Seismic Assessment of RC Buildings Using Nonlinear Static Pushover Analysis

Textbook, 2018

106 Pages, Grade: 1


Table of Contents



Table of Contents

List of Figures

List of Tables


1 Introduction
1.1 Forward
1.2 Performance Based Design
1.3 Seismic Analysis of RC Structure
1.4 Research Objectives
1.5 Outline

2 Literature review
2.1 General
2.2 Force and Performance Based Seismic Design Methods
2.2.1 Force Based Design Methods (FBD)
2.2.2 Performance Based Seismic Design Methods (PBD)
2.3 Structural Analysis Types
2.3.1 Linear Procedures
2.3.2 Nonlinear Procedures
2.4 Seismic Performance Criteria
2.4.1 FEMA 356 (ASCE2000)
2.4.2 Rehabilitation Objectives
2.4.3 Global Level Approach
2.4.4 Member Level Approach

3 Case Study Description & Modeling Features
3.1 Introduction
3.2 Case Study Description
3.2.1 General
3.2.2 Architectural Description
3.3 Structural Details
3.3.1 General
3.3.2 Structural System
3.4 Materials
3.5 Vertical Loads
3.6 Modeling Features
3.6.1 Introduction
3.6.2 Assumptions & Possible Scenarios
3.6.3 Input Data

4 Inelastic Modeling and Analysis of Case Study Building
4.1 Introduction
4.2 Elastic Analysis and Checks
4.2.1 Gravity Loads Analysis
4.2.2 Modal Analysis
4.3 Pushover Analysis
4.3.1 Introduction
4.3.2 Usage of Pushover Analysis
4.3.3 Limitations of Pushover Analysis
4.4 Capacity Spectrum Method CSM
4.4.1 Introduction
4.4.2 CSM Procedure as Per ATC-40 Reduction of 5% damped response spectrum Reduction of 5% damped response spectrum Point of intersection between demand and capacity curves Structure performance point
4.5 Modeling Pushover Analysis
4.5.1 Introduction
4.5.2 Definition of Plastic Hinges
4.5.3 Loads Introduction Defining initial load conditions for pushover analysis Lateral Load Patterns
4.5.4 Define Load Cases for Pushover
4.6 Results of Pushover Analysis
4.6.1 Introduction
4.6.2 Base Shear vs. Top Displacement
4.6.3 Performance Point of RD model
4.7 Assessment of the Case Study Building

5 Summary and Conclusions
5.1 Summary
5.2 Conclusions



To my father

To my mother

To my brothers

To my sister

To my precious ones

To all friends and colleagues

To my teachers

To everyone working in this field

To all of them

I literally dedicate this work


Praise is to Allah for helping me in making this research possible.

Special mention goes to my parents, brothers, sister, friends and colleagues.

List of Figures

Figure ‎1.1: Seismicity map of the Dead Sea transform region (circles represent seismic events). [SASPARM Project, 2014]

Figure ‎2.1 Force-based design process sequence [Wen-Cheng Liao, 2010]

Figure ‎ 2.2: 5% design response spectrum for seismic design [ASCE 7-16]

Figure ‎ 2.3: Statistical maximum response of a SDOF structure subjected to a base excitation

Figure ‎ 2.4: Building Capacity Curve [ATC-40, 1996]

Figure ‎ 2.5: Generalized Force-Deformation Relations for Concrete Elements or Components [FEMA 356]

Figure ‎3.1: Possible vertical irregularity formations in many buildings [SASPARM project (2), 2014]

Figure ‎3.2: Al-Ma'ajeen area in Nablus city [SASPARM project (2), 2014]

