3 Storey Rc Building-2009-Ali

Half Scale Three-Storey Infilled RC Building;A Comparison of Experimental and Numerical Models

A Dissertation Submitted in Partial Fulfilment of the Requirements

for the Master Degree in

Earthquake Engineering

By

Hassan Ali

Supervisors:

Dr. Roberto Nascimbene

Dr. Rui Pinho

May, 2009

Istituto Univeritario di Studi Superiori

Universita degli Studi di Pavia

The dissertation entitled “Half Scale Three-Storey Infilled RC Building; A Comparison of Ex-perimental and Numerical Model”, by Hassan Ali, has been approved in partial fulfillment ofthe requirements for the Master Degree in Earthquake Engineering.

Dr. Roberto Nascimbene

Dr. Rui Pinho

Abstract

ABSTRACT

The present work reports the comparison between the experimental and numerical model of 3Dthree storey RC infilled building. The experimental model is similar to SPEAR structure butwith major differences such as introduction of infill panels and reduced scale (i.e. 1:2). Exper-imental test was conducted on the Shake Table at European Centre for Training and Researchin Earthquake Engineering (EUCENTRE), Pavia Italy. Testing phases consist of the seismicexcitation applied to building using a natural accelerogram scaled at different levels of PGA, inorder to observe the development of the collapse mode and the overall resistance of the build-ing. SeismoStruct a fibre based Finite Element Program has been used for implementation ofNumerical Model. The main feature of the current work is the use of infill panel and rigiddiaphragm in the model. The hysteric parameters of Infill panel are first calibrated with experi-mental test which are then used in the model to accurately perform the Dynamic Time Historyanalysis. Finally the results of the Numerical and experimental model are compared.

Keyword: SPEAR structure; Scaled Structure; SeismoStruct; Infill Panel; Rigid Diaphragm andCalibration of Infill Panel.

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Acknowledgements

ACKNOWLEDGEMENTS

I would like to express my deep and sincere gratitude to my supervisor Dr.Rui Pinho. His wideknowledge and logical way of thinking have been a great value for me. I am also deeply gratefulto my supervisor Dr.Roberto Nascimbene for his detailed and constructive comments, and forhis important support throughout this work. His understanding and personal guidance haveprovided a good basis for the present thesis.

I wish to express my sincere thanks to Dr.Qaisar Ali, Director Earthquake Engineering Centerand Dr.Akhtar Naeem Khan, Head of Department, Civil Engineering, N-W.F.P University ofEngineering & Technology, Peshawar, Pakistan, who introduced me to the field of EarthquakeEngineering. Their ideals and concepts have a remarkable influence on my career. Dr.Qaisar Alihas been an inspirational throughout my graduate studies. The financial support for my entiremaster program from N-W.F.P University of Engineering & Technology Peshawar, Pakistan, isgratefully acknowledged.

Many friends in ROSE School have helped me stay sane through these difficult years. I greatlyvalue their friendship and I deeply appreciate their belief in me. I am thankful to EUCENTREStaff and administration for providing me all the data required for the present work.

Last, I want to thank my parents, without whom I would never have been able to achieve somuch. They has been a constant source of love, concern, support and strength all these years. Icordially thank my son for not forgetting me, even though he had so seldomly the opportunityto see me. I especially wish to express my love for my wife who only knows the real price ofthis dissertation as we suffered and paid it together. I thank for her endless love, patience, andunderstanding.

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Index

TABLE OF CONTENTS

ABSTRACT i

ACKNOWLEDGEMENTS ii

TABLE OF CONTENTS iii

LIST OF FIGURES vi

LIST OF TABLES ix

1. INTRODUCTION 1

1.1 Organization Of the Report . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. PROJECT DESCRIPTION 3

2.1 SPEAR Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 EUCENTRE Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Similitude condition . . . . . . . . . . . . . . . . . . . . . . . . . . 4

iii

Index

2.2.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.3 Reinforcement Detail for beam and column . . . . . . . . . . . . . . 8

2.2.4 Additional Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.5 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.6 Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3. LITERATURE REVIEW 15

3.1 Infill Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.1 Micro-Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.2 Macro-Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1.3 Cyclic Behavior of Infill Panel . . . . . . . . . . . . . . . . . . . . . 19

3.1.4 Proposed model for the analysis of Infilled frames . . . . . . . . . . 19

3.1.5 Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.6 Reduction in area due to lateral displacements . . . . . . . . . . . . 25

3.1.7 Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 Rigid Diaphragm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4. NUMERICAL MODEL OF CASE STUDY 29

4.1 SeismoStruct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.2 Numerical Model of Structure . . . . . . . . . . . . . . . . . . . . . . . . 30

4.3 Calibration of Infill Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.3.1 Geometrical Parameters . . . . . . . . . . . . . . . . . . . . . . . . 39

iv

Index

5. ANALYSIS AND RESULTS 41

5.1 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2 Non-linear Time History Analysis (NTHA) . . . . . . . . . . . . . . . . . 42

6. CONCLUSIONS AND RECOMMENDATIONS 45

6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.2 Future Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

REFERENCES 47

v

List of Figures

LIST OF FIGURES

2.1 Scaled Structure on Shake Table . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Typical Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4 Beam Column Plan configuration . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.5 Typical Beam Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.6 Typical Column Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.7 Construction and Reinforcement Detail for Foundation . . . . . . . . . . . . . 10

2.8 Typical Column Reinforcement and Construction Detail . . . . . . . . . . . . . 10

2.9 Typical Beam & Slab Construction & Reinforcement Detail . . . . . . . . . . . 11

2.10 Additional Masses on Scale Structure . . . . . . . . . . . . . . . . . . . . . . 11

2.11 Additional Masses on Scale Structure, Plan . . . . . . . . . . . . . . . . . . . 12

vi

List of Figures

2.12 Additional Masses on Scale Structure, Section . . . . . . . . . . . . . . . . . . 12

2.13 Input Signal [PGA = 0.3g] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.14 Input Signal [PGA = 0.54g] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Deformation under shear load . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Variation of the ratio bw

dwfor infill frames as a function of parameter λ · h . . . . 18

3.3 Variation of the ratio bw

dwas a function of parameter λ · h according to Decanini

and Fantin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 cyclic axial behavior of masonry . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.5 Stress Strain Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.6 Modified strut models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.7 Infill panel element configuration . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.8 Shear spring configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.9 Stress state considered to evaluate the strength of masonry . . . . . . . . . . . 23

3.10 Variation of area of strut as a function of the axial strain . . . . . . . . . . . . . 26

3.11 Diaphragm constraint to model rigid floor slab . . . . . . . . . . . . . . . . . . 28

4.1 Material Inelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2 Rigid Link connection at column C2 . . . . . . . . . . . . . . . . . . . . . . . 32

4.3 (a) Displacement-Based Element Formulation, (b) Force-Based Element For-mulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.4 Layout of Infill panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

vii

List of Figures

4.5 Reinforcement Detail of Beam and Columns . . . . . . . . . . . . . . . . . . . 34

4.6 Force-Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.7 Force-Displacement, Trial 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.8 Force-Displacement, Trial 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.9 Force-Displacement, Final Calibrated . . . . . . . . . . . . . . . . . . . . . . 38

5.1 Experimental Results for Col 6 . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2 Comparison of Displacement Time History for Col 6 . . . . . . . . . . . . . . 44

viii

List of Tables

LIST OF TABLES

2.1 Scale factors for model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Average Compressive Strength of concrete . . . . . . . . . . . . . . . . . . . . 13

2.3 Average values of yield strength of specimens . . . . . . . . . . . . . . . . . . 13

4.1 Default Values for Calibration of Infill Panel . . . . . . . . . . . . . . . . . . . 36

4.2 Intermediate Values for Calibration of Infill Panel . . . . . . . . . . . . . . . . 37

4.3 Final Values for Calibration of Infill Panel . . . . . . . . . . . . . . . . . . . . 38

4.4 Parameters contributing most . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.1 Estimated Vibration Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2 Empirical Eq. and SeismoStruct result . . . . . . . . . . . . . . . . . . . . . . 42

ix

Chapter 1. Introduction

1. INTRODUCTION

It has been observed that frame infill panel are mostly used as interior partition walls andexternal walls in building according to the requirement of the usage. But they are seldom usedin numerical calculation. The main reason for not including is complexity of analytical modelsfor infill panel and not adequate knowledge.

