Oct 12, 1992 - reinforced concrete frame buildings, wall buildings, dual wall-frame buildings bridges, towers, timber structures, Steel structure, masonry buildings and retaining wall. It is considered that (DDBD) ..... After calculation of the period, these spectrum graphs are used to deduce the expected response of this ...
COMPARISON BETWEEN FORCE BASED DESIGN AND DIRECT DISPLACEMENT BASED DESIGN FOR REINFORCED CONCRETE FRAME OR WALLED STRUCTURES
by Ahmed Alaa Eldin Ismail Mohamed Fawzy Elansary B.Sc. Civil Engineering, Cairo University, 2008.
A Thesis submitted to the Faculty of Engineering at Cairo University In partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE in STRUCTURAL ENGINEERING
FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2010
COMPARISON BETWEEN FORCE BASED DESIGN AND DIRECT DISPLACEMENT BASED DESIGN FOR REINFORCED CONCRETE FRAME OR WALLED STRUCTURES
by Ahmed Alaa Eldin Ismail Mohamed Fawzy Elansary B.Sc. Civil Engineering, Cairo University, 2008.
A Thesis submitted to the Faculty of Engineering at Cairo University In partial Fulfillment of the Requirements for the Degree of
MASTER OF SCIENCE in STRUCTURAL ENGINEERING
Under the supervision of
Prof.Dr.Adel Galal El-Attar
Prof.Dr. Abd El-Hamid I.Zaghw
Professor of Reinforced Concrete Structures
Professor of Reinforced Concrete Structures
Structural Engineering Department
Structural Engineering Department
Faculty of Engineering
Faculty of Engineering
Cairo University
Cairo University
FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2010
COMPARISON BETWEEN FORCE BASED DESIGN AND DIRECT DISPLACEMENT BASED DESIGN FOR REINFORCED CONCRETE FRAME OR WALLED STRUCTURES
by Ahmed Alaa Eldin Ismail Mohamed Fawzy Elansary B.Sc. Civil Engineering, Cairo University, 2008.
A Thesis submitted to the Faculty of Engineering at Cairo University In partial Fulfillment of the Requirements for the Degree of
MASTER OF SCIENCE in STRUCTURAL ENGINEERING Approved by the Examining Committee
_____________________________________________________ Prof.Dr. Adel Galal El-Attar, Thesis Main Advisor _____________________________________________________ Prof.Dr. Abd El-Hamid I.Zaghw, Thesis Advisor _____________________________________________________ Prof.Dr. Moustafa Fouad El-Kafrawy, Examiner _____________________________________________________ Prof.Dr. Mohamed Nasser Darweesh, Examiner _____________________________________________________ FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2010
ABSTRACT Many problems were found in forced based design (FBD) such as the assumed stiffness of the structure elements, inappropriate R-factor, and others. So an alternative design approach was very important to be used instead of (FBD) consequently the researchers resorted to the performance based design (PBD). (PBD) is considered one of the most important modern concepts in the earthquake engineering. It attempts to study the behavior of the building under seismic forces with accurate methods -rather than the forced based design at which a lot of formulas are considered empirical rules. One of the important approaches based on the (PBD) are the direct displacement based design. (DDBD) which is considered an accurate and best equipped method which shows the deficiencies of conventional (FBD) and it is characterized by its simple procedures which can be applied on different types of structures such as reinforced concrete frame buildings, wall buildings, dual wall-frame buildings bridges, towers, timber structures, Steel structure, masonry buildings and retaining wall. It is considered that (DDBD) gives more accurate solution for certain category of the structures since damage of different structural elements is related to the strain at each one. The objective of this thesis is to apply DDBD on different reinforced concrete frame buildings with 2, 4, 8, 12, 16, and 20 number of storeys and on 12-storey building contains shear walls at certain direction such as we calculate the base shear force at each case, finally compare the value of base shear forces calculated by DDBD with these ones calculated by FBD. Four computer programs have been used in our analysis of the studied buildings which are SAP, ETABS, Seismostruct, and IDARC to perform a pushover analysis and get the displaced shape corresponding to the drift limit at the first floor. i
The effective parameters that are found to significantly affect the base shear force were the displaced shape of the building at its inelastic phase, the ground acceleration, the period of the building, the soil type, the geometry of the building, and the mass of the building, so parametric studies were made on each of them. The results of the analysis show that the (DDBD) is suitable for moment resisting frame buildings which have number of storeys more than 8 and for high values of ground accelerations, while it gives small base shear forces for buildings which have number of storeys less than 8 storeys for low values of ground accelerations. For ground acceleration of value about 0.55g, for the moment resisting frame buildings which have number of storeys larger than 8, the value of the base shear force calculated by DDBD is approximately equal to the base shear force by FBD.
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ACKNOWLEDGEMENT
I would like to express my gratitude to my research supervisors Professor Dr. Adel Galal El-Attar and Professor Dr Abd El-Hamid I.Zaghw for their continuous help, patience and guidance to me through my research, they provided me with valuable advices, latest references, and clarified lots of basic concepts to me, I wish to thank them for their efforts, great suggestions, and reviewing the manuscript which participated in enhancing thesis.
I would also like to proselyte this work to my parents who encouraged me to reach my goals, my grandfather (Dr.Aboul wafa Abd El a~kher) who usually pushes me to achieve progress in my career and always tell me to make a lot of researches, my sister (mira), and her husband (Ahmed Saleh), my brother (Mahmoud), all my relatives, all my professors in faculty of engineering
who participated in building my knowledge, and all my friends.
