Analysis of Reinforced Concrete Structures for Earthquakes: A Review of Research Studies, Summaries of Engineering

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UILU-ENG-78-

e. ~ CIVIL ENGINEERING STUDIES

STRUCTURAL RES~ARCH SERIES NO. 457

Metz Reference Room

Civil Engineering Department

BI06 C. E. Building

University of Illinois

Urbana, Illinois 61801

ANALYSIS OF REINFORCED CONCRETE

FRAME-WALL STRUCTURES FOR

STRONG MOTION EARTHQUAKES

By

KATSUHIKO EMORI

and

WILLIAM C. SCHNOBRICH

A Report on a Research Project Sponsored by THE NATIONAL SCIENCE FOUNDATION Research Grant ENV 74-

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Univsrsity of Illinois

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UNIVERSITY OF ILLINOIS

at URBANA-CHAMPAIGN URBANA, ILLINOIS DECEMBER 1978

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ACKNOWLEDGMENT

The writers would like to express their special gratitude to Professor Mete A. Sozen of the University of Illinois for his invaluable comments and help. Deep appreciation is also due Dr. T. Takayanagi and Mr. D. A. Abrams, former and current research assistants at the University of Illinois for providing the authors with information from their analytical and experi- mental studies. The numerical calculations were performed on the CYBER 175 System of the Computing Services Office of the University of Illinois. The work was supported by U. S. National Science Foundation Grant No. ENV 7422962. The support is gratefully acknowledged.

CHAPTER

iv

TABLE OF CONTENTS Page

 - 1.1 Introductory Remarks -------------------------------------- INTRODUCTION - 1.2 Review of Previous Research ------------------------------- - 1.3 Object and Scope ------------------------------------------ 

• 2 STRUCTURAL SYSTEM AND MECHANICAL MODELS ------------------------ - 2.12.2 StructuralAn Analytical System .Model ----------------------------------------- for Frame-Wall Structures ------------- - 2.3 Mechanical Models for Structural Components ---------------
• 3 FORCE-DEFORMATION RELATIONSHIPS FOR CANTILEVER BEAM MODELS ----- - 3.23.1 ConcentratedIntroductory SpringRemarks Model-------------------------------------- and Multiple Spring Model ------- - 3.3 Layered Model --------------------------------------------- - 3.4 Additional Considerations for Each Model ------------------
• 4 ANALYTICAL PROCEDURE ------------------------------------------- - 4.1 Introductory Remarks -------------------------------------- - 4.2 Basic Assumptions ----------------------------------------- - 4.3 Analytical Models ----------------------------------------- - 4.44.5 StructuralStatic Analysis Stiffness -------------------------------------------45 Matrix ------------------------------- - 4.6 Dynamic Analysis ------------------------------------------
  • 5 HYSTERESIS RULES AND NUMERICAL EXAMPLES ------------------------ - 5.1 Introductory Remarks - _____________________________________ - 5.2 Degrading Trilinear Hysteresis Rule ----------------------- - Experimental Results -------------------------------------- 5.3 Comparison of Computed Hysteresis Loop with - 5.4 Effect of Axial Load --------------------------------------
  • 6. COMPUTED RESULTS -----------------------------------------------
       • 6.1 Introductory Remarks --------------------------------------
       • 6.2 Static Analysis -------------------------------------------
         • the Exterior Columns -------------------------------------- 6.36.4 DynamicEffect ofAnalysis Changing ------------------------------------------66 Axial Load at the Base of

v

Page 7 SUMMARY AND CONCLUSIONS ---------------------------------------- 78 7.1 Summary --------------------------------------------------- 78 7.27.3 ConclusionsRecommendations ----------------------------------------------- for Further Studies ----------------------- (^7980) LIST OF REFERENCES ---------------------------------------------------- 82 APPENDIX A DETAILS OF STIFFNESS MATRICES _________________________________ ~ B COMPUTER PROGRAM FOR NONLINEAR RESPONSE ANALYSIS OF REINFORCED CONCRETE FRAME-WALL STRUCTURES ------------------- C NOTATION ------------------------------------------------------