Recent studies have shown that the use of masonry infill panel has a significant not only onthe strength and stiffness but also on the energy dissipation mechanism of the overall structure.Neglecting the effects of masonry infill can lead to inadequate assessment of structural damageof infilled frame structures subjected to intense ground motions.

Current scope of the work is to compare the experimental results with the numerical simulation.The experimental model is a reduced scale multi-storey building with infill panel and openings.Experimental test comprises of a shaking table test at the TREES Lab EUCENTRE, Pavia, Italy.The building is a representation of older building in Southern Europe without earthquake design.It has been designed only for gravity loads. The research at TREES Lab is aimed at verifyingefficiency and accuracy of the rules for seismic assessment and repair of existing buildingsincluded in the Italian Code OPCM 3274 and recently included in the new Italian TechnicalRegulations for Construction through the use of numerical simulations and experimental testson a building representative of the construction in the years 50-60 in Italy.

The Finite Element package used for numerical verification is SeismoStruct. The software isa fibre-element based program capable of taking into account both geometric non-linearity andmaterial inelasticity. To account for the inelastic deformations of masonry panel, the four nodemasonry panel element developed by Crisafulli is used. Each panel is represented by six strutmembers, to carry axial load across two opposite diagonals and shear from top to the bottom ofthe panel.

1

Chapter 1. Introduction

The slab of the scaled building is very rigid. It is therefore necessary to correctly distribute theinertia forces through out the structure. Hence use of rigid diaphragm nodal constraint approachthat makes use of Lagrange Multiplier is opted for the numerical model. This approach ofmodeling slab as rigid diaphragm is a reliable way of modeling the presence of very stiff floorsin this type of irregular structures (Pinho et al. 2008).

1.1 ORGANIZATION OF THE REPORT

The dissertation is organised into six chapters covering from the theoretical backgroundof infill panel & rigid diaphragm to their implementation in SeismoStruct for analysis.A brief description of each chapter is given below: Chapter 2 provides a brief introduction oforiginal SPEAR project. It includes the main objectives with brief characteristics of the SPEARbuilding. After the introduction of the SPEAR project a detail overview of the present casestudy (i.e. EUCENTRE project) is mentioned. The case study is a reduced scale (1:2) of theoriginal SPEAR building tested at EUCENTRE, Pavia Italy. The main difference between thisbuilding and SPEAR is; reduce scale and introduction of infill panel.

Chapter 3 delves on with the literature review of infill Panel & rigid diaphragm. The infill panelmodel used in this study is the one developed by Crisafulli and implemented by Blandon inSeismoStruct.

Chapter 4 deals with the calibration of infill panel with experimental data. The descriptionof geometrical and material properties used for numerical model are discussed.The Finite ele-ment code used for this case study is SeismoStruct, a fibre element based program capable ofpredicting large displacement.

Chapter 5 presents the results of two analysis i.e. Eigenvalue & Dynamic Time History Analysisboth with displacement based element formulation and force based element formulation. In theend a comparison between numerical and experimental data is presented.

Chapter 6 finally presents the summary of the whole work along with the conclusion.

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Chapter 2. Project Description

2. PROJECT DESCRIPTION

2.1 SPEAR PROJECT

A series of experimental test were conducted by European Laboratory for Structural As-sessment (ELSA), at ISPRA Italy under the research project financed by European commission.The project was named as Seismic Performance Assessment and Rehabilitation (SPEAR). Sev-eral partners within Europe and around the world participated in the project, with the leadingrole played by ELSA. The project aim was to develop simple assessment and rehabilitationstrategy for existing RC structures which were designed only for gravity loads and are typicalof non-seismic design. These comprise a major part of building structure in Europe and manyparts of the world. From social and economic point of view, it was not feasible to replace theseexisting structures with new construction, nevertheless to achieve an acceptable seismic level;these structures must be assessed and retrofitted.

Under the SPEAR project, a Pseudo Dynamic test of a full scale three-storey reinforcedconcrete (RC) building (torsionally unbalanced) was tested. The structure is a simplification ofan actual three-storey building designed by Fardis (2002). The building is a representative ofolder construction in Greece, Portugal, Southern Europe and many parts of the world, withoutprovisions for earthquake resistance Pinho et al. (2008). It was designed only for gravity loadsusing the concrete design code used in Greece between 1954 & 1995. The materials and con-struction practice are the one used in Southern Europe (Italy and Portugal) in early 70’s. TheSPEAR structure is regular in elevation but have plan irregularity in both directions, which is atypical configuration of non-earthquake design.

Some of the main features of the structure are:

• For longitudinal reinforcement smooth bars are used.

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• Minimum amount of stirrups are provided.

• Beam-column joint connection is provided without stirrups.

• Lap splices are located just above the joints.

Infill walls and stairs were not included in the test structure. For detail description ofthe structure, along with the experimental and numerical activity of the SPEAR project can befound at Negro et al. (2004), Molina et al. (2004), Molina et al. (2005).

2.2 EUCENTRE PROJECT

The present study is focused on the experimental work recently carried out at EuropeanCentre for Training and Research in Earthquake Engineering (EUCENTRE, Pavia, Italy). Theanalyzed experimental model is a three storey two bay RC structure similar to SPEAR structurebut with reduced Scale i.e. 1:2. The test is part of the activities programmed in the researchprojects ”Numerical and experimental assessment of recommendations for existing RC build-ings included in the ”OPCM 3274” and ”Use of innovative materials for strengthening andreparation of RC structures in high seismicity areas”. The project is financed by the Italian CivilProtection department and the foundation CARIPLO of Milan Italy.

The project intend to verify the seismic assessment and retrofitting techniques throughnumerical simulation by means of conducting experimental test on buildings representative ofolder construction in Italy. The building is tested with natural accelerograms scaled at differentlevels of PGA. Although the building is similar to SPEAR but with many differences, the mostimportant differences are: reduce scale (i.e. 1:2), use of infill walls with openings, earthquakewill be applied only in one direction (Marazzi et al. 2007).

2.2.1 Similitude condition

For real dynamic test of scaled models on shake table, Cauchy & Froude law must be sat-isfied. The Cauchy law is adequate for phenomenon in which restoring forces are derived fromstress-strain constitutive relationship, while Froude law applies to cases where gravity forcesare important. Thus for the realistic modeling of non-linear dynamic response of structure bothsimilitude laws must be satisfied Sullivan et al. (2004). The simultaneous satisfaction of Cauchyand Froude similitudes leads to scale factors represented in Table 2.1. (assuming Ep

Em= 1 i.e.

