Study on Reinforced Concrete Frame with Solid Infill Masonry using Artificial Neural Network (ANN) RC Infill Wall Model in ANSYS (Ajay Gupta)

TRIBHUVAN UNIVERSITY INSTITUTE OF ENGINEERING

PULCHOWK CAMPUS DEPARTMENT OF CIVIL ENGINEERING M .Sc. Program in Structural Engineering Thesis No: SS00147

STUDY ON REINFORCED CONCRETE FRAME WITH SOLID INFILL BRICK MASONRY USING ARTIFICIAL NEURAL NETWORK

AJAY KUMAR GUPTA

February, 2011

TRIBHUVAN UNIVERSITY INSTITUTE OF ENGINEERING

PULCHOWK CAMPUS DEPARTMENT OF CIVIL ENGINEERING M .Sc. Program in Structural Engineering Thesis No: SS00147

STUDY ON REINFORCED CONCRETE FRAME WITH SOLID INFILL BRICK MASONRY USING ARTIFICIAL NEURAL NETWORK

A Thesis Submitted By AJAY KUMAR GUPTA

In partial fulfillment of the requirement for the degree of

MASTER OF SCIENCE IN

STRUCTURAL ENGINEERING

February, 2011

COPYRIGHT © The author has agreed that the Library, Department of Civil Engineering, Institute of Engineering, Pulchowk Campus, may make this thesis freely available for inspection. Moreover, the author has agreed that permission for extensive copying of this thesis for scholarly purpose may be granted by the professor who supervised the thesis work recorded herein or, in his absence, by the Head of the Department or concerning M.Sc. program coordinator or the Dean of the Institute in which thesis work was done. It is understood that the recognition will be given to the author of this thesis and to the Department of Civil Engineering, Institute of Engineering, Pulchowk Campus, in any use of the material of this thesis. Copying or publication or other use of the thesis for financial gain without approval of the Department of Civil Engineering, Institute of Engineering, Pulchowk Campus and the author’s written permission is prohibited. Request for permission to copy or to make any other use of the material of this thesis in whole or in part should be addressed to:

………………………….. Head Department of Civil Engineering Pulchowk Campus Institute of Engineering Lalitpur, Nepal.

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CERTIFICATE This is to certify that the work contained in this thesis entitled “Study on Reinforced Concrete Frame with Solid Infill Brick Masonry using Artificial Neural Network” submitted by Mr. Ajay Kumar Gupta (Roll No. 065/MSS/r/102) for the award of partial fulfillment of the degree of Master of Science in Structural Engineering of Institute of Engineering, Tribhuvan University, Kathmandu is a bonafide record of work carried out by him under my supervision and guidance, no part of it has been published or submitted elsewhere for the award of degree.

………………………………..

…………………….

Assoc. Prof. Prajwal Lal Pradhan

Date

Department of Civil Engineering Institute of Engineering Pulchowk Campus Lalitpur, Nepal

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ACKNOWLEDGEMENT

I would like to express my deep gratitude to my thesis supervisor, Assoc. Prof. Dr. Prajwal Lal Pradhan his valuable guidance, expertise, encouragement and critical suggestion without whom, this thesis could not come in this complete form. I highly appreciate his scholastic attitude and pragmatic thinking over thesis problems. I also express my gratitude to Mr. Shashidhar Ram Joshi, HOD, Department of Electronics, Pulchowk campus for giving me the concept of Artificial Neural Network. He has allowed me to attend the full semester course afford by the Electronics department for the M.Sc. students of that department. He has also helped me during my thesis period. Special appreciation goes to all the teachers of the Department of Civil Engineering, Pulchowk Campus, especially Prof. Dr. Prem Nath Maskey, Prof. Dr. Hikmat Raj Joshi and Dr. Jishnu Subedi for their kind support and suggestions during the entire thesis period. I owe a debt of gratitude to many other seniors and colleagues who provided technical support and social encouragement, especially Mr. Sujan Tripathi, Mr. Dinesh Gupta, Mr. Anup Chaudhary, Mr. Arvind Jha and Mr. Chandan Karna. And they, all, by virtue of proximity, became living sounding boards of ideas. Finally, I would like to express my profound gratitude to my family for their continuous support and encouragement during my study period.

Ajay Kumar Gupta (065/MSS/r/102)

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TRIBHUVAN UNIVERSITY INSTITUTE OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING M .Sc. Program in Structural Engineering

ABSTRACT Student: Ajay Kumar Gupta

Supervisor: Dr. Prajwal Lal Pradhan

Despite being the most common construction practice throughout the ages, infills have not found the space it deserves, in the structural design. There is lack of proper and easy method to consider the effect of the in-filled. So, this research is a small effort in the search of the alternative approach for analyzing the infill frames. The FEM Models are normally incapable of considering all the effecting factors such as non-linear behavior of the infill materials, lack of fit, non-homogeneity of the materials, etc. This research gives some idea to the structural engineer how to guess initially the parameters of interest during the design of infills. Structural design process is an iterative process and an approximate initial guess can reduce the time and cost involved in the analysis. The tentative design parameters can be predicted using the Artificial Intelligence and this computing power of the modern day computers has been used to fulfill the intended purpose. The data sets, which are generated by computer from the simulation of the infill-frame structure done in sophisticated software (ANSYS v10.0) capable of non-linear analysis, are used for the training of Neural Network. Few other unique data sets are taken for the validation of the Network trained. The comparison of the results from the ANN and that of software were in reasonable agreement with each other except in few rare cases.

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TABLE OF CONTENTS COPYRIGHT © ……………………………………………………………………………………….

i

CERTIFICATE ………………………………………………………………………………………..

ii

ACKNOWLEDGEMENT …………………………………………………………………………….

iii

ABSTRACT ……………………………………………………………………………………………

iv

LIST OF TABLES ……………………………………………………………………………………..

vii

LIST OF FIGURES …………………………………………………………………………………… viii LIST OF SYMBOLS …………………………………………………………………………………..

ix

CHAPTER 1: INTRODUCTION ……………………………………………………………………

1

1.1 Infilled Frames

1

1.2 Background

2

1.3 Why this Study ?

3

1.4 Objectives of the Study

5

1.5 Methodology

5

1.5.1 Review of Literature

6

1.5.2 Collection of Input Data

6

1.5.3 Modeling of the Structure

7

1.5.4 Analysis of the Structure

7

1.5.5 Result Validation

7

CHAPTER 2: REVIEW OF LITERATURE …………………………………………………………

8

2.1 General

8

2.2 Experimental Studies

8

2.3 Analytical Studies

9

2.4 About ANN

12

2.4.1 Back-Propagation Neural Network

13

2.4.2 The Back-Propagation Training Algorithm

14

CHAPTER 3: REINFORCED CONCRETE INFILL FRAME MATERIALS …………………….. 16 3.1 General

16

3.2 Masonry

16

3.3 Bricks

17

3.4 Mortar

18

3.5 Reinforced Concrete

19

v

CHAPTER 4: FINITE ELEMENT MODEL …………………………………………………………. 22 4.1 About ANSYS

22

4.2 Modelling Strategy

23

4.2.1 Calibration of the Model

23

4.2.2 Dimensions of the Model

23

4.3 Description of the Models

24

4.3.1 Element used in Modeling

24

4.3.2 Boundary Conditions Imposed

25

4.3.3 Overview of the Materials Used

26

4.3.4 Model Descriptions

27

4.3.5 The Outputs

27

4.4 Preparation of the Training sets

28

CHAPTER 5: TRAINING THE DATA SETS USING ANN ………………………………………... 30 5.1 Introduction to NeuNet Pro

30

5.2 Development of ANN Tool

30

CHAPTER 6: RESULTS AND DISCUSSIONS ……………………………………………………..

32

6.1 Parametric Studies

32

6.2 Geometric Parameters

33

6.2.1 Influence of wall thickness

34

6.2.2 Influence of Aspect Ratio

35

6.2.3 Influence of Bricks

37

6.2.4 Influence of Mortar

37

6.3 Variation of stiffness

38

6.4 Effective width of equivalent diagonal strut

40

6.5 Validation of Neural Network

42

CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS ……………………………………. 48 7.1 General

48

7.2 Conclusions

50

7.3 Recommendations for the future works

51

APPENDIX ……………………………………………………………………………………………… 53 A. ANSYS Contour Result Plot

53

B. Output Result from ANSYS

55

REFERENCES ………………………………………………………………………………………….. 70

vi

LIST OF TABLES Table 2-1: Analogy between biological and artificial neural networks

13

Table 3-1: Types and Properties of Bricks (Pradhan, P.L., 2009)

17

Table 3-2: Types and Properties of Mortar (Pradhan, P.L., 2009)

19

Table 3-3: Properties of concrete and rebars used in analysis

20

Table 4-1: Material properties used in analysis (Pradhan, P.L., 2009)

26

Table 4-2: Designation of Models used for analysis

27

Table 6.1: Parameters of Interest

32

Table 6-2: Parametric characteristics of infilled frames analysed

33

Table 6-3: Response variation due to wall thickness

35

Table 6-4: Response variation due to aspect ratio

36

Table 6-5: Response variation due to Bricks

37

Table 6-6: Response variation due to Mortar

38

Table 6-7: Comparison of strut widths

41

Table 7-1: Comparison of Results obtained from ANSYS and ANN

43

Table A-1: ANSYS Results for Span 3m

55

Table A-1: ANSYS Results for Span 3.5m

58

Table A-1: ANSYS Results for Span 4m

61

Table A-1: ANSYS Results for Span 4.5m

64

Table A-1: ANSYS Results for Span 5m

67

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LIST OF FIGURES Figure 1-1: Structure of Artificial Neural Network model

3

Figure 1-3: Flow Chart for Analysis of Infill Wall using ANN

6

Figure 2-1: Single Diagonal Strut Models (Smith and Carter 1969)

9

Figure 2-2: Geometric characteristics in Equations. (2-8) and (2-9)

12

Figure 2-3: Biological Neural Network

13

Figure 2-4: Typical Back-Propagation Network

14

Figure 3-1: Stress-strain characteristics of different bricks used.

18

Figure 4-1: Plane stress element used for Modeling

24

Figure 4-2: Beam3 element used for Modeling Beam and Column

25

Figure 4-4: Sample model prepared for the analysis

26

Figure 4-5: Salient nodal points considered for the output

28

Figure 5-1: Back-propagation Neural Network used for Training

31

Figure 5-2: Error reduction graph during Back-propagation Neural Network Training

31

Figure 6-1 : Infilled frames with different Aspect Ratios

34

Figure 6-2: Variation of displacement with span

39

Figure 6-3: Variation of stiffness with load

40

Figure 6-4 : Equivalent Strut Model

41

Figure 6-5 : Comparison of actual versus predicted data

42

Figure A-1 : Displacement contour plot

53

Figure A-2 : Stress Intensity contour plot

53

Figure A-3 : Shear Stress contour plot

54

Figure A-4 : X-axis Stress contour plot

54

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LIST OF SYMBOLS t

thickness of the infill

h

height of the infill

ℓ

length of the infill

θ

inclination of infill with the horizontal

d

diagonal length of infill

h’

height of the frame, measured between the centerlines of the beams

l’

span of the frame, measured between the centerlines of the columns

Wds

width of the diagonal strut

λh

non-dimensional parameter given by Smith

λ’

non-dimensional parameter given by FEMA

Ic

moment of inertia of the columns

Ed

young’s modulus of the infill material

Ef

young’s modulus of the material constituting the frame

Fi

total number of inputs of neuron i in the network

p

number of step

xi(p)

input of ith node in pth step

yj(p)

output of jth node in pth step

wij

weight assigned to a hidden layer node in between ith and jth nodes

δk

error in the output

σ

stress at a node

ε

strain at a node

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CHAPTER 1: INTRODUCTION 1.1 Infilled Frames Infill-frames have been used in many parts of the world over a long time. In these structures, exterior masonry walls and/or interior partitions, usually regarded as nonstructural architectural elements, are built as an infill between the frame members. However, the usual practice in the structural design of infill-frames is to ignore the structural interaction between the frame and infill. This implies that the infill has no influence on the structural behaviour of the building except for its mass. This would be appropriate if the frame and infill panel were separated by providing a sufficient gap between them. However, gaps are not usually specified and the actual behaviour of infill frames observed during past earthquakes shows that their response is sometimes wrongly predicted. Infill-frames have often demonstrated good earthquake resistant behaviour, at least for serviceability level earthquakes in which the masonry infill can provide enhanced stiffness and strength. It is expected that this structural system will continue to be used in many countries because the masonry infill panels are often cost-effective and suitable for temperature and sound insulation purposes. Hence, further investigation of the actual behaviour of these frames is warranted, with a goal towards developing a displacement-based approach to their design. Masonry panels, which contribute a large proportion of the mass of the infillframe, normally consist of anisotropic materials with a wide range of strength, deformation and energy dissipation properties. Unlike other conventional materials such as concrete and steel which have, to some extent, standard properties. Masonry materials vary significantly from one country to another based on the local constituent materials (the bricks and the mortar) and workmanship. Different local materials are used to produce masonry units with different shapes; they might be solid or hollow units with different hole-sizes and hole arrangements. In many countries, situated in seismic regions, reinforced concrete frames are infilled by brick masonry panels. Although the infill panels significantly enhance both the stiffness and strength of the frame, their contribution is often not considered mainly because of the lack of knowledge of the composite behavior of the frame and the infill. In multistory structures, the frames are generally well engineered in accordance with the state of knowledge of the day and to the building practice of 1

every country, whereas the infill panels are considered non-structural. The reason for the negligence is the high amount of non-linearity and non-homogeneity involved in the analysis making the analysis portion extremely tedious and monotonous. Thus computers can be extremely useful in such scenario. The computing capabilities of the computers can be used to deal with the problems imposed due to the inconsistent characteristics of the infill.

1.2 Background Infill frame construction represents a common type of construction in urban areas. Infill walls change the behavior of frames considerably under lateral loads and affect mainly the strength, rigidity, energy dissipation, etc. characteristics. In the conventional design, the building frames are designed for dead and live loads. Hence, they cannot withstand lateral loads, especially when they are very tall. On the other hand, post-earthquake damage reports often note poorly detailed reinforced concrete frames that have failed due to localized forces produced by the infill. Any attempt to increase the size of the structural elements to withstand these occasional loads is both expensive and undesirable. The concept of the infill frame considers the integral structural action of walls and slab with the frames, and provides increased lateral force resisting capacity for frames. The use of computers as we all know is inevitable these days in any portion of the structural design of any type of the structures. And the use of artificial intelligence in the field of computers is one of the most fascinating and interesting as the use these days is recommended in almost any field of real life and practical applications. The field being related to computer applications has not found much of the place in structural field and especially in the context of Nepal the use has been found to be very limited. The method based on the Artificial Neural Networks (ANN) can accommodate all parameters and uncertainties like non-linear behavior of infill, lack of fit at the frame infill interface, non-homogeneity of the materials. The main advantage of this method is that the size of the output vector can be increased to meet all the requirements. The inherent tolerance mechanism and the ability to learn from the new patterns (data sets) make it an ideal method. The origins of Artificial Neural Networks (ANN) are in the field biology. The biological brain consists of billions of highly interconnected neurons forming a neural 2

network. Human information processing depends on this connectionist system of nervous cells. Based on this advantage of information processing, neural networks can easily exploit the massively parallel local processing and distributed storage properties in the brain. Generally speaking, an ANN is an informational system simulating the ability of a biological neural network by interconnecting many simple neurons (Fig. 1-1). The neuron accepts inputs from a single or multiple sources and produces outputs by simple calculations, processing with a predetermined non-linear function. Therefore, the primary characteristics of an ANN can be presented as following: (1) the ability of learning; (2) distributed memory; (3) fault tolerance and (4) operating in parallel.