Figure ‎3.3: Typical section in an unreinforced masonry stone wall

Figure ‎3.4: Top view of the case study

Figure ‎3.5: Ground floor plan view of the case study

Figure ‎3.6: Repeated floors 1 to 5 plan view of the case study

Figure ‎3.7: Elevation view of the case study

Figure ‎3.8: Columns grids of the case study

Figure ‎3.9: Foundation system

Figure ‎3.10: Beams distribution

Figure ‎3.11: Assumed divisions of elevator-well shaft

Figure ‎3.12: Typical section for poor and good confined concrete column

Figure ‎3.13: Unconfined concrete stress-strain curve

Figure ‎3.14: confined concrete stress-strain curve

Figure ‎3.15: Section in slab in cm

Figure ‎4.1: Resulting reinforcement area in mm[2] of slab beams

Figure ‎4.2: Typical pushover curve and performance levels

Figure ‎4.3: Load control vs. displacement control

Figure ‎4.4: CSM procedure components and determination of performance point

Figure ‎4.5: Example modal participation factors and modal mass coefficients

Figure ‎4.6: Convert Sa vs. T for 5% damping into ADRS format

Figure ‎4.7: Bilinear representation of capacity spectrum

Figure ‎4.8: Derivation of energy dissipated by damping

Figure ‎4.9: Reduced response spectrum

Figure ‎4.10: Performance point (intersection point of demand and capacity

Figure ‎4.11: Pushover curves in X-direction for the two models

Figure ‎4.12: Pushover curves in Y-direction for the two models

Figure ‎4.13: Pushover curve in term (Sa-Sd), X-direction

Figure ‎4.14: Plastic hinges distribution at performance point due to pushover load in X-direction in RD model

Figure ‎4.15 : Pushover curve in term (Sa-Sd), Y-direction

Figure ‎4.16: Plastic hinges distribution at performance point due to pushover load in Y-direction in RD model

List of Tables

Table ‎2.1: Combinations of Structural and Non-structural Levels to form Building Performance Levels [ATC-40, 1996]

Table ‎ 2.2: FEMA 356 rehabilitation objectives (adapted from ASCE 2000)

Table ‎ 2.3: Structural performance levels and damage (Adapted from ASCE 2000)

Table ‎ 2.4: FEMA 356 modeling parameters and numerical acceptance criteria for

Table ‎ 2.5: FEMA 356 modeling parameters and numerical acceptance criteria for nonlinear procedures - RC columns (adapted from ASCE 2000)

Table ‎ 2.6: FEMA 356 modeling parameters and numerical acceptance criteria for nonlinear procedures - RC beam-column joints (Adapted from ASCE 2000)

Table ‎3.1: Soil classification [ASCE 7-16]

Table ‎3.2: Characteristics of structural elements

Table ‎3.3: The characteristic of the used materials

Table ‎3.4: Summary of adopted vertical loads

Table ‎4.1: modal participating mass ratios for the RD model

Table ‎4.2: modal participating mass ratios for the FS model

Table ‎4.3 : Structural behavior types for the quality of seismic resisting system

Table ‎4.4: : Values for damping modification factor K

Seismic Assessment of RC Buildings Using Nonlinear Static Pushover Analysis


Anas M. Fares


In Palestine, The seismic design of new buildings is mandatory. However, there are many existing buildings were mostly designed under the influence of gravity loads. Such buildings may stand vulnerable to earthquakes and thus need to be strengthened; so that they become safe. To achieve the required level of strengthening, advanced analysis and assessment tools must be used.

There is a lack of studies in Palestine that provide practical "know-how" guidelines for local engineers on the assessment of existing buildings against seismic loads. Generally, the guidelines written in foreign codes (e.g. the ASCE or FEMA) are very broad and general and may pose a challenge to local engineers regarding the consistency of their implementation. This study bridges this gap between local engineers and international codes by putting these guidelines into action through a practical case study.

Generally, four procedures are available for seismic analysis of buildings: two linear procedures, and two nonlinear procedures. The nonlinear procedures include the nonlinear static procedure (NSP) and nonlinear dynamic procedure (NDP). NSP's are deemed to be very practical tools to assess the nonlinear seismic performance of structures. On the other hand, NDP's require detailed input data, and it is very time-consuming, which is a relevant drawback in design offices, where the deadlines are restrictive. Also, this method does not exist in Palestine neither local earthquake records, nor specialized powerful programs for NDP. This makes the NSP best choice for practical assessment of buildings.

The study objective in this book is to demonstrate an assessment methodology through studying a local existing building, which was designed under gravity loads only. Based on the above, the case study building is assessed using an NSP that is called capacity spectrum method (CSM) as per ATC-40. The behavior of the structure is generated using nonlinear pushover analyses.

The seismic assessment was conducted based on FEMA 356 performance criteria. According to FEMA 356, there are two approaches for seismic evaluation: global-level and member-level with three performance levels, which are immediate occupancy (IO), life safety (LS) and collapse prevention (CP). In addition, seismic design requirements that are mentioned in ASCE 7-10 were conducted in order to assess the building for irregularities.

