73-6 and EERC 73-22. University of California. Berkeley. April 1973. Revised September 1973 and August 1975. Keshavarzian,M. and Schonobrich.W.C.. Analytical Model for the Nonlinear Analysis of Reinforced Concrete Structures. 1983 Annual Convention . ACI. Los Angeles. California. March. 20-25. Neshavarzian.M. and Schonobrich.w.0.. Computed Nonlinear Seismic Response of Reinforced Concrete Wall-Frame Structures. Structural Research Series. Civil Engineering Studies. University of Illinois. Urbana- Champaign. Ill.. No.515. May 1984. Kikichi.K. and Yoshimura.K.. Effect of Vertical Component of Ground Motions and Axial Deformation of Columns on Seismic Behavior of Reinforced Concrete Building Structures. Proceedings. Eighth World Conference of Earthquake Engineering. San Francisco. California. U.S.A.. Section 6.3. Vol.IV. 1984. pp. 599- 606. Meyer.0. and Roufaiel.M.S.L.. Analysis of Damaged Concrete Frames Buildings. Technical Report to the National Science Foundation. Columbia University in the City of New York. May. 1983. Mcniven.H.D. and Stanton.J.F.. Towards an Optimum Model for the Response of Reinforced Concrete Beams to Cyclic 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 98 Loads. Earthquake Engineering and Structural Dynamics. Vol.11. pp. 299-312. 1983. Newmark. N.M.. and Hall. W.J.. Procedures and Criteria for Earthquake Resistant Design. National Bureau of Standards. Building Science Series 46. February 1973. Otani. S.. SAKE - A Computer Program for Inelastic Response of Reinforced Concrete Frames to Earthquake. Structural Research Series. Civil Engineering Studies. University of Illinois. Urbana-Champaign. Ill.. No.413. 1974. Otani.S.. Hysteresis Models of Reinforced Concrete for Earthquake Response Analysis. Proceedings. Eighth World Conference of Earthquake Engineering. San Francisco. California. U.S.A.. Section 6.3. Vol.IV. 1984. pp. 551- 558. Park. R. and Paulay.T. . Reinforced COhCPEtB Structures. by John Wiley & Sons.Inc.. 1975. Povell.G.H. and Row.D.G.. Influence of Analysis and Design Assumptions on Computed Inelastic Response of Moderately Tall Frames. Report No.EERC 76-11. April. 1976. Earthquake Engineering Research Center. University of California. Berkeley. California. Soleimani.D.. Reinforced Concrete Ductile Frames under Earthquake Loadings with Stiffness Degradation. Ph.D. Dissertation. University of California. Berkeley. December. 1978. Sozen.M.A. and Saiidi.M.. Simple and Complex Models for Nonlinear Seismic Response of Reinforced Concrete Structures. Structural Research Series. Civil Engineering Studies. University of Illinois. Urbana- Champaign. Ill.. No.465. August. 1979. Shibata. A. and Sozen. M.A.. Substitute-Structure Method for Seisuuc Design in Reinforced Concrete. Journal of the Structural Division. ASCE. Vol. 102. 8T1. January 1976. pp. 1-18. Structural Engineers Association Of California. Recomended Lateral Force Requirements and Commentary. SEAOC Seismology Committee. 1980. Takeda. T.. Sozen. M.A. and Nielsen. N.N.. Reinforced Concrete Response to Simulated Earthquakes. Journal of the Structural Division. ASCE. Vol. 96. No. ST12. December 1970. pp. 2557-2573. 40. 41. 42. 99 Tansirikongkol. V. and D.A. Pecknold. Approximate Modal Analysis of Bilinear MDF Systems Subjected to Earthquake. CiVil Engineering Studies. Structural Research Series. No. 449. University of Illinois. Urbana. August 1978. Wen. R.K.. and J.G.. Janssen. Dynamic Analysis of Elasto-Inelastic Frames. Proceedings. Third World Conference on Earthquake Engineering. New Zeland. January 1965. Vol. II. pp. 713-729. Wiggins. J.H.. Jr. and Moran. D.F.. Earthquake Safety in the CitY Of Long Beach Based on the Concept 0f Balance Risk. J.H. Wiggins Company. Redondo Beach. California. September 1971. APPENDIX A THE MATHEMATICAL MODEL APPENDIX A THE MATHEMATICAL MODEL A.1 Introduction The purpose of this appendix is to present the essential features of the mathematical model for the inelastichysteretic behavior of reinforced concrete members used in the analysis program. As mentioned previously the model was that proposed by Meyer and Roufaiel[28] which is a modified version of the Takeda model. The modification includes accounts of the effects of the finite size of the plastic regions as well as the axial and shear forces. The accuracy of the model was demonstrated in [28] by analyZing numerous members and structures. The results showed that the model is very effective in predicting the cyclic nonlinear behavior of reinforced concrete frame members. The model requires the specification of only a few material properties of steel and concrete in order to simulate the complete 1381183101“ under CYCIIC loads. TOO 101 A.2 Material Constitutive Laws A.2.1 Reinforced Steel The stress-strain curve for steel is shown in Fig.