Figure 1-1: Structure of Artificial Neural Network model

1.3 Why this Study ? With the advancement of computational technology and ever going increasing trend of research activities, the demand for inelastic design is increasing day by day. The term inelastic is associated to material whose stress-strain diagram is non-linear. But, the usual practices follow only the linear stress-strain relationships. The linear relations are acceptable only for the small deformations. Whereas, in most of the cases when the deformation becomes too large, structural members undergo failure before the strains become finite. Such a situation can be frequently observed in infill frame structures. Infill frames are widely constructed using brick masonry infill walls. Since the brick masonry wall possesses highly heterogeneous material, non-linear studies become inevitable. Thus, for the analysis of infill frames, the models which can account for nonlinear behavior of individual materials must be used. For this, 3

non-linear characterization of the materials is quite essential to formulate. These days, engineering practices demand more and more new additional materials. Whose stressstrain behaviors are still not known or they have to be tested in laboratories. For the very common materials like bricks, concrete and mortars, which have a long history, people still are adopting linear relations for stress-strain curve. In the early days, computational challenges and efforts have made people compelled to accept the state of linear assumption. Now the advancement in computational technology stipulates more precised computational techniques, which can minimize the gap between realistic value and the approximation. Structural engineering involves understanding of material behavior, laws of mechanics, intuition, past experience or expertise and analysis techniques. The modern computer can bring speed, efficiency and accuracy in analysis of structures. But to computerize the areas such as conceptual design, modeling of natural phenomenon and material behavior, damage assessment etc., is extremely difficult as it requires human expertise. Structural design is an iterative process. The initial design is the first step in design process. Though the various aspects of structural design are controlled by many codes and regulations, the structural engineer has to exercise caution and use his judgment in addition to calculations in the interpretation of the various provisions of the I.S 456–2000 code to obtain an efficient and economic design. After the design process the designer makes an overall guess about the possible optimum solution consistent with designer’s experience, knowledge, constraints, and requirements. The analysis of the structure is then carried out using initial design. Based on the results of the analysis a re-design of the structure is carried out if any of the constraints is not satisfied. The efficiency of the design process depends heavily on initial guess. A good initial design reduces the number of subsequent analysis–design cycles. This phase is extremely difficult to computerize as it needs human intuition. In recent years efforts have been made to computerize the initial design process using artificial neural networks as they can learn from available designs during training process. Artificial neural network is a new technology emerged from approximate simulation of human brain and has been successfully applied in many fields of engineering. Neural networks and genetic algorithm demonstrate powerful problem solving ability. They are based on quite simple principles but take advantage of their mathematical nature in terms of non-linear 4

iteration. Neural networks with Back Propagation (BP) learning can be an extremely powerful tool for the prediction of subsequent design parameters.

1.4 Objectives of the Study The overall picture of the analysis of infill wall panels is still so vague in structural engineering fields. The amount of non-linearity involved due to heterogeneity in the materials presents complex design scenario for structural engineers. The presence of whole infill is found to be neglected in design studios. The research work is intended to produce some useful design criteria in the case of infill wall panels and easy prediction of the macro response of the wall panels with the use of artificial intelligence techniques. The summary can be listed as below − To determine the nonlinear response (using material non-linearity) of the composite action between brick infill walls and reinforced concrete frame, under in plane lateral load. − To compare the results obtained from a series of analysis of infill of different aspect ratios, thickness and materials. − To determine the equivalent diagonal strut thickness of infill wall useful in SEDS (Single Equivalent Diagonal Strut) Model. − To train the computer for the development of ANN tool for the prediction of non linear results associated with the infill masonry wall. − To

predict

the

infill

wall

response

parameters

of

interest

instantaneously without any real modeling and with much of accuracy desired.

1.5 Methodology The analysis comprise of a series of steps which are briefed as under in a systematic manner.

5

Non-linear Analysis of Infill

Identification of Material Properties (Non-linear)

Modelling & Analysis

Density, Poisson’s ratio & Stress-Strain curve of Brick

2D Modelling of Infill Wall Frame

Density, Poisson’s ratio & Stress-Strain curve of Mortar

2D Non-linear Analysis of RC Infill Wall

Training & Validation of Neural Network

Training Neural Network with Trainee Data Sets

Verification of Result obtained from Trained Network

Density, Poisson’s ratio & Stress-Strain curve of Reinforced Concrete

Figure 1-3: Flow Chart for Analysis of Infill Wall using ANN

1.5.1 Review of Literature The various literatures related with the works were searched and reviewed. In this regard, the literatures concerned with the traditional masonry infills, steel frame with infills, etc. were searched. Experimental and analytical studies conducted in the past were referred simultaneously. 1.5.2 Collection of Input Data The data regarding the material non-linearities and other properties were collected from previous researches and published journals. The dimensions of the infill to be used for the analysis were concluded from the practice being availed in this part of the country.

6

1.5.3 Modeling of the Structure Four different Ansys elements are used for preparation of Reinforced Concrete infill model in Ansys. Three different materials reinforced concrete, brick and mortar are considered. In which Ansys element Plane42 is used for both brick and mortar, and the element Beam3 is used for both beam and column. Link10 element is used for connection between line and plane element. Using these three elements 2D model is prepared in Ansys. Different aspect ratios were considered providing the data sets a wide range and two thickness of infill were used for analysis. 1.5.4 Analysis of the Structure The infill was modeled as a planar structure and hence the analysis was also done for the in-plane lateral loading. Since the non-linear analysis was found to quite time-consuming, static analyses were done for different models in advanced software. 1.5.5 Result Validation The responses obtained from the analytical analyses were used as data sets to train the Neural Network and then the trained network was used for the validation of other data sets for the quick prediction of the responses.

7

CHAPTER 2: REVIEW OF LITERATURE 2.1 General Recent earthquakes have clearly shown that the damages done to the buildings with infills were considerable less than those without infills and the difference was quite a bit significant. Therefore, the structural contribution of infill walls cannot simply be neglected particularly in regions of moderate and high seismicity where, the frame–infill interaction may cause substantial increase in both stiffness and strength of the frame. A review of analysis and design provisions related to masonry infill RC frames in seismic design codes of different countries shows that only a few codes have considered the effect of infill in analysis and design of masonry infill RC frames (Kaushik et al. 2006). On the other hand, the stiffness and strength of the infill frames are not taken care of by most of the codes. Hence, the behavior of infill frames needs to be studied extensively in order to develop a rational approach or guidelines for design.

2.2 Experimental Studies Hinged steel-frame with solid infill tested under monotonic loading were found to lose their load carrying capacity at ultimate stage by cracking of mortar joints along the compressive diagonal of the infill wall (Polyakov, 1948). About 45 single storey, single bay frames with reinforced concrete infill of reduced scale (between 1/8 and 3/8) were studied under monotonic loading (Benjamin& Williams, 1950). The influence of infill geometry, amount and direction of reinforcement in the wall, and column reinforcement were studied on ductility and load carrying capacity of the frame. Another study on steel frames with brick work, and concrete in-filling showed that the stiffness and the strength of the steel frame was greatly increased under the composite action of frame and masonry infill wall panel (Holmes, 1960). Several full-size tests were carried out to determine the behaviour of infill steel frames subjected to racking or shear loading. Tests on single storey steel frame with reinforced concrete and brick infill under lateral load led to semi-empirical methods for accounting effect of infill (Holmes, 1962). Infill walls were modelled as equivalent diagonal strut and the ultimate lateral load carrying capacity of the infill 8

frame expressed as a function of geometry of frame and infill, and of the compressive strength of the infill.

2.3 Analytical Studies Analytical models that have been developed to estimate lateral stiffness and strength of the infill frames include the equivalent frame model, the single diagonal strut model, and the multi-diagonal strut model. The equivalent frame model is based on the concept of equivalent frame, where members have the properties of the composite sections of the actual structure (Liauw 1972, Kodur et al. 1998). The equivalent diagonal strut model is the most simplified yet reasonably accurate macromodel. This is usually done by modeling the infill panel as a single diagonal strut connected to the two compressive diagonal corners. The key to this approach lies in determination of effective width of equivalent diagonal strut. In the last few decades, several attempts have been made to compute the effective width of diagonal strut for infill frames (Holmes 1961, Smith and Carter 1969, Mainstone 1971, Liauw and Kwan 1984, Paulay and Priestley 1992).

Figure 2-1: Single Diagonal Strut Models (Smith and Carter 1969)

9

During the last three decades, different approaches have been proposed for the prediction of the ultimate strength of infill steel frames subjected to monotonic lateral load. Holmes (1961) proposed that the infill wall be replaced by an equivalent diagonal strut having a width equal to one-third of the diagonal length of the infill wall. Stafford Smith (1966) proposed an expression relating the width of the equivalent strut to the properties of the frame and infill wall. The width of the equivalent strut varied with value of the following non-dimensional factor:

 E th 3 sin 2θ   λ h =  c 4Es I  

1/ 4

(2-1)

Where, Ec = elastic modulus of the infill material, ksi Es = elastic modulus of the frame material, ksi t = thickness of the infill wall, inches h = height of a single story, inches 4

I = moment of inertia of the frame columns, inch

θ = slope of the infill diagonal relative to horizontal

Stafford Smith and Carter (1969) further related the width of the equivalent strut not only to factor λh, but also to the variation of the elastic modulus of the infill material at different stress levels. Makino (1984) proposed a simplified formula to calculate the width of the equivalent strut based on Stafford Smith and Carter’s work. In his formula, the width of the equivalent strut was only related to the diagonal length of the infill wall or the thickness of the infill wall. Liauw and Kwan (1983a) expressed the equivalent strut width as a fraction of hcosθ: b=

0.86 (h cos θ) ≤ 0.45(h cos θ) λh

(2-2)

where, the non-dimensional factor parameter λh is defined in Eq. (1). This relation was obtained by parametric study using the finite element method. There has been a concern by some researchers (Meharbi et al. (1994), AlChaar (2002), and Al-Chaar et al. (2003a, 2003b)) that the single equivalent diagonal strut does not predict satisfactorily the lateral stiffness of infill frame. It is therefore 10

important to compare the width of diagonal strut of solid infill frames obtained from several empirical relationships available in the literature with that obtained by the finite element analysis. The following relations have been considered.

WdS =

d 3

l WdS = 0.58  h

−0.445

(λh )0.335d  l 

(2-3)

(Smith and Carter 1969)

(2-4)

(Mainstone 1971)

(2-5)

(Liauw and Kwan 1984)

(2-6)

0.064

h

WdS = 0.16λ−h0.3 d

WdS =

(Holmes 1961)

(0.95h cosθ ) λ.h

WdS =

d 4

(Paulay and Priestley 1992) (2-7)

WdS =

d 8

(Angel At. Al 1994)

(2-8)

(FEMA 274, 1997)

(2-9)

WdS = 0.175(λh )

−0.4

d

FEMA 356

The Federal Emergency Management Agency (FEMA) code 356 explains clearly enough how to take infills into account: the effect of infills has to be considered by a FEM analysis or, alternatively, by introducing a diagonal pin-jointed strut equivalent to the infill. For the first option no more is said, unlike the second one, which is derived from an experimental observation: under lateral forces the frame tends to separate from the infill near the windward lower and leeward upper corners of the infill mesh. For FEMA 356 the equivalent strut is to have the same thickness and modulus of elasticity as the infill panel (but it is not clear along which direction the modulus of elasticity must be calculated) while the width w is given by the following equation W − 0.4 = 0.175(λ ' h') d

λ' = 4

Ed tSin(2θ ) 4E f I c h

(2-10) (2-11)

11

Figure 2-2: Geometric characteristics in Equations. (2-8) and (2-9)

2.4 About ANN Machine learning involves adaptive mechanisms that enable computers to learn from experience, learn by example and learn by analogy. Learning capabilities can improve the performance of an intelligent system over time. The most popular approaches to machine learning are Artificial Neural Networks and Genetic Algorithms. A neural network can be defined as a model of reasoning based on the human brain. The brain consists of a densely interconnected set of nerve cells, or basic information-processing units, called neurons. The human brain incorporates nearly 10 billion neurons and 60 trillion connections, synapses, between them. By using multiple neurons simultaneously, the brain can perform its functions much faster than the fastest computers in existence today. Each neuron has a very simple structure, but an army of such elements constitutes a tremendous processing power. A neuron consists of a cell body, soma, a number of fibers called dendrites, and a single long fiber called the axon. Our brain can be considered as a highly complex, non-linear and parallel information-processing system. Information is stored and processed in a neural network simultaneously throughout the whole network, rather than at specific locations. In other words, in neural networks, both data and its processing are global rather than local. Learning is a fundamental and essential characteristic of biological 12

neural networks. The ease with which they can learn led to attempts to emulate a biological neural network in a computer.

Figure 2-3: Biological Neural Network

An artificial neural network consists of a number of very simple processors, also called neurons, which are analogous to the biological neurons in the brain. The neurons are connected by weighted links passing signals from one neuron to another. The output signal is transmitted through the neuron’s outgoing connection. The outgoing connection splits into a number of branches that transmit the same signal. The outgoing branches terminate at the incoming connections of other neurons in the network. Table 2-1: Analogy between biological and artificial neural networks

Biological Neural Network Artificial Neural Network Soma Dendrite Axon Synapse

Neuron Input Output Weight

2.4.1 Back-Propagation Neural Network

The network computes its output pattern, and if there is an error or in other words a difference between actual and desired output patterns, the weights are adjusted to reduce this error. A training set of input patterns is presented to the network. In a back-propagation neural network, the learning algorithm has two phases. 13

First, a training input pattern is presented to the network input layer. The network propagates the input pattern from layer to layer until the output pattern is generated by the output layer. If this pattern is different from the desired output, an error is calculated and then propagated backwards through the network from the output layer to the input layer. The weights are modified as the error is propagated. 2.4.2 The Back-Propagation Training Algorithm

Step 1: Initialisation -Set all the weights and threshold levels of the network to random numbers uniformly distributed inside a small range:  2.4 2.4    − ,+ Fi   Fi

(2-12)

Figure 2-4: Typical Back-Propagation Network

Step 2: Activation- Activate the back-propagation neural network by applying inputs x1(p), x2(p),…, xn(p) and desired outputs yd,1(p), yd,2(p),…, yd,n(p). (a) Calculate the actual outputs of the neurons in the hidden layer:  n  y j ( p ) = sigmoid ∑ xi ( p ).wij ( p ) − θ j   i =1 

(2-13)

Where, n is the number of inputs of neuron j in the hidden layer, and sigmoid is the sigmoid activation function. 14

(b) Calculate the actual outputs of the neurons in the output layer:  m yk ( p ) = sigmoid ∑ x jk ( p ).w jk ( p ) − θ k    j =1

(2-14)

Where, m is the number of inputs of neuron k in the output layer.

Step 3: Weight training- Update the weights in the back-propagation network propagating backward the errors associated with output neurons. (a) Calculate the error gradient for the neurons in the output layer:

δ k ( p) = y k ( p).[1 − y k ( p)].ek ( p) Where, ek ( p ) = y d ,k ( p ) − y k ( p )

(2-15) (2-16)

Calculate the weight corrections: ∆w jk ( p ) = α . y j ( p) − δ k ( p )

(2-17)

Update the weights at the output neurons: (2-18)

w jk ( p + 1) = w jk ( p ) + ∆w jk ( p )

Step 4: Iteration- Increase iteration p by one, go back to Step 2 and repeat the process until the desired error criterion is satisfied.

