A THESIS REPORT

PUSH OVER ANALYSIS OF MULTI STORIED RCC

BUILDINGS USING SAP 2000

A Thesis Submitted

In Partial Fulfillment of the Requirements

For the degree of

MASTERS OF TECHNOLOGY

IN

STRUCTURAL ENGINEERING

Submitted by

N. JYOTHSNA

Regd No: 15781D2006

Under the guidance of

B. Rajashekar (Associate Professor)

DEPARTMENT OF CIVIL ENGINEERING

SRI VENKATESWARA COLLEGE OF ENGINEERING AND TECHNOLOGY

(Autonomous)

(Approved by AICTE, Accredited by NBA, New Delhi,

Accredited by NAAC, Bangalore & Affiliated to JNTUA, Ananthapuramu)

R.V.S Nagar, Tirupati Road, Chittoor-517127, Andhra Pradesh

MAY 2017

CHAPTER 1

INTRODUCTION

1.1 General

Recent improvement in numerical methods and computer technology/ software has revealed a whole new world to explore for the scientists and researchers. Research in civil engineering has reached too much wider horizons then what one could have ever imagined. The development in the computer science and technology was accepted by the structural engineer as it saved a lot of human time and effort as the analysis and design of the structure are repeated processes, the need for the cumbersome processes of iterations and redesigning were reduced to giving simple cyclic programmed tasks to the computer.

Earlier the intension of the structural designer was to design a structure that can resist the earthquake induced forces, which resulted in brittle structure having structural components with heavy sections and hence high cost of construction. An important development in the designing procedures came in the form of limited states. The introduction of the limit state methodologies gave rise to the advancement of performance based design of the structure. This gave slender members and economy in construction costs and reduction time required for the construction with better performance level. The usage of ductility, for dissipation of the energy released by the earthquake to the structure gave the designers sufficient space for judging the performance of the structures and monitoring the same while designing. The design of the structure based on the presentation under the loading may be the predicted by modeling the structure mathematically. This can be efficiently done by any of the software available in the market, for structural modeling analysis and design. The prediction of the performance of the structure, designed for a specified pattern of loadings and level of safety holds good importance for the practicing structural design engineers.

In the simplest case, seismic design can be viewed as a two step process. The first and usually most important one is the conception of an effective structural system that needs to be configured with due regard to all important seismic performance objectives, ranging from serviceability considerations to life safety and collapse prevention. This step comprises the art of seismic engineering. since no rigid can, or should be imposed on the engineers creativity to devise a system that not only fulfills seismic performance objectives but also pays tribute to functional and economic constraints imposed by the owner, the architect and other professionals involved in the design and construction of building. By default this process of creation is based on judgment, experience, and understanding of seismic behavior rather than rigorous mathematical formulations. Rules of thumb for strength and stiffness targets, based on the fundamental knowledge of ground motion and elastic and inelastic dynamic response characteristics, should be sufficient to configure and rough size an effective structural system.

There are many available techniques for the analysis of the structure and to evaluate their performance under the given loading the most accurate among them being the non linear time history analysis. For the structure with importance or seismic hazard, some other conventional methods have been developed called as non linear static methods (NSPs) the results obtained from these procedures may or may not be accurate.

1.2 Importance of seismic analysis

The prediction of the response of the structure to a particular type of loading is of utmost importance for the design of structure. Fundamentally the codes and previous experience provide us with a lot of information regarding the type of loads and their intensities for different types of structures and the site conditions. The analysis procedure to be adopted purely depends upon the engineers choice as per the accuracy of the work required.

The non linear time history analysis can be regarded as the most accurate methods of seismic demand prediction and performance evaluation of structures. However, this method requires the selection of the appropriate set of ground motion, detailed site conditions and also a numerical tool to handle the analysis of the data, which is in many cases computationally expensive.

In this way the non linear static analysis (NSPs) or also called as push over analysis can simply be introduced as an effective alternative technique. On this method, structural performance is evaluated using nonlinear behavior of the structure for estimation of the strength and deformation capacities. The results are compared with demand at the consequent performance levels.

Using either of the two methods, the performance of the structural system can be monitored under the subjected loading. Huge amount of research is being carried out on the NSPs for seismic evaluation of structures.

