An-Najah National University Faculty of Graduate Studies EXPLORING THE RELATIONSHIP BETWEEN THE DEFLECTION AMPLIFICATION FACTOR AND THE TIME PERIOD OF REINFORCMENT CONCRETE – MOMENT RESISTING FRAME STRUCTURES By Murad Ribhy Hussin Bsharat Supervisors Dr. Monther Dwaikat Dr. Munther Diyab Ibrahim This Thesis is Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Structural Engineering, Faculty of Graduate Studies, An-Najah National University, Nablus, Palestine. 2024 II EXPLORING THE RELATIONSHIP BETWEEN THE DEFLECTION AMPLIFICATION FACTOR AND THE TIME PERIOD OF REINFORCMENT CONCRETE – MOMENT RESISTING FRAME STRUCTURES By Murad Ribhy Hussin Bsharat This thesis was Defended Successfully on 12/06/2024 and approved by Dr. Monther Dwaikat Supervisor Signature Dr. Munther Diyab Ibrahim Co-Supervisor Signature Dr. Abdulsamee Halahla External Examiner Signature Dr. Mohammad Samaaneh Internal Examiner Signature III Dedication This thesis is dedicated to my dear parents who have encouraged and supported me. Also, to my great family and friends. IV Acknowledgment First of all, I am thankful to the almighty God for granting me good health, strength and peace throughout the research period. I would like to thank everyone who has contributed to accomplishing this thesis. I would want to express my heartfelt gratitude to my academic advisor Dr. Monther Dwaikat and Dr. Munther Diyab Ibrahim. for their extraordinary support in this project process. I think the completion of this project would not have been possible without their guidance and support. I would like to sincerely thank my family and friends for their endless support and encouragement throughout the project. V Declaration I, the undersigned, declare that I submitted the thesis entitled: EXPLORING THE RELATIONSHIP BETWEEN THE DEFLECTION AMPLIFICATION FACTOR AND THE TIME PERIOD OF REINFORCMENT CONCRETE – MOMENT RESISTING FRAME STRUCTURES I declare that the work provided in this thesis, unless otherwise referenced, is the researcher’s own work, and has not been submitted elsewhere for any other degree or qualification. Murad Ribhy Hussin Bsharat . Student's Name: Murad Ribhy Hussin Bsharat Signature: 2024/06/12 . Date: VI List of Contents Dedication ....................................................................................................................... III Acknowledgment ............................................................................................................ IV Declaration ....................................................................................................................... V List of Contents ............................................................................................................... VI List of Tables ................................................................................................................ IX List of Figures................................................................................................................ X List of Appendices ....................................................................................................... XI Abstract ......................................................................................................................... XV Chapter One: Introduction and Literature Review ........................................................... 1 1.1 Overview .............................................................................................................................. 1 1.2 Definition of Deflection Amplification Factor (Cd) ....................................................... 2 1.3 Research Significance ........................................................................................................ 2 1.4 Objectives ............................................................................................................................ 3 1.5 Structure of the Thesis: ...................................................................................................... 3 1.6 Overview .............................................................................................................................. 4 1.7 Special Moment Resisting Frames (SMRF) ................................................................... 5 1.8 Deflection Amplification Factor by Different Codes. ................................................... 5 ASCE 7-22 ............................................................................................................... 5 UBC97 standard ....................................................................................................... 6 Eurocode 8 ............................................................................................................... 7 1.9 Seismic loading ................................................................................................................... 8 Palestine Seismicity ................................................................................................. 8 Response Spectrum ................................................................................................. 8 Time History Records .............................................................................................. 9 Time History Matching to Response Spectrum ..................................................... 10 1.10 Modeling Nonlinear Behavior ....................................................................................... 10 Fiber Hinges ........................................................................................................ 10 Material ............................................................................................................... 11 Hysteresis Loops ................................................................................................. 15 1.11 Literature Review ............................................................................................................. 16 1.12 The Fundamental Period Value ...................................................................................... 19 1.13 Analysis tool (SAP 2000 software) ................................................................................ 20 VII Verification through comparison with Anil K. Chopra textbook: ...................... 21 Validation through .............................................................................................. 22 Validation through Real Testing ......................................................................... 23 1.14 Parameters Affecting on the Deflection Amplification Factor .................................. 24 1.15 Literature Review summary ........................................................................................... 25 Chapter Two: Modeling and Results .............................................................................. 26 2.1 Overview ............................................................................................................................ 26 2.2 Cases Details for Analysis ............................................................................................... 26 2.3 Model Description ............................................................................................................ 27 2.4 Materials and Sections ..................................................................................................... 27 2.5 Loads and Boundary Conditions .................................................................................... 28 2.6 Seismic Loads for Parametric Cases .............................................................................. 