15

CHAPTER 3: REINFORCED CONCRETE INFILL FRAME MATERIALS 3.1 General Reinforced Concrete, mortar & brick are the major components of masonry units. Masonry possesses distinct directional properties due to the mortar joints. A number of influence

factors (such as anisotropy of units, size of units, mortar

thickness, material properties of units and mortar, arrangement of bed as well as head joints, and quality of workmanship) make simulation of masonry structures extremely difficult. The frame-masonry interaction in infill makes it even harder for the computer simulation.

3.2 Masonry Masonry is the building of structures from individual units laid in and bound together by mortar; the term masonry can also refer to the units themselves. The common materials of masonry construction are brick, stone such as marble, granite, travertine, limestone; concrete block, glass block, and tile. Masonry is generally a highly durable form of construction. However, the materials used, the quality of the mortar and workmanship, and the pattern in which the units are assembled can significantly affect the durability of the overall masonry construction. Masonry units, such as brick, tile, stone, glass brick or concrete block generally conform to the requirements specified in the 2003 International Building Code (IBC) Section 2103. Masonry is commonly used for the walls of buildings, retaining walls and monuments. Brick and concrete block are the most common types of masonry in use in industrialized nations and may be either weight-bearing or a veneer. Concrete blocks, especially those with hollow cores, offer various possibilities in masonry construction. They generally provide great compressive strength, and are best suited to structures with light transverse loading when the cores remain unfilled. Filling some or all of the cores with concrete or concrete with steel reinforcement (typically rebar) offers much greater tensile and lateral strength to structures.

16

Masonry is broadly classified as i) Stone masonry and ii) Brick masonry. Apart from the load-bearing capacity, the following aspects also are considered while selecting the most suitable type of masonry unit: (a) adequate thermal and sound insulation capacity of masonry, especially in the case of external walls, (b) reduction of the weight of the building in order to reduce the seismic loads, and (c) economy of construction.

3.3 Bricks A brick is a block of ceramic material used in masonry construction, usually laid using various kinds of mortar. The term brick refers to small units of building material, often made from fired clay and secured with mortar, a bonding agent comprising of cement, sand, and water. Long a popular material, brick retains heat, with-stands corrosion, and resists fire. Masonry construction are being made of either burnt clay brick, concrete or light-weight concrete units in different sizes and shapes, either solid or perforated. As a rule, they must meet national standard requirements. When selecting the most suitable type of unit, one has to consider, apart from the load-bearing capacity, the following aspects: 1. That can provide adequate thermal and sound insulation capacity, especially in external walls. 2. Which can minimise the weight of the building and of seismic horizontal forces. 3. Which can optimise the cost of construction. Table 3-1: Types and Properties of Bricks (Pradhan, P.L., 2009)

Material

Types

Modulus of Elasticity E (N/m2)

Poisson's Ratio ν

Density ρ, (kg/m3)

Brick

MB LB

3.022 E9 2.387 E9

0.09

1700

Build houses using brick masonry is a common practice in this part of the world. Generally there can be a few types of brick available anywhere in the world. Here also we intend to use three different types of brick, based on their properties and not dimensions. The types of the brick and their corresponding properties used in the modeling are tabulated in Table 3-1. 17

Figure 3-1: Stress-strain characteristics of different bricks used.

3.4 Mortar Mortar is a mixture of sand, lime and Portland cement, mixed with water to a workable consistency. It is used as a bond in masonry or for covering a wall. Mortar are referred as any of various bonding materials used in masonry, surfacing, and plastering, especially a plastic mixture of cement or lime, sand, and water that hardens in place and is used to bind together bricks or stones. Sometimes, additives are added to mortar to improve its workability, or for other reasons. Mortars must be sufficiently strong, durable, capable of keeping the wall intact, and must create a water-resistant barrier. It is applied with a bricklayer's trowel, and sets solid in a few hours. There are many different mixes and admixtures used to make mortars with different performance characteristics. According to the classification used in Euro Code 6, different types of mortar are used in masonry construction some of them are: 1. General purpose mortar, use in joints with a thickness greater than 3 mm and in which only dense aggregates are used. 2. Thin-layer mortar, designed mortar for use in joints between 1 mm and 3 mm in thickness.

18

3. Lightweight mortar, designed mortar with a dry hardened density lower than 1500 kg/m3. 4. Pre-batched mortar, consisting of constituents batched in a plant, supplied to the building site and mixed there under factory specified proportions and conditions. 5. Site-made mortar, composed of primary constituents batched and mixed on the building site. The types of the mortar and their corresponding properties used here for modeling are stated as below. Table 3-2: Types and Properties of Mortar (Pradhan, P.L., 2009)

Material

Composition

Modulus of Elasticity E (N/m2)

Poisson's Ratio ν

Density ρ, (kg/m3)

Mortar

1:4 1:6

3.651 E9 2.616 E9

0.17

1780

Figure 3-2: stress-strain characteristics of different mortar used

3.5 Reinforced Concrete Concrete is a mixture of cement (usually Portland cement) and stone aggregate. When mixed with a small amount of water, the cement hydrates form microscopic opaque crystal lattices encapsulating and locking the aggregate into a rigid structure. Typical concrete mixes have high resistance to compressive stresses (about 4000 psi (28 Mpa); however any appreciable tension (e.g., due to bending) will 19

break the microscopic rigid lattice, resulting in cracking and separation of the concrete. For this reason, typical non-reinforced concrete must be well supported to prevent the development of tension. A rebar (short for reinforcing bar), also known as reinforcing steel, reinforcement steel, or a deformed bar, is a common steel bar, and is commonly used as a tensioning device in reinforced concrete and reinforced masonry structures holding the concrete in compression. It is usually formed from carbon steel, and is given ridges for better mechanical anchoring into the concrete. Rebars were known in construction well before the era of the modern reinforced concrete. The name is taken from an extinct species of African jungle snakes used in tribal wars. The cast iron used for rebars is of very high quality, and they can resist corrosion on them for extremely long periods. If a material with high strength in tension, such as steel, is placed in concrete, then the composite material, reinforced concrete, resists not only compression but also bending and other direct tensile actions. A reinforced concrete section where the concrete resists the compression and steel resists the tension can be made into almost any shape and size for the construction industry. The common practice observed in this part of Nepal and almost everywhere in the country is to use reinforced concrete for frame materials and brick masonry for infill materials. So here we have intended to get closer to the real practice by modeling the structure using these four distinct materials and use their non-linear characteristics as far as possible. The properties of the concrete and the reinforcing bars used for the modeling purpose are listed as under: Table 3-3: Properties of concrete and rebars used in analysis

Material

Modulus of Elasticity E (N/m2)

Poisson's Ratio ν

Density ρ, (kg/m3)

Reinforced Concrete

2.549E+10

0.15

2500

20

Figure 3-3: Stress-Strain Characteristics of Reinforced Concrete

21

CHAPTER 4: FINITE ELEMENT MODEL 4.1 About ANSYS The finite element method is a numerical procedure that can be used to obtain solutions to a large class of engineering problems involving stress analysis, heat transfer, electromagnetism, and fluid flow. ANSYS software is the software of choice for structural dynamics, material modeling, fast fluid flow, impact and blast and shock response at many leading institutions worldwide. An integrated ANSYS software tightly integrates the preprocessing, post-processing and analysis modules for maximum productivity. ANSYS software is not an average explicit finite element or Computational Fluid Dynamics (CFD) program. From the very beginning, ANSYS developed this technology to handle, naturally and effectively, the non-linear behavior of fluids and structures in an integrated fashion. A key component is the seamless way that users can couple sophisticated material models with a fluid structure program. ANSYS software is different from other explicit programs in a number of ways: − Integrated and coupled response of fluids, structures and materials. − Multiple solvers including finite element, CFD and Smooth Particle Hydrodynamics (SPH) as well as the coupling between FE and

the

other solvers. − Use of materials with strength, such as metals, in all solvers, in addition to fluids and gasses. − Comprehensive remapping capabilities from FE to CFD and vice versa. − Interactive GUI with leading edge visualization. − Solvers seamlessly integrated pre- and post-processors.

22

4.2 Modelling Strategy A parametric study is performed to obtain lateral stiffness of infill frames with varying aspect ratios. The FE model is prepared for the purpose. The FE model is first calibrated using published results of experimental specimens available in the literature. This calibrated model is used in the parametric study to determine the lateral stiffness of infill frames. The width of equivalent diagonal strut for the infill frame using other established relations is compared to that estimated from the FE method. That is, equivalent width of diagonal strut is to be determined that will give correct approximation of lateral stiffness. In the parametric study, five parameters, i.e., aspect ratio, brick property, mortar property, thickness of infill and lateral load are varied considerably to get the sufficient data for Neural Network training. A single-bay single-story is considered for the study and their lateral stiffness is determined by non-linear analysis considering material non-linearity. The single-bay single-story infill frame considered is shown in figure bellow. Thus a total of 200 models have to be analysed in the parametric study. All the analyses are performed using the software ANSYS v10.0. 4.2.1 Calibration of the Model

Experimental results available in the published literatures are used to calibrate the FE model (Table 5-1). The influence of the following four factors namely, (a) modulus of elasticity of reinforced concrete, (c) modulus of elasticity of brick and (d) modulus of elasticity of mortar are considered in the analysis. Other data are taken as the provisions in the relevant codes. 4.2.2 Dimensions of the Model

− Frame section comprising of beam of size 300mm x 350mm and column section of size 300mm x 300mm. − Length of the panels varying from 3m to 5m, c/c of columns, at an interval of 0.5m. − Single storey single bay frame panel of height 3m. − Brick masonry infill of two different thicknesses of 110mm and 230mm. 23

− Mortar thickness of 12mm provided in between consecutive bricks.

4.3 Description of the Models The finite element model shown above is prepared using ANSYS. The material properties and the elements used for analytical study are described as under. 4.3.1 Element used in Modeling

Four different Ansys elements are used for preparation of Reinforced Concrete infill model in Ansys. Three different materials reinforced concrete, brick and mortar are considered. In which Ansys element Plane42 is used for both brick and mortar, and the element Beam3 is used for both beam and column. Link10 element is used for connection between line and plane element. Using these three elements 2D model is prepared in Ansys.

Plane42 element can be used either as a plane element (plane stress or plane strain) or

as an axi-symmetric element for 2D analysis of structure. According to name of the element Plane means aerial, 4 means four nodes i.e. quadrilateral and 2 means two degree of freedom (translations in the nodal x and y directions) at each nodes.

Figure 4-1: Plane stress element used for Modeling

Beam3 is a linear element. This element is used for modelling of the members which

has bending capabilities. The element has three degrees of freedom at each node, translations in the nodal x and y directions and rotation about the nodal z-axis.

24

Figure 4-2: Beam3 element used for Modeling Beam and Column

Link10 is a linear element. This element is used where only compressive or tension

property of the material has to be considered. When it is used as compressive only, at that time tension property of that material is taken to be zero. This element is used for modelling of cable, non-tension element etc.

Figure 4-3: Link10 element used for Modeling Frame-Infill Interface

4.3.2 Boundary Conditions Imposed

Two degrees of freedom are considered for all the nodes of infill. The displacements in X- and Y- directions in the plane of frame are considered at all nodes for the infill and for this Plane42 element is used. The element having translations in the nodal x and y directions and rotation about the nodal z-axis i.e. Beam3 element is used for modelling of Beam and Column. Link10 element is used for connection between Frame (i.e. line element) and infill (i.e. Plane42 element) by taking only compression feature of this element.

25

Figure 4-4: Sample model prepared for the analysis

4.3.3 Overview of the Materials Used

Three different materials reinforced concrete, brick and mortar are used for modeling to incorporate the complex heterogeneity involved in the infill as far as possible. The area for the link element is computed using average spacing of the link elements throughout the run of the infill and the thickness of the beam and column element. The material non-linearity is also considered. An overview of the material properties used for the analysis purpose is presented in the tabular form below. Table 4-1: Material properties used in analysis (Pradhan, P.L., 2009)

Material

Remarks

Reinforced Concrete Brick Mortar

MB LB 1:4 1:6

Modulus of Elasticity E (N/m2)

Poisson's Ratio ν

Density ρ, (kg/m3)

2.549E10

0.15

2500

0.09

1700

0.17

1780

3.022 E9 2.387 E9 3.651 E9 2.616 E9

26

4.3.4 Model Descriptions

The above mentioned materials and geometries were combined to generate the models which ensured the combination of materials in a systematic way and thus creating the desired variation in the analysis that was intended to be given to this research. The respective combination of geometries with their respective material properties are given in the table below. Table 4-2: Designation of Models used for analysis

Aspect Ratios

Brick

Machine Made Brick 1 Local Brick 0.86 0.75 0.67 0.60

Mortar

Wall Thickness (mm)

110 230 110 1:6 230 110 1:4 230 110 1:6 230 Same as in Aspect Ratio 1 Same as in Aspect Ratio 1 Same as in Aspect Ratio 1 Same as in Aspect Ratio 1 1:4

Model Designation 11-MB4 23-MB4 11-MB6 23-MB6 11-LB4 23-LB4 11-LB6 23-LB6

4.3.5 The Outputs

The model prepared was described above and the outputs taken were limited to the specific points as described below. All the points could not be considered for the output so the salient points which were considered to be of considerable interest were only considered. The reactions and moments were noted at both the supports along with the top roof displacement and then the stresses and strains were also noted down for the points as shown below in the figure.

27

σ RU,ε RU

σ LU,ε LU

σ C,ε C

σ LB,ε LB Hz

σ RB,ε RB Hz

ML

L

R

MR V

Figure 4-5: Salient nodal points considered for the output

Where, HzL

-

Horizontal reaction at Left Support.

HzR

-

Horizontal reaction at Right Support.

V

-

Vertical Reaction at each Support

ML

-

Moment at the Left Support.

MR

-

Moment at the Right Support.

σLB, εLB

-

Stress and Strain at the Bottom-Left corner.

σLU, εLU

-

Stress and Strain at the Upper-Left corner.

σC, εC

-

Stress and Strain at the Center of the Infill.

σRB, εRB

-

Stress and Strain at the Bottom-Right corner.

σRU, εRU

-

Stress and Strain at the Upper-Right corner.

4.4 Preparation of the Training sets Total of 200 sets of data were prepared and organized in a schematic manner in order to feed them in the neural network. The non-linear analysis results from 28

Ansys were taken as the reference for the preparation of the training sets. Another 16 data sets were also prepared using Ansys for validation purpose. The 200 data sets that were collected for the training purpose of the neural network comprised of variation of single height, five spans, two brick-types, two mortar-types, two thicknesses of infill and five loads thus making a total of 5 x 2 x 2 x 2 x 5 = 200 models to be analysed. The validating 16 data sets were taken in order to check the accuracy of the data predicted from the trained network.

29

CHAPTER 5: TRAINING THE DATA SETS USING ANN 5.1 Introduction to NeuNet Pro NeuNet Pro is a complete neural network development system. Neural networks can be used for pattern recognition, data mining, market forecasting, medical diagnosis, sports handicapping, and almost any activity where you need to make a prediction based on our data. The graphical user interface incorporated in the software makes it extremely easy to operate and handle while providing flexibility in operation and handling as well. The user is allowed to choose manually which rows as well as fields are to be trained and which rows’ values are to be predicted after the training is accomplished. However the field that can be predicted is limited to one for greater accuracy. The user is allowed to select from available classic Backprop algorithms. Records containing missing values are automatically detected and handled. Algorithms are fully compiled and optimized for extremely fast operation. Backprop algorithm allows one output value to be predicted using up to 255 input values. Backprop allows up to 128 neurons in the hidden layer. Users are allowed to browse through data table while comparing actual versus predicted.