Based on the nonlinear pushover analysis and the assessment of the building, it was found that the building suffers from vertical irregularities and concentration of plastic hinges at the ground floor.

This book paves the way to further research on seismic assessment of existing buildings with effective tools for judging the efficiency and suitability of retrofitting techniques.

1 Introduction

1.1 Forward

Palestine is a seismic zone that it is located along the Dead Sea Transform, which is an extension of ground faults separating the Arabian and African plates as shown in Figure 1.1. The seismic history of the region indicates the occurrence of destructive earthquakes. The last devastating earthquake that hit the area was in 1927, which claimed the lives of dozens of residents under the rubble of their homes. [SASPARM Project, 2014]

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.1: Seismicity map of the Dead Sea transform region (circles represent seismic events). [SASPARM Project, 2014]

Unfortunately, this bloody history was not enough motivation to work on mitigating the seismic risk or retrofitting of old buildings in this region. There is, however, a glimmer of hope in improving the level of construction by spreading awareness among the society and the designers. The first step was adopting a decision by the Palestinian Engineers Association (PEA), which imposes seismic design as compulsory for new facilities.

The (PEA) decision is a step towards seismic risk mitigation. The (PEA) did not issue a mandatory decision regarding the status of existing buildings. Most of the existing buildings are vulnerable to earthquake events. Ignoring the existing buildings in term of earthquake resistance can cause the following problems:

1. High risk for citizens in event of earthquakes.
2. The risk of closure of major roads or important facilities, which hinders relief efforts.
3. Expensive damage to private and public properties.
4. Legal dilemma: difficulty in specifying responsibility regarding the collapse of buildings that were not designed to resist earthquakes.

One reason behind ignoring the existing buildings is the lack of systematic procedures for evaluating such buildings and for identifying the weaknesses and risks in these buildings, which makes it difficult to adopt retrofitting policies that would improve seismic resistance of such buildings.

In this study, a procedure of using existing method for evaluation of existing buildings, and how to judge their behavior in earthquake events will be displayed. The applicability of the presented methods will be demonstrated through a case study building. This research will provide useful and practical information for engineers who maybe in need for tools to evaluate existing buildings.

1.2 Performance Based Design

Performance based seismic design (PBD) is a new approach to earthquake resistant design. It is more realistic than force based design methods that are based on prescriptive and mostly empirical code formulations. (PBD) is a recent method to design buildings based on predictable and target seismic performance. Therefore, performance objectives such as immediate-occupancy (IO), life-safety (LS), or collapse prevention (CP) are used to define the state of the building when exposed to earthquake loads. In one sense, performance based seismic design is a limit-state design extended to cover the complex range of performance requirements faced by earthquake engineers. There has been much researches on PBD, and many researches tried to come up with the most realistic and accurate procedures for PBD [Chopra, 2012].

One common procedure is the capacity spectrum method (CSM) through pushover analysis. In this study, this method of PBD will be presented and demonstrated through a case study building to provide a tool for local engineers to assess structures against seismic behavior.

1.3 Seismic Analysis of RC Structure

Current seismic design codes in the world are generally carried out by linear static procedures (LSPs), such as equivalent lateral force (ELF) and response spectrum methods (RSA). However, the designed structures can be exposed to large inelastic deformations in strong earthquake events, which are inaccurately accounted for in the current force-based design methods. The drawbacks of (LSPs) will be discussed in chapter two in this thesis.

The most realistic design method must account for the development of plastic deformations in the structure during an earthquake event. In addition, hysteretic behavior of the structure during earthquake event must be considered, in order to predict the capacity of the structure to resist earthquake loads and not to exceed the designed limit level.

The nonlinear time-history analysis method meets the previous consideration. However, it requires high accuracy in the selection of characteristics and assumptions to reach the correct results, and requires very powerful tools for the calculation-intensive nonlinear analysis.

In the last two decades, the need for simple evaluation tools for existing buildings led to new methods related to performance-based approach. These include the nonlinear static analysis (pushover analysis). The main idea in this procedure depends on estimating the capacity curve (pushover curve) and the demand response spectrum curve. The pushover curve represents the behavior of the structure during the elastic and plastic range until collapse, while the demand curve represents the magnitude of predicted earthquake force. The point of intersection between these two curves is called the performance point

The pushover curve (or capacity curve) can be generated by subjecting the structure to one lateral load pattern or more depending on the natural fundamental modal shapes. Then, increase the magnitude of these loads monotonically to generate a nonlinear inelastic force-deformation relationship curve. The load vector is usually chosen to be representative of the load acting on the structure while vibrating in its first mode as a fundamental mode to be compatible with the seismic response of the building.