4


the model and prototype have the same material properties). The acceleration scale is unitywhile time scale is square root of geometrical scale λ. This means that in model the time scaleis compressed by a factor

√1λ

, therefore the accelerogram applied to the structure have shorterdurations, higher frequency and the same accelerations. Another important consequence of thesimilitude law, is the increase of the mass of the model relative to the reference prototype (ρbecome inversely proportional to the geometric scale factor λ). This relations imposes difficul-ties in terms of either finding non-standard high density material, or adding mass to the modelwithout influencing its stiffness. In the present study additional masses are applied on the scaledmodel as discussed in Section 2.2.4.

Parameter Symbol Scale Factor Scale Factor(Cauchy) (Cauchy + Froude)

Length L Lp/Lm = λ Lp/Lm = λModulus of Elasticity E Ep/Em = e = 1 EpEm = e = 1Specific mass ρ ρp/ρm = ρ = 1 ρp/ρm = ρ = λ−1

Area A λ2 λ2

Volume V λ3 λ3

Mass m λ3 λ2

Displacement d λ λ

Velocity v 1 λ12

Acceleration a λ−1 1Weight w λ3 λ2

Force F λ2 λ2

Moment M λ3 λ3

Stress σ 1 1Strain ε 1 1Time t λ λ

12

Frequency f λ−1 λ− 12

Table 2.1: Scale factors between prototype and model, adapted from Sullivan et al. (2004)

2.2.2 Geometry

An overview of the test building along with plan and elevations are presented in Fig-ure 2.1, Figure 2.2 and Figure 2.3. The scaled model is regular in elevation but non-symmetricin plan with a storey height of 1.5 m between floors. The slab thickness for all floors is 0.08m(80mm). All beams have equal dimensions of 0.125 x 0.25m (125 x 250mm). The cross sectiondimension of column C2 is 0.125 x 0.375m (125 x 375mm) whilst all remaining columns are0.125 x 0.125m (125 x 125mm). The plan layout with beam and column configuration is shownin Figure 2.4.

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The frame was filled by nonstructural masonry infilled walls. Elevation A & C consistsof door opening (525 x 1050 mm) and (400 x 1050 mm) at each floor level. Similarly elevationD contains window opening (600 x 650 mm) at each floor. Elevation B contains solid infill,without openings. The general layout of the location and dimension of infill and opening areshown in Figure 2.2 and Figure 2.3.

Figure 2.1: Scaled Structure on Shake Table

Figure 2.2: Typical Plan

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Figure 2.3: Elevation

Figure 2.4: Beam Column Plan configuration

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2.2.3 Reinforcement Detail for beam and column

Column longitudinal reinforcement consists of 6mm smooth round bars. Lap splicing ofcolumn reinforcement is made above floor level which is typical of non-earthquake resistantdetailing. Column stirrups are provided by 3mm bars with 90◦ overlapping hook. Minimumspacing between stirrups is 70 mm.

Typical beam reinforcement consists of 6 mm and 10 mm bars, depending on the loadingcondition. For bottom reinforcement out of four bars two bars are bent up along the columndirection while remaining two is anchored in the joint with a 180◦ hook. Stirrups or transversereinforcement comprises of 3mm bars with 90◦ overlapping hook and minimum spacing of 55mm.

Some of the beam directly intersects with other beam which creates a beam to beam joint.The design is based on weak column strong beam, which is opposite to the current seismic de-sign procedure. Also none of the transverse reinforcement from beam and column continueswithin the joint, which makes the beam-column joint weakest point during earthquake excita-tion. Typical layout of section of a beam and column along with reinforcing detail is presentedin Figure 2.5 and Figure 2.6. Figure 2.7, Figure 2.8 and Figure 2.9 shows typical constructionstages of the experimental model. It can be clearly seen from the reinforcement pictures takenat the time of construction that the experimental model lacks seismic resistant reinforcementdetailing.

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Figure 2.5: Typical Beam Reinforcement

Figure 2.6: Typical Column Reinforcement

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Figure 2.7: Construction and Reinforcement Detail for Foundation

Figure 2.8: Typical Column Reinforcement and Construction Detail

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Figure 2.9: Typical Beam & Slab Construction & Reinforcement Detail

2.2.4 Additional Masses

In order to comply with the similitude condition, additional masses are applied to thespecimen. These include permanent and live load modified and increased, as discussed in Sec-tion 2.2.1. For the present study additional masses consists of unreinforced concrete havingspecific mass, ρ = 2400kg/m3. The position of additional masses are shown in the Figure 2.10,Figure 2.11 and Figure 2.12.

Figure 2.10: Additional Masses on Scale Structure

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Figure 2.11: Additional Masses on Scale Structure, Plan

Figure 2.12: Additional Masses on Scale Structure, Section

2.2.5 Material Properties

The materials used for the scale specimen such as concrete, steel and infill were cho-sen such that they fulfill the requirements of similitude conditions. The concrete compressive

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strength test was carried out on cubes of 150mm sides. The results of the test are presented inthe following Table 2.2. The table provides average values for each element on each floor. Thecylinder strength of concrete are obtained by following relation:

fc × 1.2 = fcu (2.1)

where fc = Cylinder Compressive Strengthfcu = Cube Compressive Strength

Compressive Strength

Element Cylinder [MPa] Cube [MPa]

Column 1st Floor 38 32Beam 1st Floor 52 43Column 2nd Floor 39 33Beam 2nd Floor 52 43Column 3rd Floor 33 27Beam 3rd Floor 44 36

Table 2.2: Average Compressive Strength of concrete

Steel bars of diameter 3mm, 6mm and 10mm are chosen for the scaled model. Tensilestrengths tests were made on the specimen and the results of only the yield values are presentedin Table 2.3. For every diameter bar three specimen were tested, average of the three values arechosen for the numerical model.

Yield Strength

Dia Specimen1 [MPa] Specimen2 [MPa] Specimen3 [MPa]

10mm 286 300 -06mm 366 360 36503mm 801 800 801

Table 2.3: Average values of yield strength of specimens

The specimen infill panels are made of cellular concrete Gasbeton RDB. The infills areconstructed after the construction of frame. Thickness of infill panel is 50mm. Geometricalconfiguration of infill panel is presented in Figure 2.3.

2.2.6 Testing Procedure

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(a) Input Signal The input signal selected for the test is Herceg-Novi record of 1979,Montenegro earthquake. It was divided into minor, moderate and severe earthquake. Minorintensity excitation (PGA = 0.02g) are designed to access the elastic response of the structureand its dynamic properties through the calculation of the natural frequencies and mode shapes.Moderate (PGA = 0.30g) & severe intensity (PGA = 0.54g) were applied to the structure tostudy the inelastic response of the structure for assessment. To conform with the time similitudecondition, time history of the original accelerogram was compressed by a factor 1/

√2.