(A.1). The bilinear curve consists of an elastic part where 37 (A. 1) and an iflQlfiSth part With strain hardening ratio f f _ su sy. 1 ps. 6 - e E ”‘2’ su 8? S where fsy and £8? are the yield stress and strain respectively. fan is the ultimate stress. and esu is the strain at ultimate stress. A.2.2 Concrete The proposed stress-strain curve for confined concrete (confined by transverse or hoop steel). Fig.(A.2) may be completely determined DY specifying the following three parameters: 1) uniaxial strength of plain (unconfined) concrete. fc; 102 2) strain at fc. €03 3) volumetric ratio 0f confinement Steel given DY ua 3(b.+ d”)A p: n n (A. 3) b -d -S S where b and d are the width.and depth 0f the confined core. A8 18 the hoop Steel cross-sectional area. and S is the hoop steel spacing. F18.(A.3). Initially A”s 18 equal to the shear reinforcement (stirrups) determined for the member in the preliminary design phase. Referring to Fig. (A.2). the Parameters that define the stress-strain curve are related to the preceding three basic parameters as fOllOWS: fcu : ac fc (A 4) ecu = cc 60 (A 5) 2 fcy ‘ 3 fcu (A 6) e - 1 E (A 7) cy ' 3 cu ' Gm, : BC ch (A 8) where ac and BC are factors which.account for the confinement steel effect on concrete strength and ultimate 103 strain. respectively. These factors are determined from the empirical expressions. a 1 + 10 p" (A.9) c 8c 2 + 600 p" (A.10) The cut-off pOint of the unloading branch. 0.2 fcu is chosen empirically. A.3 Primary Moment-Curvature Relationship The primary moment-curvature relationship of a beam section can be derived using conventional reinforced theory only. A typical primary moment-curvature curve is shown in Fig. (A.4). The bending moment Mm is associated With the curvature 7m at WhiCh the concrete strain reaches the crushing strain Gm. Thus. the primary moment-curvature relationship is valid up to the crushing 0f the concrete cover at which.point the section is regarded as having failed. A.4 Hysteretic Behavior of Reinforced Concrete Under load reversals. the stiffness of a reinforced concrete member changes due to the cracking 0f the concrete and debonding effects at the steel-concrete interface. In 104 the computer program. a modified Takeda-type model is used to represent hysteretic moment-curvature relationships. Fig.(A.5). The model has five basic branch types. 1- Elastic loading and unloading; 2- Inelastic loading; 3- Inelastic unloading; 4- Inelastic reloading during closing of cracks in which the "pinching effect” is considered.( to be described in section A.5) 5- Inelastic reloading after closing of cracks. In branches 1 and 2 the stiffnesses are: (EI)1 : (EI)e ( elastic range ) and (EI)2 = p (Elle In order to compute (EI)3 for branch 3 define. MI. I: - maXimum moment and curvature reached. in the positive direction during the current load cycle. M;. e; - maximum.moment and curvature reached in the previous load cycles in the negative direction. It follows that. M = p -( ¢I(EI)1 - u*) (A.11) 0 1 - p 1 + 1 + H1 773" ’1 ' raw “'1’“ ‘o. O I 105 in which the point (no. ’0) is on a line drawn from ( MI. fl) parallel to branch 1. M- - u if = f 0 (A. 13) 7x - ’0 M g; : ’0 - -:g- (A.14) (EI) "I (EI)3 : ’+ - ’+ (A.15) 1 r The definitions of (EI)4 and (EI)5 are based on the pinching effect as described in the next section. A.5 Shear Effect on Hysteretic Behavior In a reversed loading cycle. preViously opened cracks tend to close. leading to an increase in stiffness and the characteristic "pinched” shape of the moment-curvature curve. Experimental work indicated that when the maximum nominal shear stress. vmax’ is less than 3.5 r f’cthe hysteresis loops would be stable. When v is greater than 3.5 r f’c . stiffness degradation would result in "pinched” load-deformation curves. In order to include this effect in the mathematical model. the stiffness of a section is assmmed to be represented DY two straight line segments. F18. (A.5). where: 106 (0.¢r) - point of reloading (Mp.¢p) - pinching point (Mx.fix) - point of resumed inelastic loading (Hn’fin) - point of no "pinching" The line segment 4 represents reloading before the closing of shear cracks. The line segment 5 represents reloading after the closing of shear cracks. From Fig.