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TABLE OF CONTENTS
Page - ABSTRACT …………………………………………………..………………i - ACKNOWLEDGEMENT…………………………………………………...iii -TABLE OF CONTENTS……………………………….………….….……...iv -LIST OF TABLES……………………………………………………..….….ix -LIST OF FIGURES……………………………………………………………x Chapter (1) INTRODUCTION………………….…………………………….1 1.1 Background…………………………………………………………….1 1.2 Forced based design, (FBD)………………….……………………….2 1.3 Displacement based design, (DBD)…………………………………..3 1.4 Work on the thesis……………………………………………………..4 Chapter (2) LITERATURE OF PREVIOUS WORK…………………………7 2.1 Background……………………………….……………………………7 2.2 Development of displacement based seismic design…………………8 2.2.1 Force-based /displacement checked……………….………………8 2.2.2 Deformation calculation based design…………….………………5 2.2.3 Deformation specified based design…………………………….....9 2.2.4 Choice of design approach…………………………………...…….9 2.3 Fallacies in Earthquake Engineering………………………...….…10 2.3.1. Fallacy of design of elastic acceleration spectra…………….…11 2.3.2 The refined analysis myth……………………………………….13 iv
2.3.3. (Strength = Safety) is fallacy…………………………………….14 2.3.4 The myth of maximized energy absorption………………………14 2.3.5. Myths and fallacies related to reinforced concrete design detailing ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,16 2.4 Basic Correct concepts in seismic Design…………………………..16 2.4.1. The Elastic Stiffness of concrete members……………….……..16 2.4.1.1 General………………………………………………..……16 2.4.1.2. Elastic stiffness of circular columns………………………18 2.4.1.3 Elastic stiffness of rectangular columns……………….…..19 2.4.1.4 Elastic stiffness of rectangular walls (shear walls)……..….19 2.4.1.5 Elastic stiffness of flanged beams………………………….20 2.4.1.6 Yield drift of frames………………………………….…….21 2.4.1.7 Results……………………………………………….……..22 2.5 Some problems with Multi-Modal Analysis………………….…….23 2.5.1 Advantages of Multimodal Analysis…………………………..…23 2.5.1.1 How higher mode effects are considered in "Equivalent lateral force design"………………………………………………..……23. 2.5.1.2 How Torsional effects is considered in "Equivalent lateral force design"………………………………………………………..……24 2.5.2 Design higher modes effects by multi-modal analysis………….24 2.5.2.1 General……………………………………………………25 2.5.2.2 Higher mode effects in cantilever wall from time history analysis……………………………………………………………….…..26 2.5.2.3 Modified Modal Superposition (MMS) for design forces in cantilever wall……………………………………………………………27 2.5.2.4 Consequences for capacity design………………………..…28.
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2.5.2.5 Higher mode effects in frame buildings from time history analysis…………………………………………………………….………28 2.5.3 Torsional response of building structures……………………...…28 2.5.4 Conclusions……………………………………………………….29 2.6 Comparison between Forced Based Design (FBD) and Displacement Based Design (DDBD)………………………………………………..…..29 2.6.1 General………………………………………………………...….29
2.6.2 Forced based design method……………………………..33 2.6.3 Direct displacement design method……………………..…37 2.6.3.1 Steps of DDBD for reinforced concrete moment resisting frame buildings……………………………………………………..38 2.6.3.2 Steps of DDBD for reinforced concrete wall buildings ………………………………………………………………………46 2.6.3.3 Steps of DDBD for reinforced concrete duel wall-frame buildings…………………………………………………………….47 2.6.4 Some implications of DDBD………………………………..49 2.6.4.1 Influence of seismic intensity on base shear strength………49 2.6.4.2 Influence of building height on required frame base shear strength…………………………………………………………………….51 Chapter (3) PLOTTING THE DISPLACEMENT RESPONSE SPECTRUM………………………………………………………………….53 3.1 Background…………………………………………………………...53 3.2 Deducing the DRS from the acceleration response spectrum, ARS……………………………………………………………………….54 3.3 Deducing the displacement response spectrum, DRS, from first principles……………………………………………………………57 Chapter (4) ANALYSIS BY PROGRAMS……………………………….66 4.1 Introduction…………………………………………………………66 vi
4.2 Modeling of moment resisting frame buildings…………………66 4.2.1 Modeling using 2D-IDARC program……………….……….…69 4.2.2 Modeling using SAP program…………………………………..67 4.2.3 Modeling using SEISMOSTRUCT program………..………….83 4.3 Modeling of dual frame-wall building………………………………96 4.3.1 Modeling using SAP program………………………………….98 4.3.1 Modeling using ETABS program………………………………98 Chapter (5) RESULTS………………………………………………………99 5.1 Results for frame buildings………………………………………….99 5.1.1 Comparison between the Inelastic displaced shape of the studied buildings…………………………………………………………………99 5.1.2 Comparison between the base shear calculated by FBD and the base shear by DDBD at different ground accelerations……………………103 5.1.3 Comparison between the base shear calculated by FBD and the base shear by DDBD at constant ground accelerations……………………107 5.1.4 Comparison between the periods of the studied frames………..109 5.1.4.1 The empirical equation from the Egyptian code…………..110 5.1.4.2 Period from the DDBD procedure………………………….110 5.1.4.3 Period from the modal analysis of the SAP model (with non reduced moment of inertia of the cross sections…………………..110 5.1.4.4 Period from the modal analysis of the SAP model (with reduced moment of inertia of the cross sections)………………….111 5.1.5 Comparison between the stiffness of the studied frame buildings.114 5.1.5.1 Using pushover analysis from SAP program…………….…114 5.1.5.2 Using pushover analysis from Seismostruct program……..114. 5.1.5.3 Using DDBD procedure……………………………………114 5.2Resuls for wall and dual frame-wall buildings……………………117 vii
5.2.1 Comparison between the Inelastic displaced shape ………117 5.2.2 Comparison between the base shear calculated by FBD and the base shear by DDBD ……………………………….………………………119 5.2.3 Comparison between the periods ……………………….………121 Chapter (6) CONCLUSIONS AND RECOMMENDATIONS FOR FUTUTRE WORK…………………………………………………………122 6.1 conclusions………………………………………………………….122 6.1.1 Frame buildings………………………………………………122 6.1.2 Dual frame-wall building……………………………………..123 6.2 recommendations for future work………………………………123 Appendix A…………………………………………………………………..124 References……………………………………………………………………127
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LIST OF TABLES
Table 2.1.yield curvature for different structural members Table 2.2 Force reduction factor for different types of structural systems in the Egyptian code for loads Table 2.3.Code drift limits for different systems and different levels for damage Table 2.4.Approximate relations for calculating the displacement at a certain damping ratio from the displacement for damping ratio=5% Table 3.1 seismic parameters of acceleration response spectrum (Type 1) for different soil types Table 3.2 seismic parameters of acceleration response spectrum (Type 2) for different soil types Table 4.1 Numerical presentation of the displaced shape in Seismostruct program Table 5.1 Calculation of the base shear for the studied frames at constant ground acceleration Table 5.2 Periods of studied buildings from different methods Table 5.3 Stiffness of studied buildings using different methods Table 5.4 Periods of the studied frame-wall building at both directions
