UNIVERSITI PUTRA MALAYSIA

EVALUATION OF IDEALIZED CAPACITY CURVE GENERATION FOR REINFORCED CONCRETE FRAMED-STRUCTURES SUBJECTED TO

SEISMIC LOADING

MEHRDAD SEIFI

FK 2008 41

EVALUATION OF IDEALIZED CAPACITY CURVE GENERATION FOR REINFORCED CONCRETE FRAMED-STRUCTURES SUBJECTED TO

SEISMIC LOADING

By

MEHRDAD SEIFI

Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia, in Fulfilment of the Requirement for the Degree of Master of Science

September 2008

DEDICATION

Dedicated to my parents and my brother owing to their precious support during my studies

EVALUATION OF IDEALIZED CAPACITY CURVE GENERATION FOR REINFORCED CONCRETE-FRAMED STRUCTURES SUBJECTED TO

SEISMIC LOADING

By

MEHRDAD SEIFI

September 2008

Chairman : Associate Professor Jamaloddin Noorzaei, PhD

Faculty : Engineering

The designing of R/C framed structures subjected to seismic excitation generally is

performed by linear elastic method, while current trend of the codes of practice is

moving toward increasing emphasis on evaluating the structures using nonlinear static

pushover (NSP) approaches. Recently, several NSP approaches, with varying degree of

vigor and success have been proposed. In this study, initially a comparative study has

been made among different nonlinear static methods for adopting the most suitable

method of extracting the capacity curve of R/C framed structures. Then, a program was

developed to overcome the difficulties of graphical iterative procedure of idealization

proposed by FEMA-356.

Subsequently, the comparative tool which is a combination of the superior NSP method

detected and the developed program was used to investigate the effects of significant

structural variables on idealized parameters of capacity curves of population of R/C

framed structures. Eventually, the applicability of replacing the time-consuming NSP

procedure by ANN for deriving the capacity curve was tested. The outcomes

demonstrated the outperformance of interstorey-based scaling adaptive pushover in

addition to high precision of the developed program. Furthermore, the distinct effects of

each one of the considered structural variables on idealized parameters were unveiled.

Finally, an acceptable performance of ANN as an alternative to NSP procedure was

observed.

Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai memenuhi keperluan untuk ijazah Sarjana Sains

PENILAIAN DALAM PENGHASILAN KAPASITI LENGKUNGAN DIIDEALKAN UNTUK STRUKTUR KONKRIT-BERSANGGA DIDEDAHKAN

KEPADA GELOMBANG

Oleh

MEHRDAD SEIFI

September 2008

Pengerusi: Professor Madya Jamaloddin Noorzaei, Ph.D. Fakulti: Kejuruteraan Rekaan struktur konkrit bersangga berdasarkan rangsanagn gempa biasanya terbentuk

daripada kaedah linear elastic method , sementara itu pendekatan sekarang mengenai

kod proktis sentiasa meningkat kehadapan dengan menekankan pengukuran struktur

menggunakan kaedah nonlinear static pushover (NSP). Terbaru, beberapa kaedah NSP

dengan pelbagai sudut vigor telah mencapai kejayaan. Dalam kajian ini , biasanya kajian

perbandingan telah dibuat dikalangan kaedah ‘non linear static method’ yang berbeza

untuk memilih kaedah yang paling sesuai dalam meningkatkan kapasiti lengkuk struktur

konkrit bersangga. Seterusnya program telah dibina untuk mengatasi masalah graphical

interactive procedure yang dicadangkan oleh FEMA-356.

Selepas itu , alat perbandingan yang mengandungi kombinasi kaedah NSP telah dikesan

dan program tersebut telah digunakan untuk menyiasat kesan perubahan pada struktur

berdasarkan populasi parameter lengkung keupayaan struktur konkrit bersangga.

Kesudahannya, keterapan perubahan prosedur pengukuran masa NSP daripada

ANN untuk mengukur kapasiti lengkungan telah diuji. Keputusan yang ditunjukkan

daripada keupayaan program inter storey based scaling pushover yang dibina

mempunyai ketepatan yang tinggi. Sebagai tambahan, kesan berlainan pada pelbagai

struktur pada parameter dapat dilihat. Akhir sekali, keupayaan ANN sebagai alternative

pada prosedur NSP diiktiraf atau diterimapakai.

ACKNOWLEDGEMENTS

Allah, the dominion of the heavens and the earth belongs to him. No son has he be

gotten nor has he a partner in his dominion. It is he who created all things and ordered

them in due proportions (Holly Quran 25:2).