(A.6). we have: if fl : fl (A.15) n r (Eh-(m) e Mn : (EI)e- fin (A.17) where (EI) : ;——:—; x r Introducing a pinching factor. (1p. WhiCh represents the effect of shear stress on the hysteresis behavior and writing. Mp : up Mn (A.18) = a - A.1 7p p fin ( 9) With the empirical equation. Qp:0.4—-d—-0.5 (A.20) where a up - 0 if -E— < 1 5 a = 1 if -2— > 4 107 a shear span( in a typical building frame. a = L/2.) d effective depth.of the beam the pinching effect is now completely defined. A.6 Tangent Stiffness Matrix To compute the tangent stiffness of a general frame member. the element is subdivided into three regions. Fig.(A.7): a) an inelastic region 0f length X1 at node 1. having the average stiffness (ET)1: b) an inelastic region of length x at node J. having the .1 average stiffness (EI)J; c) a central region of length (L - x1 - xJ). hav1ng the initial elastic stiffness (EI)e. 108 For the six planar degrees of freedom identified in Fig.(A.7). the tangent stiffness of this frame element can be written as x11 0 0 x14 0 0 K22 R23 0 K25 K26 K33 0 K35 K36 [Xe] : synm. 1 “44. 0 0 K55 K56 K66 the coefficients _ EA K11 ' K44 ‘ 'K14 ‘ L are assumed to remain constant. K33. K36. K65 are Obtained from their flexibility. which.can be computed DY integrating the moment-curvature expression over the entire length 0f the member. Defining (EI)e Qi : :- (A.21) (EI)1 (EI)e Q = _ (A.22) J .— (I)J the stiffness ratios for the end of the regions 1 and J. the flexibility coefficients are given DY 109 f11 = ———1———§[(oJ-1) x: - (01-1) (L-x1)3+ Q1L3] (A.23) 3(EI)eL fJJ :-———l———§[(ol-1) x: - (01-1) (L-xJ)3+ QJLBJ (A.24) 3(EI)eL f - 1 [(o -1) x2 (1 6 L - x ) + 1J 3(EI) L8 J J J e + (Q -1) x2 (1 6 L - x ) + L3/2] (A.25) 1 1 ‘ 1 Then for stiffness coefficients. x = f / ( f f - £2 ) (A.26) 33 JJ 11 JJ 1J k = f / ( f f - fa ) (A 27) 66. 11 11 JJ 1J ' k - - f / ( f f - £3 ) (A 28) 36 ‘ 1) 11 JJ 11 ° and the remaining coefficients follow from statics. K23 : - K35 : ( K33 + K36 ) / L (A.29) K26 : - K56 : ( K36 + K66 ) / L (A.30) 2 K22 - K55 - - K25 - ( K33 + 2 K36 + K66)/L (A.31) The length x and stiffness ratio 01 of the plastic region 1 at node i depend on the current branch of the moment- curvature diagram. For the initial elastic loading and unloading the member end WhiCh has not experienced any inelasticity. 31 is taken as zero and 01 equal to one. For inelastic loading the length 0f the plastic region is determined DY 110 x = 1 -L (A. 32) assuming that moments vary linearly along the beam length. For inelastic unloading. x1 will be assumed to remain the maximum plastic region length reached in all the previous inelastic loading cycles. A.7 Axial Load Effect The effect of gravity loads on story shear and moment through the lateral story displacement was considered in the program. This phenomenon. known as the P-A effect. is considered using the usual geometric stiffness matrix for the beam.member. As mentioned previously. the axial load is assumed to remain constant and equal to the grav1ty load effect present at the beginning 0f the ground motion. A.8 Strength Degradation During Cyclic Loading Under load reversals. not only the stiffness of a reinforced concrete member decreases. but also its strength deteriorates if the member is strained beyond a certain critical load level. Then. the maximum.load required to deform.the member to a given level of deformation decreases. Strength degradation and the corresponding critical load are 111 functions of several variables. such as the degree of confinement and the value of axial force. Experiments have indicated that [28] the strength degradation commences when the concrete cover reaches the failure strain em. as defined in Equation (A.8). The terminal point (Mm.¢m) of the moment-curvature curve. Fig.(A.4). had been defined as the point associated with the curvature at which the concrete strain reaches the value em. It is also observed that once the concrete strain Gthas been exceeded members would fail after only a very few cycles. Therefore. for practical purposes. the curvature associated With Em is defined as the point Of failure. That is. the small amount Of energy that would be dissipated in those few cycles is ignored in the model. A.9 Damage Factor The damage factor is defined as H ¢ m x -— for M > M H! fim x y damage factor : = 0 for Mx < MY where l‘ly is the yield moment of the member section (Fig.