28 2.7 Designing and Analysis ................................................................................................... 29 Validation of the Model ......................................................................................... 29 Analysis of Parametric Study ................................................................................ 30 2.8 Analyze result and Calculating the Deflection Amplification Factor (Cd )............... 31 Chapter Three: Result Analysis and Cd -Factor Evaluation ........................................... 34 3.1 Overview ............................................................................................................................ 34 3.2 Parametric Study ............................................................................................................... 34 3.3 Analysis Results ................................................................................................................ 34 3.4 Results and Discussion ................................................................................................ 35 Correlation B Cd and Building Characteristics ...................................................... 36 The Effect of Time Period on Cd ........................................................................... 37 The Effect of Span Length on Cd ........................................................................... 39 The Effect of Floor Height on Cd ........................................................................... 40 The Effect of Number of Bays on Cd ..................................................................... 41 3.5 Proposed Equation for Cd ................................................................................................ 42 Regression Analysis ............................................................................................... 43 Residual ................................................................................................................. 44 Validate the Equation ............................................................................................. 45 Chapter Four: Conclusion and Recommendation ........................................................... 46 4.1 Overview ............................................................................................................................ 46 4.2 Conclusions ....................................................................................................................... 46 4.3 Proposed Equations .......................................................................................................... 47 4.4 Recommendations and Future Studies ........................................................................... 48 VIII References ....................................................................................................................... 49 List of Abbreviations ...................................................................................................... 53 Appendices ...................................................................................................................... 55 ب ............................................................................................................................... الملخص IX List of Tables Table 1: General properties of the RC framed structures used in Study ........................ 26 Table 2: General for Data Concrete B 350 and ASTM A615 ........................................ 27 Table 3: Response Spectrum properties .......................................................................... 29 Table 4: Computation of the Cd value for parametric study .......................................... 32 Table 5: Analysis results for 36 case studies .................................................................. 35 Table 6: A correlation table was generated using Excel ................................................. 36 Table 7: Regression Statistics for equation to compute Cd value .................................. 43 Table 8: Coefficients of equation to compute Cd value ................................................. 44 Table 9: ANOVA table by SPSS software for Cd equation ........................................... 45 Table 10: Root Mean Squared Error of the fitted model ................................................ 45 X List of Figures Figure 1: The Vecchio and Emara (1992) frame a) Structural details.b) Comparing between The Vecchio and Emara (1992) frame and SAP2000 pushover ..... 23 Figure 2: Geometric and design layout of prototype RC farm a) concrete reinforcement and sections b) real modal for testing ........................................................... 24 Figure 3: Time-history before and after matched with response spectrum for Z=0.3 by Seismomatch and SAP 2000 ......................................................................... 31 Figure 4: Hysteresis Loop and Hinge Performance ........................................................ 32 Figure 5: Elastic and inelastic displacement for each floor by linear and nonlinear analysis for three-time history records........................................................................ 33 Figure 6: The relationship between the periodic time and Cd factor .............................. 37 Figure 7: Influence of Structure Time Period on Seismic Force and Inelastic displacement when Transition from Elastic to Inelastic Behavior through Modal Response Spectrum Analysis ........................................................................................ 38 Figure 8: Variation of the Cd concerning the span length (5m and 7m) while altering the number of floors a) 4-bays and 3.5 m floor height b) 3-bays and 3 m height floor) 3-bays and 3.5 m floor height ............................................................. 39 Figure 9: Variation of the Cd Factor concerning the Floor height (3m, and 3.5m) while altering the number of floors a) 3-bays and 7 m Span length b) 3-bays and 7 m Span length ............................................................................................... 41 Figure 10: Variation of the Cd Factor concerning the number of bays (3,4, and5) while altering the number of floors a) 5m Span length and 3 m floor height b) 6m Span length and 4 m floor height c) 6m Span length and 4 m floor height .. 42 XI List of Appendices Appendix A: Tables ........................................................................................................ 55 Table A. 1: Cd value According of in NEHRP Recommended Provisions for the structure systems ............................................................................................................................ 55 Table A. 2: Deflection amplification factor in different building codes ........................ 55 Table A. 3: Time-History record properties ................................................................... 55 Table A. 4: Comparison of models for confined and unconfined concrete .................... 55 Table A. 5: Geometric and design layout of prototype RC frame .................................. 56 Table A. 6: General properties of the RC framed structure used in macro modeling .... 56 Table A. 7: SIDL account details .................................................................................... 56 Table A. 8: models Specifications reinforcement employed in the Research ................ 56 Table A. 9: Model Summary (Regression Statistics ) for Time-period Equation .......... 58 Table A. 10: ANOVA for Time-period .......................................................................... 