One can

interactively experiment with field values while observing effect on the prediction. Data mine anomalies by performing a descending sort on difference between actual and prediction. Perform graphical data mining by clicking mouse on scatter graph and confusion matrix. While browsing data, rows may be interactively check marked for export.

5.2 Development of ANN Tool The data obtained from the linear analyses were trained using a sophisticated Artificial Neural Network. The network consisted of 5 inputs and a single output every-time the training was done, i.e. a single output field was predicted every-time the training was done, for greater accuracy. The network comprised of five nodes in a single hidden layer. The model of the network that was used for the training purpose is shown below (Figure 5-1). Taking Ansys results as the reference, the verification was done regarding the accuracy of the trained network. In total, 200 sets of data were used as training sets and 16 data sets were used for validating the results obtained from the neural network. 30

Figure 5-1: Back-propagation Neural Network used for Training

Figure 5-2: Error reduction graph during Back-propagation Neural Network Training

31

CHAPTER 6: RESULTS AND DISCUSSIONS 6.1 Parametric Studies In previous chapter, a finite element model developed for simulating the infilled frame which was of interest in this study. As stated in Section 4.2 and 4.3, the finite element model was developed in order to supplement the generally adopted construction practices. It was also pointed out that material characteristics were taken as per the availing practices in this part of the country. In this chapter, the finite element model that was developed will be used to investigate the influence of several parameters. The parameters investigated are those that relate to choices that ordinarily need to be made in the design process, such as geometric sizes, material properties and strength parameters. In Table 6.1 a list of parameters that may be of interest is shown. The geometric parameters investigated are: the overall dimensions of infilled frames, thus, aspect ratio; the wall thickness. Under material properties are considered the elasticity modulus of Brick and the Mortar Units. The influence of infill to the overall Frame-infill structure is considered under the strength criterion; however this study is limited to the plane of the infill. Table 6.1: Parameters of Interest

Geometric

Material Properties

Strength

Aspect Ratio

Modulus of Elasticity of Brick

In-plane Lateral

Thickness of wall

Modulus of Elasticity of Mortar

Stiffness

The variation is the parameters on the above mentioned interest are tabulated below making the sum total number of analysed models 200. Combination of five aspect ratios, two thicknesses of wall, two different bricks, and two different mortars are anylysed for five loading conditions. The schematic variation in the considered parameters is shown in the table below.

32

Table 6-2: Parametric characteristics of infilled frames analysed

Analyses

Aspect Ratios

Brick Machine Made Brick

1 – 40

1 Local Brick

41 - 80 81 – 120 121 – 160 161 – 200

0.85 0.75 0.67 0.60

Wall Mortar Thickness (mm) 110 1:4 230 110 1:6 230 110 1:4 230 110 1:6 230 Same as in 1 - 40 Same as in 1 - 40 Same as in 1 - 40 Same as in 1 - 40

Lateral load (KN) 100,200,300,400,500 100,200,300,400,500 100,200,300,400,500 100,200,300,400,500

6.2 Geometric Parameters In Table 6-2 a summary of the geometric characteristics of the two hundred types of infilled frames analysed is given. Three geometric parameters, namely, aspect ratio and thickness of wall in the infill are included in the study. The aspect ratio is defined as h/l where h is the height of the infilled frame and l is its length. Five aspect ratios, 0.6, 0.67, 0.75, 0.85 and 1.0 were used in the analyses. The corresponding infilled frames, shown in Figure 6.1, are 3.0 m high by 5.0 m wide, 3.0 m high by 4.5 m wide, 3.0 m high by 4.0 m wide and 3.0 m high by 3.5 m wide and 3.0 m high by 3.0 m wide respectively. The first geometric parameter is the aspect ratio. The variation is shown in the table above ranging from 0.6 to 1.0. The second geometric parameter studied is the thickness of the wall. The thickness is either 110 mm or 230 mm. First forty analyses were done as per stated in the table above and the subsequent analyses were carried out considering the same variation as in 1 – 40. In conformity with the materials used in the experiments and the validation of the ANSYS model, the properties of the materials used in the analyses are as shown in Table 4.1

33

(a) Aspect Ratio 1.0 (3m x 3m)

(b) Aspect Ratio 0.86 (3m x 3.5m)

(c) Aspect Ratio 0.75 (3m x 4m)

(d) Aspect Ratio 0.67 (3m x 4.5m)

(e) Aspect Ratio 0.6 (3m x 5m) Figure 6-1 : Infilled frames with different Aspect Ratios

6.2.1 Influence of wall thickness

The table shown below shows that the ratios of stiffness and stresses at main and the off-diagonal points of infilled frames with 230 mm thick infill walls to those of infilled frames with 110 mm thick infill walls. These results indicate that there is a 34

near linear relationship between the wall thickness and the infilled frame stiffness, as well as between the wall thickness. The Ratio of stiffness is increasing as the aspect ratio is decreasing, i.e., the ratio of stiffness is increasing with increase in the span. However, the trend for the ratio of stress and strain is opposite. The ratio of stresses and strains at the specified nodal points seems to be decreasing with the decrease in aspect ratio (i.e. increase in span). Table 6-3: Response variation due to wall thickness Aspect Ratios

1

0.85

0.75

0.67

0.6

Ratio of Stresses

Ratio of Stresses

Model Designation

Ratio of Stiffness

σLU

σC

σRU

εLU

εC

εRU

MB-4

1.060

0.565

0.508

0.509

0.566

0.508

0.511

MB-6

1.067

0.569

0.518

0.518

0.570

0.518

0.512

LB-4

1.063

0.569

0.513

0.513

0.569

0.513

0.513

LB-6

1.070

0.574

0.523

0.523

0.574

0.523

0.515

MB-4

1.076

0.511

0.508

0.507

0.512

0.508

0.507

MB-6

1.086

0.516

0.520

0.520

0.517

0.519

0.510

LB-4

1.080

0.508

0.512

0.512

0.509

0.512

0.507

LB-6

1.091

0.511

0.522

0.522

0.512

0.522

0.512

MB-4

1.091

0.527

0.509

0.510

0.524

0.509

0.508

MB-6

1.102

0.527

0.520

0.518

0.523

0.519

0.514

LB-4

1.104

0.579

0.513

0.513

0.576

0.513

0.528

LB-6

1.114

0.565

0.523

0.523

0.561

0.522

0.531

MB-4

1.101

0.524

0.508

0.508

0.527

0.509

0.506

MB-6

1.117

0.529

0.518

0.518

0.531

0.518

0.507

LB-4

1.107

0.571

0.518

0.519

0.571

0.514

0.512

LB-6

1.139

0.567

0.521

0.521

0.564

0.515

0.507

MB-4

1.114

0.531

0.506

0.506

0.532

0.505

0.523

MB-6

1.131

0.533

0.512

0.512

0.534

0.511

0.506

LB-4

1.137

0.588

0.511

0.512

0.592

0.511

0.528

LB-6

1.151

0.583

0.519

0.519

0.587

0.518

0.510

6.2.2 Influence of Aspect Ratio

The influence of aspect ratio can be clearly seen on the in-plane stiffness of the infill frame and bare frame. The stiffness decreases if the aspect ratio decreases in case of the bare frame. However, the stiffness was found to increase with the decrease in aspect ratio for the infilled frame. The normalised stresses exert almost linear relationship with the change in aspect ratio. In this study the size of aperture was kept constant for respective aspect ratio as stated in table 6-2.

35

1.085

1.079

1.078

1.071

1.105

1.102

1.101

1

1

1

1

1

1

1

1

11 MB 4

11 MB 6

11 LB 4

11 LB 6

23 MB 4

23 MB 6

23 LB 4

23 LB 6

1.098

0.85

1.171

1.177

1.180

1.185

1.094

1.131

1.097

1.146

0.75

1.258

1.227

1.232

1.230

1.112

1.161

1.119

1.182

0.67

Normalised Stiffness

1

Model Designation

Table 6-4: Response variation due to aspect ratio

1.245

1.255

1.261

1.269

1.103

1.170

1.114

1.196

0.6

1

1

1

1

1

1

1

1

1

0.909

0.876

0.913

0.873

1.050

0.991

1.023

0.990

0.85

1.241

1.251

1.244

1.254

1.029

1.341

0.981

1.338

0.75

0.961

0.946

0.945

0.924

0.780

0.990

0.745

0.973

0.67

Normalised stresses

0.982

0.978

0.973

0.972

0.747

1.013

0.717

0.985

0.6

1

1

1

1

1

1

1

1

1

0.913

0.878

0.920

0.877

1.055

0.992

1.030

0.993

0.85

1.253

1.259

1.257

1.263

1.043

1.370

0.992

1.365

0.75

0.954

0.981

0.981

0.975

0.799

1.025

0.762

1.009

0.67

Normalised strains

1.030

1.024

1.020

1.020

0.773

1.061

0.742

1.032

0.6

6.2.3 Influence of Bricks

The influence of aspect ratio can be clearly seen on the in-plane stiffness of the infill frame and bare frame. The stiffness decreases if the aspect ratio decreases in case of the bare frame. However, the stiffness was found to increase with the decrease in aspect ratio for the infilled frame. The normalised stresses exert almost linear relationship with the change in aspect ratio. In this study the size of aperture was kept constant for respective aspect ratio as stated in table below. The ratio of stiffness was found to increases with decrease in aspect ratio. The stresses and strains were found to be decrease with decrease in aspect ratio and also on increase in wall thickness. Table 6-5: Response variation due to Bricks Aspect Ratios

1

0.85

0.75

0.67

0.6

Model Designation

Ratio of Stiffness

Ratio of Stresses

σLU

σC

Ratio of Stresses

σRU

εLU

εC

εRU

11 1:4

1.015

1.071

1.095

1.094

0.845

0.865

0.779

11 1:6

1.015

1.063

1.080

1.079

0.840

0.853

0.781

23 1:4

1.008

1.063

1.073

1.074

0.838

0.848

0.778

23 1:6

1.008

1.054

1.060

1.059

0.832

0.838

0.777

11 1:4

1.021

1.068

1.077

1.077

0.845

0.853

0.764

11 1:6

1.022

1.060

1.065

1.064

0.839

0.843

0.786

23 1:4

1.011

1.057

1.053

1.052

0.837

0.834

0.759

23 1:6

1.012

1.054

1.044

1.044

0.834

0.827

0.779

11 1:4

1.024

1.071

1.050

1.050

0.845

0.829

0.900

11 1:6

1.024

1.032

1.033

1.033

0.813

0.814

0.903

23 1:4

1.014

1.072

1.029

1.034

0.846

0.812

0.888

23 1:6

1.015

1.055

1.013

1.013

0.833

0.799

0.897

11 1:4

1.030

1.060

1.051

1.051

0.838

0.830

0.813

11 1:6

1.029

1.042

1.033

1.034

0.823

0.815

0.806

23 1:4

1.015

1.049

1.030

1.031

0.832

0.816

0.811

23 1:6

1.001

1.048

1.029

1.029

0.830

0.813

0.813

11 1:4

1.034

1.058

1.092

1.092

0.837

0.863

0.727

11 1:6

1.031

1.031

1.072

1.073

0.814

0.847

0.697

23 1:4

1.018

1.054

1.079

1.080

0.833

0.854

0.750

23 1:6

1.019

1.037

1.057

1.058

0.820

0.836

0.723

6.2.4 Influence of Mortar

The ratio of responses with 1:4 mortar to 1:6 mortar are tabulated below. It can be clearly seen on the in-plane stiffness of the infill frame with 1:4 mortar are slightly above to those compared to those with 1:6 mortar. The ratio of stiffness was 37

found to increases with decrease in aspect ratio. The stresses and strains were found to be decrease with decrease in aspect ratio and also with the increase in wall thickness. Table 6-6: Response variation due to Mortar Aspect Ratios

1

0.85

0.75

0.67

0.6

Model Designation

Ratio of Stiffness

Ratio of Stresses

σLU

σC

Ratio of Stresses

σRU

εLU

εC

εRU

11 MB

1.016

1.019

0.951

0.950

1.021

0.951

1.052

11 LB

1.016

1.011

0.938

0.937

1.014

0.938

1.054

23 MB

1.013

1.011

0.941

0.943

1.013

0.941

1.049

23 LB

1.014

1.002

0.929

0.929

1.006

0.929

1.048

11 MB

1.017

0.953

0.968

0.967

0.952

0.964

0.976

11 LB

1.018

0.947

0.957

0.955

0.945

0.953

1.005

23 MB

1.014

0.959

0.960

0.959

0.958

0.957

0.976

23 LB

1.014

0.957

0.952

0.952

0.955

0.948

1.002

11 MB

1.025

1.080

1.008

1.008

1.081

1.011

0.889

11 LB

1.025

1.039

0.991

0.991

1.039

0.992

0.892

23 MB

1.014

0.981

1.001

1.002

0.980

1.003

0.855

23 LB

1.015

0.966

0.985

0.982

0.965

0.987

0.863

11 MB

1.030

1.061

1.005

1.003

1.065

1.004

1.005

11 LB

1.029

1.041

0.988

0.987

1.045

0.987

0.996

23 MB

1.025

0.973

0.985

0.984

0.983

0.995

0.993

23 LB

1.010

0.972

0.983

0.981

0.982

0.991

0.995

11 MB

1.036

1.094

0.951

0.950

1.099

0.948

1.010

11 LB

1.034

1.065

0.933

0.934

1.069

0.931

0.969

23 MB

1.016

0.988

0.940

0.940

0.988

0.938

0.999

23 LB

1.016

0.972

0.921

0.921

0.972

0.919

0.961

6.3 Variation of stiffness Stiffness is defined as the resistance to the deformation. This is one parameter which can be considered of considerable interest to structural engineers. In the study conducted now, the variation of stiffness with load and span is studied. The graphs showing the variation are shown below. The deflection goes on decreasing with increase in span, i.e., the tendency of the infill to resist the horizontal load seems to be increasing and thus causing a schematic increase in the stiffness with increase in span. The stiffness of the infilled frame goes on decreasing with the application of load, i.e. the decrease in stiffness is observed for different loading values. Also the stiffness for the infilled frame with 230 mm thickness is considerably greater than the stiffness of those with thickness 110 mm. the decrease in stiffness can be observed from the graphs below. 38

(a) MB4

(b) LB4

(a) MB6

(b) LB6

Figure 6-2: Variation of displacement with span

(a) 3m

(b) 3.5m

39

(c) 4m

(d) 4.5m

(e) 5m Figure 6-3: Variation of stiffness with load

6.4 Effective width of equivalent diagonal strut The results of the finite element analyses in this research support the observation that infill walls essentially provide diagonal bracing to bounding frames. As such, the wall can be replaced with an equivalent diagonal strut. In order to evaluate the effective widths of the equivalent diagonal strut for the walls in the infilled frames analysed, it is hereby assumed that the equivalent diagonal strut is pinned to the intersection of the beams and columns at the loaded corners; the modulus of elasticity and the thickness of the strut are the same as those of the wall; and the frame connections are rigid. As stated in chapter 2, several theoretical and empirical formulae for the effective width have been proposed by various researchers. In Table 6.7 effective widths derived from the finite element analyses of rigidly connected infilled frames with 110 mm thick walls are compared with effective widths calculated from some of these expressions.