(A.8)). This factor represents the ratio between the secant stiffness at the point Of failure. and the minimum 112 secant stiffness. reached during the response. The value of damage factor equal to zero indicates that deformations have remained elastic and there is no damage. The value of damage factor equal to 1.0 indicates that the member has been loaded to the point of failure. A.10 Equations of Motions The equation Of motion Of a structure can be written in the matrix form as: n 96 + c 96 + x 90 = - u 951'‘ (A.33) where M. C. K are respectively. the structure mass. damping. and tangent stiffness matrices. The symbol Q is used here to denote increment instead of the usual symbol . Thus. QU. 96 . 96 are the incremental nodal displacement. Velocity and acceleration vectors relative to the ground. and 9&8 is the incremental ground acceleration. Using the usual assembly procedure. the structure stiffness matrix is assembled from the element stiffness matrices described in previous sections. The numerical integration technique of solving the equation of motion used was Newmark's Beta method for ' average acceleration ( Beta:1/4 )'. It is unconditionally stable for linear systems and becomes unstable only when overly large time steps are used for the analysis Of nonlinear problems. The 113 incremental velocities and displacements over a short time step are calculated from.the following equations. QU fin 9t + 1/2 96 9t (A.34) QU on 9t + 1/2 Un(9t)a + 1/4 (9t)29fi (A.35) in which 9U. 9U. 96 are change of horizontal displacement. velocity. and acceleration vectors relative to the ground motion between time step "n" and "n+1” and Un. u are velocity and acceleration vectors relative to the ground motion at the end of step "n”. Equation (A.35) can be solved to calculate the corresponding incremental acceleration: 4 (s21)(2 QM = e O. 2 '[QU - Un Qt - 1/2 Un (Qt) ] (A.35) Substituting. equation (A.36) into Equation (A.34) gives: ‘ _ 2 av ' Qt I - Q .0 a [QU Un Qt + 3/2 Un (Qt) (A.37) Substituting. equation (A.36) and Equation (A.37) into the equation of motion and re-arranging the terms yields: 1 1 9U 1 = [ A 1‘ 1 B 1 (A.38) in which. A : 4 “a + a C + K (A.39) (9t) 9t 3 = M (5%— Un + a fin — 9X‘) + + 2 C (Un - 3/2 Un Qt) (A.40) 114 From Equation (A.38) the incremental displacement can be obtained. Then the corresponding incremental velocity and acceleration vectors are given DY Equation (A.37) and Equation (A.36). STRESS 115 IDEALIZED SY esu STRAIN Fig.(A.1)- Steel stress-strain curve .2f CU cu 116 IDEALIZED CONFINED /’ ‘“\ //Z \ UNCONFINED / / /' pc Bo. \ / \ \ / \ ‘x \ .. A/ \ \ PC E / \ \ / \ \ / \ \ , \ 1:. c \\ say 6 cu STRAIN Fig.(A.2)- Adopted stress-strain curve for concrete 117 / / I 1 AR A”s (Spacing ”8”) ///' dll X¥\X.\\ Fig.(A.8) - Cross-Sectional Confined Area 118 ACTUAL MOMENT C U RVATU RE Fig. (A. 4) - Primary moment-curvature relationship for a beam section 119 120 Fig.(A.6)- Pinched reloading curve 121 ''''''''''''''''''''''''''' "(765' (61 MJ (E_I )J F)g.(A.7)- Frame Member Model 122 Fig. (A. 8)- Damage Factor APPENDIX B EXAMPLE PROBLEM OF DYNAMIC ANALYSIS m) Ce' US ca 28 123 APPENDIX B EXAMPLE PROBLEM OF DYNAMIC ANALYSIS A three-story one-bay frame was analyzed by the program. The accelerations values of the first 12 secs of the 1940 El Centro (NS) record were amplified by a factor of one. and used as the base motion of the structure. The analysis was carried out at every 0.02 sec. The total execution time was 28 minutes on an IBM Personal Computer. I NPUT DATA 124 iif§l§§i§§§§§§§§lf§i§§§fifiiiiifif{fiiifiifiiffiiifi 1 1 1 NONLINEAR ANALYSIS OF REINFORCED CONCRETE 1 1 1 1 STRUCTURES * 1 1 1 DYNANIC ANALYSIS 1 1 1 1111111111111111111111111111111111111111111111111111 * INPUT DATA PROSRAN 1 1111111111111111111111111111111111111111111111111111 i by 1 1 Aecio Freitas Lira ! §{§§§{§{§§§§O{§§§§l§§§§§§§5859895§§§§iiefi{iiiiill}! NOTE FOR CORRECTING DATA: 111111111111111111111111 (I) NEN DATA : TYPE THE NUNBER IN OETNEEN I l (I) CORRECT DATA : TYPE THE VARIABLE NUNOER IN BETNEEN I I : USE OPTION 2 : LIST DATA TO OBTAIN TNE VARIABLE NONBER. 11111111111111111111111111111111111111111111111111 125 INPUT DATA FILE NAHE =EXAHPLE INPUT DATA OPTION 0: NEN DATA 1: CORRECT DATA 2: LIST DATA 3: END =0 TYPE THE TITLE OF THE PROBLEH : EXAHPLE FOR DISSERTATION 1111111111111111111 GENERAL INFORNATION 1111111111111111111 (lllll NUMBER OF NODAL POINTS=8 (ZTIZJ NUNDER OF CONTROL NODEG FOR X-Y GENERATION=4 (3)I3l NUNBER OF NODE GENERATION COHNANDS=2 (4)14] NUNBER OF IERO DISPLACEHENTS CONNANDS=2 (6)16] NUMBER OF HASS GENERATION COHHANDS=I (7)17] DATA FOR CHECKING ONLY I: RUN 1: CHECK ONLY =0 ARE ALL THE DATA CORRECT (YIN) [Y]?: Y 126 1111111111111111111111111 CONTROL JOINT COORDINATES 1111111111111111111111111 TOTAL NUMBER OF CONTROL COMMANDS: 4 CONTROL COMMAND NUMBER= I ( IBlIIIl NODE NUMBER = l I lI)[IIl X-COORDINATE = I ( 12)[121 Y-COORDINATE = 49' ARE ALL THE DATA CORRECTTY/N) IY]?: Y CONTROL COMMAND NUMBER: 2 ( l3lIlBl MODE NUMBER 3 2 ( IAIIlIl I-COORDINATE 8 25B 1 151(12] Y-COORDINATE 8 400 ARE ALL THE DATA CORRECTIY/N) [Y]?: Y CONTROL COMMAND NUMBER8 3 ( lb)[lll NODE NUMBER = 7 ( 17)[Ill X-COOROINATE = O ( 181(121 Y-COORDINATE = I ARE ALL THE DATA CORRECTTY/N) IYl?: Y CONTROL COMMAND HUMBER= A I IRIIIBJ MODE NUMBER 3 O I ZBlllll I-COORDINATE 3 25. I 211112] Y-COORDINATE 8 O ARE ALL THE DATA CORRECTIY/N) [Y]?: Y 127 111111111111111111111111 NODE GENERATION COMMANDS 111111111111111111111111 TOTAL NUMBER OF CONTROL COMMANDS= 2 CONTROL COMMAND NUMBER= I I 22)II3] FIRST NODE NUMBER = I I 231114] LAST MODE NUMBER = 7 I 241(151 NUMBER OF NODES TO BE GENERATED=2 I 251116] DIFFERENCE BETNEEN TNO SUCESSIVE NODES=2 ARE ALL THE DATA CORRECTIY/N) [Y]?: Y CONTROL COMMAND NUMBER8 2 I 26IIl3l FIRST NODE NUMBER = 2 I 271(14] LAST NODE NUMBER = B I 281115] NUMBER OF MODES TO BE GENERATED=2 I 291(161 DIFFERENCE BETNEEN TNO SUCESSIVE NODES=2 ARE ALL THE DATA CORRECTIYIN) [Y]?: Y 128 §§§!§lilffliiiiiiiilliNH)“ ZERO DISPLACEMENTS COMMANDS 111111111111111111111111111 1: FOR FIXED D.O.F. B: FOR FREE D.O.F. TOTAL NUMBER OF CONTROL COMMANDS= 2 CONTROL COMMAND NUMBER= I I 3B)I17] FIRST NODE IN THE GROUP=I I 311118] CODE FOR X-DISPLACEMENT=D I 321I191 CODE FOR Y-DISPLACEMENT=B I 331(201 CODE FOR ROTATION=B I 341121] LAST NODE IN THE SROUP=6 I 351(22] DIFFERENCE BETNEEN TNO SUCESSIVE NODES=I ARE ALL THE DATA CORRECTIY/N) [Y]?: Y CONTROL COMMAND NUMBER3 2 I 361(17] FIRST NODE IN THE GROUP=7 I STIIIBJ CODE FOR I-DISPLACEMENT=1 I 381119] CODE FOR Y-DISPLACEMENT=I I 391(20] CODE FOR ROTATION=I I ABII2Il LAST NODE IN THE GROUP=B I 411(22] DIFFERENCE BETNEEN TNO SUCESSIVE NODES=I ARE ALL THE DATA CORRECTIY/NI [Y]?: Y 129 IHNCONDCCCSSDSNC‘INDSNI’} MASS GENERATION COMMANDS 111111111111111111111111 TOTAL NUMBER OF CONTROL COMMANDS= l CONTROL COMMAND NUMBER= I I 42)123l FIRST NODE NUMBER IN THE GROUP=I I 43)[241 I-MASS=B.OGS I IAIIZSI Y-NASS=B.B65 I 45)I26] ROTARY IMERTIA=I I 461127] LAST NODE NUMBER IN THE GROUP=6 I 47)[29] DIFFERENCE BETNEEN TNO SUCESSIVE NODES=I ARE ALL THE DATA CORRECTIY/N) [Y]?: Y 11111111111111111 LOAD CONTROL DATA 11111111111111111 INPUT NUMBER OF NODAL STATIC LOAD COMMANDS=2 FIRST MODE MUMBER=I FORCE IN THE X-DIR.=D FORCE IN THE Y-DIR.=-25.B MOMENT =ID67.I LAST MODE NUMBER=5 DIFF. BETNEEN NODES=2 FIRST NODE NUMBER=2 FORCE IN THE I-DIR.=I FORCE IN THE Y-DIR.=-25.B MOMENT =-IB67.I LAST MODE NUMBER=6 DIFF. BETNEEN MODES=2 . 130 I 481129] GRAVITY ACCELERATION =384 I 49)I3Dl NUMBER OF INTEGRATION STEPS FOR DYNAMIC ANALYSIS =GBO I SBIISI] INTEGRATION TIME STEP SIZE=0.02 I SIII32] FACTOR TO BE APPLIED TO GROUND ACCELERATION RECORD IN THE HORIZONTAL DIRECTION =I.O I SZIIIS] FACTOR TO BE APPLIED TO TIME COORDINATE ACCELERATION IN THE X-DIR. =I.O I 551136] ABS. VALUE OF THE MAX. DISPLACEMENT=SO ARE ALL THE DATA CORRECTIY/N) [Y]?: Y 131 1111111111111111111111111111111111111111111111111 EARTHQUAKE ACCELERATION CONTROL - DAMPING FACTORS 1111111111111111111111111111111111111111111111111 '\ 561137] NUMBER OF TIME-GROUND ACCELERATION PAIRS DEFINING THE HORIZONTAL DIRECTION INPUT =22B A SBII39] CODE FOR PRINTING ACCELERATION AS INPUT: I DO NOT PRINT ACCELERATION RECORD I PRINT ACCELERATION RECORD =O A 591140] NUMBER OF STEPS TO SKIP NHEN PRINT=I A GBIIAIl TITLE TO IDENTIFY RECORD 1 ELCENTRO : CALTEC I : CALTEC 2 : CALTEC 3 : CALTEC 4 3 u. CALTEC 5 TAFT SAN FERNANDO OTHER =1 QQNO~M%HN I GIIIAZJ MASS PROPORTIONAL DAMPING FACTOR: ALPHA =B.397 I 62)I43] TAMGENT STIFFNESS PROPORTIONAL DAMPING: BETA =B.OBBGG ARE ALL THE DATA CORRECTIY/N) IYI?: Y 11111111111111 OUTPUT CONTROL 11111111111111 I GAIIASI NUMBER OF NODES I-DISPLACEMENT IS REDUIRED=I ARE ALL THE DATA CORRECTIYIN) IY]?: Y *“NHNNHI’GMCEHIEECDNMINSNDENNIIEANINHNARE LIST OF MODES FOR X-DISPLACEMENT TIME HIGTORIES 11111111111111111111111111111111111111111111111 TOTAL NUMBER OF MODES FOR X-DISPLACEMENT= 1 INPUT NUMBER= I I SGIIABI SPECIFY 'NHOUT' NODE NUMBER=I IS THE DATA CORRECTIYINI [Y]?: Y 11111111111111111111 BEAM ELEMENT CONTROL 11111111111111111111 I TOIISSI NUMBER OF MEMBERS IN THE STRUCTURE=9 I 71)I54] REINFORCING STEEL PROPERTY TYPES=I I 721(551 NUMBER OF CONCRETE PROPERTY TYPES=2 ARE ALL THE DATA CORRECTIY/N) [Y]?: Y 1111111111111111111111111111 REINFORCING STEEL PROPERTIES 1111111111111111111111111111 STEEL PROPERTIE NUMBER= I I TSIISGJ MODULUS OF ELASTICITY=29OBB I TAIISTI STRAIN HARDENING RATIO=O.BI I TSIISB] YIELD STRESS=GB I TGIISVI ULTIMATE STRAIN=B.BIS ARE ALL THE DATA CORRECTIY/N) IY]?: Y 133 11111111111111111111 