1.3 Pushover analysis (Non Linear Static procedure):

The Non Linear Static procedure is also called as “Pushover Analysis” it uses simplified Non Linear Techniques in order to estimate the deformations occurred in a structure due to seismic loads. The performance based design of a structure has given rise to non linear static methods. In past two decades majority of researches has been implemented for the study of Pushover Analysis. These researches mainly focused on the range of applicability, merits, and demerits of those methods respectively. After finding various deficiencies and Limitations in those methods considerable measures have been taken to improve it to their maximum extent.

1.4 NONLINEAR DYNAMIC PROCEDURE (NDP)

The Nonlinear Dynamic Procedure is also known as nonlinear time history analysis is the best way to assess the performance of structure subjected to seismic forces. Nonlinear dynamic procedure utilizes the combination of ground motion records with a detailed structural model for analysis. Hence, the results of analysis are reliable with relatively low uncertainty. Instead of this, the calculated responses are very sensitive to the characteristics of the individual ground motion used as seismic input. Therefore, for getting a realistic result, several analyses are required using different ground motion. It requires considerable judgment and experience to perform and this can only be used within its limitations. The complications and requirements for making decisions in dynamic analysis are higher when compared to static analysis.

1.5 Advantages of Pushover Analysis method:

Characteristic information which cannot be provided by elastic static and dynamic analysis can be provided by Pushover Analysis:

1.) Realistic force demands of potentially brittle elements.

2.) It can also estimate the deformation demands on in elastically deformed elements, in order to dissipate the energy.

3.) Strength deterioration effect of any particular element in a structure and stability of entire structure can be determined.

4.) Certain crucial areas where inelastic deformation is expected to be occurred can be identified.

5.) Strength irregularities can be identified in both plan and Elevation.

6.) Inter storey drifts can be estimated.

7.) Strength and stiffness discontinuity can be identified.

8.) Hinge properties at joints can be identified.

Nowadays various guideline methods such as ATC-40(1996), FEMA 356/357(2000), ATC-55(2005), FEMA-440(2005), ASCE 41-06(2007) etc., are being prominently used for analysis of structure using Non Linear Static methods.

1.6 Objectives of the study

The present work aims at the following objectives:

1. Evaluation of the applicability of Non Linear Static methods to predict the performance of the reinforced concrete framed buildings in various seismic hazards to meet the performance requirement.

2. Evaluation of performance of the structure using model pushover analysis method.

3. To compare and identify differences among the pushover analysis methods given by international standards.

4. Compare weather capacity curve is reaching the demand curves as per the requirement

5. Combination of responses obtained from different modes of the structure and comparison of results

6. To illustrate the effects of higher mode of structure on its responses.

1.7 Scope of the study

The present work aims at an objective indicating the consequence of higher mode shapes on a building and its significance in calculating the response of the structure. The building studied in this segment is a reinforced concrete moment resisting frame designed for gravity and seismic loads using Non Linear Static Pushover Analysis. The structure is evaluated in accordance with sesmic code IS1893:2002 using Model Pushover Analysis (MPA) and Pushover Curves using different international standard codes with the help of the SAP2000V18 (csi ltd) analysis engine is determined.

1.8 Organization of thesis

Chapter 1 is the discussion of the importance of earthquake hazards analysis procedures adopted for the structures and brief introduction to the earthquake design philosophy in the seismic codes of India. The scope and objectives of the study has also been discussed.

Chapter 2 deals with the various literature that have been published on the energy based pushover analysis and seismic evaluation techniques.

Chapter 3 covers the complete study on pushover analysis and energy based pushover analysis and the procedure to be adopted in the present analysis and also discusses the need for performance based design.

Chapter 4 gives detail explanation modeling of structure using inelastic Analysis

Chapter 5 completely takes care of the case study of a building under considerations and the various building data surveys done to gather the information for modeling of the structure.

Chapter 6 copes up with the numerical study and presentation of results of pushover analysis method for the current building under study.

Chapter 7 details the discussions drawn from the present work and the further scope of study.

CHAPTER 2

LITERATURE REVIEW

2.1GENERAL

The general philosophy for earthquake resistant design of structure has undergone some major changes in the past 15 years; following are some of the most devastating earthquakes all over the world. The prediction of the earthquake response of the structure became more significant for the engineers to design the structures and this became much easier with the availability of seismic data and software enhancement.