58 Table A. 11: Coefficients for Time-period Equation ...................................................... 58 Table A. 12: Cd calculation details for case1 ................................................................. 58 Table A. 13: Cd calculation details for case2 ................................................................. 59 Table A. 14: Cd calculation details for case3 ................................................................. 59 Table A. 15: Cd calculation details for case 4 ................................................................ 59 Table A. 16: Cd calculation details for case 5 ................................................................ 59 Table A. 17: Cd calculation details for case 6 ................................................................ 60 Table A. 18: Cd calculation details for case 7 ................................................................ 60 Table A. 19: Cd calculation details for case 8 ................................................................ 60 Table A. 20: Cd calculation details for case 9 ................................................................ 60 Table A. 21: Cd calculation details for case 10 .............................................................. 61 Table A. 22: Cd calculation details for case 11 .............................................................. 61 Table A. 23: Cd calculation details for case 12 .............................................................. 61 XII Table A. 24: Cd calculation details for case13 ............................................................... 62 Table A. 25: Cd calculation details for case 14 .............................................................. 62 Table A. 26: Cd calculation details for case15 ............................................................... 62 Table A. 27: Cd calculation details for case 16 .............................................................. 63 Table A. 28: Cd calculation details for case 17 .............................................................. 63 Table A. 29: Cd calculation details for case 18 .............................................................. 63 Table A. 30: Cd calculation details for case19 ............................................................... 64 Table A. 31: Cd calculation details for case20 ............................................................... 64 Table A. 32: Cd calculation details for case 21 .............................................................. 64 Table A. 33: Cd calculation details for case 22 .............................................................. 65 Table A. 34: Cd calculation details for case23 ............................................................... 65 Table A. 35: Cd calculation details for case24 ............................................................... 66 Table A. 36: Cd calculation details for case 25 .............................................................. 66 Table A. 37: Cd calculation details for case26 ............................................................... 66 Table A. 38: Cd calculation details for case27 ............................................................... 67 Table A. 39: Cd calculation details for case28 ............................................................... 67 Table A. 40: Cd calculation details for case29 ............................................................... 68 Table A. 41: Cd calculation details for case30 ............................................................... 68 Table A. 42: Cd calculation details for case31 ............................................................... 69 Table A. 43: Cd calculation details for case32 ............................................................... 69 Table A. 44: Cd calculation details for case33 ............................................................... 70 Table A. 45: Cd calculation details for case34 ............................................................... 70 Table A. 46: Cd calculation details for case35 ............................................................... 71 Table A. 47: Cd calculation details for case36 ............................................................... 71 Appendix B: Figures ....................................................................................................... 72 XIII Figure B. 2: Seismic Hazard Map and Seismic Zone Factor (Source ESSEU, Earth Sciences and Seismic Engineering Unit at NNU ) ....................................... 72 Figure B. 3: Design response spectrum .......................................................................... 72 Figure B. 4: Recordings adopted by the International Building Code (IBC) ................. 73 Figure B. 5: Time history matching to response spectrum by Sap 2000 which matched before by Seisomatch software ..................................................................... 73 Figure B. 6: Fiber hinge .................................................................................................. 74 Figure B. 7: Concrete area with effective confinement .................................................. 74 Figure B. 8: Stress-Strain curve ...................................................................................... 75 Figure B. 9: Stress- Strain Model proposed .................................................................... 76 Figure B. 10: Proposed Stress-Strain curve .................................................................... 77 Figure B. 11: Stress-strain Curve for steel reinforcement .............................................. 77 Figure B. 12: Takeda Hysteresis Mode .......................................................................... 78 Figure B. 13: Kinematic Hardening hysteresis model .................................................... 78 Figure B. 14: Deflection amplification factor for different story levels in ordinary and special MRF .................................................................................................. 79 Figure B. 15: Variation of Fundamental Period with Structural Height ......................... 79 Figure B. 16: Validation through a Single Degree of Freedom (SDOF) Approach ....... 80 Figure B. 17: Validation via Analysis of a Concrete Frame ........................................... 80 Figure B. 18: Geometric and design layout of prototype RC frame ............................... 81 Figure B. 19: Column Axis plan ..................................................................................... 81 Figure B. 20: 3D ETABS model ..................................................................................... 82 Figure B. 21: Three time histories record using for analysis .......................................... 82 Figure B. 22: Mander Confined and unconfined Concrete model for concrete B350 by the SAP2000 Software ........................................................................................ 83 Figure B. 23: Stress - strain curve for reinforcements steel by the SAP2000 Software . 83 Figure B. 24: The sequential formation of plastic hinges ............................................... 84 XIV Figure B. 25: Single –deree freedom system .using by Anil K. Chopra ........................ 84 Figure B. 26: Ductility demand for elastoplastic system due to El Centro ground motion ...................................................................................................................... 85 Figure B. 27: A correlation was generated using SPSS .................................................. 85 Figure B. 28: The residual errors for Cd equation devloped by regression analysis ...... 