First of all, I would like to express my deepest gratefulness to my supervisor Assoc.

Prof. Dr. Jamaloddin Noorzaei for his patient direction, encouragement, cooperation, full

support and close consultation throughout the research and thesis writing. In addition,

special thanks are due to Assoc. Prof. Dr. Mohamad Saleh Jaafar for his invaluable

comments, guidance, consultation and support throughout the thesis. I also appreciate

for advice and suggestions of Prof. Dr. Waleed Thanoon.

Secondly, I would like to express my sincere gratitude to my parents and my brother

who encourage and support me to do my researches. This goal has not been reached

without their everlasting love.

Finally, I would like to express my gratitude to my friends and colleagues too

neumerous to mention here, some of them are Mr.Avakh, Mr. Hadi, Mr. Hakim, Mr.

Hejazi, Mr. Homayooni, Mr. Javidmoayyed, Mr. karimoddiny, Mr. Kohrangi, Mr.

Pakanahad, Mr. Yazdanpanah and Mr. Zamani. Your nice help, I would never forget.

I certify that an Examination Committee met on 14 July 2008 to conduct the final examination of Mehrdad Seifi on his Master of Science thesis entitled “Evaluation of Idealized Capacity Curve Generation for Reinforced Concrete-Framed Structures Subjected to Seismic Loading” in accordance with Universiti Pertanian Malaysia (Higher Degree) Act 1980 and Universiti Pertanian Malaysia (Higher Degree) Regulations 1981. The committee recommends that the student be awarded the Master of Science.

Members of the Examination Committee were as follows: Bujang Kim Huat, PhD Professor Faculty of Engineering University Putra Malaysia (Chairman)

Ir. Abang Abdullah Abang Ali, PhD Professor Faculty of Engineering University Putra Malaysia (Internal Examiner)

Thamer Ahmed Mohammed, PhD Associate Professor Faculty of Engineering University Putra Malaysia (Internal Examiner)

Pradeep Bhargava, PhD Professor Department of Civil Engineering Indian Institute of Technology Roorkee (External Examiner)

______________________________ HASNAH MOHD. GHAZALI, PhD Professor/Deputy Dean School of Graduate Studies Universiti Putra Malaysia Date: 26 August 2008

This thesis was submitted to the senate of Universiti Putra Malaysia and has been accepted as fulfillment of the requirement for the degree of Master of Science.

The members of the Supervisory Committee were as follows: Jamaloddin Noorzaei, PhD Associate Professor Faculty of Engineering University Putra Malaysia (Chairman) Mohammad Saleh Bin Jaafar, PhD Associate Professor Faculty of Engineering University Putra Malaysia (Member) Waleed A. M. Thanoon, PhD Professor Faculty of Engineering University of Technology Petronas (Member)

______________________________ AINI IDERIS, PhD Professor and Dean School of Graduate Studies Universiti Putra Malaysia Date: 11 September 2008

DECLARATION

I hereby declare that the thesis is based on my original work except for quotations and citations which have been duly acknowledged. I also declare that it has not been previously or concurrently submitted for any other degree at UPM or other institutions.

______________________________ MEHRDAD SEIFI

Date: 22 September 2008

TABLE OF CONTENTS

Page DEDICATION ii ABSTRACT iii ABSTRAK v ACKNOWLEDGEMENTS vii APPROVAL SHEETS viii DECLARATION x LIST OF TABLES xv LIST OF FIGURES xvii LIST OF ABBREVIATIONS xx CHAPTERS