Newer analysis methodologies are being proposed with focus on a realistic characterization of seismic structural damage and its direct incorporation in the design methodology. In addition, a major emphasis is given to the characterization of all the uncertainties in the process of design. In general, these approaches are categorized under performance-based seismic design (PBSD). The various ways of modeling structural damage for PBSD lead to various design approaches. The most commonly adopted approach for PBSD so far is the displacement-based design approach, where the design criterion is set usually by a limit on the peak roof (inelastic) displacement, the peak (inelastic) inter-story drift, or the peak ductility demand, etc.

Generally when the earthquake hits a structure, before actual failure of the building, it passes both the linear and non linear stages. The linear analyses have been the source of the interest of the researchers as mentioned before but the nonlinearity of the structures has now taken the stage. The strength of the structure and could be utilized with application of several limit states for a monitored performance and damage.

As mentioned in various codes and papers by number of researchers, nonlinear time history analysis (NL-THA) can be regarded as the most accurate method of seismic demand prediction and performance evaluation of the structures. In an ideal world there would be no debate about the proper method of the demand prediction and performance evaluation at low performance levels other then inelastic time history analysis that predicts with sufficient reliability the forces and cumulative deformation (damage) demands in every element of the structural system is the final solution . The implementation of this solution requires the availability of the set of ground motion records (each with three components) that account for the uncertainties and differences in severity, frequency characteristics. And duration due to the rupture characteristic tics and distances of the variation fault that may cause motion at the site. It requires further the capabilities to model adequately the cyclic load deformation characteristics of all important elements of the three dimensional soil- foundation structure systems and the availability of efficient tools to implement the solution process within the time and financial constraints imposed on an engineering office.

There is a need to work towards this final solution, but we also need to recognize the limitations of today’s state of knowledge and practice, at this time none of afore mentioned capabilities have been adequately developed and efficient tools for implementation do not exist, Recognizing these limitations, the task is to perform an evaluation process that is relatively simple, but captures the essential features that significantly affect the performance goal. In this context, the accuracy of demand prediction is desirable, but this is hardly possible since neither seismic input nor capabilities are known with accuracy.

The non linear static analysis named here after Pushover Analysis (POA) had been simply introduced as an effective alternative technique to the NL-THA. In this method, structural performance is evaluated using static non linear analysis for estimation of the strength and deformation capacities of the structure. The use o f the POA dates back to the 1970’s, but only after gaining importance during the last 10-15 years have dedicated publications started to appear on the subject. Initially the majority concentrated on discussing the range of applicability of the method and its advantages and disadvantages, compared to the elastic or non linear dynamic procedures.

2.2 Non Linear Static Procedures

The ATC-40 document has been a source of great knowledge for researchers working on the NSPs (capacity Spectrum Method and Coefficient Method etc). Excerpts from the documents that would give a better picture of the pushover analysis have been presented in the following paragraph discussing the background and the development of the performance based analysis.

The essence of virtually all seismic evaluation procedures is a comparison between some measures of the demand that earthquakes place on a structure to a measure- of the capacity of the building to resist. Traditional design procedures characterize demand and capacity as force. Base shear (total horizontal force at the lowest level of the building) is the normal-parameter that is used for the purpose. The engineer calculates the Base shear demand that would be generated by a given earthquake, or intensity of ground motion, and compares this to the base shear- capacity of the building. The capacity of the building is an estimate of the base shear that would be acceptable. If the building were subjected to a force equal to its base shear capacity some deformation and yielding might occur in some structural elements, but the building would not collapse or reach an otherwise undesirable overall level of damage. If the demand generated by the earthquake is less than the capacity then the design is deemed acceptable.

The first formal seismic design procedures recognized that the earthquake accelerations would generate forces proportional to the weight of the building with the advancement of the understanding of the structural dynamics and empirical knowledge of the actual behavior of the building, the basic procedure was modified to reflect the fact that the demand generated by the earthquake accelerations was also a function of the stiffness of the structure. Engineers also began to recognize the inherently better behavior of some buildings over others. Consequently, they reduced seismic demand based on the characteristics of the basic structural material and system. The motivation to reduce seismic demand for design came because engineers could not rationalize theoretically hoe structures resisted the forces generated by earthquake. This was partially the result of their fundamental assumption that structures resisted loads linearity without yielding or permanent structural deformation. An important measure, the capacity of structure, to resist seismic demand is a property known as ductility. “Ductility is the ability to deform beyond initial yielding without failing abruptly”. A glass rod would snap if it is attempted to bend with force, where as a steel rod would snap if it is attempted to bend with force, where as a steel rod can be bend without breaking. This property is a critical component of structural capacity.