Figure 2.13: Input Signal [PGA = 0.3g]

Figure 2.14: Input Signal [PGA = 0.54g]

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Chapter 3. Literature Review

3. LITERATURE REVIEW

3.1 INFILL PANEL

It has been observed in the past, that design of buildings is done without taking into ac-count the effect of the infill, mainly because of lack of research and experimental work. Thegeneral idea behind ignoring infill panel during analysis was its highly non-linear nature. Themost important factors contributing to the nonlinear behavior of infilled frames arise from mate-rial nonlinearity, which required complex computational techniques for design. Recent studieshave shown that behavior of RC frames filled with masonry infill panel can significantly increasethe stiffness, strength and energy dissipation characteristics of framed structures.

In order to fully understand the behavior of infill panel and its mode of failure, severalanalytical models have been proposed by researchers around the world. These models can beclassified into two main groups, namely micro-models (local) and macro-models (simplified).

3.1.1 Micro-Models

These models are represented by using Finite Element method. Mallick and Severn (1967)were the first one to use this approach. Different elements were used to model this approachsuch as beam elements for surrounding frame, plane frame element for representing infill andinterface element for frame and panel interaction. The benefit of using finite element approachis to study in detail all possible modes of failure but its use is limited due to the greater computa-tional effort and time required in analysis & modeling. For further detail on micro-models basedon finite element apporach, readers can refer to work of Mallick and Severn (1967), Gooman(1968), Stafford (1962), Riddington and Stafford Smith (1977), KIng and Pandey (1978), Liauwand Kwan (1984), Rivero and Walker (1984), Dhanasekar (1985), Chrysostomou (1991), Shing(1992), Syrmkezis and Asteris (2001) as suggested by Smyrou (2006).

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3.1.2 Macro-Models

In order to overcome the complexity and computational requirement using micro-models,research has been done to simplify the modeling of infill panel with a single element. The mainidea has been to study the global effects of infill panel on structures under lateral loads.Since first attempts from Polyakov (1956), analytical and experimental tests have shown thata diagonal strut with appropriate mechanical properties can provide a solution to the problem.Several authors have modified the characteristics of single strut model with multi strut configu-rations to better understand the effect of,micro-cracking in the corner of the infill panel due totensile stresses and higher shear strength of the infill panel relative to the frame. A brief reviewof the expressions developed because of these experimental work is presented below.

Figure 3.1: Deformation under shear load (Paulay and Priestley 1992)

(a) General Properties of Diagonal Strut Based on elastic studies Polyakov (1956)conducted one of the first analytical studies on infilled frames. He considered the effect of infillin each panel as equivalent to diagonal bracing. In 1961, Holmes took the idea and suggestedthat infill panel can be replace by an equivalent pin-jointed diagonal strut. He proposed that thediagonal strut to have the same material and thickness as the infill panel. The width of strut wastaken equal to one third of the strut length as shown in the Figure 3.1 i.e.

bw =dw

3(3.1)

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Stafford (1966) performed a series of test on square steel infilled frames. He observed thatcontact length between the wall and frame is related to the width of the strut. From the experi-mental result he proposed the following relation for finding the contact length between the walland infill frame.

z =π

2λ(3.2)

λ = 4

√Emtwsin(2θ)

4EcIchw

(3.3)

where λ represents the relative stiffness between the RC frame and the wall. Em is the elasticmodulus of the masonry, θ the angle of the diagonal strut with the beams, Ec and Ic representselastic modulus and moment of inertia of concrete column respectively.

Paulay & Priestley took a conservatively high value for the width of equivalent strut. Accordingto them, a high value of bw will result in a stiffer structure. The relation given by them is asfollows:

bw = 0.25dw (3.4)

Mainstone (1971) conducted tests on small scale specimens(h = 406mm) diagonally loaded incompression and proposed the following expression:

bw = 0.16λ−0.3h dw (3.5)

Klingner and Berter (1978) based on scale test done by Mainstone (1971) proposed the follow-ing the equation:

bw

dw

= 0.175(λ · h)−0.4dw (3.6)

Liauw and Kwan (1984) found the following relation from previous experimental data:

bw =0.95hmcosθ√

λ · h(3.7)

In the above equation it was assumed that θ is equal to 25◦ and 50◦. These values represent thelimit values for practical situations. Crisafulli (1997) compared the variation of the parameter λh

with the ratio of bw

dwand found out that the ratio bw/dw decreases as λh increases. The variation

is presented in the Figure 3.2.

17


0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

λ−h

b w/d

w

Holmes

Paulay & Priestley

Mainstone

Liauw & Kwan (25)

Liauw & Kwan (50)

Figure 3.2: Variation of the ratio bwdw

for infill frames as a function of parameter λ · h

Decanini and Fantin (1987) for the first time considered the fact of cracked and uncrackedmasonry effect and proposed two sets of equations based on the results from the framed masonrytested under lateral forces. The variation is plotted in the Figure 3.3.

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10

λ−h

b w/d

w

UncrackedCracked

Figure 3.3: Variation of the ratio bwdw

as a function of parameter λ ·h according to Decanini andFantin

18


3.1.3 Cyclic Behavior of Infill Panel

In this section, the model proposed by Crisafulli (1997) for the hysteric behavior of ma-sonry subjected to cyclic loading is described. The model is capable of taking into account thenon-linear response of masonry in compression. As the model allows to take into account thevariation of struts cross section as a function of the axial deformation experienced by element, itis possible to consider the loss of stiffness due to shortening of the contact length between frameand panel as the lateral load increases. Stress Strain relation for the hysteric model proposed areshown Figure 3.4 and Figure 3.5.

Figure 3.4: General characteristics for cyclic axial behavior of masonry (Crisafulli 1997)

Decanini and Fantin (1987) from experimental results showed that the equivalent width of thestrut decreases by about 20% to 50%, due to cracking of masonry panel. The main advantage isthat it allows the user to control the variation of stiffness and the axial strength of the masonrystrut.

3.1.4 Proposed model for the analysis of Infilled frames

As discussed previously for macro-modeling of infilled frames, equivalent diagonal strutrepresentation is used. Crisafulli (1997) adopted the same approach, considering a multi-strutformulation as shown in the Figure 3.6. An initial study was carried out to see the limitations

19


Figure 3.5: Stress Strain Curve (Crisafulli 1997)

of single strut model and influence of different multi strut model on response of the structure.The main focus was on stiffness of the structure and in the actions induced in the surroundingframe.

Figure 3.6: Modified strut models Crisafulli (1997)

20


Numerical results obtained from three strut models were compared with a finite elementmicro-model formulation. The area of the equivalent strut was kept constant and static lateralload was applied assuming linear elastic behavior. Nonlinear effects were considered for finiteelement model to represent the separation of panel frame interface.

Results from the test shows that, stiffness of the infilled frame is similar in all cases. Itdecrease slightly for two and three strut model, however there was significant change in stiffnessfor three strut model depending on the contact distance hz, which is function of contact lengthz. It was also observed from the results that single strut model under-estimated the bendingmoment, two strut model showed much larger values while three strut model constituted betterapproximation with the finite element model.

It was concluded from the results, although single strut model represent good estimationof stiffness of the infilled frame and axial forces by lateral forces. However, a more refinedmodel is required which could give realistic values for bending moment and shear force inframes.

(a) Description of proposed model Crisafulli proposed a new multi-spring model whichis intended to represent the shear failure of masonry. The model accounts separately for thecompressive and shear behavior of masonry using a double truss mechanism and a shear springin each direction. It was assumed that both struts are parallel and are separated by a verticaldistance equal to hz.