40

Figure 6-4 : Equivalent Strut Model

The finite element (FE) effective widths have been determined by replacing the infill wall with a strut that results in the same infilled frame stiffness as from the corresponding finite element analysis. Calculations based on Mainstone (1971) method, and the FEMA 306 (1998) method are in reasonable agreement with each other while that obtained from the current FE analyses shows the results on a higher side for the estimates of the effective widths of the equivalent diagonal struts.

Table 6-7: Comparison of strut widths Aspect Ratio

1

0.86

0.75

MB4

FEM Wds (m) 0.364

FEMA Wds Factor (m) of FE 0.398 1.093

Mainstone Wds Factor (m) of FE 0.417 1.146

Angel Wds Factor (m) of FE 0.473 1.299

MB6

0.371

0.405

1.091

0.422

1.138

0.473

1.275

LB4

0.369

0.403

1.091

0.421

1.140

0.473

1.282

LB6

0.376

0.409

1.089

0.426

1.133

0.473

1.258

Model Designation

MB4

0.403

0.438

1.086

0.458

1.138

0.519

1.289

MB6

0.417

0.445

1.067

0.464

1.113

0.519

1.245

LB4

0.413

0.443

1.072

0.463

1.120

0.519

1.258

LB6

0.423

0.450

1.064

0.468

1.107

0.519

1.228

MB4

0.454

0.481

1.059

0.503

1.109

0.569

1.253

MB6

0.459

0.489

1.065

0.510

1.110

0.569

1.239

LB4

0.456

0.486

1.067

0.508

1.114

0.569

1.248

LB6

0.464

0.495

1.066

0.514

1.108

0.569

1.226

41

0.67

0.6

MB4

0.483

0.527

1.090

0.551

1.140

0.621

1.285

MB6

0.497

0.535

1.077

0.558

1.122

0.621

1.249

LB4

0.492

0.533

1.083

0.556

1.130

0.621

1.262

LB6

0.501

0.542

1.082

0.563

1.123

0.621

1.239

MB4

0.536

0.575

1.072

0.600

1.120

0.674

1.258

MB6

0.542

0.584

1.078

0.608

1.122

0.674

1.244

LB4

0.538

0.582

1.081

0.606

1.126

0.674

1.254

LB6

0.546

0.591

1.083

0.613

1.124

0.674

1.235

6.5 Validation of Neural Network After the training of the network was done, the predicted output was compared with the standard outputs obtained from the analysis done in Ansys. The corresponding maximum error was noted down. This process was repeated for all the 16 outputs and results were tabulated below. A sample error comparison chart for the displacement-output is shown as below. The dots show the predicted data and the diagonal line corresponds to the actual data.

Figure 6-5 : Comparison of actual versus predicted data

This was done for all the 16 outputs those were desired to be produced from the network. The validation of the predicted data sets was done in reference to those data sets from Ansys analysis. The predicted data and the desired data and their corresponding difference in percentage which indicates the accuracy of the predicted data are shown in the table below. 42

ANN

ANSYS

-99997

-150000

163970

74302

97579

12.911

2033

-4795728

-606176

-4817533

6144

3.870E-07

-9.583E-04

-1.900E-04

-1.418E-03

1.047E-06

Responses

Hz L (N)

Hz R (N)

V (N)

M L (N-m)

M R (N-m)

Disp (mm)

σLB (N/m2)

σLU (N/m2)

σC (N/m2)

σRB (N/m2)

σRU (N/m2)

εLB

εLU

εC

εRB

εRU

9.798E-07

-1.443E-03

-1.947E-04

-1.004E-03

3.928E-07

5980

-4989542

-611721

-4737439

1849

13.168

98226

75393

163451

-149503

-100329

250

Load

Model

6.381

1.768

2.496

4.808

1.487

2.661

3.570

0.915

1.215

9.022

1.988

0.663

1.468

0.317

0.331

0.332

% Error

8.407E-07

-1.003E-03

-1.347E-04

-7.266E-04

3.035E-07

4348

-3718866

-430130

-3475204

1118

16.589

132500

97796

231990

-213150

-136850

ANSYS

11-MB4

Table 7-1: Comparison of Results obtained from ANSYS and ANN

9.091E-07

-1.095E-03

-1.366E-04

-7.915E-04

3.382E-07

4268

-4037448

-434327

-3565439

1074

16.473

132989

97432

232805

-211241

-135908

ANN

450

8.128

9.162

1.444

8.933

11.428

1.853

8.567

0.976

2.597

3.879

0.701

0.369

0.373

0.351

0.896

0.689

% Error

2.883E-07

-4.427E-04

-5.894E-05

-3.319E-04

1.556E-07

2093

-1511038

-197155

-1653769

528

7.064

56706

41834

99461

-91505

-58495

ANSYS

2.672E-07

-4.558E-04

-5.702E-05

-3.175E-04

1.648E-07

1876

-1508890

-189955

-1858448

465

6.934

56212

41200

98058

-89219

-57538

ANN

150

7.299

2.959

3.261

4.335

5.901

10.370

0.142

3.652

12.377

11.894

1.842

0.871

1.516

1.411

2.498

1.635

% Error

2.181E-06

-2.276E-03

-3.942E-04

-1.985E-03

8.622E-07

10183

-6231407

-993716

-6301922

4778

24.421

179010

138530

293230

-267510

-182490

ANSYS

23-MB4

2.320E-06

-2.172E-03

-3.937E-04

-1.962E-03

8.048E-07

10634

-5653019

-1009572

-5778220

5438

24.434

179778

139091

292447

-268607

-182535

ANN

350

6.336

4.592

0.144

1.161

6.652

4.430

9.282

1.596

8.310

13.810

0.054

0.429

0.405

0.267

0.410

0.024

% Error

ANN

ANSYS

-100560

-149440

163550

75332

98313

13.163

2129

-4953283

-643746

-4967742

6881

3.856E-07

-9.901E-04

-2.026E-04

-1.467E-03

1.078E-06

Responses

Hz L (N)

Hz R (N)

V (N)

M L (N-m)

M R (N-m)

Disp (mm)

σLB (N/m2)

σLU (N/m2)

σC (N/m2)

σRB (N/m2)

σRU (N/m2)

εLB

εLU

εC

εRB

εRU

9.972E-07

-1.476E-03

-1.939E-04

-1.061E-03

3.405E-07

6180

-5091107

-630214

-4798553

1896

13.337

98861

75896

163207

-149582

-100822

250

Load

Model

7.466

0.602

4.295

7.187

11.689

10.189

2.483

2.102

3.124

10.956

1.322

0.557

0.749

0.209

0.095

0.261

% Error

2.146E-06

-2.120E-03

-3.675E-04

-1.535E-03

3.745E-07

12541

-6165900

-1165171

-6470576

5772

24.498

179240

138180

293250

-267490

-182510

ANSYS

11-MB6

1.866E-06

-2.075E-03

-3.544E-04

-1.655E-03

3.337E-07

10981

-5832554

-1119811

-5717876

5819

24.706

180898

139530

292111

-268872

-181804

ANN

450

44

13.062

2.122

3.568

7.831

10.919

12.443

5.406

3.893

11.633

0.815

0.850

0.925

0.977

0.388

0.517

0.387

% Error

2.883E-07

-4.427E-04

-5.894E-05

-3.319E-04

1.556E-07

2093

-1511038

-197155

-1653769

528

7.064

56706

41834

99461

-91505

-58495

ANSYS

2.672E-07

-4.558E-04

-5.702E-05

-3.175E-04

1.648E-07

1876

-1508890

-189955

-1858448

465

6.934

56212

41200

98058

-89219

-57538

ANN

150

7.299

2.959

3.261

4.335

5.901

10.370

0.142

3.652

12.377

11.894

1.842

0.871

1.516

1.411

2.498

1.635

% Error

8.339E-07

-1.061E-03

-1.438E-04

-7.226E-04

3.230E-07

4873

-3890035

-457402

-3603996

1179

16.879

133400

99041

231490

-212210

-137790

ANSYS

23-MB6

9.100E-07

-1.123E-03

-1.374E-04

-7.968E-04

3.444E-07

4457

-4183064

-451793

-3646379

1089

16.809

133916

98977

233048

-212342

-135330

ANN

350

9.125

5.911

4.451

10.274

6.619

8.539

7.533

1.226

1.176

7.575

0.414

0.387

0.064

0.673

0.062

1.785

% Error

ANN

ANSYS

-100640

-149360

163420

75703

98491

13.249

1938

-4435134

-562581

-4489361

5461

4.740E-07

-1.218E-03

-2.225E-04

-1.671E-03

1.270E-06

Responses

Hz L (N)

Hz R (N)

V (N)

M L (N-m)

M R (N-m)

Disp (mm)

σLB (N/m2)

σLU (N/m2)

σC (N/m2)

σRB (N/m2)

σRU (N/m2)

εLB

εLU

εC

εRB

εRU

1.428E-06

-1.708E-03

-2.298E-04

-1.258E-03

4.279E-07

5980

-4800765

-578272

-4587174

1757

13.459

99194

76678

162810

-149124

-100821

250

Load

Model

12.464

2.187

3.298

3.310

9.735

9.501

6.936

2.789

3.428

9.321

1.586

0.714

1.288

0.373

0.158

0.180

% Error

2.181E-06

-2.276E-03

-3.942E-04

-1.985E-03

8.622E-07

10183

-6231407

-993716

-6301922

4778

24.421

179010

138530

293230

-267510

-182490

ANSYS

11-MB4

2.320E-06

-2.172E-03

-3.937E-04

-1.962E-03

8.048E-07

10634

-5653019

-1009572

-5778220

5438

24.434

179778

139091

292447

-268607

-182535

ANN

450

45

6.336

4.592

0.144

1.161

6.652

4.430

9.282

1.596

8.310

13.810

0.054

0.429

0.405

0.267

0.410

0.024

% Error

3.589E-07

-4.778E-04

-7.053E-05

-3.663E-04

1.756E-07

1676

-1371119

-173548

-1490799

487

7.124

56862

42077

99367

-91406

-58594

ANSYS

3.662E-07

-4.338E-04

-7.342E-05

-3.683E-04

1.954E-07

1801

-1329601

-175490

-1690440

446

6.913

56070

41032

98049

-89400

-57519

ANN

150

2.025

9.191

4.100

0.541

11.268

7.477

3.028

1.119

13.392

8.546

2.952

1.393

2.483

1.326

2.194

1.835

% Error

8.354E-07

-1.210E-03

-1.592E-04

-8.288E-04

3.664E-07

3901

-4157936

-402957

-3275523

1166

16.832

133160

98821

231590

-212670

-137330

ANSYS

23-MB4

8.799E-07

-1.316E-03

-1.678E-04

-9.125E-04

4.162E-07

4268

-3812790

-414469

-3411099

1029

16.632

133232

98036

231613

-210674

-136552

ANN

350

5.335

8.815

5.407

10.101

13.585

9.406

8.301

2.857

4.139

11.726

1.187

0.054

0.795

0.010

0.939

0.566

% Error

ANN

ANSYS

-101230

-148770

162970

76832

99283

13.524

1886

-4587630

-602243

-4663352

6338

4.003E-07

-1.158E-03

-2.395E-04

-1.741E-03

1.365E-06

Responses

Hz L (N)

Hz R (N)

V (N)

M L (N-m)

M R (N-m)

Disp (mm)

σLB (N/m2)

σLU (N/m2)

σC (N/m2)

σRB (N/m2)

σRU (N/m2)

εLB

εLU

εC

εRB

εRU

1.448E-06

-1.734E-03

-2.342E-04

-1.254E-03

3.638E-07

6180

-4926436

-600434

-4657419

1803

13.637

99877

77282

162562

-148815

-101758

250

Load

Model

6.097

0.385

2.222

8.329

9.117

2.492

5.642

0.300

1.521

4.432

0.832

0.598

0.585

0.250

0.030

0.521

% Error

2.556E-06

-2.367E-03

-4.249E-04

-1.957E-03

9.378E-07

11861

-6328377

-1065036

-5828512

4986

25.135

181010

141160

292140

-266310

-183690

ANSYS

11-MB4

2.327E-06

-2.180E-03

-3.983E-04

-1.890E-03

8.283E-07

10981

-5708711

-1048822

-5683134

5622

25.550

182771

143211

291252

-267203

-183992

ANN

450

46

8.961

7.908

6.253

3.422

11.679

7.425

9.792

1.522

2.494

12.753

1.652

0.973

1.453

0.304

0.335

0.165

% Error

3.892E-07

-5.372E-04

-7.377E-05

-3.958E-04

1.816E-07

1947

-1459303

-185955

-1561059

492

7.179

57013

42311

99277

-91285

-58715

ANSYS

3.584E-07

-4.830E-04

-7.096E-05

-3.835E-04

2.011E-07

1876

-1449315

-183159

-1751616

451

7.063

56395

41680

97952

-88847

-57684

ANN

150

7.930

10.096

3.807

3.101

10.738

3.622

0.684

1.504

12.207

8.306

1.610

1.084

1.492

1.335

2.671

1.756

% Error

9.738E-07

-1.278E-03

-1.710E-04

-8.593E-04

3.768E-07

4522

-3821021

-430671

-3392969

1130

17.094

133730

99861

230400

-211110

-137890

ANSYS

23-MB4

8.800E-07

-1.339E-03

-1.682E-04

-8.957E-04

4.227E-07

4457

-3980147

-432644

-3492311

1043

16.980

134214

99622

231858

-210329

-136786

ANN

350

9.625

4.795

1.651

4.242

12.185

1.443

4.164

0.458

2.928

7.684

0.665

0.362

0.239

0.633

0.370

0.800

% Error

From the above tables it can be noted that the percentage of error in prediction of data from the ANN tool so developed is varying from maximum of 13.81% to minimum of 0.01%. Hence ANN can be taken as a powerful tool for the prediction of initial design parameters related to any field especially if the mass data regarding that field is available. For the data sets given above it can be noticed that error percentage is relatively high in stress and strain fields whereas the error percentage is almost negligible in reaction fields (displacements, shear and vertical reaction). This is a good sign that the parameters of interest was predicted more accurately by the tool so developed and the variation in data predicted for stress and strain fields can be attributed to the reason that the data taken was not uniform enough as the recognisation of nodes at the exact place was almost impossible for all the models prepared thus creating a more varying data for the training sets itself and hence the prediction showing the results afterwards.

47

CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS 7.1 General Infilled frame has been studied by various researchers; this research represents the yet another effort to investigate the behaviour of infill walls using various materials. The peculiarities of brick and mortar combinations along with varying thickness being practiced traditionally are still unknown. It was therefore considered necessary to carry out an experimental and numerical investigation in order to describe the structural behaviour of such infilled frames. The influence of several geometrical, material and interface parameters on this behaviour has been investigated. In this research the behaviour of reinforced concrete frame infilled with brick masonry units subjected to in-plane lateral loads has been described. Simplified expressions for prediction of the stiffness and other macro responses of these types of infilled frames have been proposed. Infill walls are already commonly used as partitions and claddings on building structures. Accounting for their contribution in resisting loads leads to more efficient use of materials. Evaluating the stiffness and strength of the infills also leads to reduced risks of damage to the infills, bounding frames and the finishes. This in turn can lead to significant reductions in maintenance and rehabilitation costs of buildings. The literature review includes modelling of infilled frames by replacing the infill wall by strut models with best possible result outcomes. Work on infilled frames was initiated in 1940s. Modelling of infilled frames and further development in this area happened by late 1960s. Studies on monotonic behaviour of infilled frames under lateral load were carried out in the 1970s. Similarly, cyclic tests, full scaled tests and nonstructural infill frame tests were carried out during the 1980s and 90s. Studies were concentrated primarily in two distinct areas, namely on materials and on modelling of infilled frames. Basic properties were studied of bricks, mortar and masonry wallets. Infill frame models were developed that describe the different failure modes. These models include strut models, effective column width model and micro-models. Over the years, several different analytical approaches were proposed. But, the equivalent -strut method gained the most popularity among practitioners.