86 Figure B. 29: Cd normalization through dividing the coefficient (Cd) for each system by the minimum Cd value versus the floor number ........................................... 87 Figure B. 30: General Structural Response .................................................................... 87 Figure B. 31: Elastic and inelastic displacement through each floor by linear and nonlinear time history analysis for three records .......................................................... 88 Appendix C: Validation of the model for design ............................................................ 97 Appendix D: Model Design .......................................................................................... 101 XV EXPLORING THE RELATIONSHIP BETWEEN THE DEFLECTION AMPLIFICATION FACTOR AND THE TIME PERIOD OF REINFORCEMENT CONCRETE -MOMENT RESISTING FRAME STRUCTURES By Murad Ribhy Hussin Bsharat Supervisors Monther Dwaikat Dr. Munther Diyab Ibrahim Abstract The deflection amplification factor (Cd) is an important parameter in seismic design. Cd is essential in seismic design according to the American Society of Civil Engineers minimum design load standards (ASCE7-16) especially for the drift check and for the calculation of the seismic separator distance. Contractors face difficulty in implementing seismic separation, especially in high-rise buildings. The seismic separator is computed in ASCE7-16 depending on the Cd factor by calculating the inelastic displacement, which is crucial for calculating the seismic separation. Cd remains constant for the same structural system, as per ASCE7-16, regardless of the building characteristics such as (time period which depends on span length, story height and numbers of bays). The goal of this work is to obtain a Cd value for each building based on the building’s characteristics, which helps in reducing the width of the seismic separator, especially for high-rise buildings. To achieve this goal, various parameters associated with building characteristics that may influence Cd value were studied. 36 case studies of square-shaped building models with varying numbers of floors, floor height, span length, and the number of bays were analyzed using both linear and nonlinear time history analysis. Three-time history records that match the response spectrum in SAP2000 and seismomatch are used to compute Cd. On the other hand, the computer software, ETABS was used for the structural design considering both gravity and seismic loads. Results from the analysis show that ASCE 7-16 is conservative in presenting Cd values and that Cd varies depending on the characteristics of the building. The results show that XVI the value of Cd decreases with increasing span length, story height, number of bays, and time period (Tn). The results of this study were used to develop an equation to estimate Cd based on the building characteristics. Keywords: Deflection amplification factor, Cd, SMRFs, Time history, Response Spectrum, nonlinear displacement, liner displacement, fiber hinge. 1 Chapter One Introduction 1.1 Overview In regions prone to earthquakes, ensuring the safety and structural integrity of buildings is crucial. Designing structures that can withstand earthquakes involves various factors, including the deflection amplification factor (Cd). Cd value is very important for high-rise buildings because it's used to determine the seismic separator and check drift. Cd is crucial for calculating inelastic displacement. Engineers use Cd by multiplying it with elastic displacement to find the resulting inelastic displacement. This value is then utilized to calculate the seismic separation between two buildings. Construction of high- rise buildings based on may conservative Cd values taken from ASCE Code 7-16, which do not take into account the characteristics of the building. A challenge arises from the role that the Cd value plays in determining the seismic separator, as it gives a large distance between two adjacent buildings that is difficult to apply when carrying out building construction. Previous research and insights from books on the dynamics of structures suggest that the Cd factor may decrease as the building height (and hence the period of the building) increases (Chopra, 2017). If an equation is developed to obtain a Cd value that takes into account the building properties, a specific Cd value can be calculated for each building. This is in contrast to the ASCE7-16 code, which adopts precise values for the identical structural system. This approach can reduce the distance of the seismic separation between buildings if the Cd value is less than ASCE7-16 code, as a result addressing an assignment that engineers face at some point of the implementation of constructing construction. The improvement of an equation (mathematical expression) governing the Cd value represents a large advancement in displacement-based layout methodologies. This development complements the precision and reliability of seismic design, supplying engineers worldwide with the ability to fine-tune designs to achieve targeted performance levels. 2 1.2 Definition of Deflection Amplification Factor (Cd) Cd, which referred to as the deflection amplification issue, is a critical parameter used in structural engineering to assess the quantity to which the deflection of a building is multiplied mainly occasions. Indeed, it assists engineers in comprehending and forecasting how expertise and predicting how a shape will reply to external forces. Further, by using taking Cd into consideration and controlling the degrees of deflection, engineers can make certain that homes continue to be safe. Cd represents the ratio of the expected displacement, throughout a seismic occasion (most inelastic displacement) to the deflection determined the usage of elastic evaluation (ASCE7-sixteen, 2017). It quantifies how a great deal the buildings movement is magnified for the duration of an earthquake compared to its motion beneath ordinary conditions. This parameter performs a function in layout and assessment presenting insights, into structures dynamic behavior in the course of earthquakes and helping in designing buildings to withstand seismic forces effectively. 1.3 Research Significance This study seeks to address a major engineering hurdle of seismic separation, especially when designing high-rise buildings. The hurdle revolves around a critical factor known as Cd. Engineers usually rely on Cd to check the drift and determine the separation distance between two adjacent buildings. In high-rise buildings, structural seismic separation becomes a large distance when using ASCE7-16, which creates challenges for implementation. Cd value remains constant in ASCE7-16 for same structural system regardless of the specific characteristics of the building. Hence, the aim is to obtain a specific Cd value for building based on it is characteristics, which value may be less than the code value based on previous studies suggested that the Cd coefficient tends to decrease with increasing building height which will be discussed in the chapter two. This enables the hurdle seismic separator solution, which is affected by the value of the Cd. The aim of this thesis is to understand how structure characteristics (span length, story height, number of bays, and time period (Tn)) effect on the Cd for buildings with the RC- SMRF structural system. It also aims to explain the effects of building characteristics on 3 Cd by creating an empirical equation through which the value of Cd is calculated based on the building’s characteristics, if the results of the analysis allow. 