The seismic demand curve (response spectrum curve) is a representation of the earthquake-induced response to the building, and it is presented in terms of peak acceleration-time relationship. Capacity curve (generated earlier by pushover analysis) must be converted from MDOF into an equivalent SDOF in a format representing peak acceleration and peak displacement. The resulting curve is called capacity spectrum curve. Then response spectrum is also converted into acceleration-displacement response spectra format (ADRS). Both curves are plotted as spectral acceleration with spectral displacement. The response spectrum curve must be reduced such that it accounts for reduction in stiffness and absorbed energy during earthquakes event. The performance point is determined as the intersection of the capacity spectrum and the reduced seismic demand curve.

This method of thinking is gaining popularity among earthquake engineers, and represents a basis for performance based design approach.

1.4 Research Objectives

The main objective of this work is to present a methodology for evaluating performance of existing buildings under seismic loads. Non-linear static procedure will be used in studying the existing building.

The general objectives in this study are the following:

A. Present a methodology for the seismic assessment of existing buildings.
B. Progress step towards spreading the awareness of seismic performance based analysis and design that gives a clear impression about the realistic behavior of the structure under seismic loads.

The objectives above can be attained by achieving the following tasks:

i. Selection of a representative existing building as a demonstration vehicle for the methodology.
ii. Software for doing the nonlinear pushover analysis will be selected and then verified through comparison to manual calculations for some selected cases.
iii. Establishment of a three-dimensional model that simulates the existing building using the program in order to understand its behavior.
iv. Performing pushover analysis using both material and geometric non- linearity's, in order to draw the capacity curve of the modeled building.
v. Establishing the performance point of the structure based on the intersection of capacity and demand curves.
vi. Identifying acceptable performance target for the selected building using relevant codes and standards and logical judgment.

1.5 Outline

This book will be organized according to the following structure:

1. Chapter1: The seismic history of area will be presented. Brief talk about performance based design is presented. Also objectives and scope of the work will be discussed briefly.
2. Chapter 2: A brief review for analytical methods that are used in the design and analysis of structures for seismic loads is presented. In addition, this chapter talks about the criteria used by FEMA 356, which evaluates seismic performance for overall structure and member performance level.
3. Chapter 3: This chapter describes the case study building: site, architectural geometry, structural system, material, and loads. In addition, it talks about assumptions adopted for modeling the building.
4. Chapter 4: In this chapter, modal and static analyses are done to generate modal shapes, and to check static gravity loads. Then pushover methodology is illustrated. After that, the capacity spectrum method used by ATC-40 is explained. Then, modeling pushover features that consist of definition of lateral load patterns and cases, and the plastic hinges properties are presented. Results of pushover analysis are summarized. Then, the performance level of the building is determined based on the results from pushover and the guidelines given by FEMA 356.
5. Chapter 5: This chapter contains the summary and conclusions.

2 Literature review

2.1 General

This chapter gives a brief introduction to the methods used in seismic analysis and design, and seismic performance criteria. Elastic analysis methods and their major limitations are outlined. After that, performance based design methodology is illustrated and the performance levels are explained.

2.2 Force and Performance Based Seismic Design Methods

Earlier methods of seismic design were based on idealization of earthquake as a lateral force in what called a force-based method. Recently, (PBD) has been widely used by the researchers since the events of 1994 Northridge Earthquake, which was devastating and a very costly earthquake in U.S. history, and 1985 Mexico earthquake. The goal of PBD is to develop design methodologies that produce structures of predictable and intended seismic performance under stated levels of seismic hazards [SEAOC, 1995]. Then the international codes developed guidelines based on PBD to assess and rehabilitate existing buildings, such as ATC-40 (1996) and FEMA 273 (1997).

2.2.1 Force Based Design Methods (FBD)

Traditional seismic design codes in the world are generally based on elastic analysis methods, where earthquake is presented as static forces. This comes in contrast to reality, where the structures can be exposed to large inelastic deformations in strong earthquake events, and this is not accurately accounted for in current force-based design methods.