Figure 3.7: Infill panel element configuration,Crisafulli (1997)

21


Figure 3.8: Shear spring configuration,Crisafulli (1997)

In order to simplify the application of the proposed model, three different sets of nodes areconsidered for the development of panel namely, External, Internal and Dummy nodes. Externalnodes are connected to the frame while internal nodes are defined by a horizontal and verticaloffset xoi and yoi. The vertical and horizontal offsets are used to represent the reduction of thedimensions of the panel due to the depth of the frame members. Four dummy nodes are requiredto define one end of the strut members, which is not connected to the corners of the panel. Thedetails are shown in Figure 3.7 and Figure 3.8.

One spring element is used to describe the shear behavior of the panel element. The spring isconnected to two diagonally opposite internal nodes depending on the direction of the shearforce. The limitation of the proposed model is that the potential plastic hinges which coulddevelop along the length of the columns can not be considered in the model.

(b) Compressive Strength fn The expression for compressive strength of diagonal strut asproposed by Decanini and Fantin (1987) can be estimated by following expression:

Rc = f′

mθAms (3.8)

where Ams is the area of the equivalent strut i.e. Ams = bw × t and f′

mθ is the strength ofmasonry when diagonally loaded at an inclination, θ.Mann and Muller (1982) developed a failure theory for unreinforced masonry subjected to shear

22


and compressive stresses based on equilibrium considerations. Crisafulli (1997) modified thetheory assuming a linear distribution of stress by considering the shear and normal stressesin the bed joint, τ and fn. Axial stresses parallel to the bed joint were neglected based onequilibrium consideration. Expressing the failure criterion in terms of principal stresses f1 andf2, the following equations can be used:

fn = f1 sin2 θ (3.9)

τ = f1 sin θ cos θ (3.10)

In the above equation f1 is assumed to be positive. The above equations are derived under theassumption that principal stresses f2 developed in the masonry panel is not significant.

Figure 3.9: Stress state considered to evaluate the strength of masonry,Crisafulli (1997)

(c) Element Stiffness The total element stiffness is distributed in a given proportionto the strut and to the shear spring. The stiffness of the shear spring Ks can be calculated as afraction γs of the total stiffness of the masonry strut. Since the area of both struts are assumedto be equal such that the combination of the shear spring and the two masonry struts resultsin a total stiffness equal to the stiffness of the single strut model. The strut stiffness and shearstiffness are computed as follows:

KS = γsAmsEm

dm

cos2 θ (3.11)

KA = (1− γs)AmsEt

2dm

(3.12)

Tensile Strength, f ′t: Although analytical and experimental results show that the tensile strength

of masonry is usually much smaller than the compressive strength, therefore, f ′t can be assumed

to be zero in the analysis. However, research have shown that a value equal to 10% of the com-pressive strength can be approximated. It has been introduced in the model to gain generality.

23


Strain at maximum stress, ε′m: It represents the strain at maximum stress and its value vary

from 0.002 to 0.005. It influences via the modification of the secant stiffness of the ascendingbranch of stress-strain curve.Ultimate Strain, εu: It controls the descending branch of the stress-strain curve. For a largevalue such as εu = 20ε

′m, a smooth decrease of the compressive stress is obtained.

Closing strain, εcl: Closing strain presents the limiting strain at which cracks are closed par-tially and compressive stresses are resisted. For very large values such as εcl = εu is notconsidered in the analysis. Typical value range between 0 and 0.003.Elastic Modulus, Emo: This parameter represents the initial slope of the stress-strain curve. Alarge variation in its value is reported because of masonry being made up composite material,each have distinct properties. Empirical equations have been proposed for the evaluation ofelastic modulus of masonry by various researchers. Most of these equations define the secantmodulus at a stress level between 1/3 and 2/3 of maximum compressive stress. According to(Crisafulli), these values can underestimate the initial stiffness of the infilled frame and to obtaina better approximation for the strength envelope, he assumed the following expression:

Emo ≥2f

′

mθ

ε′m

(3.13)

3.1.5 Input Parameters

In order to describe the hysteric behavior of strut, several geometrical, mechanical and em-pirical parameters were described by (Crisafulli). Crisafulli proposed a range of recommendedvalues obtained from experimental tests. A list of input parameters along with definition andrecommended values are presented in this section:Unloading stiffness factor, γun: This parameter controls the slope of the unloading branch ofthe envelope curve. The variation of this parameter modifies the internal cycles, and not theenvelope. Its value ranges from 1.5 to 2.5, however it is assumed to be γun ≥ 1.0.Reloading strain factor, αre: It defines the point on the strength envelope, where the reloadingcurve reach the strength envelope. Its value ranges from 0.2 to 0.4. Crisafulli (1997) used avalue of 1.5 for non-linear analysis of infilled frames.Strain inflection factor, αch: This parameter predicts the strain at which the reloading curvehas an inflection point. Its value range between 0.1 and 0.7. This parameter controls the fatnessof the hysteresis loops.Complete unloading strain factor,βa: This parameter defines the auxiliary point used to de-fine the plastic deformation after complete unloading. Its values typically range between 1.5and 2.0.Stress inflection factor, βch: It defines the stress at which the reloading curve exhibits an in-

24


flection point. Its value vary from 0.5 to 0.9.Zero stress stiffness factor, γplu: This parameter defines the modulus of the hysteric curve atzero stress after complete unloading in proportion to initial modulus. Its value vary between 0and 1.Reloading stiffness factor, γplr: It defines the reloading stiffness modulus, after complete load-ing has taken place. Its value is greater than one but typical value range between 1.1 to 1.5 to fitexperimental data.Plastic unloading stiffness factor, ex1: It controls the influence of εun in the degradation of thestiffness. Values ranging from 1.5 and 2.0 have been used.Repeated cycle strain factor, ex2: This parameter increases the strain at which the envelopecurve is reached after an envelope curve is reached. Its value may typically vary between 1.0and and 1.5. It is used to represent cumulative damage inside repeated cycles.Reduction shear factor, alphas: This empirical parameter represents the ratio between themaximum shear stress and the average stress in the panel, and may range between 1.4 and 1.65.

3.1.6 Reduction in area due to lateral displacements

It has been assumed in the proposed model that the area of the equivalent strut variesas a function of axial displacements, as shown in the Figure 3.10. The effect of strength andstiffness degradation due to cracking of the panel was not considered in the previous models.Even though there is insufficient information to estimate the practical values but it is introducedin the model to gain generality. Experimental results of Decanini and Fantin showed that thewidth of the strut decreases by about 20 % to 50 % due to cracking of the masonry infill panel.However, the results were obtained under the assumption that the modulus E remains constant,whereas the current model considers a variable modulus Crisafulli (1997). In the Figure 3.10,ε1 and ε2, the strains for reduced and residual areas define a linear reduction of the initial area,they can be taken as 1/10(ε′

m) and 1/2 (ε′m) (Blandon 2005).

25


Figure 3.10: Variation of area of strut as a function of the axial strain

3.1.7 Openings

Experimental tests have shown that presence of openings significantly change the be-haviour of infilled frames by reduction of strength and resistance. Due to the variability inlocation and size of openings, exact prediction of strength and stiffness of infilled frame is dif-ficult to predict. (Mosalam and Ayala) observed that infilled frames with openings show moreductile behaviour and less strength then solid infill. He performed experiments on two struc-tures, one having symmetric windows while other having symmetric doors. Initial stiffnesswas reduced in both the cases but he observed, frame with window openings show no reduc-tion of the maximum strength while for frame with door as opening strength was reduced 20%approximately.