CONCRETE PROPERTIES 11111111111111111111 CONCRETE PROPERTIE NUMBER= I I 77IIGBl CONCRETE STRENGTH: Fc=3 I TGIIGII STRAIN AT MAXIMUM STRESS: Eo=0.002 I 79)IG2] CONFINEMEMT RATIO: RO=B.BBB ARE ALL THE DATA CORRECTIY/N) [Y]?: Y CONCRETE PROPERTIE NUMBER= 2 I BBIIGBl CONCRETE STRENGTH: Fc=3 I BIIIGIl STRAIN AT MAXIMUM STRESS: E0=B.BB2 I BZIIGZI CONFINEMEMT RATIO: RO=B.BBB ARE ALL THE DATA CORRECTIYIN) IYI?: Y 134 11111111111111111 MEMBER PROPERTIES 11111111111111111 I BSIIGSl MEMBER NUMBERINEGATIVE VALUE FOR SYMMETRIC SECTION) =-I I BAIIGAI NODE NUMBER AT END OF THE MEMBER=I I 851165] NODE NUMBER AT THE OTHER END=2 I BG)IGS] STEEL TYPE NUMBER: IF THIS VALUE IS ZERO ALL THE INFORMATION EXCEPT NODE NUMBERS HILL BE THE SAME AS THE PRECEDING ELEMENT =I I BTII67] CONCRETE TYPE NUMBER=I ARE ALL THE DATA CORRECTIY/N) [Y]?: Y 11111111111111111111111111 CROSS SECTIONAL PROPERTIES - MEMBER NUMBER= I 11111111111111111111111111 I 89)I691 MAGNITUDE OF AXIAL LOAD DUE TO GRAVITY=B I SBIITBI ' HT ' IHEIGHTI=3B I 9I)I7Il ' BB ' INIDTH-BOTTOM)=IB I 921172] ' DCB 'ICOVER-BOTTOMI=3 I 931I73] ' ASB 'IREINF.-BOTTOM)=2.4 ARE ALL THE DATA CORRECTIY/NI [Y]?: Y 135 11111111111111111 MEMBER PROPERTIES "1111111111111" ( 97) 1131 m mmmsmvs mus son svmsmc sscnmu =-2 I 9111141 no»: mm AT sun or me MEMBER=3 I 991155) me NUMBER AT ms omen mm (11mm 51551 ms sums: . IF ms mu: IS 2110 ALL n1: 1110111110): EXCEPT none NUMBERS 1111 as we sent as me mesons £12151: =1 ARE ALL THE DATA CORRECTIYINI [Y]?: Y 136 "1111111111111" MEMBER PROPERTIES 11111111111111111 (IIIIISST HEMBER MUMBERINESATIVE VALUE FOR SYHMETRIC SECTION) =-3 (IIZIIAAI NODE NUMBER AT END OF THE HEMDER=5 (II3)[65] MODE NUMBER AT THE OTHER END=6 (IIAIIbbl STEEL TYPE NUMBER: IF THIS VALUE IS ZERO ALL THE INFORMATION EXCEPT NODE MUNIERS MILL BE THE SAME AS THE PRECEDINB ELEHENT =0 ARE ALL THE DATA CORRECTIY/HI [Y]?: Y 137 11111111111111111 MENBER PROPERTIES 11111111111111111 (125)I63I NEMBER NUMBERINESATIVE VALUE FOR SYMMETRIC SECTION) =-4 IIZGIIAAI NODE NUMBER AT END OF THE MENBER=5 (IZTIIBSI NODE NUNBER AT THE OTHER ENO=7 (IZOTIAAI STEEL TYPE NUMBER: IF THIS VALUE IS ZERO ALL THE INFORMATION EXCEPT NODE NUMBERS HILL BE THE SAME AS THE PRECEDINB ELEMENT =1 (IZBII67I CONCRETE TYPE NUNBER=2 ARE ALL THE DATA CORRECTIY/N) [Y]?: Y 11111111111111111111111111 CROSS SECTIONAL PROPERTIES - HENBER NUMBER= 4 11111111111111111111111111 (ISIII69I MASNITUDE OF AXIAL LOAD DUE TO SRAVITY=75 (132)?!“ ' HT ' (IEISHTPZB (I33IITII ' BB ' INIDTH-BOTTOMT=2B (ITAIITZI ' DCB '(COVER-BOTTON)=2 (135II731 ' ASB '(REINF.-BOTTOM)=2 ARE ALL THE DATA CORRECTIY/NI [Y]?: Y 138 {flifllI’MD‘lD‘li‘l MEMBER PROPERTIES 11111111111111111 (139)I63] MEMBER NUMBER(NEBATIVE VALUE FOR SYMMETRIC SECTION) =-5 (IABIIAAI NODE NUMBER AT END OF THE MEMBER=6 (IAI)I65] NODE NUMBER AT THE OTHER END=8 I142)I66] STEEL TYPE NUMBER: IF THIS VALUE IS ZERO ALL THE INFORMATION EXCEPT NODE NUMBERS HILL BE THE SAME AS THE PRECEDINS ELEMENT =B ARE ALL THE DATA CORRECTIY/N) IYI?: Y 139 11111111111111111 MEMBER PROPERTIES 11111111111111111 (153)[631 MEMBER NUMBERINEBATIVE VALUE FOR SYMMETRIC SECTION) =-6 (ISAIIBAI NODE NUMBER AT END OF THE MEMBER=3 (ISSIIBSI NODE NUMBER AT THE OTHER END=5 (ISAIIbbl STEEL TYPE NUMBER: IF THIS VALUE IS ZERO ALL THE INFORMATION EXCEPT NODE NUMBERS HILL BE THE SAME AS THE PRECEDINS ELEMENT =1 (ISTIIBTI CONCRETE TYPE NUMBER=2 ARE ALL THE DATA CORRECT(Y/N) [Y]?: Y 11111111111111111111111111 CROSS SECTIONAL PROPERTIES - MEMBER NUMBER= b 11111111111111111111111111 {ISBTIBBI MAGNITUDE OF AXIAL LOAD DUE TO BRAVITY=JD (IGOIITBI ' HT ' IHEIBHT)=ZB (IbI)ITII ' BB ' (NIDTH-BOTTOM)=2B (I62II721 ' DCB '(COVER-BOTTOM)=2 (163)I73] ' ASB '(REINF.-BOTTOM)=2 ARE ALL THE DATA CORRECTIYIN) [Y]?: Y 140 {fliffli’i‘l’ilfl’ifl MEMBER PROPERTIES 11111111111111111 (167)I63] MEMBER NUMBERINEBATIVE VALUE FOR SYMMETRIC SECTION) =-7 LIABIIBAI NODE NUMBER AT END OF THE MEMBER=I (IBBIIBSI NODE NUMBER AT THE OTHER END=6 IIZBIIAAI STEEL TYPE NUMBER: IF THIS VALUE IS ZERO ALL THE INFORMATION .EXCEPT NODE NUMBERS NILL BE THE SAME AS THE PRECEDINB ELEMENT =D ARE ALL THE DATA CORRECTIY/N) IYI?: Y 141 EH§§I§§§§!A§§§N MEMBER PROPERTIES 11111111111111111 (IBIII63T MEMBER NUMBERINESATIVE VALUE FOR SYMMETRIC SECTION) =-B (IBZTIAAI NODE NUMBER AT END OF THE MEMBER=I IIBS)[65] NODE NUMBER AT THE OTHER ENO=3 IIBAIlbbl STEEL TYPE NUMBER: IF THIS VALUE IS ZERO ALL THE INFORMATION EXCEPT NODE NUMBERS NILL BE THE SAME AS THE PRECEDINB ELEMENT =1 (IBSIISTI CONCRETE TYPE NUMBER=2 ARE ALL THE DATA CORRECTIY/N) [Y]?: Y 11111111111111111111111111 CROSS SECTIONAL PROPERTIES - MEMBER NUMBER= 8 11111111111111111111111111 IIB7)I69] MAGNITUDE OF AXIAL LOAD DUE TO SRAVITY=25 IIBBIITBI ' HT ' (HEISHT)=2B (189)ITII ' BB ' (NIDTH-BOTTOM)=ZB IIBBIITZI ' DCB '(COVER-BOTTOM)=2 (IPIIITSI ' ASB '(REINF.