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LIST OF FIGUIRES
Figure 2.1 Displacement response spectrums for different damping Figure 2.2 hysteretic shapes for different models Figure 2.3 Effect of flexure strength on moment curvature curve Figure 2.4.Force-displacement relation for elastic and ductile behavior for reinforced concrete building. Figure 2.5 getting the acceleration from the ARS using the period Figure 2.6.Substitute structure representation for multi-degree of freedom frame and the force displacement relation up to failure (Elastic and inelastic stages Figure 2.7 Comparison between different formulas of damping ratio (ζ) Figure 2.8.Displacement response spectrum for different effective damping ratio Figure 2.9.Displacement and acceleration response spectrum for two buildings constructed at different seismic zone Figure 3.1 Typical shape of the displacement response spectrum Figure 3.2.Typical shape of acceleration response spectrum, ARS Figure 3.3 Representation of SDOF body and the free body diagram for it Figure 3.4 Time history record of a certain earthquake
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Figure 3.5 Displacement responses at different values of time due to a certain earthquake for the buildings have a certain period. Figure 3.6 Velocity responses at different values of time due to a certain earthquake for the buildings have a certain period. Figure 3.7 Acceleration responses at different values of time due to a certain earthquake for the buildings have a certain period. Figure 4.1 Elevation view for the studied moment resisting frame buildings Figure 4.2 Numbers of columns, beams, levels, and axes for the 12-storey building modeled by IDARC Figure 4.3 Stress strain curve of concrete Figure 4.4 Stress strain curve of reinforcing steel Figure 4.5 Part of the output file of IDARC program which shows the displacement at each level Figure 4.5 The displaced shape by the SAP program for 12-storey building Figure 4.7 The wizard of the Seismostruct program Figure 4.8 Editing of the stress strain curve of the concrete Figure 4.9 Editing of the stress strain curve of the reinforcing steel Figure 4.10 Editing of the a reinforced concrete section properties Figure 4.11 Fiber modeling for reinforced concrete cross section Figure 4.12 Determining the criteria for the program to stop its analysis Figure 4.13 Graphical presentation of the displaced shape
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Figure 4.14 Elevation view of the displaced shape Figure 4.15 Plan view for the studied duel frame-wall building Figure 4.16 Plan view for the studied duel frame-wall building [18] Figure 4.17 Three dimensional modeling of the dual frame-wall building [18] Figure 5.1 Inelastic displaced shape for 2-storey building Figure 5.2 Inelastic displaced shape for 4-storey building Figure 5.3 Inelastic displaced shape for 8-storey building Figure 5.4 Inelastic displaced shape for 12-storey building Figure 5.5 Inelastic displaced shape for 16-storey building Figure 5.6 Inelastic displaced shape for 20-storey building Figure 5.7 The ratio between the base shear calculated by DDBD and FBD for 2-storey building for different values of ground accelerations Figure 5.8 The ratio between the base shear calculated by DDBD and FBD for 4-storey building for different values of ground accelerations Figure 5.9 The ratio between the base shear calculated by DDBD and FBD for 8-storey building for different values of ground accelerations Figure 5.10 The ratio between the base shear calculated by DDBD and FBD for 12-storey building for different values of ground accelerations Figure 5.11 The ratio between the base shear calculated by DDBD and FBD for 16-storey building for different values of ground accelerations Figure 5.12 The ratio between the base shear calculated by DDBD and FBD for 20-storey building for different values of ground accelerations xii
Figure 5.13 Calculation of the base shear for the studied frames at constant ground acceleration Figure 5.14 the periods of the studied buildings using different methods. Figure 5.15 Stiffness of studied buildings from different methods Figure 5.16 Displaced shape by (DDBD), and pushover analysis by SAP and ETABS in x-direction for the dual frame-wall building Figure 5.17 Displaced shape for dual frame wall building in y-direction using SAP, and ETABS programs Figure 5.18 The base shear force for dual frame-wall building using different methods Figure 5.19 Periods of the studied frame-wall building at bath directions
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Chapter 1 INTODUCTION 1.1 Background: Nowadays applying lateral earthquake loads on buildings became an essential procedure in the design of structures so as to get the maximum possible straining actions in the structure elements. Researchers always look for the best method to be used to consider the seismic forces. Many approaches were developed starting from simplified methods of estimating the base shear as a constant factor from the building weight [15] and then the forced based design –adopted in most of current codes including the Egyptian one- to the latest approach for seismic which is called the performance based design (PBD). During the late 19th and 20th centuries, the effect of earthquake on the structures became one of the most important interests of the structural designers in Japan, Italy, and the United States. This was due to the occurrence of multiple earthquakes such as: 1855 Edo in Japan, 1891 Mino-Awari in the United States, and 1908 Messina in Italy [15]. Earthquake engineering began at the end of the 19th century when some European engineers suggested designing the structures considering a small percent of the building weight to be applied laterally on the building so as to simulate the effect of earthquake on the structures. This idea is adopted and developed in Japan at the beginning of the 20th century [15]. The concept of response spectrum is the introduced such that a spectrum of all possible responses is plotted for very wide range of periods for the structures. After calculation of the period, these spectrum graphs are used to deduce the expected response of this structure when it is subjected to a certain earthquake.