1.4 Objectives The primary goal of this study is to reevaluate the Cd, in conventional Reinforced Concrete Special Moment Resisting Frames (RC-MRFs) that commonly used in Palestine. This reassessment involves using nonlinear time history analysis tools to investigate how the Cd is influenced by structural time periods (related to mass and stiffness) and structural geometry (span length, story height, and the number of bays). To achieve this goal, the research begins with a thorough literature review to examine recent studies on the Cd, aiming at gaining insights into the subject. Subsequently, nonlinear time history analysis is applied to understand the relationship between the deflection amplification factor for RC-MRFs and the structural geometry and time period. A simplified equation has been devloped for the defliction amplification factor (Cd). using statistical regression. 1.5 Structure of the Thesis This thesis unfolds by way of presenting distinctive chapters, every contributing to the overall exploration. Chapter One: Introduction and Literature Review: The thesis opens with a short but comprehensive introduction in the first chapter. This Chapter This chapter seeks to address the research problem and highlight its importance within this field. On the other hand, presents an in-depth examination of the associated challenges with modeling (specifically issues pertaining to simulating fiber hinges) using linear or non-linear time-history analyses. It also treats validation and verification of the analysis tool, material nonlinearity, review literature relevant to this study. Chapter Two: Modeling and Analysis: In this Chapter, this thesis delves into the intricacies of modeling particularly focusing on the hurdles associated with portraying fiber plastic hinges. The chapter also delves into computing both inelastic displacements using linear and nonlinear time history analyses to determine the Cd value. 4 Chapter Three: Proposed Equation for Cd : The Chapter Three holds significance within the thesis framework. It showcases the effects of the analysis for 36 scenarios highlighting the Cd particular characteristics of each parametric study. An examination of the collected records is carried out to explain how every parametric study (each building characteristic) influences Cd, observed with the aid of a formulation for locate the Cd value based based on building characteristics. Chapter Four: Conclusions and Recommendations: Acting as a repository for discoveries within the thesis Chapter Four consolidates research findings into conclusions and offers evidence-based totally suggestions critical, for seismic engineering. 1.6 Overview Understanding seismic engineering is understanding how structures perform under dynamic forces, especially those caused by earthquakes. The Deflection Amplification Factor is a key parameter in this understanding of structural dynamics, which depends on for the most part about Cd. The need for Cd and its importance in seismic design, especially in drift and seismic separator is explains extensively by this thesis. Through linear and nonlinear time-history analysis, a software like SAP2000 will calculate the Cd value by getting elastic and inelastic displacement. Cd value is an important parameter in seismic design. screening drifts that govern the dimensions of concrete sections and the distance between adjacent buildings (seismic separator). This chapter examines the various methods of calculating Cd from engineering codes and literature. After that the design criteria of Special Moment Resisting Frames (SMRFs) are collected based in ACI-318. Also, linear and non-linear time-history analyses are carried out. 5 1.7 Special Moment Resisting Frames (SMRF) SMRFs (Special Moment Resisting Frames) are utilized to withstand under the influence of lateral loads such as wind or earthquake force. Generally, composed of beams and columns interconnected by strong joints that allow them to transfer lateral loads from the building down through connections all the way driven into ground. SMRFs add a measure of stability and stiffness to the building, especially in Seismic regions because they help it sustain multiple loads that result from lateral movement respectively. In Guidelines for ACI detailing of special moment resisting frames, designing criteria are given with respect to material properties, Proper reinforcement detailing, including column and beam reinforcement, ensures adequate ductility and confinement for concrete by ties under seismic loading. Beam-column joint design is crucial, requiring sufficient strength and ductility through special detailing like confinement and shear reinforcement. 1.8 Deflection Amplification Factor by Different Codes. The deflection amplification factor is crucial in design, so engineers refer to engineering codes to find the factor value. However, each code has its own method for determining this factor value. This section will explain how to find the factor value in the main engineering codes. ASCE 7-22 For seismic analysis and design, seismic force-resisting systems are categorized in ASCE- 7-16's Table 12.2-1, further divided for different types of vertical elements. FEMA P-695 (2009b) establishes a methodology for quantifying seismic system performance, addressing parameters like R, over-strength factor (Ω0), and deflection amplification factor (Cd). These are collectively termed "seismic design coefficients." Future systems are likely to adopt this methodology, with existing coefficients subject to review. Height limits, specified for over 50 years, have evolved based on expert judgment from organizations like the NEHRP Provisions Update Committee and the ATC-3 project team, adjusting over time based on observations and testing, albeit with subjective values (ASCE7-16, 2016). 6 To Compute Cd, determine the values of ∆ 𝑚𝑎𝑥 and ∆e for the specific seismic loading scenario under consideration from liner and non-liner time history. Shown (Uang, 1991) that the force reduction and deflection amplification factors for strength design can be expressed by the following formulas, and Figure B .30 in Appendix B explain the General Structural Response : 𝐶𝑑 𝑅 = µ𝑠 𝑅µ = ( ∆𝑚𝑎𝑥 ∆𝑦 ) ( 𝐶𝑒 𝐶𝑦 ) = ( ∆𝑚𝑎𝑥 ∆𝑦 ) ( ∆𝑒 ∆𝑦 ) = ∆𝑚𝑎𝑥 ∆𝑒 (1) Where: ∆𝑚𝑎𝑥∶ maximum inelastic drift. ∆𝑒∶ maximum elastic drift ∆𝑒∶ maximum yielding drift. 𝐶𝑒: elastic base Shear Ratio. 𝐶𝑦 ∶ yielding base Shear Ratio. Divide the maximum inelastic displacement (δi) by the maximum elastic displacement(𝛿𝑒): 𝐶𝑑 = 𝛿𝑖 ∗ 𝐼/ 𝛿𝑒 (2) Where:  (δi): the maximum inelastic displacement  (𝛿𝑒) ∶maximum elastic displacement divided on reduction force factor (R).  I: Important Factor UBC97 standard The UBC code obtained the Cd value for SMRFs through a comprehensive analysis of structural behavior data, empirical correlations, and engineering expertise, similar to the approach followed by other seismic design codes like ASCE. Within the UBC97 standard, the calculation for the nonlinear displacement value is outlined as follows (International Code Council, 1997). 𝛥𝑚 = 𝛽𝑅𝑢𝛥𝑠 (3) 7 𝑚 0.7 𝑅𝑢𝑠 (4) The equation No.4 simplify to find Cd to Equation No. 5, where β is set at 0.7, and it can be formulated as: 𝐶𝑑 = 0.7𝑅𝑢 (5) 𝛥𝑠: Maximum inelastic displacement of the structure. 𝑚: Maximum elastic displacement of the structure. Rμ: Coefficient of ductility behavior. Eurocode 8 Euro code 8, the deflection amplification factor (often denoted as q) is used to account for increased deflections in structural elements during seismic events, taking into consideration the nonlinear behavior of the structure. The calculation of Cd is a bit more complex and may involve several steps. Here is a simplified overview of how to compute the deflection amplification factor in Eurocode 8 (Solomos, Pinto, & Dimova, 2008): The Deflection Amplification Factor (Cd) which called (𝑞) can be calculated according Eurocode 8 using in the following equation: 𝑞 = (𝑆𝑑 / 𝑆𝑎) ∗ (𝑇 / 𝑇𝑜) ∗ 𝜇 (6) Where:  Sd: is the design response spectrum acceleration at the structure's period T.  