Current building codes use static (ELF) procedures for seismic design of regular structures. A brief sequence of the procedure is illustrated in Figure 2.1.

ELF is used for buildings with relatively short periods, but for buildings with relatively long periods, (ELF) procedure could be inaccurate, and the structure must be designed using other procedures [Chopra, 2012].

The design lateral forces acting on any structure depend on vibration properties of the structure and the site classification. Based on the estimated fundamental modal behavior of the structure, formulas are specified for calculating base shear, and then lateral forces are distributed over the height of the building accordingly. Static analysis of the building for these forces provides the design forces, including shears and overturning moments for the different stories and structural elements. [Chopra, 2012].

In these methods, the inelastic behavior of the building is incorporated as a reduction factor "R" of the base shear force.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.1 Force-based design process sequence [Wen-Cheng Liao, 2010]

Figure 2.2 shows the process of determining the design base shear as used in ASCE 7-16. The seismic base shear force is generally reduced by a factor (R/I), where (R) represents the force reduction factor depending upon inherent ductility of the structural system, and (I) represents occupancy factor in order to increase the design base shear force for more important buildings according to the category of the building.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.2: 5% design response spectrum for seismic design [ASCE 7-16]

Then lateral design base shear force is distributed along the building height at the floor levels according to the following formulas:

Abbildung in dieser Leseprobe nicht enthalten


Fx: Shear force at floor x

Cvx: Vertical distribution factor

V: Total design shear force at the base of the structure

wi&wx: The portion of the total effective seismic weight of the structure located or assigned to Level i or x

hi&hx: The height from the base to Level i or x

k: An exponent related to the effect of modal shape and period as follows:

For structures having a period of 0.5 s or less, k = 1. For structures having a period of 2.5 s or more, k = 2. For structures having a period between 0.5 and 2.5 s, k shall be 2 or shall be determined by linear interpolation between 1 and 2.

Elastic analysis is performed to determine the required member strengths. After members design for strength, a deflection amplification factor, Cd, according to ASCE 7, is then used to multiply the calculated drift obtained from elastic analysis to check the specified drift limits. The process is repeated in an iterative manner until the strength and drift requirements are satisfied.

Response spectrum depends on computing the statistical peak response of a structure when subjected to a base excitation as shown in Figure 2.3. Each of the vibration modes are assumed to respond independently as a SDOF system. Design codes specify response spectra which determine the base acceleration applied to each mode according to its period.

Response Spectrum Analysis (RSA) is used to determine peak displacements and member forces due to support accelerations from each mode of vibration. The "Complete Quadratic Combination" (CQC) method for combining correlated modal responses is generally used to determine the peak response of the structure. This is equivalent to the "Square Root of the Sum of Squares" (SRSS) method if the modes are uncorrelated. RSA is considered as a dynamic procedure. [Chopra, 2012]. The method involves the calculation of only the maximum values of the displacements and member forces in each mode using smooth design spectra that are the average of several earthquake motions.

[This figure has been removed by the editorial staff for copyright reasons.]

Figure 2 . 3: Statistical maximum response of a SDOF structure subjected to a base excitation

The major limitations and weaknesses of the force based design methods in current codes procedures such as (ELF) and response spectrum analysis (RSA) can be summarized as:

i. In many past earthquakes, it has been observed that in many cases, collapse occurred due to local column damage. This means that safety cannot be guaranteed when the sequence of damage is not clear. [Moehle and Mahin, 1991]. In addition, the distribution of elastic forces depends on stiffness of structural members, which is not accurate, since stiffness of structural members change due to the resulting plastic damage.
ii. Nonlinear dynamic analyses research done by Villaverde (1991) showed that using the code distribution of lateral forces, without accounting for the fact that a structure would enter inelastic state during a major earthquake, could be the primary reason leading to numerous upper story collapses during the 1985 Mexico City Earthquake. [Villaverde, 1991]
iii. The plastic drift calculated in ELF by using Cd factor or similar factors is not accurate especially for degrading (“pinched”) hysteretic behavior and energy dissipation characteristics. [Chao and Goel, 2006]
iv. Ductility of higher modes could be different from the ductility of the fundamental modes. Therefore, using the same force reduction factor (R) in all modes may underestimate the higher mode effects in terms of internal forces. [Priestly, 2003]
v. The factor (R) is considered constant for any building with the same structural system.
vi. A response spectrum is obtained from an accelerogram by running this record in several single degree of freedom (SDOF) systems with different periods of vibration. The value of the response spectrum corresponding to a certain period is obtained taking the maximum response of the SDOF with that period. As a consequence the duration effects of the dynamic response are ignored, which may not be valid in the case of plastic responses. [Priestly, 2003]