Instead of comparing forces, nonlinear static procedures use displacements to compare seismic demand with capacity of a structure. This approach includes consideration of the ductility of the structure on an element by element basis. The inelastic capacity of a building is then a measure of its ability to dissipate earthquake energy. The current trend in seismic analysis is toward these simplified inelastic procedures.

The NSP may be used for any structure and any Rehabilitation Objective, with the following exceptions and limitations:

1. The NSP should not be used for structures in which higher mode effects are significant, unless an LDP evaluation is also performed.

2. To determine the response, if higher modes are significant a model response spectrum analysis should be performed for the structure using sufficient modes to capture 90% mass participation and a second response spectrum analysis should be performed considering only the first mode participation. Higher mode effects should be considering significant if the shear in any story calculated from the modal analysis considering all modes required obtaining 90% mass participation exceeds 130% of the corresponding story shear resulting from the analysis considering only the first mode response. When an LDP is performed to supplement an NSP for a structure with significant higher mode affects, the acceptance criteria values for deformation- controlled actions (m values) may be increased by a factor

3. The NSP should not be used unless comprehensive knowledge of the structure has been obtained.

2.3 Literature survey:

Force and displacement based POA and CSM have been discussed extensively in various papers and articles by many authors. Major criticisms can be summarized in the following two points.

• The imposed force/displacement profile, although based on model analyses or other source of experience and observation, seem hardly capable of simulating the behavior of the structure throughout the deformation history up to collapse. The risk being that, by imposing a displacement profile, strain localization may be underestimated and that by imposing a force profile, the capability of the structure to redistribute force and energy dissipation is neglected.

• The equivalent damping used to scale the displacement spectrum is obtained from assumption and equations containing a substantial degree of approximation. The equivalent damping is generally found from the energy dissipation which in turn is obtained from the monotonic force displacement response of the structure(capacity curve found from POA)

In the attempt to consider higher mode effect higher mode effect, paret et.al and sasaki et al. suggested the simple, yet efficient, multi-mode Pushover procedure (MMP). This method comprises several pushover analyses under forcing vectors representing the various modes deemed to be excited in the dynamic response. The results obtained from the analysis of the structure in different modes are then combined using a suitable combination rule (discussed in detail in chapter 4). The results obtained using this method were closer to that the time history analysis and were also enhances because of the consideration of the higher modes responses being considered.

Chopra and Geol developed a method called multimode pushover analysis (MPA) for estimating inter story drifts in framed structure at higher modes are considered. Later, the ATC-55 project attempted to apply this procedure towards estimating story- shears and over turning moments in addition to floor- displacement and inter-story drifts. The project encountered some problems pointing out reverse lint the third mode pushover of a three- story steel moment- resisting frame building. This setback indicates that increments in roof displacement are in a direction opposite to the base –shear, which may happen depending on the mechanism that get developed within the structure that is the effect of various modes.

Fig2.1: Floor displacements and story drifts at the right frame of unsymmetrical-plan system U2 determined by MPA using CQC and ABSSUM combination rules and non-linear RHA.

Peng pan, makotoohsaki proposed another nonlinear MPA procedure. In their paper “nonlinear Multimodal Pushover analysis method for spatial structures” the authors have discussed in detail the applicability and procedure of the MPA methods. They pointed out some shortcomings of the MPA procedure as it is not necessary straightforward to extend the conventional pushover analysis method to spatial structures primarily due to the following reasons:

1. Most of the existing methods are strongly dependent on the properties of the regular frame and use base shear and roof displacement.

2. Spatial structures commonly have multiple dominant vibration modes, which are all indispensable for determining the structural response.

3. The dominant vibration modes may significantly interact with each other particularly when the response increases to plastic range.

4. The MPA procedure has been conducted in two different ways, in the first one the SRSS rule is applied to the response of the structure, where as in the 2nd procedure, it is applied to the model, forces are first combined using multiple rules to defined the equivalent static forces, the forces are applied to the structure to obtain the response for each combination and the maximum value among the multiple combinations is taken as the final response.