48

Several modifications were proposed in the equivalent strut models. The outcomes of this research are in reasonable agreement with the one proposed by FEMA356. A series of two hundred full scale analyses was conducted using finite element model to simulate each model. The finite element model was used to carry out parametric studies. The model utilises 4-noded plane stress elements for masonry units, 2-noded link elements for frame-to-wall contact and again 2-noded beam element for the modelling of beam and column. A simplified approach to formulate an equivalent strut width for the infills has been proposed in this research. With the aid of software, reactions, deflections and other responses at several nodes on each specimen were recorded. Load deflection responses showed that infills increased the stiffness of frames by 2.5 times. Non-linear elastic behaviour was prescribed for frame-to-wall contact and thin-layer joints. Linear elastic behaviour was assumed for steel. Material properties used in this model were obtained from estimations based on the available literature. The finite element model has been used to study the influence of several geometric, material and interface parameters. These parameters included the aspect ratio of the infilled frame, the thickness of the infill wall, the elasticity modulus of the bricks and the mortars. It has been concluded that composite infilled frame action is optimum in infilled frames with aspect ratios less than or nearly equal to one. In relatively squat infilled frames, the wall dominates the behaviour while the frame’s contribution diminishes. On the other hand, for relatively slender infilled frames, bending deflections increasingly overshadow composite action of the bounding frame and infill walls. In general, most geometrical parameters have the highest relative influence on the stiffness of square infilled frames. A comparison of effective widths of equivalent diagonal struts derived from finite element analyses in this study with those derived from other methods from literature showed that a width of the diagonal proposed by FEMA length is a good, though a bit underestimated, approximation. The data thus obtained from the structural analyses were then fed into the neural network and the network was trained for as many cycles as possible to reduce the mean RMS error. The neural network was trained to predict one output at a time for the prediction of a particular response. The results predicted from the trained network and those from the ANSYS were compared and found to be in reasonable 49

accuracy. Thus based on this study, ANN model was found to be reasonably accurate for the structure like infilled frame where the degree of non-linearity is very high. And hence the ANNs are expected to be applicable to other civil engineering problems, and may have wider applications in other engineering problems.

7.2 Conclusions The following conclusions are drawn from this study: − Three strut models considered, two performed okay but the one fitting best with the current FE analyses is the one proposed by FEMA; the locations for the strut and the formula for the calculation of their strut width best represent the scenario of an infill bounded by reinforced concrete frame. − The combination of material constituting masonry units have a wider influence on the stiffness and stress- strain responses developed in the infill and each case has to be investigated peculiarly to know the exact response rather than treating complete masonry infill as a single unit. − The responses from the non-linear analysis of the infill model prepared in ANSYS were used as training data sets. Standard Neural Network software was used to train the network and later some data sets were used for validation of the results predicted. The results were found to be satisfactory with error ranging from 0.01% minimum to 13.81% maximum. − For the quick prediction of the design parameters, neural network can be extremely useful. The network needs to be trained with data sets of similar types though. A typical neural network was fed into 200 data sets as training data sets for the training purpose and the network with just one hidden layer containing 5 nodes produced accuracy as high as 99.99%. However the accuracy on the predicted data heavily depends upon the anomalies present in the data that is being used to train the network. The research conducted above makes it clear that infill materials present a very complex scenario for structural engineers when it comes to the simulation of the real structures in computers. The material heterogeneity and complex interaction among several infill-masonry components make it extremely difficult to idealise the 50

structure and thus the computer simulation to represent the characteristics of the infill becomes extremely tedious and monotonic. Thus the prediction of correct initial design parameters, if possible, can be a boon to structural engineers. These days computers come with extra-ordinary computing capabilities and hence computing powers of modern day computers can be used to an optimum extent to predict the responses of the infill due to in-plane lateral load analysis. This is where the Artificial Neural Networks can be extremely useful.

7.3 Recommendations for the future works Keeping the time frame in mind, all the possible combination of parameters are taken into account in this research. However the scope for the development never perishes. Recommendations are hereby made from the point of view of the future continuation of this research. The above issues can be experimentally investigated without any major changes to the existing setup used in this work. The limitations being the high costs and practical difficulties involved in conducting large-scale tests, it is essential that experimental tests should be carried out hand-in-hand with numerical analyses. As encountered in this investigation, although modelling nonlinear behaviour of brick masonry walls and frame-to-wall interfaces is by no means easy, numerical modelling can be powerful contributor in understanding and interpreting the experimental behaviour. It is recommended that the numerical analyses conducted in this investigation should be extended into the cracking and post cracking range. This would facilitate an assessment of the ultimate load and give a more realistic assessment of the margin between the cracking (service) loads and the ultimate load. This in turn would assist in determining the appropriate safety factors in the design guidelines. It is hereby recommended that this research should be continued, generally, in the following order:

− Experimental investigation of infilled frames The infilled frames analysed in this study should be studied experimentally as for the correct prediction of their responses and verification of the responses derived analytically here in this study. 51

− Variation in masonry properties Although some variation in the properties of masonry units are considered in the current study, a broad investigation on the influence of masonry properties on response parameters is felt necessary as strength of a masonry wall depends on the individual properties of brick units and mortar mix. − Reversal cyclic loading All the analyses carried in the current research are under monotonic loading of the infilled frame. However it can be interesting to study the responses of the infill under the reverse cyclic loading for any structural engineer. − Generation of more data sets for the training purpose Due to the time limitations, only two hundred sets of data were prepared and fed into the neural network for its training purpose. It has to be noticed the error in the double digits is an outcome of limitation on the data sets being used for the training purpose. To get even better accuracy at least 500 data sets has to be used for the training purpose, thus making the prediction of responses more accurate.

52

APPENDIX A. ANSYS Contour Result Plot

Figure A-1 : Displacement contour plot

Figure A-2 : Stress Intensity contour plot

53

Figure A-3 : Shear Stress contour plot

Figure A-4 : X-axis Stress contour plot

54

B. Output Result from ANSYS Table A-1: ANSYS Results for Span 3m Input

Reactions Brick

Load (KN)

HzL (N)

ML (N-m)

MR (N-m)

1:4

MB

100

-42976

1:4

MB

200

-85901

-57024

93155

31126

36911

5.88350

-114100

185750

63191

74552

12.04600

0.11

1:4

MB

300

-128270

-171730

278220

95425

112400

18.28000

0.11

1:4

MB

400

0.11

1:4

MB

500

-170410

-229590

370720

127600

150230

24.51000

-212200

-287800

463090

159980

188260

30.82300

0.11

1:4

LB

100

-43132

-56868

92979

31447

37115

5.96880

0.11

1:4

LB

200

-86227

-113770

185420

63803

74935

12.20900

0.11 0.11

1:4

LB

300

-128860

-171140

277730

96344

112960

18.52100

1:4

LB

400

-171230

-228770

369960

129010

151110

24.88200

0.11

1:4

LB

500

-213330

-286670

462030

161930

189480

31.33900

0.11

1:6

MB

100

-43069

-56931

92936

31509

37183

5.99620

0.11

1:6

MB

200

-85691

-114310

185380

63819

75049

12.24000

0.11

1:6

MB

300

-127850

-172150

277750

96210

113030

18.53400

0.11

1:6

MB

400

-169660

-230340

370060

128700

151130

24.87400

0.11

1:6

MB

500

-211450

-288550

462320

161250

189280

31.24100

0.11

1:6

LB

100

-43221

-56779

92756

31838

37393

6.08470

0.11

1:6

LB

200

-86058

-113940

185040

64438

75429

12.40300

0.11

1:6

LB

300

-128420

-171580

277210

97216

113660

18.80100

0.11

1:6

LB

400

-170530

-229470

369260

130170

152050

25.26600

0.11

1:6

LB

500

-212670

-287330

461220

163290

190550

31.77800

0.23

1:4

MB

100

-42568

-57432

93712

30112

36251

5.60320

0.23

1:4

MB

200

-85231

-114770

187330

60393

72610

11.26100

0.23

1:4

MB

300

-127870

-172130

280400

91606

109690

17.18300

0.23

1:4

MB

400

-170160

-229840

373410

122880

146880

23.13700

0.23

1:4

MB

500

-212200

-287800

466360

154250

184170

29.13600

0.23

1:4

LB

100

-42655

-57345

93614

30292

36365

5.65120

0.23

1:4

LB

200

-85383

-114620

187150

60719

72818

11.34600

0.23

1:4

LB

300

-128120

-171880

280120

92113

110020

17.31900

0.23

1:4

LB

400

-170510

-229490

373040

123570

147310

23.32200

0.23

1:4

LB

500

-212700

-287300

465910

155080

184680

29.35300

0.23

1:6

MB

100

-42583

-57417

93664

30198

36310

5.62830

0.23

1:6

MB

200

-85304

-114700

186900

61140

73166

11.47500

0.23

1:6

MB

300

-127630

-172370

279870

92495

110400

17.45200

0.23

1:6

MB

400

-169620

-230380

372790

123910

147730

23.46600

0.23

1:6

MB

500

-211180

-288820

465670

155360

185130

29.51000

0.23

1:6

LB

100

-42669

-57331

93560

30388

36432

5.67940

0.23

1:6

LB

200

-85469

-114530

186700

61496

73392

11.57100

0.23

1:6

LB

300

-127890

-172110

279580

93020

110730

17.59300

0.23

1:6

LB

400

-169990

-230010

372410

124600

148160

23.64900

0.23

1:6

LB

500

-211750

-288250

465210

156220

185650

29.73500

Mortar

0.11 0.11

HzR (N)

Displacement

V (N)

Thickness (m)

55

(mm)

Stress (N/m2)