vii

LIST OF FIGURES

Figure Page

2.1 REINFORCED CONCRETE FRAME-WALL TEST STRUCTURE ------------------ 110 2.2 REINFORCEMENT DETAILS OF STRUCTURAL COMPONENTS ----------------- 111 2.3 DEFORMATION MODES OF FRAME-WALL STRUCTURES --------------------- 113 2.4 CURVATURE DISTRIBUTION ALONG A CANTILEVER BEAM ----------------- 114 2.5 MECHANICAL MODELS USED IN INVESTIGATION ------------------------ 115 3.1 IDEALIZED STRESS-STRAIN RELATIONSHIPS FOR CONCRETE AND STEEL FOR THE CONCENTRATED SPRING AND MULTIPLE SPRING MODELS --------- 116 3.2 DISTRIBUTIONS OF STRESS AND STRAIN OVER A CROSS SECTION -------- 117 3.3 IDEALIZED MOMENT-CURVATURE RELATIONSHIP USED FOR THE CONCENTRATED SPRING MODEL -------------------------------------- 118 3.4 IDEALIZED MOMENT-ROTATION RELATIONSHIP USED FOR THE CONCENTRATED SPRING MODEL -------------------------------------- 118 3.5 IDEALIZED MOMENT-CURVATURE RELATIONSHIP FOR EACH SPRING OF THE ~JLTIPLE SPRING MODEL ----------------------------------- 119 3.6 IDEALIZED STRESS-STRAIN RELATIONSHIPS USED WITH THE LAYERED MJJEl -------------------------------------------------- 120 3.7 DISTR!SJTIJNS OF STRESS AND STRAIN OVER A CROSS SECTION OF THE LAYERED MODEL ------------------------------------------- 121 3.8 INSTA~~[ S MOMENT-CURVATURE RELATIONSHIPS FOR THE L~Y~~[J ~ECTION OF THE LAYERED MODEL ----------------------- 122 3.9 BONJ s~ rp ~ C~ANISM -------------------------------------------- 123 3.10 COMP';;;::SC, OF COMPUTED BOND SLIP WITH EXPERIMENTAL DATA -------- 124- 3.11 TYPICA~ LQ~J-D!SPLACEMENT CURVES FOR INELASTIC ANALYSIS -------- 125 4.1 DEFORMED SYAPES OF A CONCENTRATED SPRING MODEL AND AN EQUIV.~LENT SIMPLE BEAM MODEL ---------------------------- 126 4.2 TYPICAL MEMBERS IN GLOBAL COORDINATES SYSTEM ------------------- 127 4.3 MULTIPLE SPRING MODEL ------------------------------------------ 128 4.4 APPLICATION OF THE LAYERED MODEL TO 1ST STORY EXTERIOR COLUMNS ----------------------------------------------- 129

ix

Figure Page

6.14 RESPONSE WAVEFORMS FOR STRUCTURE FW-2, RUN- USING HYSTERESIS MODELS 1 AND 2 -------------------------------- 167 6.15 MOMENT-ROTATION RELATIONSHIPS OF THE FLEXURAL SPRING AT THE 5TH LEVEL LEFT EXTERIOR BEAM ---------------------------- 169 6.16 MOMENT-ROTATION RELATIONSHIPS OF THE FLEXURAL SPRING USING HYSTERESIS MODELS 1 AND 2 AT THE 5TH LEVEL LEFT EXTERIOR BEAM ----------------------------------- 171 6.17 MOMENT-ROTATION RELATIONSHIPS OF A FLEXURAL SPRING AT THE BASE OF THE LEFT COLUMN --------------------------------- 172' 6.18 MOMENT-CURVATURE RELATIONSHIPS OF THE FLEXURAL SPRING AT THE BASE ELEMENT OF THE WALL -------------------------------- 174 6.19 BASE OVERTURNING MOMENT VS. TOP-STORY DISPLACEMENT RELATIONSHIPS OF THE STRUCTURES -------------------------------- 175 6.20 RESPONSE WAVEFORMS FOR AXIAL FORCE AT THE BASE OF THE LEFT COLUMN --------------------------------- 177 6.21 COMPUTED STRUCTURAL YIELD PATTERNS (STRUCTURE FW-1, RUN-1) ----- 179 6.22 OBSERVED CRACK PATTERNS IN STRUCTURE FW-2, RUN-2 --------------- 183 6.23 BASE SHEAR VS. TOP-STORY DISPLACEMENT RELATIONSHIPS OF STRUCTURE FW-2 USING CONCENTRATED SPRING MODEL AND LAYERED MODEL -------------------------------------------------- 184 6.24 MOMENT-CURVATURE RELATIONSHIPS OF THE LAYERED SECTION AT THE BASE OF THE COLUMNS ------------------------------------- 185 6.25 LOADING PATH AT THE BASE OF THE EXTERIOR COLUMNS --------------- 186 6.26 BASE SHEAR VS. TOP-STORY DISPLACEMENT RELATIONSHIPS OF STRUCTURE FW-2 USING CONCENTRATED SPRING MODEL AND LAYERED MODEL FOR SINGLE CYCLE OF LOADING ------------------ 187 6.27 MOMENT-CURVATURE RELATIONSHIPS OF THE LAYERED SECTION AT THE BASE OF THE COLUMNS FOR SINGLE CYCLE OF LOADING --------- 188 6.28 BEHAVIOR OF THE LAYERED SECTION AT THE BASE OF THE COLUMNS FOR SINGLE CYCLE OF LOADING --------------------- 189 B. 1 FLOW DIAGRAM OF COMPUTER PROGRAM FOR NONLINEAR RESPONSE ANALYSIS OF REINFORCED CONCRETE FRAME-WALL SYSTEMS -------------

understood. In analyzing reinforced concrete structures in the inelastic range, many phenomena arise which have to be taken into consideration, such as cracking, crushing of concrete, yielding, strain hardening of reinforcing steel, and bond slip, to name a few. These characteristics make the analysis complicated. In this study, the analysis of idealized reinforced concrete plane frame-wall structures will be treated on the basis of certain assumptions such as the substitute frame structure, fixed inflection point locations in members, concentrated mass at each floor level, etc. These assumptions are made to simplify the analysis while not markedly affecting its accuracy_ The study presented is limited to plane structures of laboratory test specimens.