Bertoldi et al. proposed a set of expressions for calculation of reduction coefficient rac. Theexpressions are given below:

rac = 0.78e−0.322 ln Aa + 0.93e−0.762 ln Ac ≤ 1 (3.14)

In the above expression,Aa[%] = Ratio of opening area / infill area andAc[%] = Ratio of opening length / infill lengthAn infill panel with opening can be considered effective, if the following criteria is met:

Aa(%) ≤ 25 (3.15)

Ac(%) ≤ 40 (3.16)

26


Due to a large number of variables and uncertainties involved, there is not much agreementon this topic among the research community. However the effect of openings can be takeninto account by reducing the value of strut area A1 as described by (Smyrou 2006) that is,if agiven infill panel features openings of 15% to 30% with respect to the area of the panel, goodresponse predictions might be obtained by reducing the value of A1 (i.e. its stiffness) by a valuethat varies between 30% and 50%.

3.2 RIGID DIAPHRAGM

To enforce certain types of rigid body behaviour constraints are used. They are use toconnect different parts of the model. The advantage of using constraints is that it reduces thenumber of equations to be solved and will usually result in increased computational efficiency.The type of behaviours that can enforced by constraint are, naming a few such as rigid body,rigid diaphragm, etc.A rigid diaphragm constraint causes all of its constrained joints to move together as a planardiaphragm that is rigid against membrane deformation. Effectively all constrained joints areconnected to each other by links that are rigid in plane but do not effect out of plane. Thisconstraint can be used to model:

• concrete floors in building structures, which typically have very large in-plane stiffness.

• diaphragm in bridge superstructure.

The use of diaphragm constraint for building structure eliminates the numerical accuracyproblem created, when large in-plane stiffness of a floor diaphragm is modeled with a membraneelement. It is also very useful in the lateral dynamic analysis of buildings, as it results ina significant reduction in the size of the eigen value problem to be solved (Computers andStructures. 2004).

27


Figure 3.11: Diaphragm constraint to model rigid floor slab, Adapted from (Computers andStructures. 2004)

28

Chapter 4. Numerical Model of Case Study

4. NUMERICAL MODEL OF CASE STUDY

In this chapter numerical model of the scaled building is presented. The non-linear finite elementprogram used for current work is SeismoStruct (SeismoSoft 2008). SeismoStruct is a fibreelement-based program freely available from Internet. Modeling of any kind of structures iseasily done because of its Graphical user Interface. Also the calibration of infill panel andnumerical model of the structure in SeismoStruct is presented in detail.

4.1 SEISMOSTRUCT

SeismoStruct is a Finite Element package capable of predicting the large displacementbehavior of space frames under static or dynamic loading, taking into account both geomet-ric nonlinearities and material inelasticity. SeismoStruct accepts static as well as dynamic ac-tions and has the ability to perform eigenvalue, nonlinear static pushover (conventional andadaptive), nonlinear static time-history analysis, nonlinear dynamic analysis and incrementaldynamic analysis.

To model geometric nonlinearity, both local (beam-column effect) and global (large dis-placements/rotations effects) sources of geometric nonlinearity are automatically taken into ac-count in SeismoStruct. Since a constant generalised axial strain shape function is assumed inthe adopted cubic formulation, it results that its application is only fully valid to model the non-linear response of relatively short members and hence a number of elements (3-4 per structuralmember) is required for the accurate modeling of structural frame members.

For accurate estimation of structural damage distribution, the spread of material inelas-ticity along the member length and across the section area is explicitly represented through theemployment of a fibre modeling approach as shown in Figure 4.1. The sectional stress-strainstate of beam-column elements is obtained through the integration of the nonlinear uni-axial

29


stress-strain response of the individual fibers in which the section has been subdivided. If asufficient number of fibres (200-400 in spatial analysis) is employed, the distribution of mate-rial nonlinearity across the section area is accurately modeled. Two integration Gauss pointsper element are then used for the numerical integration of the governing equations of the cubicformulation. If a sufficient number of elements is used (5-6 per structural member) the spreadof inelasticity along member length can be accurately estimated.

Figure 4.1: Material Inelasticity

4.2 NUMERICAL MODEL OF STRUCTURE

The software has been used extensively in the past by many authors for verifying theexperimental model with the numerical one, however none of the studies carried out modelingof 3D irregular frames with infill panel and rigid diaphragm. Therefore the current study triesto verify the response of FE model with experimental results.

Uni-axial nonlinear constant confinement model, that follows the constitutive relationshipproposed by (Mander, Priestley, and Park 1988) and the cyclic rules proposed by Martinez-Rueda and Elnashai (1997) is used for modeling concrete . The confinement effects providedby the lateral transverse reinforcement are incorporated through the rules proposed by (Mander,Priestley, and Park 1988) whereby constant confining pressure is assumed throughout the entirestress-strain range. Five parameters must be defined to describe the model completely. Theseare Compressive strength, tensile strength,strain at peak stress,confinement factor and specificweight. The confinement factor (kc) is the ratio between the confined and unconfined compres-sive stress of the concrete. In current study its value is taken equal to 1.0 because transverse

30


reinforcement of all members is very small to produce an effective concrete confinement. Thecompressive strength values used for the model are presented in Table 2.2. The values for otherparameters are given below as they are constant for all sections.

• Tensile strength, ft = 0.001 N/mm2

• Strain at peak stress, εc = 0.002 mm/mm

• Confinement factor, kc = 1.0

• Specific weight, γ = 24 kN/m3

A uni-axial bilinear stress-strain model with kinematic strain hardening is used to for steel.Three parameters must be defined to describe the model completely, modulus of elasticity, yieldstrength, and strain hardening parameter. Values of yield strength for the model are given inTable 2.3. The values for others parameters are given below:

• Elastic Modulus, Es = 200000 N/mm2

• Strain hardening, µ = 0.004

Inelastic frame elements are used to model 3D-beam column elements both with dis-placement base formulation and force base formulation. The number of section fibres for dis-placement base formulation or integration points for force base formulation used in sectionequilibrium computations carried out at each of the element’s Gauss section needs to be de-fined. The ideal number of section fibers, sufficient to guarantee an adequate reproduction ofthe stress-strain distribution across the element’s cross-section, varies with the shape and mate-rial characteristics of the latter, depending also on the degree of inelasticity to which the elementwill be forced to. For the current study, number of section fibers used for displacement base for-mulation is 300 whereas number of integration points use are 4 for force base formulation.

The distributed mass applied to beam and column elements consists of self weight ofthe frame and additional masses obtained from similitude condition. The total mass of thestructure is 51.83 tons. In SeismoStruct geometry of the structure being modeled is a three-step procedure. In the first step all structural and non-structural nodes are defined, after whichnodes are connected through element connectivity and finally the process is then concludedwith the assignment of structural restraints, which fully characterise the structure’s boundaryconditions. Centerline dimensions for beams and columns are used to accurately model the

31


structure. All beams are 125 x 250mm while except column C2 which is 125 x 375mm theremaining columns are 125 x 125mm. Rigid links are used to connect elements at column C2as shown in the Figure 4.2.