Input Thickness (m) 0.11

σLB

σLU

σC

σRB

σRU

MB

Load (KN) 100

1.846E+03

-1.627E+06

-2.237E+05

-1.453E+06

2.259E+03

1:4

MB

200

3.581E+03

-2.730E+06

-4.416E+05

-2.580E+06

4.450E+03

Mortar

Brick

1:4

0.11 0.11

1:4

MB

300

5.371E+03

-3.791E+06

-6.595E+05

-3.648E+06

6.671E+03

0.11

1:4

MB

400

7.194E+03

-4.904E+06

-8.800E+05

-4.694E+06

8.881E+03

0.11

1:4

MB

500

9.044E+03

-5.945E+06

-1.101E+06

-5.605E+06

1.108E+04

0.11

1:4

LB

100

1.881E+03

-1.513E+06

-2.068E+05

-1.313E+06

2.089E+03

0.11

1:4

LB

200

3.654E+03

-2.551E+06

-4.087E+05

-2.352E+06

4.128E+03

0.11

1:4

LB

300

5.472E+03

-3.555E+06

-6.101E+05

-3.306E+06

6.166E+03

0.11

1:4

LB

400

7.378E+03

-4.567E+06

-7.933E+05

-4.227E+06

8.009E+03

0.11

1:4

LB

500

9.357E+03

-5.561E+06

-9.795E+05

-5.055E+06

9.901E+03

0.11

1:6

MB

100

1.688E+03

-1.524E+06

-2.354E+05

-1.502E+06

2.376E+03

0.11

1:6

MB

200

3.339E+03

-2.673E+06

-4.643E+05

-2.663E+06

4.693E+03

0.11

1:6

MB

300

5.051E+03

-3.781E+06

-6.947E+05

-3.755E+06

7.016E+03

0.11

1:6

MB

400

6.808E+03

-4.865E+06

-9.249E+05

-4.689E+06

9.346E+03

0.11

1:6

MB

500

8.594E+03

-5.978E+06

-1.155E+06

-5.600E+06

1.167E+04

0.11

1:6

LB

100

1.728E+03

-1.429E+06

-2.200E+05

-1.380E+06

2.223E+03

0.11

1:6

LB

200

3.418E+03

-2.532E+06

-4.353E+05

-2.452E+06

4.397E+03

0.11

1:6

LB

300

5.156E+03

-3.545E+06

-6.509E+05

-3.418E+06

6.570E+03

0.11

1:6

LB

400

6.982E+03

-4.571E+06

-8.470E+05

-4.280E+06

8.569E+03

0.11

1:6

LB

500

8.869E+03

-5.623E+06

-1.046E+06

-5.106E+06

1.059E+04

0.23

1:4

MB

100

9.394E+02

-8.260E+05

-1.121E+05

-7.363E+05

1.133E+03

0.23

1:4

MB

200

1.858E+03

-1.654E+06

-2.265E+05

-1.486E+06

2.288E+03

0.23

1:4

MB

300

2.729E+03

-2.228E+06

-3.369E+05

-2.022E+06

3.404E+03

0.23

1:4

MB

400

3.614E+03

-2.788E+06

-4.470E+05

-2.570E+06

4.520E+03

0.23

1:4

MB

500

4.511E+03

-3.292E+06

-5.569E+05

-3.125E+06

5.633E+03

0.23

1:4

LB

100

9.662E+02

-7.689E+05

-1.030E+05

-6.678E+05

1.039E+03

0.23

1:4

LB

200

1.916E+03

-1.565E+06

-2.116E+05

-1.354E+06

2.138E+03

0.23

1:4

LB

300

2.813E+03

-2.099E+06

-3.147E+05

-1.864E+06

3.180E+03

0.23

1:4

LB

400

3.724E+03

-2.624E+06

-4.179E+05

-2.352E+06

4.218E+03

0.23

1:4

LB

500

4.648E+03

-3.105E+06

-5.216E+05

-2.847E+06

5.271E+03

0.23

1:6

MB

100

8.812E+02

-8.857E+05

-1.219E+05

-8.163E+05

1.228E+03

0.23

1:6

MB

200

1.706E+03

-1.574E+06

-2.393E+05

-1.492E+06

2.414E+03

0.23

1:6

MB

300

2.532E+03

-2.159E+06

-3.563E+05

-2.078E+06

3.594E+03

0.23

1:6

MB

400

3.380E+03

-2.711E+06

-4.722E+05

-2.694E+06

4.766E+03

0.23

1:6

MB

500

4.247E+03

-3.265E+06

-5.891E+05

-3.252E+06

5.948E+03

0.23

1:6

LB

100

9.096E+02

-8.317E+05

-1.135E+05

-7.480E+05

1.146E+03

0.23

1:6

LB

200

1.766E+03

-1.493E+06

-2.261E+05

-1.386E+06

2.284E+03

0.23

1:6

LB

300

2.622E+03

-2.055E+06

-3.368E+05

-1.940E+06

3.402E+03

0.23

1:6

LB

400

3.499E+03

-2.582E+06

-4.474E+05

-2.495E+06

4.515E+03

0.23

1:6

LB

500

4.390E+03

-3.108E+06

-5.591E+05

-3.007E+06

5.650E+03

56

Input Thickness (m) 0.11

Strain

Mortar

Brick

1:4

MB

Load (KN) 100

0.11

1:4

MB

200

1.115E-06

-8.231E-04

-1.330E-04

-7.871E-04

2.050E-06

0.11

εLB

εLU

εC

εRB

εRU

5.745E-07

-4.934E-04

-6.736E-05

-4.463E-04

1.034E-06

1:4

MB

300

1.672E-06

-1.142E-03

-1.986E-04

-1.108E-03

3.055E-06

0.11

1:4

MB

400

2.240E-06

-1.477E-03

-2.650E-04

-1.423E-03

4.068E-06

0.11

1:4

MB

500

2.816E-06

-1.791E-03

-3.315E-04

-1.695E-03

5.076E-06

0.11

1:4

LB

100

7.377E-07

-5.821E-04

-7.883E-05

-5.115E-04

1.315E-06

0.11

1:4

LB

200

1.433E-06

-9.751E-04

-1.558E-04

-9.100E-04

2.610E-06

0.11

1:4

LB

300

2.146E-06

-1.358E-03

-2.326E-04

-1.274E-03

3.898E-06

0.11

1:4

LB

400

2.894E-06

-1.744E-03

-3.025E-04

-1.624E-03

5.247E-06

0.11

1:4

LB

500

3.671E-06

-2.123E-03

-3.735E-04

-1.937E-03

6.640E-06

0.11

1:6

MB

100

5.291E-07

-4.594E-04

-7.091E-05

-4.592E-04

9.844E-07

0.11

1:6

MB

200

1.047E-06

-8.050E-04

-1.399E-04

-8.086E-04

1.942E-06

0.11

1:6

MB

300

1.584E-06

-1.139E-03

-2.093E-04

-1.136E-03

2.902E-06

0.11

1:6

MB

400

2.134E-06

-1.465E-03

-2.786E-04

-1.416E-03

3.866E-06

0.11

1:6

MB

500

2.694E-06

-1.801E-03

-3.478E-04

-1.688E-03

4.844E-06

0.11

1:6

LB

100

6.824E-07

-5.462E-04

-8.388E-05

-5.347E-04

1.251E-06

0.11

1:6

LB

200

1.350E-06

-9.658E-04

-1.659E-04

-9.436E-04

2.474E-06

0.11

1:6

LB

300

2.036E-06

-1.352E-03

-2.481E-04

-1.310E-03

3.697E-06

0.11

1:6

LB

400

2.757E-06

-1.743E-03

-3.229E-04

-1.636E-03

4.973E-06

0.11

1:6

LB

500

3.503E-06

-2.144E-03

-3.988E-04

-1.949E-03

6.298E-06

0.23

1:4

MB

100

2.924E-07

-2.505E-04

-3.377E-05

-2.263E-04

5.251E-07

0.23

1:4

MB

200

5.785E-07

-5.017E-04

-6.822E-05

-4.567E-04

1.051E-06

0.23

1:4

MB

300

8.497E-07

-6.727E-04

-1.015E-04

-6.188E-04

1.568E-06

0.23

1:4

MB

400

1.125E-06

-8.406E-04

-1.346E-04

-7.841E-04

2.079E-06

0.23

1:4

MB

500

1.404E-06

-9.922E-04

-1.677E-04

-9.521E-04

2.589E-06

0.23

1:4

LB

100

3.789E-07

-2.958E-04

-3.927E-05

-2.603E-04

6.746E-07

0.23

1:4

LB

200

7.517E-07

-6.027E-04

-8.069E-05

-5.278E-04

1.350E-06

0.23

1:4

LB

300

1.103E-06

-8.035E-04

-1.200E-04

-7.237E-04

2.015E-06

0.23

1:4

LB

400

1.461E-06

-1.003E-03

-1.593E-04

-9.101E-04

2.674E-06

0.23

1:4

LB

500

1.823E-06

-1.186E-03

-1.989E-04

-1.100E-03

3.333E-06

0.23

1:6

MB

100

2.762E-07

-2.678E-04

-3.674E-05

-2.503E-04

5.031E-07

0.23

1:6

MB

200

5.347E-07

-4.744E-04

-7.208E-05

-4.558E-04

1.003E-06

0.23

1:6

MB

300

7.938E-07

-6.502E-04

-1.073E-04

-6.325E-04

1.492E-06

0.23

1:6

MB

400

1.060E-06

-8.165E-04

-1.422E-04

-8.183E-04

1.979E-06

0.23

1:6

MB

500

1.332E-06

-9.833E-04

-1.774E-04

-9.855E-04

2.467E-06

0.23

1:6

LB

100

3.591E-07

-3.189E-04

-4.325E-05

-2.907E-04

6.464E-07

0.23

1:6

LB

200

6.972E-07

-5.703E-04

-8.619E-05

-5.367E-04

1.289E-06

0.23

1:6

LB

300

1.035E-06

-7.838E-04

-1.284E-04

-7.482E-04

1.918E-06

0.23

1:6

LB

400

1.382E-06

-9.846E-04

-1.706E-04

-9.599E-04

2.548E-06

0.23

1:6

LB

500

1.734E-06

-1.185E-03

-2.131E-04

-1.154E-03

3.178E-06

57

Table A-1: ANSYS Results for Span 3.5m Input

Reactions

Displacement (mm)

Thickness (m)

Mortar

Brick

Load (KN)

HzL (N)

HzR (N)

V (N)

ML (N-m)

MR (N-m)

0.11

1:4

MB

100

-41315

-58685

79952

30142

37526

5.425

0.11

1:4

MB

200

-83003

-117000

159550

60994

75564

11.055

0.11

1:4

MB

300

-124450

-175550

238960

92222

113930

16.785

-234500

318280

123580

152440

22.571

-293630

397540

155060

191050

28.404

0.11

1:4

MB

400

-165500

0.11

1:4

MB

500

-206370

0.11

1:4

LB

100

-41508

-58492

79753

30565

37801

5.534

-116620

159170

61813

76091

11.267

0.11

1:4

LB

200

-83383

0.11

1:4

LB

300

-125090

-174910

238350

93513

114760

17.118

0.11

1:4

LB

400

-166590

-233410

317380

125490

153670

23.061

0.11

1:4

LB

500

-207910

-292090

396290

157720

192760

29.083

-58537

79812

30438

37721

5.507

61750

76121

11.257

0.11

1:6

MB

100

-41463

0.11

1:6

MB

200

-83077

-116920

159180

0.11

1:6

MB

300

-124280

-175720

238450

93233

114690

17.072

-234920

317620

124900

153440

22.960

-293880

396590

156960

192480

28.948

0.11

1:6

MB

400

-165080

0.11

1:6

MB

500

-206120

0.11

1:6

LB

100

-41657

-58343

79606

30875

38004

5.620

-116500

158780

62613

76673

11.478

0.11

1:6

LB

200

-83495

0.11

1:6

LB

300

-124990

-175010

237800

94610

115580

17.425

0.11

1:6

LB

400

-166270

-233730

316670

126930

154740

23.476

-292370

395270

159790

194270

29.664

36733

5.110

0.11

1:6

LB

500

-207630

0.23

1:4

MB

100

-40721

-59279

80528

28917

0.23

1:4

MB

200

-81494

-118510

161040

57869

73491

10.230

-177390

241300

87342

110600

15.518

0.23

1:4

MB

300

-122610

0.23

1:4

MB

400

-163830

-236170

321250

117410

148200

20.935

0.23

1:4

MB

500

-204740

-295260

401200

147480

185820

26.365

0.23

1:4

LB

100

-40824

-59176

80421

29146

36881

5.169

-118300

160830

58322

73785

10.347

0.23

1:4

LB

200

-81704

0.23

1:4

LB

300

-122910

-177090

240980

88014

111040

15.691

0.23

1:4

LB

400

-164230

-235770

320830

118310

148780

21.168

-294710

400670

148610

186550

26.656

36799

5.135

0.23

1:4

LB

500

-205290

0.23

1:6

MB

100

-40774

-59226

80481

29019

0.23

1:6

MB

200

-81757

-118240

160820

58333

73798

10.367

-176950

240760

88426

111400

15.798

0.23

1:6

MB

300

-123050

0.23

1:6

MB

400

-163860

-236140

320640

118630

149130

21.266

0.23

1:6

MB

500

-204420

-295580

400470

148910

186950

26.778

-59118

80366

29263

36956

5.198

58808

74105

10.489

0.23

1:6

LB

100

-40882

0.23

1:6

LB

200

-81967

-118030

160600

0.23

1:6

LB

300

-123370

-176630

240440

89123

111840

15.977

-235690

320200

119580

149730

21.509

-294950

399910

150110

187710

27.084

0.23

1:6

LB

400

-164310

0.23

1:6

LB

500

-205050

58

Stress (N/m2)