1 INTRODUCTION 1

1.1 Brief Background 1

1.2 Problem Statement 4

1.3 Objectives of the Study 5

1.4 Scope of the Work 5

1.5 Limitation of the Study 7

1.6 Layout of the Study 7

2 LITERATURE REVIEW 10

2.1 Introduction 10

2.2 Overview on the Origin of Performance-Based Design Engineering (PBDE) 11

2.3 Nonlinear Static Pushover (NSP) Analysis, Background and Fundamentals 12

2.3.1 Traditional Pushover Theoretical Background 14

2.3.2 Fundamental Concepts on Pushover 16

2.4 Challenges and Enhancements on Pushover Analysis 17

2.5 Recent Studies on Application of Pushover in PBDE Domain 29

2.6 Critical Discussion on Proceeding of Pushover Analysis

2.7 Artificial Neural Network (ANN) and Applications in PBD 36

2.7.1 Neural Networks Basics 37

2.7.2 Classification of Neural Networks 38

2.7.3 Designing Neural Network 40

2.7.4 ANN Applications in Performance-Based Design Engineering 42

2.8 Justification of Selecting the Proposed Problem 46

2.9 Concluding Remarks 50

3 METHODOLOGY AND COMPUTER CODIFICATIONS 52

3.1 Introduction 52

3.2 Overall View of Implemented Study 53

3.3 Addressing Format 55

3.4 Preliminary Modeling and Analysis 56

3.4.1 Vertical and Lateral (Seismic) Loading 57

3.4.2 Preliminary Modeling and Analysis Criteria 58

3.4.3 Displacement Control 59

3.5 Designing Criteria 60

3.6 Detailing 60

3.7 Finite Element Modeling 61

3.7.1 Finite Element Idealization of Framed Structure 63

3.7.2 Modeling of R/C Section 64

3.7.3 Constitutive Modeling 64

3.8 Loading 69

3.8.1 Gravitational Load 69

3.8.2 Lateral Load Distribution 69

3.8.3 FEMA-356 Approaches 69

3.8.4 Adaptive Pushover Analysis (APA) Methods 70

3.9 Incremental Dynamic Analysis (IDA) 76

3.10 Comparative Study among Applied Methods 77

3.11 Comparative Study among Applied Methods 81

3.11.1 FEMA-356 Bilinear Idealization Criteria 82

3.11.2 Necessity of Programming 83

3.11.3 Surmounting the Major Problem of Programming 83

3.11.4 Computational Algorithm 84

3.12 Influence of Structural Variable on Idealized Capacity Curve 88

3.13 Replacing Artificial Neural Network (ANN) 89

3.13.1 Feedforward Back Propagation Neural Network 90

3.13.2 Accelerated Training of a Multilayer Neural Network 92

3.13.3 Selection of Entering Data 93

3.13.4 Representing the Data 93

3.13.5 Structuring the Network 94

3.13.6 Training and Testing of Networks 95

3.14 Concluding Remarks 97

4 RESULTS AND DISCUSSION 99

4.1 Introduction 99

4.2 Preliminary Analyze, Design and Detailing of Residential R/C Frame Structures 100

4.2.1 Analyze and Design 102

4.2.2 Detailing 104

4.3 Finite Element Modeling 107

4.4 Generation of Loading Pattern by Conventional and Adaptive NSP Methods 111

4.5 Earthquake Record Applied through IDA and NSP Analysis 113

4.6 Performance Evaluation of Different NSP Methods 114

4.6.1 Capacity Curve Evaluation 115

4.6.2 Assessing of Interstorey Drifts 119

4.6.3 Selection of the Outstanding Method 123

4.7 Capacity Curve Bilinear Idealization 124

4.7.1 Generation of Bilinear Idealized Curve by Using the Developed Program 124

4.7.2 Results of Applying Methods for Other Frame Structures 131

4.8 Influence of the Structural Variable Parameters on Idealized Capacity Curve 135

4.8.1 Achievement of Comparative Tool 135

4.8.2 Generation of Idealized Capacity Curve for Population of R/C Buildings 135

4.8.3 Discussion on the Results 138

4.8.4 Elapsed Time for Computational Procedure, Uniqueness of Outcomes 140

4.9 Extraction of Idealized Capacity Curve by Substitutable ANN Approach 140

4.9.1 Configuration of Appropriate ANNs 141

4.9.2 Selection of ANNs 142

4.9.3 Extraction of errors and Data Analyzing 146

4.10 Concluding Remarks 148

5 CONCLUSIONS AND RECOMMENDATION FOR FUTURE SCOPES 151

5.1 Conclusions 151

5.2 Recommendation for future works 157

REFRENCES 158

APPENDICES 164

BIODATA OF STUDENT 183

LIST OF PUBLICATIONS 184

LIST OF TABLES

Table Page 1.1 Some of recent destructive earthquakes 2

2.1 Preliminary ideas on pushover analyze 33

2.2 Criticism of preliminary NSP methods 33

2.3 Enhancements and advanced method on NSP procedure 34

2.4 Recent investigations related on pushover analysis 36

2.5 Applications of artificial neural network (ANN) in Performance-based design engineering (PBDE) 46

3.1 The whole possible types of structural models on the bases of the adopted variables 56

4.1 Modeled structures utilized during study 100

4.2 Material properties for the selected case study 101

4.3 Lateral load distribution along the height of 6f3s4l4b3 by UBC-97 code 102

4.4 Storey drift ratio for 6f3s4l4b3 103

4.5 Column sections of 6f3s4l4b3 106

4.6 Beam sections of 6f3s4l4b3 106

4.7 Feature of selected structural sections 107

4.8 Defined concrete parameters for the 6f3s4l4b3 model 108

4.9 Defined Steel parameters for the 6f3s4l4b3 model 107

4.10 Assumed element lengths during study 109

4.11 Section properties of b11 as a template of R/C T-sections 110

4.12 Section properties of C1 as a template of RC rectangular sections 110

4.13 Computation of lateral load based on FEMA-356 approaches 111

4.14 Characteristics of El-Centro record 114

4.15 Roof displacement-Base Shear (Capacity Curve) computed by different methods 116

4.16 Absolute Relative Percentage Error (ARPE) of Base Shear calculation by different NSP methods vs. IDA results 117

4.17 Inter-storey drifts computed by different method for 0.54%, 0.93%and 2.00% of structure height as the total drift 120

4.18 Relative Percentage Error (RPE) of drift estimations by different NSP method vs. IDA-max results 121

4.19 Relative Percentage Error (RPE) of drift estimations by different NSP methods vs. IDA results 122

4.20 Mean of Absolute Relative Percentage Error (MARPE) of computed Inter-Storey drifts by different NSP methods 123

4.21 Measuring the accuracy of estimated capacity curve for 6f3s4l4b3 126

4.22 Final results for 6f3s4l4b3 128

4.23 Final results for 5f2s3.5l4b3 131

4.24 Structural variable parameters vs. corresponding extracted nonlinear parameter (Idealized capacity curve parameter) 136