Chandrashekaran and Anubhab Roy highlighted the need of a completely up-to-date and versatile method of a seismic analysis of a 10 storey RC frame building using response spectrum method, based on Indian Standard code provisions and base shear, storey-shear and storey drifts were computed. The same structure was also analyzed by Model Pushover Analysis (MPA) to determine the structural response for the same acceleration spectra used in the earlier case. The major focus of study was to bring out the superiority of POA method over the conventional dynamic analysis method recommended by the code. Comparison of the results obtained from the above analysis procedures show that the response spectrum method underestimates the response of the system. It was also shown that model participation of higher modes contributes to better results of the response distribution along the height of the building. Also pushover curves were plotted to illustrate the displacement as a function of base shear.

The Energy Based Pushover Analysis was first proposed in 1984 by Zahra and Hall, they argued that the cumulative energy dissipated due to cyclic plastic deformation occurring in structure (that is the hysteretic energy) is directly related to seismic damage in structure. The argument was in favor of considering the hysteretic energy demand as design criterion is that it can directly account for the cumulative nature of damage in the structure and the dynamic nature of earthquake. The methodology was proposed but no further work was done due to intensity of work Involved and lesser resources availability of different software to perform difficult cyclic procedures, the researchers turned to the EBPOA.

Recognizing that the roof displacement may not always is the best index as a basis for establishing the properties of so called “Equivalent Single Degree of Freedom” (ESDF) systems. Hernandez-Montes et al developed an alternative index, known as an Energy Bases Displacement.

Enrique Hernandez-Montes et al in their paper “An Energy Based Formulation for first and higher mode POA.” have discussed that existing nonlinear static (pushover) methods of analysis establish the capacity curve of the structure with respect to the roof displacement. Rather than viewing pushover analysis from the perspective of roof displacement, the energy absorbed (or the work done) in the pushover analysis is considered in this procedure. Simple relations were established for energy based displacement that is equivalent to the spectral displacement obtained by conventional pushover analysis methods, within the linear elastic domain. Extensions to the nonlinear domain allow pushover curves to be established that resemble traditional first mode pushover curve to be established that resemble traditional first mode pushover curves and which correct anomalies observed in some higher mode pushover curves. The same was explained with application of a modified Multimode Pushover Analysis procedure using Yielding point spectra.

Subsequently, Tjhin et al. showed that using energy-based displacement instead of roof displacement, improves pea roof displacement estimation to establish the properties of the first mode ESDF system. Meanwhile, experiences from recent earthquake show that the behavior of irregular buildings is significantly different from that the behavior of irregular buildings is significantly different from that of regular ones. According, the UBC code started to differentiate between irregular and regular buildings. Hence, parameters such as resistance ratio, stiffness, mass and geometrical irregularities of a story, with respect to neighboring stories, were considered. Also as mentioned in the SEAOC code, another type of irregularity is irregularity due to the difference in story elevation, which is sometimes extremely essential for architectural reasons.

The necessity of an energy-based design procedure for further seismic design guidelines has been emphasized by many researchers, including a few attempts at providing a framework for such design procedures. Discussions of these efforts can be found in Gosh and Collins (2006) and Prashant (2008). The first significant step in a hysteretic energy-based design is the estimation of hysteretic energy demand due to the design ground motion scenario. With the computing facilities available today, this estimation for a specific structure under a certain earthquake ground motion is not difficult, although it is computation intensive. However, one has to apply this detailed method-nonlinear response history analysis (nlrha) of a multi- degree of freedom (MFDOM) model- for each individual structure separately, making this direct method unsuitable for incorporating in a general purpose design methodology based on hysteretic energy demand. Thus, it becomes necessary to use some approximate method for estimating the energy demand that can be easily incorporated in seismic design codes. Such a method will also be useful for the energy based performance assessment/evaluation of existing structures and for the purpose of energy based design checking

Prasanth et al (2008) used a model pushover analysis or MPA based (chopra and Goel, 2002) approximate method to estimate the hysteretic energy demand in a structure when it is subjected to an earthquake ground motion. Although their method was limited only to symmetric-in-plan building structures, the results obtained for three such framed structure subjected to various earthquake scenarios were satisfactory and the method was deemed suitable for adopting in energy based design and evaluation guidelines science it could use hysteretic energy response spectra.