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On Monday, October 12, 1992, an earthquake of magnitude 5.4 struck Egypt at 3:15 P.M at local time, at lasted for about 30 seconds. The earthquake was centered about 20 Km south of Cairo. An estimated number of 541 were killed, about 6500 were injured, about 20000 were displaced from their houses, about 350 structures were collapsed, and 8000 were damaged. There was no seismic design code in Egypt before this earthquake and most of buildings were not designed for earthquake loads. A first draft seismic design code for Egypt had been in preparation and was published a few days after the earthquake. This draft seismic code divides Egypt into two zones. The first one covers most of Egypt including Cairo, this zone expected to have a maximum earthquake magnitude value of about 6.0. While the second zone is expected to have a maximum earthquake of a magnitude of 7.0, this area includes the cities in Red Sea, South Sinai, El-Fayum, and Aswan. The first draft was mainly taking about the method of calculation for the base shear force and applying it to structures so as to take the effect of the earthquake into consideration in the design process [14]. The base shear force is an estimate of the maximum expected lateral force that may occur due to seismic ground motion at the base of a structure. Calculations of base shear (V) depend on, soil conditions at the site where the building will be constructed, the distance between the building and the geological fault position, the probability of occurrence of the earthquake, and the fundamental (natural) period of vibration of the structure when subjected to dynamic loading.
1.2 Forced based design is ,(FBD): The first procedure is based on calculating the base shear force expected to be applied by the earthquake using the acceleration response spectrum and the expected elastic period of the building, then the concept of equivalent static
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lateral force procedures was adopted which is putting of static loads on a structure with magnitudes and direction that closely approximate the effects of dynamic loading caused by earthquakes. Concentrated lateral forces due to dynamic loading tend to occur at each floor in buildings, where concentration of mass is existed. Furthermore, concentrated lateral forces tend to be larger at higher elevations in a structure. Thus, the greatest lateral displacements and the largest lateral forces often occur at the top level of a structure (particularly for tall buildings). These effects are modeled in equivalent static lateral force procedures of the IBC and UBC by placing a force at each story level in a structure.
1.3 Displacement based design, (DBD): This approach uses the displacement response spectrum as a basis for calculating the base shear force. It also depends on studying the building considering its inelastic phase. This thesis presents the fundamentals of the new seismic design method known as direct displacement based design (DDBD) which is considered one of the simplest design approaches for the analysis of the multi degree of freedom structures. In this method, the structure is characterized by the secant stiffness and equivalent elastic damping of an equivalent single degree of freedom structure. This design is based on achieving a specified displacement limit state defined either by material strain limits or non-structural drift limits obtained from design codes under the design level seismic intensity. The characterization of the structure using the substitute structure avoids many problems inherent in force-based design, (FBD) where initial stiffness is used to determine an elastic period which is now adopted in most of the building codes [8].
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1.4 Work on the thesis: Reinforced concrete moment resisting frames are used as a part of seismic force-resisting systems together with shear walls or alone without shear walls in the buildings that are designed to resist earthquakes. Beams, columns, and beam-column joints in moment resisting frames buildings are proportioned and detailed so as to resist flexural, axial, and shearing actions that result from seismic forces and gravity loads. In this thesis we have applied our analysis on six moment resisting frame buildings–without any shear walls- buildings of different heights and a 12-storey dual frame-wall building. Firstly, we have showed some advantages in direct displacement based design which pushed the researchers towards to this new approach. In the contrary we have showed some disadvantages in the forced based design. We showed the various steps used in each procedure to get the base shear. Secondly, we have discussed the analysis process which was performed by different programs so as to make sure of the suitability of the displaced shape equation used in the proposed procedure. Thirdly, we have showed different methods which can be used to deduce the displacement response spectrum which is considered one of the most important procedures in the displacement response spectrum Fourthly, we have showed a comparison between the base shear force calculated by the forced based design and the other calculated by the direct displacement based design for the studied buildings at different ground acceleration values. Comparisons between the periods and stiffness given by different analysis programs were outlined for the studied buildings. Finally, we have outlined the conclusions which we derived from our work and showed the ranges of suitability of the direct displacement based design then we stated some recommendation which may be carried for future work by 4
which we can refine or add some modifications to the current procedure such that we can totally replace the FBD with the DDBD for all types of structures. The thesis is consisted of six chapters .Each of them is briefly outlines in the following few lines. Chapter1: INTRODUCTION Starting by motivation of discussing this point and make detailed study to compare between the old procedures and the new ones used in estimating the seismic forces on reinforced concrete structures as it is considered one of the most common building which any structure designer must face it during his career life. Chapter2: LITERATURE REVIEW Discussing the basic concepts of the forced based seismic design, (FBD) and the displacement based seismic design ,(DBD). It shows some deficiencies in the FBD and –in the contrary-some other advantages of DBD. It describes the gradual steps for developing the latest procedures of DDBD. Finally it outlines the step by step procedures included in FBD and DDBD which are used after this in the reaming thesis. Chapter3: PLOTTING THE DISPLACEMENT RESPONSE SPECTRUM ,(DRS) At this chapter we have showed different approaches for deducing the displacement response spectrum as it is considered an essential step in applying the DDBD. The first approach derives the DRS from the acceleration response spectrum, ARS .This method is used in all analyses in the thesis however it is considered an approximate method .while the second approach derives the DRS from first principles using dynamic analysis such that it integrates the equation of motion of a single degree of freedom to find the displacement at different periods 5
Chapter4: ANALYSIS BY PROGRAMS In this chapter, we have discussed the programs used in our thesis which were SAP, IDARC, and Seismostruct. These programs were used to perform pushover analysis for the different studied buildings and from them we deduced the displaced shape of each building. We also used them to derive the base shear needed to achieve the predetermined displacement at the first floor. A step by step procedure for each program were outlined in details to show the modeling process of each building , defining the stress strain curves of the materials used, defining the cross section of the structure elements, assigning the loads, defining the criteria at which the program stops, and displaying the outputs. Chapter5: RESULTS In this chapter, we have discussed the outputs resulting from our analysis of the studied buildings. We discussed the plot of the displaced shape for each building with different analysis programs, the plot of the ratio between the base shear calculated by FBD and DDBD, comparison between the periods for all buildings, and a comparison between the stiffness of each building calculated from our previously stated programs. Chapter6: CONCLUSIONS AND RECOMMENDATIONS FOR FUTUTRE WORK In this chapter, we have outlined the conclusions which can be derived from our study based on the results for our studied buildings. Finally, we have recommended by some techniques which can be used for future researchers.