Figure 4.2: Rigid Link connection at column C2

Finally, to correctly distribute the inertia forces in the structure, rigid diaphragm approachis used. In SeismoStruct, nodal constraints are implemented through the use of either PenaltyFunctions or Lagrange Multipliers. For the present study nodal constraints approach that makesuse of Lagrange Multiplier is implemented as suggested by Pinho et al. (2008). A 3D view ofthe structure both with Displacement base formulation and Force base element formulation isshown in Figure 4.3.

32


(a) (b)

Figure 4.3: (a) Displacement-Based Element Formulation, (b) Force-Based Element Formula-tion

4.3 CALIBRATION OF INFILL PANEL

Due to the complex nature of the masonry infill panel, the model is calibrated with theexperimental results. The experimental test was performed on a single bay single storey 2Dreinforced concrete frame with infill panel. It was conducted in the laboratory of Departmentof Structural Mechanics, University of Pavia. The infill was constructed from masonry blocksof cellular RDB Gasbeston having a height of 250 mm, thickness of 300 mm and length of625 mm. The layout of the wall along with the reinforcement detail of beam and columns ispresented in Figure 4.4 and Figure 4.5, Penna (2006).

33


Figure 4.4: Layout of Infill panel adapted from Penna (2006)

Figure 4.5: Reinforcement Detail of Beam and Columns,(adapted from Penna (2006))

34


The cyclic test was performed by repeated cycles of loading until a horizontal displace-ment of 33mm (1.2 % of panel) was raeched. The results of the test interms of force-horizontaldisplacement is shown in Figure 4.6.

−40 −30 −20 −10 0 10 20 30 40−500

−400

−300

−200

−100

0

100

200

300

400

500Force − Displacement

Displacement[mm]

For

ce [k

N]

1.20%1.00%0.80%0.60%0.40%0.20%0.10%Interp

Figure 4.6: Force-Displacement,(adapted from Penna (2006))

To accurately measure the response of the numerical model with the experimental results,Inelastic infill panel are included in the model. A four-node masonry panel element, developedby (Crisafulli 1997) and implemented in SeismoStruct by (Blandon 2005), is used for the mod-eling of the nonlinear response of infill panels in framed structures. Each panel is representedby six strut members; each diagonal direction features two parallel struts to carry axial loadsacross two opposite diagonal corners and a third one to carry the shear from the top to the bot-tom of the panel as shown in Figure 3.7 and Figure 3.8. The axial load struts use the masonrystrut hysteresis model, while the shear strut uses a dedicated bilinear hysteresis rule.

The empirical parameters as described in Section 3.1.5 were first calibrated with experimentalresults. Axial load struts use seventeen parameters to define strut hysteresis model while shearstrut uses four empirical parameters to completely define the bilinear hysteresis model. Otherthan these empirical parameters, there are few geometrical and material parameters. A detailoverview of both the parameters are given in Section 3.1.

35


The default values provided in SeismoStruct help and recommended by Smyrou (2006)were used as an initial trial. Initial few trails were run to adjust the value of compressive strengthand Initial Young Modulus to control the maximum values of base shear force. The values arepresented in Table 4.1 while the results of the analysis are shown in Figure 4.7.

Default Values

Em 1900 fm 1.25 ft 0.575ε

′m 0.0012 εu 0.024 εcl 0.003

ε1 0.0003 ε2 0.0006 γun 1.7αre 0.2 αch 0.7 βa 2.0βch 0.9 γplu 1.0 γplr 1.1ex1 3.0 ex2 1.0 τo 0.3µ 0.7 τmax 1.0 αs 1.5

Table 4.1: Default Values for Calibration of Infill Panel

−40 −30 −20 −10 0 10 20 30 40−500

−400

−300

−200

−100

0

100

200

300

400


Displacement[mm]

For

ce [k

N]

MeasuredSeismoStrcut

Figure 4.7: Force-Displacement, Trial 1

As mentioned in the study of Smyrou (2006), the most influential parameters that controlsthe shape of hysteresis loops, fatness of the loops and the tangent modulus corresponding to theplastic strain are γun, αch and ex1. These three parameters infact decide the amount of energy

36


dissipated during cyclic loading. Therefore a second trial was done by changing the valuesof these three parameters in the range give by (Crisafulli 1997). The values are provided inTable 4.2 while the result of the analysis are given in Figure 4.8.

Intermediate Values

Em 1900 fm 1.25 ft 0.2ε

′m 0.0012 εu 0.024 εcl 0.003ε1 0.0003 ε2 0.0006 γun 2.5αre 0.2 αch 0.1 βa 1.5βch 0.9 γplu 1.0 γplr 1.5ex1 1.75 ex2 1.5 τo 0.3µ 0.5 τmax 1.25 αs 1.25

Table 4.2: Intermediate Values for Calibration of Infill Panel

−40 −30 −20 −10 0 10 20 30 40−500

−400

−300

−200

−100

0

100

200

300

400


Displacement[mm]

For

ce [k

N]


Figure 4.8: Force-Displacement, Trial 2

Analysis results of second trial shows that the unloading part does not match exactly theexperimental results and some pinching is still observed during the unloading and reloading part.To remove those pinching, parameters which were less influential were modified to accuratelyrepresent the experimental results, such as closing strain, strut area reduction strain and residual

37


strut area strain. Out of range value for closing strain,εcl = 0.004 is used to better approximatethe experimental result. Strut area reduction strain ε1 and residual strut area strain ε2 values usedare 0.0001 and 0.001. Furthermore the value of unloading stiffness factor is change to defaultvalue while strain inflection factor is taken as 0.1, which is same as supposed in second trail.The final results are presented in Table 4.3 and results of the analysis are shown in Figure 4.9.

Final Values

Em 1900 fm 1.25 ft 0.2ε

′m 0.0018 εu 0.076 εcl 0.004ε1 0.0001 ε2 0.001 γun 1.7αre 0.2 αch 0.1 βa 1.5βch 0.9 γplu 1.0 γplr 1.5ex1 1.75 ex2 1.5 τo 0.3µ 0.5 τmax 1.25 αs 1.25

Table 4.3: Final Values for Calibration of Infill Panel

−40 −30 −20 −10 0 10 20 30 40−500

−400

−300

−200

−100

0

100

200

300

400


Displacement[mm]

For

ce [k

N]


Figure 4.9: Force-Displacement, Final Calibrated

The important parameters that contributed most in the calibration of the infill panel arepresented in the Table 4.4.

38


Parameters Contributing Most to Infill Panel Calibration

Parameters Default Intermediate Final

ε′m 0.0012 0.0012 0.0018

ε′m 0.024 0.024 0.076

εcl 0.003 0.003 0.004ε1 0.0003 0.0003 0.0001ε2 0.0006 0.0006 0.001γun 1.7 2.5 1.7αch 0.7 0.1 0.1ex1 3.0 1.75 1.75

Table 4.4: Parameters contributing most

4.3.1 Geometrical Parameters

Once the infill panel parameters for experimental results were calibrated in SeismoStruct,they were used for the current analysis. However the geometrical parameters were updatedaccording to the geometry of the structure. These are described below:

Thickness of the panel: As described in Section 2.2.5, the infill panels are made up of cellularconcrete Gasbeton RDB having thickness 50 mm.