Sa: is the design ground acceleration.  T: is the fundamental natural period of the structure.  To: is the reference period, usually taken as 1 second.  𝜇 : Ductility Reduction Factor Table A.1 in Appendix A displays the usage of Cd in the NEHRP Recommended Provisions. The subsequent table provides a visual representation of deflection amplification factors within a range of building codes explain in table A .2 in Appendix A. 8 1.9 Seismic loading Palestine Seismicity Palestine is an active seismic region with seismic foci concentrated in areas influenced by the Arabah Valley, the Jordan Rift Valley, the Dead Sea vicinity, and the southern extent of the Sea of Galilee. These seismic influences are connected to fault lines associated with the Depression Zone, demarcating regions between Palestine and Jordan. Noteworthy fault lines include the Fara'a Rift occurring in 1759 (El-Hussain, Sader, & Juhari, 2018). multiple seismic foci are situated, with up to five epicenters located about 10 to 12 kilometers beneath the surface (Meghraoui, 2015). Also, the Carmel Fault, impacting cities like Nablus, Ramallah, and Jerusalem. Near the Dead Sea, Carmel region exhibits activity every 200 to 300 years, with the most recent destructive earthquake. Palestine experiences recurring earthquakes in various regions. The northern Tiberias region and the Galilee Finger encounter earthquakes approximately every 800 years (Marco et al. 2003). Recent earthquake engineering studies reveal that Palestine region has a medium or medium-high level of seismic hazard (Monteiro, Dursun, & Andrade, 2016). Analyzing the Earthquake Acceleration (PGA) map for Palestine provides insights into ground shaking intensities' distribution.] This map outlines peak ground accelerations resulting from seismic events, helping identify zones with varying seismic hazard levels (Zones 1, 2A, 2B, and 3) (Filippou, 2013). The Palestinian Engineers Association mandates earthquake-resistant building design following international codes and local codes like UBC97 or IBC 2012. Figure B.1 in Appendix B illustrates the Seismic Hazard Map and Seismic Zone Factor (Source: ESSEU, Earth Sciences and Seismic Engineering Unit at NNU). Response Spectrum The response spectrum, as defined in ASCE 7-16, is a graphical representation depicting the maximum response of a structure to seismic ground motions across different frequencies. It gives engineers the basics of how to analyze and design structures that are safe for seismic forces. This picture is very important to measure the dynamic response 9 under seismic, which helps practical research in earthquake engineering for construction safety and durability. Some key parameters for design spectral acceleration in ASCE 7-16 SDS stands for short- period design spectral response acceleration (usually 0.2 seconds). SD1 indicates the spectral response acceleration at 1 second-period, corresponding to a segment of steady velocity in the spectrum. TL marks the transition from this constant-velocity segment to the constant-displacement segment. Understanding these parameters is very vital for seismic analysis and designing which helps an engineer to know the behavior of a structure under earthquake loads and making it safe in case of all earthquakes (Ghosh, 2014). Figure B.2 in Appendix B shows the ASCE-7-16 design response spectrum. Time History Records In the realm of earthquake engineering and structural dynamics, time-history records are datasets that capture ground motion during seismic events. They provide information on ground acceleration, velocity and displacement for instruction on how to move during earthquakes. They help us understand the impacts of earthquakes on structures by telling us how long they last. Besides, they involve frequency content that tells us about energy distribution at different frequencies thus affecting response of a structure. Amplitude measurements in the records quantify the strength of shaking experienced during earthquakes. The ASCE7-10 code, which is section 16.14, prescribes specific requirements for seismic analysis. These include the use of at least three ground motion record sets in order to ensure a comprehensive evaluation of structural response to ground motions. This means that a minimum of three sets of ground motion records must be used in any analysis. If there are less than seven sets, the design parameters will be based on the maximum values obtained from all the analyses. Conversely, where seven or more records are involved in an analysis, design can be based on average values derived from the analysis. Although using seven or more ground movements is useful, for the sake of more case studies and available technical capabilities, only three combinations are used. 10 Figure B.3 in Appendix B illustrates the earthquake record format adopted by the International Building Code (IBC). Table A.3 in Appendix A shows the characteristics of three ground records used in both linear and nonlinear time-history analysis. Time History Matching to Response Spectrum In seismic engineering and analysis, aligning ground motion time records with specific response spectra is crucial, particularly in Palestine where the seismic hazard is different from other locations. In order to better understand how structures interact with potential seismic loads. It requires selecting and modifying time history records to accurately simulate local seismic events. This involves utilizing software tools like SeismoMatch and SAP2000, which facilitate the matching of temporal structural response profiles to response spectra. SeismoMatch uses specialized algorithms for spectral matching, while SAP2000 reconciles the process involves refining chronological data by iteratively comparing it with response spectra. Figure B .4 in Appendix B demonstrates successful times the alignment between the time-history and response spectram. The procedure for Spectrum Matching has shown that achieving a good match is easier when extending the matching period beyond the period range of interest. This is why spectrum matching is required within the range of 0.8 times the lower period (Tlower) to 1.2 upper period (Tupper). Hence, a good match achieved is when the average acceleration spectrum computed from the matched records in each direction stays within 10% above or below the target spectrum across the period range of interest (ASCE7-16, 2017). 