2.2.2 Performance Based Seismic Design Methods (PBD)

As mentioned in chapter1, performance based seismic design is a limit-state design that is extended to cover the wide range of performance requirements. The performance objectives such as immediate occupancy, life-safety, or collapse prevention (structural stability) are used to define different states of the building when exposed to earthquake loads, see Figure 2.4.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.4: Building Capacity Curve [ATC-40, 1996]

In performance based seismic design, capacity spectrum is an important description and evaluation for the performance of the structure. There are two basic elements in PBSD method, namely seismic demand and capacity spectrum. The seismic demand represents the earthquake ground motion and it can be observed in terms of spectral accelerations imposed on structures by earthquakes.

The seismic capacity spectrum represents the elastic and inelastic behavior of structure, which is converted from base shear force versus top displacement into spectral acceleration and spectral displacement for equivalent SDOF. The resulting curve is known as the capacity spectrum curve for the building. The process to determine capacity curve relies on the use of nonlinear static analysis (pushover method). The performance point is defined as the intersection point between demand and capacity spectra where the ductility and energy dissipation of structure are matched.

According to FEMA 356, the target performance objectives are divided into two types, Structural Performance Levels (SP-n, where n is a designated number) and Non-structural Performance Levels (NP-n, where n is a designated letter). These may be specified independently, however, the combination of the two determines the overall building performance level. Table 2.1 shows possible overall combination. [FEMA 356, 2000]

A description of the structural performance level objectives as per [ATC-40] can be summarized as:

1. Immediate Occupancy (SP-1): Limited structural damage with the basic vertical and lateral force resisting system retaining most of their pre- earthquake characteristics and capacities.
2. Damage Control (SP-2): A placeholder for a state of damage somewhere between Immediate Occupancy and Life Safety.
3. Life Safety (SP-3): Significant damage with some margin against total or partial collapse. Injuries may occur with the risk of life-threatening injury being low. Repair may not be economically feasible.
4. Limited Safety (SP-4): A placeholder for a state of damage somewhere between Life Safety and Structural Stability.
5. Structural Stability (SP-5): Substantial Structural damage in which the structural system is on the verge of experiencing partial or total collapse. Significant risk of injury exists. Repair may not be technically or economically feasible, which meets collapse prevention in FEMA 356.
6. Not Considered (SP-6): Placeholder for situations where only non- structural seismic evaluation or retrofit is performed.

Table 2.1: Combinations of Structural and Non-structural Levels to form Building Performance Levels [ATC-40, 1996]

Abbildung in dieser Leseprobe nicht enthalten

Non-structural Performance Levels are defined as:

i. Operational (NP-A): Non-structural elements are generally in place and functional. Back-up systems for failure of external utilities, communications and transportation have been provided.
ii. Immediate Occupancy (NP-B): Nonstructural elements are generally in place but may not be functional. No back-up systems for failure of external utilities are provided.
iii. Life Safety (NP-C): Considerable damage to non-structural components and systems but no collapse of heavy items. Secondary hazards such as breaks in high-pressure, toxic or fire suppression piping should not be present.
iv. Reduced Hazards (NP-D): Extensive damage to non-structural components but should not include collapse of large and heavy items that can cause significant injury to groups of people.
v. Not Considered (NP-E): Non-structural elements, other than those that have an effect on structural response, are not evaluated.


Excerpt out of 106 pages


Seismic Assessment of RC Buildings Using Nonlinear Static Pushover Analysis
Catalog Number
ISBN (eBook)
ISBN (Book)
seismic, assessment, buildings, using, nonlinear, static, pushover, analysis
Quote paper
Anas Fares (Author), 2018, Seismic Assessment of RC Buildings Using Nonlinear Static Pushover Analysis, Munich, GRIN Verlag,


  • No comments yet.
Read the ebook
Title: Seismic Assessment of RC Buildings Using Nonlinear Static Pushover Analysis

Upload papers

Your term paper / thesis:

- Publication as eBook and book
- High royalties for the sales
- Completely free - with ISBN
- It only takes five minutes
- Every paper finds readers

Publish now - it's free