Horizontal and vertical offset: The horizontal and vertical offset is calculated from the beamand column depth. Since centerline dimension are used, external nodes are taken as the beamcolumn joints. The vertical offset for all panels is equal to half the beam depth divided by thenet height of the infill panel, i.e. 10%. In case of horizontal offset, the value of xoi varies sincethe bay length is different. This could be divided into three groups depending on the length ofthe bay i.e. 1.5m, 3m and 2.75m. For simplicity and not too much difference in the results thevalue of xoi for 3 m and 2.75 m bay length are taken equal, also the xoi value for the 3m baylength governs. Therefore the horizontal offset values for the 3m bay length is 2.2% while for1.5m bay length is 4.5%.

Equivalent contact length, hz: This parameter takes into account, the contact length betweenthe frame and infill panel, introduced as percentage of the vertical height of the panel, effectivelyyielding the distance between the internal and dummy nodes as shown in Figure 3.7. Valuesbetween 1/3 and 1/2 of actual contact length (z) may be used. The values finally implementedfor hz are 23% and 21% for 3m and 1.5m bay length respectively.

39


Area of the Strut, A1: This parameter is defined as the product of the panel thickness and theequivalent width of the strut (bw) which normally varies between 10 - 40 % of the diagonal ofthe infill panel. Area of the strut has a direct influence on the stiffness of the infill panel andsimilarly on the structure. Several expressions are developed by researchers for the evaluationof the width of the equivalent strut, for the current study the width of equivalent of strut is takenequal to 12 % of length of the diagonal. A review of these expressions is given in Section 3.1.2.Since the thickness of the panel is known, the area of the struts was computed eaisly from theabove consideration.

Area of the Strut, A2: This parameter is taken as a percentage of Strut area A1. It is assumedthat the area varies linearly as function of the axial strain as shown in Figure 3.10. The twostrains between which this variation takes place are defined in Section 3.1.6. The values of thetwo strains used for the current study are 0.0001 and 0.001 respectively.

40

Chapter 5. Analysis and Results

5. ANALYSIS AND RESULTS

This chapter summarizes the verification of the analysis and results with experimental data. Thechapter starts with the Eigenvalue analysis (EVA), results of the first four modes of the model arepresented. The second part of the chapter deals with the Dynamic Time History (DTH) analysis.The analysis is performed both for Displacement based element formulation and Force basedelement formulation. Finally the results of the analysis are compared with the experimentalresults.

5.1 MODAL ANALYSIS

To check the model reliability, elastic periods of vibrations and the corresponding de-formed shapes are computed. Seismostruct uses the efficient Lanczos algorithm for the eval-uation of the structural natural frequencies and mode shapes. The experimental results areobtained by applying a low level PGA (0.02g) to the structure and calculating the natural fre-quencies and mode shapes. The experimental data is available only for first two fundamentalfrequencies while higher frequencies were difficult to obtain from signals. Table 5.1 shows thecomparison of vibration period obtained from numerical model and experimental test. In theTable 5.1, longitudinal direction refers to the direction of accelerogram both for numerical andexperimental model while transverse direction refers transverse to the applied accelerogram.

Vibration Periods (Sec)Direction Numerical Experimental

Longitudinal 0.19 0.15Transverse 0.20 0.20

Table 5.1: Estimated Vibration Periods

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Fundamental period dominates in both the cases. It can be observed that the period of vibrationin transverse direction matches well with the experimental result, however the difference inthe values of the longitudinal direction. The experimental model seems to be more stiff in thelongitudinal direction.

Furthermore the results were checked with the Height wise empirical equation such asgiven by Crowley and Pinho (2006). The results of the numerical model are in close agreementwith the empirical equation, Table 5.2 shows the comparison of results from empirical equationand modal analysis. Deformed shapes of first four modes are given in Figure ??.

Reference Formula Value (Sec)

Crowley and Pinho (2006) Ty = 0.043H 0.19(H in meters)

Numerical Model SeismoStruct 0.19

Table 5.2: Empirical Eq. and SeismoStruct result

5.2 NON-LINEAR TIME HISTORY ANALYSIS (NTHA)

Once the numerical model is verified with EigenValue analysis, the second step is tocheck the results of the shake table test with the Non-linear Time History Analysis (NTHA)of the numerical model. The numerical model is subjected to acceleration record of PGA 0.3gand 0.54g. The Accelerogram applied to the numerical model is shown in Section (a) and it isapplied in one direction only.

The displacements obtained for each floor from seismic records are compared with those mea-sured during the shake table test.

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Figure 5.1: Experimental Results for Col 643


Figure 5.2: Comparison of Displacement Time History for Col 644

Chapter 6. Conclusions and Recommendations

6. CONCLUSIONS AND RECOMMENDATIONS

6.1 CONCLUSIONS

Effect of Infill panel have widely been ignored in the non-linear analysis of infilled frame struc-tures, mainly due to the complexity and uncertainty involved in the analysis procedure. How-ever recent studies have shown that inclusion of masonry infill in non-linear structural analysisgreatly influence not only on the strength and stiffness but also on the energy dissipation mech-anism of the structure.

The objective of this analytical investigation was to compare the response of a numerical modelhaving masonry infill and rigid diaphragm with the experimental results. The experimentalbuilding is an irregular half scale three-storey infilled reinforced concrete building tested atTREES Lab EUCENTRE. The building is typical of older construction without earthquakeresistant provision and designed only for gravity loads. It is similar to the SPEAR structure butwith major differences, such as half scale (1:2) and provision of infill panel with openings andearthquake excitation using shaking table.

SeismoStruct a fibre element-based program is used for the for the numerical modeling ofthe building. The numerical model is done both for Force-Based element formulation andDisplacement-Based element formulation. Infill panel is modeled using the model developedby Crisafulli 1997 and implemented by Blandon 2005 in SeismoStruct. The 4-node masonrypanel element takes into account both the compressive and shear behaviour of panel, using twoparallel struts and a shear spring in each direction. The configuration of the model adequatelyconsiders the lateral stiffness of the panel and masonry strength of panel. The infill panel modelis first calibrated with the experimental results. It requires 19 parameters to fully calibrate themodel, however some default values have been used which corresponds to better approximationof experimental and numerical results.

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Chapter 6. Conclusions and Recommendations

One of the main features of the numerical model is the use of rigid diaphragm. Rigid diaphragmis implemented in the model using nodal constraints with Lagrange multipliers, this optionprovides better response of numerical results than the usual truss model as shown by Pinhoet al. 2008. This approach of modeling slab as rigid diaphragm is a reliable way of modelingthe presence of very stiff floors in this type of irregular structures.

The result of the both eigenvalue analysis and non-linear time history analysis shows that theresponse of numerical model is in good agreement with the experimental results. Though certaindiscrepancies are observed in the eigenvalue analysis but it has to bear in mind the complexnature of masonry infill panel model.

6.2 FUTURE DEVELOPMENTS

There are many issues which need to be addressed in future research work. A few of them arelisted below:

• The consideration regarding to take into account the effect openings in the calculations isvery important. Lack of recommendations in this regard greatly effect on the response ofthe structure.

• Calibration of infill panel model with experimental results shows that the model worksgood for the loading and unloading part, however it still needs to be improved for thereloading part.

• Force-Based Element formulation recently implemented in SeismoStruct is used for anal-ysis, which accounts for less computation time and showed good results. Verification ofthe formulation with different geometry structure especially with masonry infill panel willbe of great interest.

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