4.25 Standardized value of models utilized for training 142

4.26 Standardized value of randomly selected models for testing 142

4.27 Comparison of ANNs predicted nonlinear parameters and the real ones 147

4.28 Trained ANNs for prediction of nonlinear parameters 150

LIST OF FIGURES

Figure Page 2.1 Multilinear and bilinear static base shear vs. roof

displacement response of an assumed MDOF structure 15

2.2 Conventional lateral load distribution: 16

2.3 Considered structural system: (a) wall; (b) frame 30

2.4 Capacity curves of buildings under different lateral load pattern and corresponding bilinear idealization 31

2.5 Main evolutions through the studies on pushover analysis 32

2.6 Biological neural network 37

2.7 Single layer neural network 38

2.8 Classification of neural networks 38

2.9 Three-layer feedforward back-propagation network 39

2.10 Procedure of a neural network designing 41

3.1 Flow chart of overall Performed Study 54

3.2 Preliminary analyze cases of model 59

3.3 Flow chart of learning process of SeismoStruct applied during this study 62

3.4 Finite element model of 6f3s4l4b3 structure 63

3.5 Fiber modeling of RC section (SeismoStruct) 64

3.6 Comparison of different compressive concrete stress-strain based curve 66

3.7 Menegotto- Pinto steel model 67

3.8 Incremental updating procedure 75

3.9 Example of information extracted from IDA

study of 20-storey moment-resisting steel frame 77

3.10 Flowchart of the program developed for extraction of absolute maximum interstorey drifts 80

3.11 Post-yield stiffness behavior of structures 82

3.12 Capacity curve bilinear idealization program Flow chart 87

3.13 Flow chart of the procedure passed for each of the 30 models created for comparative study 89

4.1 Computed loads for the 6f3s4l4b3 102

4.2 Finalized design of 6f3s4l4b3 104

4.3 Employed frame sections for 6f3s4l4b3 model 105

4.4 R/C T-Section for beams, (b11) 109

4.5 R/C rectangular section for columns, (C1) 110

4.6 Lateral load distribution for 6f3s4l4b3 model based on FEMA- 356 approaches 112

4.7 El-Centro earthquake 113

4.8 IDA-envelope of 6f3s4l4b3 for El-centro record 116

4.9 Dynamic capacity curve vs. Static capacity curves of 6f3s4l4b3 for El-centro record 118

4.10 Actual capacity curve (Blue) of 6f3s4l4b3 vs. the estimated one (Green) 127

4.11 Capacity curve of 6f3s4l4b3 vs. precise idealized bilinear one 129

4.12 Capacity curve of 5f2s3.5l4b3 (SeismoStruct Package) 130

4.13 Estimated capacity curves vs. their bilinearization 134

4.14 Schematic representation of passed and current study steps 137

4.15 Superior trained ANNs, inputs, outputs and structures 145

4.16 Connection weights histogram in 6-12-12-1 trained FFBPNN for prediction of αKe 148

LIST OF ABREVIATIONS

α Learning rate on neural network, a positive constant less than unity

eKα Post-yield stiffness of structure

β Momentum term in neural network

jΓ Modal participation factor of the j th mode

0λΔ Initial step increment in load factor of adaptive pushover

)(Pkδ Error gradient

MΔ Storey drift ratio in j th floor

PΔ load increment vector in adaptive pushover

WΔ Difference of displacement of two consecutive floors

jkwΔ Weight corrections” related to output layer of a neural network

cε Strain at peak stress for concrete

jθ Threshold on neuron j

λ Load factor of adaptive pushover

μ Strain hardening parameter of steel

ξ Damping ratio

φ Size of applied reinforcement

jφ Modal shape

21 & aa Transition curve shape calibrating coefficients of steel

43 & aa Isotropic hardening calibrating coefficients of steel

i th storey displacement due to ijD j th mode

sE Modulus of elasticity of steel

cf Compressive strength of concrete

if Storey safety

tf Tensile Strength of concrete (or) Total reduction factor

iF Proportion of load of each storey

tF Whiplash effect

yF Yielding strength of reinforcement

F Normalized scaling vector in adaptive pushover

iF Calculation of relative values of story forces

ih Height of th floor above the base. i

gI Gross moment of inertia

ek Confinement factor of concrete

eK Effective lateral stiffness of structure

0P Nominal counterpart of load vector in force based adaptive pushover