-BOTTOM)=2 ARE ALL THE DATA CORRECTIYIN) [Y]?: Y “NH THIN 142 Efllfli‘lilii!“ A! MEMBER PROPERTIES 11111111111111111 (195)I631 MEMBER NUMBERINESATIVE VALUE FOR SYMMETRIC SECTION) =-9 (I96)IAAI NODE NUMBER AT END OF THE MEMBER=2 II?7)I65] NODE NUMBER AT THE OTHER END=4 (IBBIIbbl STEEL TYPE NUMBER: IF THIS VALUE IS ZERO ALL THE INFORMATION EXCEPT NODE NUMBERS HILL BE THE SAME AS THE PRECEDINS ELEMENT =B ARE ALL THE DATA CORRECTIYIN) [Y]?: Y INPUT DATA OPTION 0: NEH DATA 1: CORRECT DATA 2: LIST DATA 3: END OUTPUT RESULTS 143 11111111111111111111111111111111111111111111111111111 DRAIN DYNAMIC RESPONSE ANALYSIS OF INELASTIC STRUCTURES bv Aecio Freitas Lira 1995 an an a no at up an asuu aunt w no in * up an m at an m up DEDOSDDDADDDCDDfiiiiiiiiiiiDiliiiiiliiiifii{iii{A}!!! INPUT FILE DATA NAME =QXAIoIe TOTAL NUMBER OF NODES = O NO. OF CONTROL MODES = 4 NO. OF NODE GENERATION COMMANDS = 2 NO. OF ZERO DISPLACEMENT COMMANDS = 2 NO. OF IDENTICAL DISPLACEMENT COMMANDS 8 O NO. OF MASS GENERATION COMMANDS 8 I DATA CHECKING ONLY = B CONTROL NODE COORDINATES NODE (”WNW X—COORD 0.". 25|.IBO LOGO 25L". Y-COORD IBBJOI IBBJII S.BOI D.A.. NODE GENERATION COMMANDS FIRS T NODE INIDE MODES I 2 LAST NO. OF 7 2 B 2 NODE DIFF 2 2 CINIPLETE NODE COORDINATES NODE DNC‘M-“N“ X-COORD I.“ 23.." LII. 25...“ IJIO 250.0|I I.IBI 250.“. Y-COORD ABA.” TGBJOI 32B.” 32B.“ 16..." 16L“. D.A.. I.BBI DISTANCE 144 145 ZERO DISPLACEMENT COMMANDS FIRST X Y ROTN LAST NODE NODE CODE CODE CODE NODE DIFF I O D O 6 I I I B I EOUAL DISPLACEMENT COMMANDS NONE ID ARRAY IFOR INTEREST) NODE X Y R I I 2 3 2 4 5 6 3 7 B 9 4 IB II I2 5 13 I4 IS 6 I6 I7 IB 7 B B D 8 I I I MASS GENERATION COMMANDS ms: 1: ' v 1111 1111 MASS mass mass 1 1.1511141 1.1511141 1.1111911 COMPLETE NODAL MASSES NODE X-MASS Y-MASS I I.B6SBOB O..65III 2 |.B65III I.I6SBOO 3 I.I6SOIO B.O65BOI 4 I.I65III O.I6SIIB 5 O.I6SDII 0.065OBI 6 I.B65IDI I.I6SBDO 7 I.IOIOII I.BOBIBB B D.BIOBII I.IIIBIB 146 R-MASS LAST NODE 6 NODE DIFF I MODIFYING FACTOR I.BO STATIC LOAD CONTROL INFORMATION STATIC LOAD CODE NO. OF NODAL LOAD COMMANDS 8 I LOADS APPLIED 2 EARTHQUAKE CONTROL INFORMATION NO. OF INTEGRATION TIME STEPS 8 6.. INTEGRATION STEP SIZE 3. ZM'OI MAGNIFICATION FACTORS FOR I EARTHQUAKE ACCELERATION 8 384... TIME 8 I... MAGNIFICATION FACTORS FOR Y EARTHQUAKE ACCELERATION 8 B... TIME 8 I... MAX. PERMISSIBLE DISPLACEMENT 8 3.... ISTATIC NODAL LOAD GENERATION FIRS T I 2 I LOAD COMPLETE STATIC NODAL LOADS NODE NO‘M-fiwa‘ X-LOAD EARTHQUAKE TITLE : EL CENTRO - NS I94. Y MOMENT LOAD LOAD -25.... 1.67.... -25.... -I.67.B.. Y-LOAD MOMENT -25.... 1.67.... -25.... -I.67.... -25.... I.67.... ~25.... -I.67.... -25.... 1.67.... -25.... -I.67.... ..... ..... ..... I.... 147 LAST MODE 5 6 NODE DIFF 2 2 NO. OF X INPUT PAIRS 22B NO. OF Y INPUT PAIRS PRINT CODE 8 I . - DO NOT PRINT I - PRINT NUMBER OF STEPS TO SKIP NHEN PRINT IDAMPING COEFFICIENTS MASS PROPORTION. ALPHA TANGEMT STIFFMESS PROPORTION, BETA TIME HISTORY OUTPUT IMTERVALS NODE DISPLACEMENTS 8 I NO. OF MODES FOR I DISPL HISTORY 8 NO. OF MODES FOR Y DISPL HISTORY 8 NO. OF MODES FOR ROTATION HISTORY= CODE FOR JOINT TIME HISTORY PRINT MODES FOR X DISPL HISTORY I 148 I. h. ..397... .....B6. 149 ELEMENT SPECIFICATION, GROUP I B E A M E L E M E N T S M I T H P L A S T I C R E G I O N S : NUMBER OF BEAMS 8 9 NUMBER OF STEEL TYPES 8 I NUMBER OF CONCRETE TYPES8 2 S T E E L P R O P E R T I E S : DATA ----COMPUTED---- TYPE NO ES PS FSY EPSSU EPSSY FSU I ..29..E+.5 ..I...E-.I ..6.I.E+.2 ..ISO.E-.I ..2.69E-.2 ..6375E+.2 C O M C R E T E P R O P E R T I E S : -------- DATA- ------ COMPUTED TYPE NO. FCP EPSO RDD FCY EPSCY FCU EPSCU EPSM I ..3...E+.I ..2...E-.2 ..B...E-.2 ..216.E+.I ..72..E-.3 ..324.E+BI ..216.E-.2 ..IA69E-.I 2 ..3...E+.I ..2...E-.2 ..B...E-.2 ..2I6.E+.I ..72..E-.3 ..32A.E+OI ..216.E-.2 ..IT69E-.I M E M B E R MEMBER D A T A : CONCRETE MO. ECCXI I .....E+.. 2 .....E*.. 3 .....E+.. 4 .....E+.. 5 .....E+.. 6 .....E+.. 7 .....E+.. B .....E+.. 9 .....E+.. TYPE ECCXJ I .....E+.. I .....E+.. I ..Q..E+.. 2 .....E+.. 2 .....E+.. 2 .....E+.. 2 .....E+.. 2 .....E+.. 