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Chapter 2 LITERATURE OF PREVIOUS WORK 2.1 Background: Current seismic design is based on forces and accelerations rather than displacements which are mainly due to some historical consideration. Before 1930’s , few structures were designed to resist earthquake actions ,then after some earthquakes occurred (USA 1933 long beach earthquake , New Zealand: 1932 Napier earthquake), researchers found that these structures showed better performance and resisted the seismic actions without significant damages. Consequently some design codes began to include the seismic design and setup the basic rules for design of structures located at high seismic regions. At first they specified an approximate value for seismic forces which was 10% of the building weight without making any relation with the building period. This force was then distributed over the building height in proportional to the mass at each floor [8]. Dynamics of structures appeared clearly during 1950’s period after which researchers began to determine dynamic characteristics of each building which was considered a nominal property for the building such as period, overall stiffness, etc. In the 1960’s design lateral forces were constructed depending on the period of the building, and the inelastic time history analysis became an accurate tool to estimate the behavior of the structure under seismic loads. It was also noticed that the structures designed according to the concepts of elasticity can survive inertia forces many times larger than those corresponding to the structure strength, this led to the development of ductility concept which showed that when a building transfers from the elastic to the inelastic behavior,
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it can dissipate seismic energy by increasing its ability to undergo the large displacements [8]. In the 1980’s more researchers tried to determine accurate values of ductility capacity for different types of structures with different connection detailing so as to be ready for usage in design codes. They resorted to experimental studies and compared them with theoretical deductions for each structure type. At the same time they tried to determine the maximum safe displacement that can occur in the building without any significant damage in its structural elements [8]. The capacity design was then introduced which aims to accurately specify the points of plastic hinges in different structural elements and determine the desired modes of failure, such as flexure failure, and the undesired modes such as the shear failure. In the 1990’s, performance based seismic design was introduced and many researchers concentrated on the concept of displacement based rather than force based design as they noticed that damage in buildings is tightly related to displacements instead of forces.
2.2 Development of displacement based seismic design [8]: 2.2.1 Force-based /displacement checked: Researchers thought that they have overcome a lot of deficiencies in force based seismic design (FBD) by introducing the new concept of displacement based seismic design (DBD) as they were persuaded that the damage is mainly based on displacement. They didn’t turn directly from FBD to DBD, but they tried at first to adopt some improvements on FBD so as to get more accurate analysis, the procedure of inserting modifications to FBD is known as force-
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based /displacement checked where they tried to use realistic determination of displacement demand for structures designed with FBD. These methods depend on using more accurate stiffness for elements of the structure in calculating the deformations, in some cases they resorted to using the inelastic time history analysis or pushover analysis so as to find the maximum displacements for the previously designed structures. If they found that the actual maximum displacements exceed the limits from the building codes, another iteration is required to be performed after increasing the stiffness of the building by changing the cross sectional dimensions of its elements. But it is clear that the concept of uniform risk at all buildings is not satisfied by this procedure. 2.2.2 Deformation calculation based design: Force-based /displacement checked approach was developed to deformation calculation based design by determining a relation between the displacement demand and the detailing at critical sections (specially the transverse reinforcement in reinforced concrete members). Deformation at elements of a certain structure (i.e.) end rotations are determined using inelastic pushover analysis or any other accurate analysis, then transverse reinforcement details are determined to make the structure elements able to achieve the previously determined end rotations. 2.2.3 Deformation specified based design: A more realistic approach was then introduced to the seismic design methods which was based on determining the actual maximum displacement of the structure -at the beginning of the design- rather than checking for the displacement at the end of design process, so these new methods ensure that all buildings will be under a uniform risk such that we avoid that some buildings will be under high risk while others are under law risk. 9
To achieve the goal of obtaining a certain maximum deformation at all buildings (according to code limits) ,Number of procedures were introduced by researchers ,all of them depend on stiffness characterization for design, Some methods adopted the initial pre-yield elastic stiffness as in conventional force based design which require some iteration so as to achieve the desired displacement. The secant stiffness to maximum displacement is utilized in some approaches based on concept of substitute structure adopted by shibata and sozen, and the use an equivalent elastic representation of hysteric damping at maximum displacement. An important advantage of these methods is that it doesn’t need to perform iterations which will save a lot of time for designers when this method is codified in building codes. Due to avoiding iterations at this procedure, it is called Direct Displacement Based Design (DDBD) methods. 2.2.4 Choice of design approach: Many researchers concluded that DDBD is a simple, accurate, and intelligent procedure for seismic design of structures. This procedure was applied to many types of structures such as frame buildings, wall buildings, dual wall-frame buildings, masonry buildings, timber structures, bridges, and piers. In this thesis we have limited our concern to reinforced concrete frame buildings, wall buildings, and dual frame-wall buildings as we think that they are the most widely used in Egypt
2.3 Fallacies in Earthquake Engineering [6]: First we will list some common incorrect concepts many designers think that they are correct but actually they are not. 10
2.3.1. Fallacy of design of elastic acceleration spectra: The Elastic acceleration response spectrum doesn't give the best means for determining the seismic response of the structure as a- The modal combination rules (same as SRSS &CQC) is not accurate to represent the inelastic response for the structure. b- Damage is related to material strain which is mainly related to maximum response displacement instead of acceleration. c- The following equal displacement approach is not accurate for calculating the displacements ∆
,
∆
1 ,
.