1.2 Review Q[ Previous Research When analyzing a reinforced concrete structural system deformed beyond its elastic range, it is obviously very important to choose an idealized element model suitable to represent the inelastic behavior of the reinforced concrete member components. Many different approaches which take into account material and geometric nonlinearities have been reported in the literature. Several of the more successful models are discribed below. Giberson[151 proposed a concentrated spring model for column and beam elements. His^ model^ consists^ of^ a^ linearly^ elastic^ member^ with^ a spring attached at each end. These springs take account of any nonlinear characteristics that occur within the members. This model for nonlinear analysis was applied to reinforced concrete multi-story

structures. This model is versatile since the spring at each end can have different curvilinear or bilinear hysteretic characteristics. Otani's[34] combined two cantilever beam model with nonlinear springs, belongs to the class of concentrated spring models. Concentrated spring models are effective for the antisymmetric moment distributions with fixed inflection points. Otani's model also demonstrates good agreement between analytical and test results. Benuska[10] presented a two-component model with the members divided into two imaginary parallel elements. There is an elastic element to represent the linear phase and an elasto-plastic element to represent a yielding characteristic. This^ model^ was^ applied^ to^ a nonlinear analysis of a 20-story open frame structure. Takizawa[45] assumed the distribution of flexural rigidity along a member element to be that of a parabolic function. This distribution is used in the determination of the member flexibility matrix. The inflection point is not fixed in this model. This model has been applied to the nonlinear analysis of a 3-story reinforced concrete frame structure. Takayanagi[421 has presented a multiple spring beam model for analyzing wall members. This model divides the member into several subelements along its longitudinal axis. Each subelement has a uniform flexural rigidity which changes based on the hysteresis loop appropriate to each subelement. This model is effective for a distribution of moment whose inflection point can lie outside of the element. A somewhat different approach to analyzing inelastic behavior of reinforced concrete members is the layering concept. This can be a very

circumstances. Yuzugullu[51] investigated the behavior of a shear wall frame system for monotonic, increasing load. Darwin[12] analyzed reinforced concrete shear panels under cyclic loading. They both obtained good correlation with experimental results. However, such a finite element analysis requires quite a large number of elements if the local stress distribution is important. Therefore this approach is costly, maybe too much so, for use on large scale reinforced concrete structural systems such as those being investigated in this study. The finite element analysis still has a very promising future but on more limited problems. 1.3 Object and Scope The objective of this study is to investigate analytically the nonlinear seismic behavior of reinforced concrete frame-wall structures and with that analysis to trace the development of a failure mechanism for these structures. First of all, three types of mechanical models a concentrated. spring beam model, a multiple spring beam model, and a layered beam model, which c~n take into account both the linear and the nonlinear behavior of such reinforced concrete cantilever beams are presented. To describe the nonlinear behavior of the reinforced concrete cantilever beams, a numerical procedure is presented for computing moments, curvatures and deflections. The selection of the analytical models, which is to be used to analyze the structure, depends upon the physical loading condition that exists. In order to establish the force-deflection relations of the '" :-

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structure, a beam-column component and a single shear wall of the structure are investigated. In this respect, for each constituent member: beams, columns, and the wall, a degrading trilinear hysteresis loop is adopted. But this hysteresis loop does not include any pinching effect which might occur in the structural components being tested. A second new hysteresis rule is therefore presented. This hysteresis rule was developed primarily for application to the beam members in this structure. Finally, the frame-wall structure is modelled as a system which has a concentrated spring model for the beam and column elements and a multiple spring beam model for the wall elements. A layered model is applied to the first story exterior columns of the structure only when the effect of changing axial force is investigated. Furthermore in this phase, a substitute-frame system has been chosen as the frame subsystem model because the structure being modelled has a geometrical symmetry aspect while the frame is subjected to antisymmetrical loading. This substitute frame system described in Chapter 2 reduces significantly the computation time. The instantaneous nonlinear characteristics of the structure being investigated are estimated and the failure processes of each constituent member under a strong earthquake motion are traced by numerically integrating the equations of motion in a step by step method. A computer program is developed to carry out the numerical calculations of the analysis. The computed results are discussed and compared with the available test results.