2 .....E+.. ECCEMTRICITIES STEEL CONNECTING TYPE EIXYI I I mflfifil l 3 I.IIIE+RI I 5 I.IIIE+OI I 5 I.IOIE+OI l 6 tflfifll I 3 D.IIOE+II I 4 I.IIIE+OI I I I.IOOE+BI 1 2 I.IOIE+OB MODES ECDYJ 2 A.IIIE+AO 4 D.IIIE+IO 5 1.100800 7 I.DII£+|I 8 I. DIEM 5 D.IIIE+IA 6 D.AlIE+II 3 I.DIIE+II 4 I.IAIE+II 150 LENGTH ..25B.E+.3 ..25..E+.3 ..25B.E+.3 ..I6..E+.3 ..I6..E+.3 ..16B.E*.3 ..I60.E+.3 ..16..E+.3 ..I6..E+.3 SCSCR. IA/L) ..5...E+.. ..5...E+.. B.SBBBE+DB ..5...E+.. B.5...E+.. B.5...E+.. B.5BB.E+B. B.5...E+.. ..5...E+.. AXIAL FORCE ..B...E+.. ..O...E+.. B....OE+.. ..75B.E+.2 B.75..E+B2 B.5...E+B2 ..5B..E+B2 ..25..E+.2 B.25..E+.2 ‘ com: X - S E C T I O N MEMBER QGNOM-“NF‘ C O M P U T E D MEMBER omwo-ua-un— HT ..3...E+.2 ..3...E+O2 ..3...E+.2 ..2...E+.2 ..2B..E+.2 ..2B.OE+.2 ..2BOBE+B2 ..2...E+.2 ..2B..E+.2 EIE I.3156E+IB U.SIfibEHB l.3156E+IB O.ITObE+IB $148651“ 0.1424E+BB I.IQZQE+IB 0.1353E+IO 0.1353E+BB D A T A : BB ..I...E+B2 ..I...E+B2 O.IB..E+OZ ..2...E+O2 B.2...E+B2 ..2B.BE+O2 ..2...E+.2 ..2B.BE+B2 ..2...E+.2 M E M B E R P p 1.1217141 1.12171-11 1.12171-11 1.9111142 1.9111142 1.1131141 1.1131141 1.1113141 1.11131-11 DCB R.SOBBE+BI B.3OBBE+BI B.3DBIE+BI I.ZBBBE+BI O.2BBBE+RI B.20BBE+BI B.ZBOBE+OI B.2OBBE+BI O.ZBBBE+BI R O P E R MYI I.3476E+.4 ..3476E+.4 ..3476E+.4 ..ZSIBE+.4 ..2518E+.4 ..2342E+.4 ..2342E+B4 ..2158E+.4 ..2158E+.4 151 ASB ..24..E+.I ..24..E+.I ..24..E+.I ..2BB.E+.I ..2B.OE+.I ..2B..E+.I ..2...E+.I ..2B..E+.I ..2...E+.I T I E S: MY2 ..3476E+.4 ..3476E+.4 ..3476E+.4 ..ZSIBE+.4 ..2SIBE+.A ..2342E+.4 ..2342E+.4 ..2ISBE+.4 ..2158E+.4 BT ..IB..E+.2 ..IB..E+.2 ..I...E+02 B. 2BOBE+B2 ..2...E+.2 ..20..E+.2 ..2BB.E+B2 ..2B..E+.2 ..2B..E+.2 EIUI ..I2BPE+.7 ..I2BPE+.7 ..I2BBE+.7 ..6789E+.6 ..6TBVE+.6 ..57TSE+.6 ..5775E+.6 ..49.7E+.6 ..49.7E+.6 DCT B.3...E+.I ..3...E+.I ..3B..E+.I B.2..BE+.I ..2...E+.I B.2BB.E+BI B.2BB.E+.I ..2...E+.I ..2...E+.I EIU2 ..I2BVE+.7 ..I2BBE+.T ..I2BBE+.7 ..6789E+.6 ..6789E+.6 ..5775E+.6 ..5775E+.6 ..49.7E+.6 ..49.7E+.6 AST ..24..E+.I ..24..E+.I ..24..E+.I B.2...E+BI ..2.0.E+.I ..2..BE+.I B. 200.E+.I ..2...E+.I ..20..E+.I EA ..I.39E+.7 ..II39E+.7 ..I.39E+.7 ..1316E+.7 ..I3I6E+.7 ..13I6E+.7 ..I316E+.7 ..13I6E+.7 ..ISI6E+.T *iiliiiiiiiiiilliiil RESULTS STATIC NODAL DISPLACEMENTS NODE mfléu-DMNU— X-DISPL Y-DISPL -....9 -....9 -....B -....B -....5 -....S ..... ..... 152 DAMMMDEMCENSMMRNNMMN ROTATION .....BI -.....GI .....33 -.....33 .....48 -.....48 ....... ....... 153 I am in step : 1 to 105 (COUNTER) I reached the first yield at step : 106 I am in step : 107 to 600 (COUNTER) NODAL DISPLACEMENT ENVELOPES 154 X-DISPLACEMEMT Y-DISPLACEMENT ROTATION NODE POSITIVE TIME NEGATIVE TIME POSITIVE TIME NEGATIVE TIME POSITIVE TIME NEGATIVE TIME 3.549 2.14 -4.132 2.4. ....5 2.14 -B..26 2.4. ..OB324 2.38 -O.BBI23 2.14 3.549 2.14 -4.131 2.4. ....7 2.4. -B..24 2.I4 B...I64 2.38 -..OQ289 5.0. 2.634 2.14 -3.B6. 2.4. ...B6 2.14 -...22 2.4. B...55. 2.4. -..B.452 5... 2.634 2.14 -3..6. 2.4. ..B.7 2.4. -...21 2.14 O..O469 2.4. -....478 2.14 1.192 2.16 -I.4.7 2.42 l...4 2.14 -...14 2.4. ..B.71. 2.4. -....511 2.14 1.191 2.16 -I.4.6 2.42 ..BB5 2.4. -...13 2.14 ....629 2.4. -....6IB 2.I4 ..... I... I.... B... ..... I... S.B.. B... 0...... B... ....... O... D.C.. O... ..OB. I... ..... O... ..... B... ....... B... ....... B... muauaump 155 PLASTIC RESULTS RATIO 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 ! CURV.DUCT.1 PLASTIC 1 DAMAGE 1 MAXIMUM MOMENT 1 i PROVIDED 4 LENGTHS i FACTOR * 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 MEMBER CU/CY LI/L LJ/L NODEI MODEJ MAX.MOM I YIELD MON. 1 35.052 ...0. 0.0.. 0.800 0.00. 0.56 2 35.052 0.845 0.02. 0.32. 0.170 1.10 3 33.052 ...26 ..041 0.208 0.295 1.09 4 27.481 0.... 8.058 0.8.. 8.519 1.11 5 27.481 0.0.. 0.049 0.0.. 0.450 1.09 6 32.716 ...13 8.0.. 0.142 0.008 1.03 7 32.716 ...26 8.0.4 ..241 ...73 1.05 8 39.188 8.80. 0.... 0.00. 0.0.. 8.83 9 39.188 0.00. 8.0.. 0.0.0 ..000 0.96 DUCTILITY DISPLACEMENT 111111111111111111111 FIRST YIELD DISPLACEMENT 8 3.1174. MAX.DISPLACEMENT AT THE TOP 8 4.13208 DISPLACEMENT DUCTILITY 8 1.32549 PLOT OPTIONS OUTPUT 44446 3 1| 11 -F 1 ~. I I -I . g . 1 o. y | n .1 ' u . I ‘1 I. P ‘I g. 1" 1. '1" 414 156 111111111111Pgfl? 3PT§3NS1111111111111 RUST FATION INPUT AT THE TOP RUCTURE C REGIONS '1.‘ 15: D On .I n B “.1 23 I?) (3') [CT " (“I H .31 z 0' L“ 4:- LJ I'J r- .. .- .. .- 1875 ABOUT PRINTING THE SCREEN: 1111111111111111111111111111111 - PRESS 'SHIFT/PRTSC' FUR PRINTING ~ PRESS 'ENTER' TNICE TO EXIT TYPE YOUR INPUT OPTION 8 157 UMDBFOIO‘IEB STRUCTURE 158 * m 4441 111111 4' I 1 U T111111 SEC I GROUND ACCELERATION I 7') 4'1“]. 7‘. .VIWWLHVI! 4' [1'1 111/11 14 7” IVVU-VVUVVVVVU; U EEEEEEEEEEEEEE q— 1—3 H I! M A 03 El! ('5 w 160 DBI'OIII‘IED STRUCTURE 161 ,__I F'” T..] L__1 __1 r__ .__J L —I I" _J L. 1::::3 £222: FIMITB SIZE OF PLASTIC REGIONS PLASTIC LENGTH DAMAGE FACTOR 1.8 L____ IILH 11111 S x 1211 3:1 1911111111111 11 7 1 0816 4108