1.10 Modeling Nonlinear Behavior Fiber Hinges The fiber hinge concept divides a reinforced concrete section into individual fibers, each following a non-linear stress-strain curve based on its material type (such as unconfined concrete, confined concrete, or steel reinforcement). This concept employs fiber hinges to distribute plasticity throughout the section, allowing for a comprehensive representation of its behavior. The section's overall response is determined by summing up the contributions of all fibers. In SAP2000, fiber hinge model can use, and calculates 11 non-linear deformations in response to internal forces within the section using advanced numerical methods and algorithms based on finite element analysis (FEA). Figure B.5 in Appendix B illustrates the behavior of fibers and materials under cyclic load. Material 1.10.2.1 Concrete Understanding the behavior of concrete in reinforced concrete sections involves considering confined and unconfined concrete models. Various models are available to study both types of concrete behavior simultaneously, while some focus solely on confined concrete. Examples include models developed by Cusson & Paultre (1995), Hoshikuma et al. (1997), Sheikh & Azumiri (1982), Martinez et al. (1984), Ahmed & Shah (1982), Al-Dash & Ahmed (1995), and Asa et al. (2001). Additionally, widely used and accurate models for selecting the most appropriate one for research purposes include those by Kent & Park (1971), Razvi & Satcioglu (1999), and Mander, Priestley, & Park (1988). Confined and Unconfined Models for Reinforced Concrete section: Confinement models examine how lateral reinforcement (such as hoops, spirals, and ties) affects the stress-strain characteristics of concrete. They are designed to capture the increased strength, ductility, and energy absorption capacity observed in confined concrete. These models utilize parameters like the confinement ratio, details of lateral reinforcement, and concrete strength to forecast stress-strain relationships. Both empirical and theoretical models can be used to provide accurate estimations of concrete confined stress-strain behavior. On other hand, Unconfined models study how stress and strain change without considering lateral reinforcement. They take into account factors such as the concrete compressive strength, tensile strength, and other material properties. These models are helpful for predicting how elements behave when they aren't heavily confined laterally. 12 Figure B.6 in Appendix B demonstrates Concrete area with effective confinement concret. The most popular methods for modeling both confined and unconfined concrete are: Kent & Park (1971) proposed that the maximum strength for both confined and unconfined concrete is the same, denoted as f’c. They suggested a curve, as shown in Figure B.7 in appendix B, which starts from the origin and increases parabolically ( known as Hognestad’s Parabola) until reaching the peak at f’c and the corresponding strain εco at 0.002. Then, it descends with one of two different straight lines. For confined concrete, which is more ductile, it descends until the point (0.5 f’c, ε50c) and continues descending to 0.2 f’c followed by a flat plateau. For unconfined concrete, it descends until the point (0.5 f’c, ε50u) and continues descending to 0.2 f’c without a flat plateau. Kent and Park assumed that confined concrete could sustain strain indefinitely at a constant stress of 0.2 f’c (Scott, 1980). Mander's model is widely used because it's simple yet effective at accounting for the effects of confinement. The study is a look into the improvement of strength and flexibility, which occur in reinforced concrete members when they are confined. For instance, this model is often used to evaluate the strength of columns when encased with stirrups (Mander, Priestley, & Park, 1988). Additionally, Also, Mander’s model is an earthquake engineering method that focuses on confined concrete which deals with circular spiral reinforcement and hoops and rectangular ties among others. These confinement methods are studied to determine how they influence concrete performance when subjected either to cyclic or monotonic type of loadings. One important point noted is the effective lateral confinement pressure coefficient (ke) which improves both strength and ductility in concrete. Also, Mander's model is concerned with the complex interactions between reinforcing elements such as materials that are used to bind together the pertaining structures and thus it gives insight in relation to the mechanics of closed-in concretes structures. When concrete is confined laterally in, its compressive strength (𝑓′cc) and corresponding strain (εcc) are significantly higher than those of unconfined concrete (𝑓′co and εco), as depicted in Figure B.8 in appendix B. Here, 𝑓′t, 𝑓′co, 𝑓′cc, εt, εco, εcc, εcu, εsp, Ec, and Esec 13 represent the tensile strength of concrete, the compressive strength of unconfined concrete, the compressive strength of confined concrete, the tensile rupture strain of concrete, the concrete strains corresponding to peak strength of unconfined concrete, the concrete strains corresponding to peak strength of confined concrete, the ultimate compressive strain of confined concrete, the strain at which the concrete cover is considered completely spalled, the modulus of elasticity of concrete, and the secant modulus of confined concrete at peak stress, respectively (Mosheer, Khamail Abdul- Mahdim, 2016). Saatcioglu & Razvi (1992) found that the lateral pressure from expanding concrete and the restraining effect of transverse reinforcement may not always be consistent. After testing concrete with strengths ranging from 30 to 130 MPa, they introduced a new model Figure B.9 in appendix B showing an exponential relationship between lateral confinement pressure and peak confinement strength. Their experiments involved changing factors like the volume ratio, spacing, yield strength, layout of transverse reinforcement, concrete strength, and section shape. Confined concrete models are created using physical engineering, empirical, and combined methods. Notably, Mander et al. (1988) and Saatcioglu & Razvi's (1992 & 1999) models are known for their effectiveness and accuracy. Mander et al. (1988) model it is practical and reliable. This model provides a straightforward yet efficient method to understand how confinement affects concrete. It accurately reflects the strength and flexibility improvement in reinforced concrete when confined. Moreover, Mander's model is commonly used to assess the strength of columns confined by stirrups. In this study, Mander et al. (1988) approach will use to determine the stress-strain relationships of both confined and unconfined concrete in different structural elements like columns and beams. The materials will use are Concrete Grade B350 and Grade 60 reinforced steel in confind concrete modal . Table A.4 in Appendix A showes Comparison of models for confined and unconfinedconcrete for by Kent & Park (1971), Razvi & Satcioglu (1999), and Mander, Priestley, and Park (1988). 14 1.10.2.2 Mander et al. (1988) Model for Tension Behavior The tension behavior according to the Mander model is divided into two linear segments as show in Figure B.8 in Appendix B : linear elastic behavior and linear behavior beyond the yield point. The linear elastic behavior is described by an equation No. 8 where stress is directly proportional to strain within the elastic range. Additionally, the model may include linear behavior beyond the yield point, described by equations No.9 and 10 that detail the stress-strain relationship under tension. (Huang, Wang, Yang, & Wei, 2023) 𝑓𝑡 ′ = 𝐸 ⋅ ϵt ′ (8) σ𝑡 = { 𝑓𝑡 ϵt ′ 2×10−4 ϵt ′ ≤ 2 × 10−4 (9) 𝑓𝑡 ( 8×10−4− ϵt ′) 6×10−4 ϵt ′ ≤ 2 × 10−4 (10) where: E: represents the modulus of elasticity ( 21 000 , MPa) 𝑓𝑡: tensile strength of con‐ crete. ϵt ′: corresponding strain. σ𝑡: tensile stress The equation represents how concrete behaves elastically in a linear fashion, with stress being directly proportional to strain within the elastic range. For non-linear behavior beyond the yield point, Mander’s model has a linear segment and possibly more sophisticated equations that can be used to describe stress-strain relationship under tension. Such equations might incorporate terms for strain hardening or softening and also ultimate stress and strain values at failure. Tensile Strength of Concrete. 