Grigorios Manoukas et al in their paper “static Pushover Analysis Based on an energy-Equivalent SDOF system: Application to spatial system”, have proposed an efficient Non linear static procedure based on energy equivalence. The energy equivalence of the structure is used as a margin to estimate the roof displacement under the monotonically increasing loads which are characterized by the model shape of the structure (the fundamental mode shape). The work done in displacing the structure is a better index to estimate the performance of the structure and to determine the characteristics of the same. The proposed methodology was demonstrated using a framed structure and the results obtained were compared with that of capacity spectrum method. Good results for the2D and 3D framed buildings can be obtained using the procedure and is applicable for the structure with regular or irregular multistory planer frames. It is clear that the methods good approximation of the roof displacements shown in this paper does not ensure analogous accuracy for other quantities of interest, e.g. plastic rotations (Manouks et al., 2006). The author concludes that the method seems to be a generalization and pointing out its advantages is not yet possible. In order to obtain secure generalized conclusions further investigations and research must be concluded.

In their paper “energy- based model push over procedure for asymmetric structures “Li et al” concluded that Energy-Based seismic evaluations of structures give clear illustrations of seismic demands made upon structure. The paper demonstrated a 3 dimensional energy based modal push over analysis (#D EMPA) method with equivalent three degree of freedom system and equal displacement rule. The lateral rotation couple effect on structure’s asymmetric plan was considered using the energy based model pushover analysis (MPA) procedure. The proposed procedure was validated against a non linear time history of a 5- story structure. The result show that the method takes higher mode effects into account and that the instability of capacity spectra, as indicated in the previous papers, will be avoided the maximum deformation obtained from EBMPA shows good agreement with a NL-THA results of the original system. The propose EBMPA procedure appears to be reliable and effective for evaluating the seismic response of asymmetric-plan structures.

Prof.MMofid (Sharif University of Tsheran) proposed a EBMPA methodology with the help of a strong base provided by Hernandez Montes et al a study of the structural performance of the models, with irregularities (i.e., mass, geometrical and irregularities due to the difference in elevation) in various aspects of a building and it has been made clear that different types of the above mentioned irregularities in elevation do not have any significant effect on the Energy-Based MPA method. Further the authors have concluded that, this method can be considered as an accurate alternative technique for NL-THA, to fairly estimate the seismic demands of structures. In their work the authors have performed the energy based pushover analysis over a number of frames and models and with changes in different parameters such as change in geometry, difference in the level of masses at similar stories, change in elevation etc., of the structure and found that the procedure yielding better results which were close to the results obtained from the NL-THA. In the concluding part, the authors of the paper suggested that the EBPOA method is the best method available which can replace the NL-THA.

“A procedure for evaluating seismic energy demand of framed structures”. The need of a better performance evaluation method for the structure has been highlighted and consequently a method is developed on the basis of the absorbed energy by the structure. Study on the energy demand in multistory frames is limited. Showed that the hysteretic energy demand in MDOF system cannot be evaluated reliably from an equivalent SDOF system; the researchers attributed the problem to the higher mode effect. This effect also made it difficult to predict the energy distribution along the height of building structures. A recent study by Chopra and Geol also showed that the seismic story drift demand along the building height can be estimated if more than one equivalent SDOF systems are considered. The analysis was conducted on MDOF system was calculated and the same was distributed to different storey levels using the procedure presented. Using this distribution of the energy different parameters and characteristics of the structure can be studied.

2.4 Appraisal of the literature:

Most of the literature found has been concentrated on the application and working of the procedure when compared to the other precise methods of analysis. Rigorous work has been done in making the method more effectively and accurate to use I as an alternative to the NL-THA. Many researchers have worked on the building responses in the higher modes and the performance of the building when higher modes are dominant. The proposed study aims at the effects of the higher modes on the response of the building, the model combination rules will be used for the combination of the responses of the building, and the model combination rule will be used for the combination of the responses as suggested by ATC-40 document.

2.5 Summary

In this chapter the complete literature review of Modal Pushover Analysis has been represented, from the proposal of the basis background of the method to how it was improved and implemented by the researchers. Major contribution of work has been made comparisons of the method with different types or methods of Non linear static push over analysis, for different types of structures, The appraisal of the study has been discussed regarding the effects of higher modes of the structure in the structural response regarding design codes and international standards.

**...(download the rest of the essay above)**