.
Equal displacement approach and equal energy approach are considered accurate at particular ranges and they are not accurate at other ranges of periods. There is no doubt that long period building provides larger displacement than short period building but highly damped buildings provides smaller displacement than low damped buildings so there are two main factors affecting the displacement of the building which are the building period and the damping of the building. When the period increases, the displacement increases but when the damping increases, the displacement decreases. Referring to figure 2.1 we can conclude the following: When the building is subjected to seismic loads, the building period will increase so the displacement will increase. In the contrary, when the building is subjected to seismic loads, the damping of the building will increase so the
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displacement will decrease. The resultant of the two previously stated factors will be different according to the zone of the initial period.
Figure 2.1 Displacement response spectrums for different damping [6]
For short period zone: The increase in displacement response due to the effect of increased period will be more than the decrease in the displacement response due to the increase in building damping
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For medium period zone: The increase in displacement response due to the effect of increased period will be approximately equal to the decrease in the displacement response due to the increase in building damping For long period zone: The increase in displacement response due to the effect of increased period will be less than the decrease in the displacement response due to the increase in building damping which will result in decrease of the resulting displacement. For very long period zone: The response displacement will not depend on either the period or the damping as -for this zone- the response displacement of the building will be approximately equal to the ground displacement. d- Acceleration response spectrum uses elastic stiffness of structures which is not correct while the effective stiffness by using factors of stiffness is not accurate. 2.3.2 The refined analysis myth: - Increase of sophistications due to making a 3-D model using a powerful computer program for the analysis of the structure doesn’t guarantee enhanced seismic performance due to: a. Using the same reduction factor (R) for all modes. b. Deflection profile for elastic modal analysis underestimates drifts in lower stories. c. Approximations in member stiffness: 13
Unrealistic estimates for member stiffness (some building codes uses the stiffness of the gross cross sections while others use the stiffness of 50% of the cross sections of the structure elements. 2.3.3. (Strength = Safety) is fallacy: If strength is increased by increasing flexure RFT (while dimensions are constant), the displacement capacity will decrease, the ultimate deflection capacity will decrease as the strength increases as a result of reduced ultimate curvature capacity. Since the displacement capacity is more fundamental to damage than strength, so safety will increase by reducing the flexure RFT (strength) and not vice versa. 2.3.4 The myth of maximized energy absorption: It is not correct that: "the best seismic performance is obtained when hysteric force displacement response absorbs the maximum possible energy". The best is for small hysteretic loops. To demonstrate this myth, three idealized hysteresis loop shapes were considered -as shown in figure 2.2 - which is elastic/perfectly plastic, degrading stiffness model typical of reinforced concrete, and non-linear elastic response appropriate for plastic hinge with unbounded prestressing tendons. All the three hysteretic shapes have the same initial stiffness, they all showed approximately equal maximum displacement response but whenever the load returns to zero, they showed different residual displacement. The elastic/perfectly plastic model and the degrading stiffness model showed residual displacement of about 80% from the maximum displacement response while the non-linear elastic response showed approximately zero residual displacement. According to the displacement approach, the decrease in residual 14
displacement reflects the enhancement in the behavior in the building so the non-linear elastic was the best solution.
Figure 2.2 hysteretic shapes for different models [6]
So according to experimental tests carried by PRESSS research [6], it was concluded that residual displacements are more important than maximum displacements, given the difficulty of straightening a bent building after the seismic application on the building. The PRESSS research found that structures with high hysteretic energy absorption tend to have larger deformations than structures with less hysteretic energy absorption. This research asserted that for case of zero residual displacement, problems of flange buckling can be avoided when plastic hinges form in beams
15
2.3.5. Myths and fallacies related to reinforced concrete design detailing: - It is correct that: "Using uniformly distributed flexure RFT in beams can give same flexure strength of the (Top &bottom) steel arrangement (when design moments are dominated by seismic effects”. * Benefits for uniform steel: a-Reduce congestion of RFT. b- Improve shear performance. c- Control for shear deformations. - Equations for development length are suspicious to be used in seismic regions.
2.4 Basic Correct concepts in seismic Design [6]: Then we will list some important basic correct concepts that must be adopted in the seismic design 2.4.1. The Elastic Stiffness of concrete members 2.4.1.1 General: - Modal analysis based on constant stiffness of the structure members is unable to provide accurate estimates of seismic forces since periods and distribution of forces are in gloss error. - Some codes consider the gross section (uncracked) stiffness which is not correct as some elements such as beams will normally be cracked under gravity loads before seismic actions.
16
- Other codes specify a reduction factor to be applied to the gross section stiffness. - Section stiffness is determined from moment curvature relationship and the beam equation Î - Experimental evidence and detailed analytical results indicate that the assumption of stiffness being independent of strength is not valid. - In fact yield curvature,
is independent of strength and hence stiffness is
directly proportional to the flexure strength. To demonstrate this fact, moment-curvature curve was plotted of three different moments according to experimental evidence as shown in figure 2.3.
Figure 2.3 Effect of flexure strength on moment curvature curve [6]
17
- So, it is not possible to perform accurate analysis of either elastic structure periods, or of elastic distribution of required strength through the structure until final member strengths have been determined. The elastic stiffness of different structural elements is given in the following sections. 2.4.1.2. Elastic stiffness of circular columns: To investigate stiffness of circular columns a parametric analysis was carried out varying axial load ratio and flexure RFT ratio using the computer program (cirman 4) or (CUMBIA) [16] Based on theoretical and experimental studies (made by Priestley) [6] which resulted in the following conclusion:“ Moment capacity is strongly affected by axial load ratio and also by amount of RFT but the yield curvature is not affected by axial load or RFT ratio. Consequently, it is found that the yield curvature is not affected by moment capacity. Average value of dimensionless curvature is given by 2.25
10%
Effective stiffness is determined from the following equation
- The ratio between effective and gross stiffness is given by: 0.13~0.91 Since the range is very large, a certain value inside this range can’t be easily assumed, it is better to use the curvature instead of assuming any value for
.