oR Transition curve initial shape parameter of steel

)( jSa Spectral amplification of the j th mode

1T Fundamental natural vibration period of structure in second

bV Base shear of structure

iw Weight of the i th floor

terV secint Base shear at the intersection point between idealized and main curve

maxV Maximum base shear among all coordinates in capacity curve

yV Effective yield strength of structure

ijw Preliminary weight of input i for neuron j

terX secint Displacement at the intersection point between idealized and main curve

six , Standardized variable value for p th model

maxx Maximum value of the specific variable among all models

minx Minimum value of the specific variable among all models

Abstract of thesis presented to the Senate of Universiti Putra Malaysia in fulfillment of the requirement for the degree of Master of Science

EVALUATION OF IDEALIZED CAPACITY CURVE GENERATION FOR REINFORCED CONCRETE STRUCTURES SUBJECTED TO SEISMIC

LOADING

By

MEHRDAD SEIFI

December 2007

Chairman : Associate Professor Jamaloddin Noorzaei, PhD

Faculty : Engineering

Under different circumstances various approaches starting from simplistic linear

static to the accurate but cumbersome, time-consuming nonlinear time-history

procedure are applicable for analysis of buildings. Performance-based design

engineering (PBDE) as one of the major domains in earthquake engineering, is

concerned with performance evaluation of structures under seismic excitation.

Nonlinear static pushover (NSP) as main product of PBDE is compromise of

simplicity and accuracy has been legitimatized and found its way into codes such as

Federal Emergency Management Agency (FEMA), Eurocode… One of the

momentous outcomes of this method is capacity curve, declares the relating between

base shear force and lateral displacement of control node.

The conventional pushover method applying in real-life engineering relies on

incremental pushing the structure with constant distribution of lateral load that is not

exempt of error. Several methods have been proposed to overcome its deficiencies by

the researchers. By criticizing them adaptive pushover analysis (APA) that considers

all deficits of conventional method seems to be more logic. Although, various

techniques have been suggested for pushover analysis, there is solidarity for

bilinearization and extraction of idealized parameters based on iterative graphical

method of FEMA. Moreover, parallel to evolution of pushover analysis procedure

they become more rigorous. Consequently, applications of artificial neural network

(ANN) as an alternative for solving PBDE problems have been noted recently. This

study focused on R/C regular 2D frames by extensive comparative study among five

alternatives of conventional and adaptive pushover, codifying a program to overcome

deficiencies of graphical iterative bilinearization method, study on effect of structural

variables on idealized parameters and just testing this issue that whether it is

applicable to use ANN as replacement of pushover for idealization.

Along the line of study, preliminary static analyze, designing and detailing, finite

element modeling including physical and material modeling as close as possible to

practical structure have been done for 30 case studies. Then, procedure of loading a

case study by five various conventional and adaptive pushover procedure and also

incremental dynamic analysis (IDA) as reference were implemented and an

comprehensive comparative study procedure in aspects of capacity curve and

interstorey drift evaluation has been made. Developing a program for accurate

bilinearization and overcoming the deficiency of graphical iterative procedure of

FEMA was the next stage. Achieving a comparative tool as combination of best NSP

method and the developed program results in extensive course of actions for

application of this tool for 30 created different models. Eventually, feed forward

back propagation method process as a prevalent type of ANN have been studied for

testing its applicability for replacing outstanding NSP method of deriving capacity

curve.