1.10.2.3 Steel Rebar Steel reinforcement Grade 60, known as ASTM A615 Grade 60 is a standardized specification for deformed and plain carbon steel bars that are used in reinforcing concrete structures. The construction industry uses this specification to enhance the tensile and yield properties of the steel bars in question. The table below gives an insight into mechanical properties specifically for ASTM A615 Grade 60. In addition to that, kinematic hysteresis loops are applied to expound on rebar behavior mechanism in 15 mechanics of materials. This is described by figure B10 page 146 (Appendix B) showing Stress-Strain Curve for Steel Reinforcement. Hysteresis Loops Hysteresis loops are commonly seen in materials such as reinforced concrete or steel when they undergo cyclic loading, such as during earthquakes (Pozo, Martínez, & Martínez, 2009). When hysteresis loops are nonlinear, it means that the structural response does not directly correspond to the applied load due to the material or structural behavior. This nonlinearity occurs when the relationship between the applied load and the resulting deformation or displacement of the structure is not linear. In other words, as the load increases or decreases, the deformation or displacement of the structure does not change proportionally, leading to a nonlinear hysteresis loop. This behavior is often observed in structures subjected to large deformations, yielding, or other nonlinear effects, where the relationship between stress and strain is not linear throughout the loading and unloading cycles, often because of factors like material yielding, stiffness reduction, or frictional effects within the structure. Various types of Hysteresis Loop Models exist, such as the Elastic, Kinematic, Degrading, Takeda, Pivot, Concrete, BRB Hardening, and Isotropic Hysteresis Models. In this study, Takeda and Kinematic Hysteresis Models will use . 1.10.3.1 Takeda Hysteresis Loops Takeda model is similar to the kinematic model but incorporates a degrading hysteresis loop based on Takeda's work, as outlined in Takeda, Sozen, & Nielsen (1970). Takeda model is simpler and does not require additional parameters, making it well-suited for analyzing reinforced concrete rather than steel due to its lower energy dissipation compared to the kinematic model . Therefore, this study will use the Takeda Hysteresis Model in SAP2000. (Sabah, Öztorun, & Sayin, 2022). Takeda model during reloading , it follows a secant line to the backbone curve in the opposite direction, starting from the maximum deformation observed in previous load cycles. This results in reduced energy dissipation as deformations increase. The accompanying Figure B.11 in Appendix B illustrates this behavior (Sengupta & Li, 2017). 16 1.10.3.2 Kinematic Hysteresis Loops Kinematic hysteresis loops are well-suited for studying the behavior of steel, such as steel bars in concrete reinforcement because the kinematic modeldissipates a lot of energy. Kinematic hysteresis behavior occurs when a material shows a delay in its response to an applied force or deformation. This means that the material's behavior is affected by its previous loading and unloading history. For instance, when a material experiences cyclic loading, like during earthquakes, it may deform during loading but not fully return to its original shape when the load is removed. This delayed response is called hysteresis, and when it's related to a material's behavior, it's called kinematic hysteresis. Figure B.12 in Appendix B depicts the configuration of kinematic hysteresis loops. According to SAP2000 software the Kinematic Hysteresis Model, a commonly observed behavior in metals where plastic deformation in one direction affects deformation in the other direction. Under kinematic hardening rules, plastic deformation in one direction influences the behavior in the other direction. Symmetrical pairs of points on the multi- linear curve are linked, even if the curve is not symmetrical, allowing some control over the shape of the hysteresis loop (Sabah, Öztorun, & Sayin, 2022) . one direction influences the behavior in the other direction. Symmetrical pairs of points on the multi- linear curve are linked, even if the curve is not symmetrical, allowing some control over the shape of the hysteresis loop (Sabah, Öztorun, & Sayin, 2022) . 1.11 Literature Review Many studies have been conducted on deflection amplification factor (Cd) and differences in the actual behavior of structures as compared to those predicted by ASCE7- 16 among others. These works were majorly focused with regards to multi-storey buildings which present unique challenges in terms of earthquake design. The objective of this part is to highlight the significant contributions made by some authors on the improvement of knowledge in this area. In this study, five different moment-resisting frames with varying numbers of stories ware analyzed by Sap20000 : three, five, seven, nine, and twelve. A nonlinear static analysis to determine their capacity curve was conducted. From these curves, the overstrength factor and ductility ratio ware derived. Finally, the deflection amplification factor was calculate. The study illuminated the comparative behaviors of Special Moment Resisting 17 Frames (SMRF) and Ordinary Moment Resisting Frames (OMRF). Specifically, SMRFs displayed higher ductility ratios and overstrength factors when juxtaposed with OMRFs. Interestingly, In both Ordinary Moment Resisting Frames (OMRF) and Special Moment Resisting Frames (SMRF), the overstrength factor specified in ASCE 7-10 is higher than the overstrength factor obtained from our analysis. As a result, ASCE 7-10 is slightly conservative. Moreover, an evident correlation emerged between the deflection amplification factor and the structure's ductility ratio. It is noteworthy that the calculated deflection amplification factors for structures with fewer than eight stories were found to be below the stipulated values in the ASCE 7-10 code. However, as the number of stories escalated, the calculated deflection amplification factors aligned more closely with the values dictated by the code. Figure B.13 in Appendix B explain Deflection amplification factor for different story levels in ordinary and special MRF. Anil K. Chopra (2012) claimed that the earthquake-induced inelastic response of a system is affected by the relative values of um (maximum inelastic displacement) and uo (peak elastic displacement resulting from earthquake-induced resisting deformation). These values rely on the system's natural vibration period (Tn) and the ground motion characteristics, with damping in the system playing a secondary role. Therefore, as it is the deflection amplification factor depends on both the elastic and maximum inelastic displacements, indicating that the factor is related to the time period of the structure. Through the case study conducted by Anil K. Chopra on Single –degree freedom system shown in the Figure B.24 in Appendix B. The graph shown in Figure B.25 in Appendix B was obtained which ductility demand for elastoplastic system due to El Centro ground motion; ꝭ=5% and normalized yield strength (f_ y) = 1, 0.5, 0.25, and 0.125. it is evident that there's a Relationship between ductility demand µ (the ratio of maximum deformation to yield deformation) and the time period (Tn). This suggests a potential relationship between Cd and (Tn). The ductility demand is notably high for shorter time periods and decreases as the time period increases. This observation supports the conclusion be quoted from Chopra's book " The ductility demand on very-short-period systems may be very large even if their strength is only slightly below that required for the system to remain elastic. Thus extremely-short-period systems (Tn