18
2.4.1.3 Elastic stiffness of rectangular columns: To investigate stiffness of rectangular columns a parametric analysis was carried out varying (axial load ratio &flexure RFT ratio) using the computer program (Recman 4) or CUMBIA [16]. Theoretical and experimental studies (made by Priestley) [6] showed the following conclusion: “Moment capacity is strongly affected by axial load ratio and also by amount of RFT but yield curvature doesn't vary much between the curves (i.e. yield curvature is not affected by axial load or RFT ratio)”. Consequently, it is found that yield curvature is not affected by moment capacity similar to circular columns. Average value of dimensionless curvature is given by 2.1
10%
Effective stiffness is determined from
- The ratio between effective and gross stiffness is given by: 0.12~0.86 Since the range is very large, a certain value inside this range can’t be easily assumed, it is better to use the curvature instead of assuming any value for
.
2.4.1.4 Elastic stiffness of rectangular walls (shear walls): To investigate stiffness of rectangular walls a parametric analysis was carried out varying (axial load ratio &flexure RFT ratio).
19
- Analysis showed that "uniformly distributed RFT"&"concentrated RFT at ends" will give almost identical flexure strength because "uniformly distributed RFT" gives enhanced shear performance. Based on theoretical and experimental studies (made by Priestley) [6] following conclusions are reached: Average value of dimensionless curvature is given by 2
5%
2
10%
concenterated RFT at ends
uniformly distributed RFT
Effective stiffness is determined from
- The ratio between effective and gross stiffness is given by:
/
.
1 /12
2.4.1.5 Elastic stiffness of flanged beams: To investigate effective stiffness of flanged beams, a certain beam cross section was considered with different RFT ratios. Analysis was carried out for both negative bending and positive bending. The following conclusion is found based on theoretical and experimental studies (made by Priestley) [6]:
20
The average of positive and negative moment is used in the effective stiffness calculations. Average value of dimensionless curvature 1.7
10%
1.9
10%
(Thus the concept of constant dimensionless yield curvature is adequate) - The ratio between effective and gross stiffness is given by: 0.16~0.45 We notice that it is very large range so we can’t assume a certain value inside this range. So, for (columns &walls & beams): The effective stiffness ratio depends on RFT ratio and axial load. But we can neglect the axial load effect in case of beams. 2.4.1.6 Yield drift of frames: For a beam column connection the yield drift Δ /2
is given by
Δ /2
Where: : The rotation of joint center due to beam flexure. : The rotation of joint center due to joint shear. 21
Δ : Flexure deformation of the column top relative to the tangent rotation at the joint center. Δ : Additional deformation of the column top due to the shear deformation of beams and columns. 0.5 3
6
1.7 / 6 1
1.7
&
0.283
0.4
0.25
0.1
0.5 - Experiments were made to check the adequacy of this equation which concluded that it is ok. - Experiments showed that ,
,
,
, ,
2.4.1.7 Results: - Analytical and experimental results showed that current force-based design using an assumed constant fraction of gross section stiffness for R.C members (regardless of flexure RFT and axial load) results in error in period and force distribution between members. - For stiffness calculations; yield curvature is an independent parameter that doesn't depend on RFT and axial load, while yield curvature depends only on member type (column, beam, wall...), the yield curvature for different members are summarized at table 2.1 it is clear that they are functions of yield strain of
22
steel, the cross sectional concrete dimensions, and span length (for R.C. frames).
Table 2.1.yield curvature for different structural members [6] Member type Circular column
2.25 /
Rectangular column
2.1 / 2 /
Rectangular cantilever wall T-section beams
1.7 /
R.C Frames
.
/
2.5 Some problems with Multi-Modal Analysis: 2.5.1 Advantages of Multimodal Analysis: There is no doubt that Multi-modal analysis is a good tool for seismic analysis such that it has the following advantages: a. Provides improved representation of higher mode effects. b. When used for 3-D model, it enables torsional response to be included in determining design forces. 2.5.1.1 How higher mode effects are considered in "Equivalent lateral force design" - In equivalent lateral force design, required flexure strengths at plastic hinges regions are determined from simplified representation of first mode inelastic force distribution. 23
- At other locations, required strengths are found from capacity design . . Where: : Required strength. : Over strength factor (due to overcapacity of material strengths). : Dynamic amplification factor (To account for higher mode effects). : Basic strength corresponding to first mode force distribution. 2.5.1.2 How Torsional effects is considered in "Equivalent lateral force design": The following steps summarized the procedure applied in design process (To take torsion into consideration) as follows 1. Calculate the force at each storey level (By distributing the base shear force at each floor level). 2. For each floor calculate the elastic stiffness of all force resisting elements 3. Distribute the force calculated at each level to all force resisting elements according to the relative stiffness between them. 4. Determine the location of the center of mass and the center of rigidity 5. Calculate the torsional polar moments of inertia for all force resisting elements (Parallel and perpendicular to the studied direction) 6. Calculate the eccentricity between the center of rigidity and the center of mass (then add the accidental eccentricity at each direction).
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7. Calculate the extreme torsional moments that can happen to the studied building. 8. Determine the force at each force resisting elements due to the maximum and minimum torsional moments. 9. For each force resisting element, determine the worst combination which will result in maximum acting force on it. 10. Design all force resisting elements on calculated maximum force on it. 2.5.2 Design higher modes effects by multi-modal analysis: 2.5.2.1 General: -The higher modes effects are directly considered in the analysis. -Bending moments, normal forces, shear forces, and displacements are determined for each mode. The procedure is: For each mode we calculate the following: * Mode shapes
and period
Participation factor Base shear force Force at each floor Modal displacement Δ
.
∑ ∑
∑
∑
. .
∑
. .
Using SRSS or CQC: to get elastic modal forces 25
Design forces are determined by dividing by "force reduction factor; R" Assuming "R" applies equally to all modes;
Design displacements are taken as equal to the elastic displacements. 2.5.2.2 Higher mode effects in cantilever wall from time history analysis: Six walls (2, 4, 8, 12, 16, and 20) stories were designed to Euro code 8 elastic acceleration response spectrum (0.4g, Soil B) [6]. Walls were designed in accordance with (DDBD, with interstorey drift =0.02), (Equivalent lateral force approach [using code periods, R=4]), 0.5
(Multimodal analysis [using
], R=4),
And (Time history analysis). Comparison of periods found that:
Comparison of (BMD and SFD) showed that:
Making the time history analysis: (Using computer program "Ruaumoko") we found that:
26
/
/
2.5.2.3 Modified Modal Superposition (MMS) for design forces in cantilever wall: Ductility primarily acts to limit "first mode response" but has little effect in modifying the response in higher modes. Shear force profile
Where: :Shear force at level i. : Lesser of (Elastic first mode response &ductile first mode response) : Elastic shear force at level i for mode 2 Moment profile:
1.1
- Comparison with time history results: From figures MMS approach provides a good representation of the time history moment profiles and shear forces at design intensity (IR=1)
27
2.5.2.4 Consequences for capacity design: Dynamic amplification factors (DAF) need to be increased and made intensity dependent (while; higher DAF should be used for critical facilities such as hospitals) 2.5.2.5 Higher mode effects in frame buildings from time history analysis: - Study has been carried out for three R.C frame buildings (using maximum drift = 0.0025) - From graphs (figure 3.12) we found that: & & &
&
/
- Additional work is required to formulate useable design methods for frame buildings. 1.2
2.5.3 Torsional response of building structures: Two criticisms can be noted at elastic multi-modal analysis for torsional response of inelastic systems. a. Stiffness estimates of various lateral force resisting elements (From chapter 2: stiffness will be unknown until design strengths and member dimensions are determined).
28
b. Once inelastic action develops in the major lateral force resisting elements, the eccentricity due to elastic stiffness distribution is not suitable and strength eccentricity is of fundamental importance. .2.5.4 Conclusions: - It was found that, as currently implemented in design practice, multi-modal analysis underestimates higher modes effects in structures that respond inelastically to seismic excitation. - Inelastic torsional response of structures is poorly representation represented by elastic analysis methods including multi modal analysis. - Elastic modal analysis is an inadequate tool for inelastic seismic design because: a. Stiffness inadequacies. b. Higher mode representation inadequacies. c. Torsional response inadequacies.
2.6 Comparison between Forced Based Design (FBD) and Displacement Based Design (DDBD): 2.6.1 General: Most of current codes–including the Egyptian-code use the forced based design (FBD) to perform the seismic analysis on different types of structures ,at this approach it is usually to estimate the elastic period and the elastic acceleration response spectrum with ζ=5% at the beginning of the design procedures, By the end of the our analysis a reduction ductility factor is used to reduce the resulting elastic forces so as to account for the ductility of the building which 29
can be achieved at the building by certain detailing specified by the building codes as shown in figure 2.4
Figure 2.4.Force-displacement relation for elastic and ductile behavior for reinforced concrete building
The ductility of the building, μ is defined by ∆ ∆ While the reduction factor, R is defined by
The values of the reduction factor are specified in the Egyptian code according to the type of the building same as shown in table 2.2
30
After designing all elements of the structure, the designer must check for the resulting displacements of the building and make sure that it doesn’t exceed the code limits. If the code limits are exceeded, the initially assumed stiffness of the structure elements must be modified, and then a new iteration must be carried out to determine the new base shear force. Recently, the researchers tend to different approach for performing the seismic analysis which is called “performance based seismic design, they found that displacement is a better indicator to the damage of the structure rather than the forces as the displacement can be easily converted to material strain which is related to damage of the structure elements through the exceedence of maximum allowable strain of the used material.
Table 2.2 Force reduction factor for different types of structural systems in the Egyptian code for loads [18]
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There are a lot of methods using performance based design such as ISDC method developed by Panagiotakes, and Fardis [1999], ISIP method presented by browning 2001, YPS method presented by Aschheim and Black 2000, INSPEC method by Chopra and Goel 2001, CASPEC method by Freshman 1998, SEAOC method, 1997, UBC version, and DDBD method developed by Priestley and Kowalsky (2000) which is adopted at this thesis (paper (5)). To start performing DDBD, the design drift of the building,
is determined
according to type of the building and performance level using the following table 2.3
Table 2.3.Code drift limits for different systems and different levels for damage [1] Drift Limit
Level 1
Level 2
Level 3
Structures without
0.010
0.025
No limit
0.005
0.025
No limit
unreinforced masonry Structures with unreinforced masonry
Since the drift is defined by the following equation
In this method, the structure is characterized by the secant stiffness and the damping at maximum displacement. Making a simple procedure -which will be outlined at this thesis- the base shear force, VB is determined which is necessary to achieve the design drift. 32
The calculated base shear is applied at the structure and the assumed level of damping is checked , then the design forces are adjusted –if it is necessary – but it is usual not necessary to adjust the forces as the adjustments are generally small [5]. The forced based design, (FBD) method and direct displacement design, (DDBD) method are simply outlined at the following steps (We notice that each procedure calculates the base shear force with different steps but finally the two procedures meet at the distribution of the base shear force on different floors step).
2.6.2 Forced based design method [17]: The following steps can be applied for reinforced concrete frame building, wall building, or duel frame-wall building. Step 1 Estimate the elastic period, T: The Egyptian code suggests empirical values for the period such that it doesn't exceed a certain upper limit /
(Sec)
H: height of the building (m). H