Input Thickness (m) 0.11

1:4

MB

Load (KN) 100

4.411E+02

-1.203E+06

-2.302E+05

-1.323E+06

2.324E+03

0.11

1:4

MB

200

1.135E+03

-2.306E+06

-4.574E+05

-2.655E+06

4.617E+03

0.11

1:4

MB

300

1.695E+03

-3.406E+06

-6.834E+05

-4.036E+06

6.903E+03

0.11

Mortar

Brick

σLB

σLU

σC

σRB

σRU

1:4

MB

400

2.265E+03

-4.549E+06

-9.102E+05

-5.430E+06

9.193E+03

0.11

1:4

MB

500

2.840E+03

-5.884E+06

-1.138E+06

-6.664E+06

1.149E+04

0.11

1:4

LB

100

4.224E+02

-1.125E+06

-2.161E+05

-1.242E+06

2.184E+03

0.11

1:4

LB

200

8.158E+02

-2.173E+06

-4.296E+05

-2.497E+06

4.337E+03

0.11

1:4

LB

300

1.212E+03

-3.183E+06

-6.415E+05

-3.764E+06

6.480E+03

0.11

1:4

LB

400

1.624E+03

-4.253E+06

-8.355E+05

-5.081E+06

8.438E+03

0.11

1:4

LB

500

2.045E+03

-5.513E+06

-1.032E+06

-6.244E+06

1.042E+04

0.11

1:6

MB

100

5.084E+02

-1.258E+06

-2.392E+05

-1.377E+06

2.422E+03

0.11

1:6

MB

200

1.161E+03

-2.383E+06

-4.731E+05

-2.634E+06

4.779E+03

0.11

1:6

MB

300

1.750E+03

-3.560E+06

-7.069E+05

-4.137E+06

7.140E+03

0.11

1:6

MB

400

2.352E+03

-4.922E+06

-9.392E+05

-5.362E+06

9.487E+03

0.11

1:6

MB

500

2.952E+03

-6.119E+06

-1.169E+06

-6.056E+06

1.181E+04

0.11

1:6

LB

100

4.378E+02

-1.181E+06

-2.263E+05

-1.308E+06

2.294E+03

0.11

1:6

LB

200

8.615E+02

-2.246E+06

-4.486E+05

-2.505E+06

4.535E+03

0.11

1:6

LB

300

1.295E+03

-3.328E+06

-6.707E+05

-3.886E+06

6.783E+03

0.11

1:6

LB

400

1.748E+03

-4.609E+06

-8.730E+05

-5.092E+06

8.825E+03

0.11

1:6

LB

500

2.202E+03

-5.904E+06

-1.077E+06

-5.823E+06

1.088E+04

0.23

1:4

MB

100

2.229E+02

-6.076E+05

-1.164E+05

-6.674E+05

1.171E+03

0.23

1:4

MB

200

4.451E+02

-1.220E+06

-2.329E+05

-1.345E+06

2.349E+03

0.23

1:4

MB

300

8.674E+02

-1.779E+06

-3.482E+05

-2.067E+06

3.514E+03

0.23

1:4

MB

400

1.145E+03

-2.321E+06

-4.626E+05

-2.743E+06

4.673E+03

0.23

1:4

MB

500

1.426E+03

-2.873E+06

-5.766E+05

-3.514E+06

5.826E+03

0.23

1:4

LB

100

2.154E+02

-5.726E+05

-1.106E+05

-6.306E+05

1.118E+03

0.23

1:4

LB

200

4.301E+02

-1.150E+06

-2.209E+05

-1.275E+06

2.231E+03

0.23

1:4

LB

300

6.302E+02

-1.689E+06

-3.304E+05

-1.963E+06

3.338E+03

0.23

1:4

LB

400

8.290E+02

-2.205E+06

-4.390E+05

-2.603E+06

4.437E+03

0.23

1:4

LB

500

1.031E+03

-2.721E+06

-5.481E+05

-3.320E+06

5.536E+03

0.23

1:6

MB

100

2.605E+02

-6.459E+05

-1.218E+05

-6.991E+05

1.229E+03

0.23

1:6

MB

200

5.154E+02

-1.272E+06

-2.429E+05

-1.411E+06

2.453E+03

0.23

1:6

MB

300

8.831E+02

-1.835E+06

-3.626E+05

-2.111E+06

3.664E+03

0.23

1:6

MB

400

1.176E+03

-2.410E+06

-4.804E+05

-2.882E+06

4.850E+03

0.23

1:6

MB

500

1.475E+03

-2.982E+06

-5.990E+05

-3.650E+06

6.065E+03

0.23

1:6

LB

100

2.270E+02

-6.102E+05

-1.166E+05

-6.687E+05

1.179E+03

0.23

1:6

LB

200

4.478E+02

-1.207E+06

-2.323E+05

-1.354E+06

2.348E+03

0.23

1:6

LB

300

6.625E+02

-1.750E+06

-3.469E+05

-2.026E+06

3.503E+03

0.23

1:6

LB

400

8.820E+02

-2.291E+06

-4.606E+05

-2.740E+06

4.650E+03

0.23

1:6

LB

500

1.105E+03

-2.824E+06

-5.752E+05

-3.468E+06

5.809E+03

59

Input Thickness (m) 0.11

Strain

1:4

MB

Load (KN) 100

1.336E-07

-3.660E-04

-6.992E-05

-4.024E-04

6.319E-07

0.11

1:4

MB

200

3.422E-07

-6.985E-04

-1.389E-04

-8.096E-04

1.262E-06

0.11

1:4

MB

300

5.110E-07

-1.031E-03

-2.076E-04

-1.224E-03

1.890E-06

0.11

Mortar

Brick

εLB

εLU

εC

εRB

εRU

1:4

MB

400

6.829E-07

-1.375E-03

-2.766E-04

-1.641E-03

2.518E-06

0.11

1:4

MB

500

8.562E-07

-1.778E-03

-3.458E-04

-2.011E-03

3.147E-06

0.11

1:4

LB

100

1.612E-07

-4.320E-04

-8.286E-05

-4.779E-04

8.237E-07

0.11

1:4

LB

200

3.111E-07

-8.317E-04

-1.647E-04

-9.632E-04

1.646E-06

0.11

1:4

LB

300

4.622E-07

-1.217E-03

-2.461E-04

-1.443E-03

2.461E-06

0.11

1:4

LB

400

6.191E-07

-1.625E-03

-3.206E-04

-1.943E-03

3.304E-06

0.11

1:4

LB

500

7.797E-07

-2.106E-03

-3.961E-04

-2.384E-03

4.169E-06

0.11

1:6

MB

100

1.592E-07

-3.828E-04

-7.289E-05

-4.188E-04

6.454E-07

0.11

1:6

MB

200

3.540E-07

-7.226E-04

-1.442E-04

-8.000E-04

1.287E-06

0.11

1:6

MB

300

5.338E-07

-1.078E-03

-2.155E-04

-1.251E-03

1.934E-06

0.11

1:6

MB

400

7.173E-07

-1.489E-03

-2.864E-04

-1.618E-03

2.584E-06

0.11

1:6

MB

500

9.008E-07

-1.854E-03

-3.567E-04

-1.825E-03

3.244E-06

0.11

1:6

LB

100

1.694E-07

-4.541E-04

-8.709E-05

-5.034E-04

8.198E-07

0.11

1:6

LB

200

3.341E-07

-8.604E-04

-1.727E-04

-9.626E-04

1.632E-06

0.11

1:6

LB

300

5.027E-07

-1.274E-03

-2.584E-04

-1.486E-03

2.445E-06

0.11

1:6

LB

400

6.795E-07

-1.762E-03

-3.365E-04

-1.944E-03

3.288E-06

0.11

1:6

LB

500

8.584E-07

-2.261E-03

-4.152E-04

-2.222E-03

4.163E-06

0.23

1:4

MB

100

6.752E-08

-1.849E-04

-3.536E-05

-2.030E-04

3.198E-07

0.23

1:4

MB

200

1.349E-07

-3.711E-04

-7.073E-05

-4.091E-04

6.401E-07

0.23

1:4

MB

300

2.615E-07

-5.398E-04

-1.057E-04

-6.297E-04

9.602E-07

0.23

1:4

MB

400

3.450E-07

-7.035E-04

-1.404E-04

-8.356E-04

1.278E-06

0.23

1:4

MB

500

4.300E-07

-8.702E-04

-1.751E-04

-1.067E-03

1.596E-06

0.23

1:4

LB

100

8.220E-08

-2.201E-04

-4.241E-05

-2.427E-04

4.212E-07

0.23

1:4

LB

200

1.641E-07

-4.420E-04

-8.471E-05

-4.906E-04

8.433E-07

0.23

1:4

LB

300

2.404E-07

-6.477E-04

-1.267E-04

-7.562E-04

1.266E-06

0.23

1:4

LB

400

3.161E-07

-8.441E-04

-1.683E-04

-1.004E-03

1.684E-06

0.23

1:4

LB

500

3.930E-07

-1.041E-03

-2.102E-04

-1.274E-03

2.102E-06

0.23

1:6

MB

100

8.139E-08

-1.971E-04

-3.712E-05

-2.127E-04

3.278E-07

0.23

1:6

MB

200

1.615E-07

-3.872E-04

-7.400E-05

-4.293E-04

6.563E-07

0.23

1:6

MB

300

2.693E-07

-5.573E-04

-1.104E-04

-6.434E-04

9.820E-07

0.23

1:6

MB

400

3.588E-07

-7.309E-04

-1.464E-04

-8.752E-04

1.309E-06

0.23

1:6

MB

500

4.499E-07

-9.042E-04

-1.826E-04

-1.105E-03

1.636E-06

0.23

1:6

LB

100

8.771E-08

-2.352E-04

-4.487E-05

-2.574E-04

4.207E-07

0.23

1:6

LB

200

1.734E-07

-4.641E-04

-8.939E-05

-5.215E-04

8.431E-07

0.23

1:6

LB

300

2.569E-07

-6.716E-04

-1.334E-04

-7.811E-04

1.261E-06

0.23

1:6

LB

400

3.423E-07

-8.782E-04

-1.773E-04

-1.052E-03

1.679E-06

0.23

1:6

LB

500

4.288E-07

-1.082E-03

-2.215E-04

-1.328E-03

2.096E-06

60

Table A-1: ANSYS Results for Span 4m Input

Reactions

Displacement (mm)

Thickness (m)

Mortar

Brick

Load (KN)

HzL (N)

HzR (N)

V (N)

ML (N-m)

MR (N-m)

0.11

1:4

MB

100

-40118

-59882

69917

29529

38302

5.147

0.11

1:4

MB

200

-80713

-119290

139610

59584

76987

10.500

0.11

1:4

MB

300

-122000

-178000

209000

90150

116000

15.900

-238000

278000

121000

155000

21.400

-297000

348000

152000

195000

26.900

0.11

1:4

MB

400

-162000

0.11

1:4

MB

500

-203000

0.11

1:4

LB

100

-40347

-59653

69710

30032

38628

5.271

-118840

139200

60575

77627

10.694

0.11

1:4

LB

200

-81158

0.11

1:4

LB

300

-122330

-177670

208410

91755

117120

16.262

0.11

1:4

LB

400

-163400

-236600

277440

123330

156920

21.943

-295600

346340

155210

196940

27.708

38500

5.226

0.11

1:4

LB

500

-204400

0.11

1:6

MB

100

-40302

-59698

69794

29826

0.11

1:6

MB

200

-81179

-118820

139250

60428

77585

10.656

-178150

208550

91358

116960

16.181

0.11

1:6

MB

300

-121850

0.11

1:6

MB

400

-162170

-237830

277670

122660

156650

21.819

0.11

1:6

MB

500

-199080

-300920

345420

156670

199130

28.474

0.11

1:6

LB

100

-40535

-59465

69576

30355

38842

5.355

-118360

138810

61484

78264

10.915

0.11

1:6

LB

200

-81636

0.11

1:6

LB

300

-122660

-177340

207840

93068

118060

16.599

0.11

1:6

LB

400

-163510

-236490

276680

125080

158180

22.403

-298970

344350

159450

200650

29.049

37355

4.789

0.11

1:6

LB

500

-201030

0.23

1:4

MB

100

-39422

-60578

70519

28067

0.23

1:4

MB

200

-78888

-121110

141030

56140

74720

9.580

-181320

211380

84611

112360

14.501

0.23

1:4

MB

300

-118680

0.23

1:4

MB

400

-158910

-241090

281530

113540

150340

19.523

0.23

1:4

MB

500

-199220

-300780

351570

142700

188520

24.591

-60453

70408

28338

37531

4.856

56687

75070

9.714

0.23

1:4

LB

100

-39547

0.23

1:4

LB

200

-79106

-120890

140810

0.23

1:4

LB

300

-119050

-180950

211050

85424

112880

14.699

-240550

281060

114670

151080

19.801

0.23

1:4

LB

400

-159450

0.23

1:4

LB

500

-199890

-300110

350990

144100

189430

24.935

0.23

1:6

MB

100

-39486

-60514

70470

28187

37434

4.818

0.23

1:6

MB

200

-79180

-120820

140850

56584

75014

9.705

-180590

210970

85569

113040

14.747

0.23

1:6

MB

300

-119410

0.23

1:6

MB

400

-159750

-240250

280950

114880

151320

19.851

0.23

1:6

MB

500

-199830

-300170

350860

144320

189740

25.008

-60380

70349

28480

37623

4.890

57161

75387

9.845

0.23

1:6

LB

100

-39620

0.23

1:6

LB

200

-79442

-120560

140610

0.23

1:6

LB

300

-119780

-180220

210630

86408

113570

14.955

-239720

280460

116060

152090

20.141

-299450

350230

145850

190730

25.382

0.23

1:6

LB

400

-160280

0.23

1:6

LB

500

-200550

61

Stress (N/m2)

Input Thickness (m) 0.11

1:4

MB

Load (KN) 100

3.331E+02

-1.732E+06

-2.428E+05

-1.531E+06

2.452E+03

0.11

1:4

MB

200

6.311E+02

-3.306E+06

-4.836E+05

-3.367E+06

4.885E+03

0.11

1:4

MB

300

9.259E+02

-4.779E+06

-7.203E+05

-5.676E+06

7.276E+03

0.11

Mortar

Brick

σLB

σLU

σC

σRB

σRU

1:4

MB

400

1.227E+03

-6.377E+06

-9.584E+05

-7.503E+06

9.678E+03

0.11

1:4

MB

500

1.525E+03

-7.956E+06

-1.191E+06

-8.529E+06

1.203E+04

0.11

1:4

LB

100

4.111E+02

-1.601E+06

-2.327E+05

-1.425E+06

2.351E+03

0.11

1:4

LB

200

7.862E+02

-3.060E+06

-4.635E+05

-3.115E+06

4.684E+03

0.11

1:4

LB

300

1.147E+03

-4.488E+06

-6.929E+05

-5.120E+06

6.999E+03

0.11

1:4

LB

400

1.514E+03

-6.022E+06

-9.040E+05

-6.855E+06

9.130E+03

0.11

1:4

LB

500

1.883E+03

-7.457E+06

-1.118E+06

-8.117E+06

1.129E+04

0.11

1:6

MB

100

2.131E+02

-1.787E+06

-2.430E+05

-1.649E+06

2.454E+03

0.11

1:6

MB

200

3.972E+02

-3.314E+06

-4.812E+05

-3.789E+06

4.864E+03

0.11

1:6

MB

300

5.928E+02

-4.711E+06

-7.162E+05

-5.590E+06

7.233E+03

0.11

1:6

MB

400

7.954E+02

-6.018E+06

-9.489E+05

-6.035E+06

9.584E+03

0.11

1:6

MB

500

1.243E+03

-5.864E+06

-1.167E+06

-6.335E+06

1.179E+04

0.11

1:6

LB

100

2.850E+02

-1.684E+06

-2.364E+05

-1.544E+06

2.388E+03

0.11

1:6

LB

200

5.384E+02

-3.113E+06

-4.685E+05

-3.448E+06

4.731E+03

0.11

1:6

LB

300

7.906E+02

-4.607E+06

-6.993E+05

-5.213E+06

7.063E+03

0.11

1:6

LB

400

1.039E+03

-6.036E+06

-9.124E+05

-6.181E+06

9.214E+03

0.11

1:6

LB

500

1.485E+03

-5.787E+06

-1.117E+06

-6.356E+06

1.129E+04

0.23

1:4

MB

100

1.681E+02

-8.693E+05

-1.234E+05

-7.642E+05

1.252E+03

0.23

1:4

MB

200

3.363E+02

-1.764E+06

-2.457E+05

-1.559E+06

2.485E+03

0.23

1:4

MB

300

4.866E+02

-2.615E+06

-3.673E+05

-2.450E+06

3.713E+03

0.23

1:4

MB

400

6.320E+02

-3.412E+06

-4.887E+05

-3.855E+06

4.934E+03

0.23

1:4

MB

500

7.786E+02

-4.130E+06

-6.085E+05

-5.264E+06

6.134E+03

0.23

1:4

LB

100

2.095E+02

-8.071E+05

-1.212E+05

-7.183E+05

1.208E+03

0.23

1:4

LB

200

4.186E+02

-1.645E+06

-2.378E+05

-1.461E+06

2.398E+03

0.23

1:4

LB

300

6.102E+02

-2.443E+06

-3.558E+05

-2.295E+06

3.591E+03

0.23

1:4

LB

400

7.941E+02

-3.174E+06

-4.735E+05

-3.505E+06

4.781E+03

0.23

1:4

LB

500

9.782E+02

-3.884E+06

-5.904E+05

-4.820E+06

5.956E+03

0.23

1:6

MB

100

1.114E+02

-9.367E+05

-1.218E+05

-8.174E+05

1.232E+03

0.23

1:6

MB

200

2.136E+02

-1.839E+06

-2.467E+05

-1.694E+06

2.493E+03

0.23

1:6

MB

300

3.046E+02

-2.632E+06

-3.687E+05

-2.836E+06

3.721E+03

0.23

1:6

MB

400

3.972E+02

-3.381E+06

-4.887E+05

-4.331E+06

4.935E+03

0.23

1:6

MB

500

4.945E+02

-4.063E+06

-6.084E+05

-5.219E+06

6.146E+03

0.23

1:6

LB

100

1.489E+02

-8.805E+05

-1.215E+05

-7.728E+05

1.230E+03

0.23

1:6

LB

200

2.891E+02

-1.753E+06

-2.426E+05

-1.603E+06

2.450E+03

0.23

1:6

LB

300

4.169E+02

-2.499E+06

-3.627E+05

-2.619E+06

3.662E+03

0.23

1:6

LB

400

5.449E+02

-3.204E+06

-4.810E+05

-4.022E+06

4.854E+03

0.23

1:6

LB

500

6.748E+02

-3.857E+06

-5.998E+05

-4.934E+06

6.055E+03

62

Input Thickness (m) 0.11

Strain

1:4

MB

Load (KN) 100

1.003E-07

-5.223E-04

-7.558E-05

-4.618E-04

1.381E-07

0.11

1:4

MB

200

1.902E-07

-1.000E-03

-1.509E-04

-1.017E-03

2.778E-07

0.11

1:4

MB

300

2.786E-07

-1.454E-03

-2.242E-04

-1.709E-03

4.162E-07

0.11

Mortar

Brick

εLB

εLU

εC

εRB

εRU

1:4

MB

400

3.699E-07

-1.947E-03

-2.984E-04

-2.261E-03

5.507E-07

0.11

1:4

MB

500

4.590E-07

-2.445E-03

-3.726E-04

-2.575E-03

6.822E-07

0.11

1:4

LB

100

1.567E-07

-6.112E-04

-9.177E-05

-5.441E-04

1.541E-07

0.11

1:4

LB

200

2.997E-07

-1.173E-03

-1.829E-04

-1.191E-03

3.091E-07

0.11

1:4

LB

300

4.374E-07

-1.729E-03

-2.735E-04

-1.954E-03

4.608E-07

0.11

1:4

LB

400

5.771E-07

-2.335E-03

-3.573E-04

-2.618E-03

6.104E-07

0.11

1:4

LB

500

7.178E-07

-2.909E-03

-4.420E-04

-3.102E-03

7.590E-07

0.11

1:6

MB

100

6.421E-08

-5.386E-04

-7.555E-05

-4.982E-04

1.612E-07

0.11

1:6

MB

200

1.197E-07

-1.006E-03

-1.497E-04

-1.142E-03

3.233E-07

0.11

1:6

MB

300

1.786E-07

-1.434E-03

-2.228E-04

-1.685E-03

4.820E-07

0.11

1:6

MB

400

2.396E-07

-1.839E-03

-2.952E-04

-1.818E-03

6.353E-07

0.11

1:6

MB

500

3.746E-07

-1.786E-03

-3.624E-04

-1.908E-03

6.819E-07

0.11

1:6

LB

100

1.087E-07

-6.429E-04

-9.315E-05

-5.902E-04

1.781E-07

0.11

1:6

LB

200

2.052E-07

-1.196E-03

-1.847E-04

-1.316E-03

3.564E-07

0.11

1:6

LB

300

3.014E-07

-1.783E-03

-2.758E-04

-1.989E-03

5.286E-07

0.11

1:6

LB

400

3.960E-07

-2.355E-03

-3.603E-04

-2.360E-03

6.994E-07

0.11

1:6

LB

500

5.660E-07

-2.236E-03

-4.407E-04

-2.423E-03

7.726E-07

0.23

1:4

MB

100

5.064E-08

-2.621E-04

-3.845E-05

-2.304E-04

6.969E-08

0.23

1:4

MB

200

1.013E-07

-5.319E-04

-7.648E-05

-4.703E-04

1.395E-07

0.23

1:4

MB

300

1.466E-07

-7.891E-04

-1.143E-04

-7.403E-04

2.103E-07

0.23

1:4

MB

400

1.903E-07

-1.033E-03

-1.521E-04

-1.164E-03

2.810E-07

0.23

1:4

MB

500

2.345E-07

-1.254E-03

-1.895E-04

-1.587E-03

3.515E-07

0.23

1:4

LB

100

7.987E-08

-3.082E-04

-4.787E-05

-2.741E-04

7.856E-08

0.23

1:4

LB

200

1.596E-07

-6.279E-04

-9.375E-05

-5.577E-04

1.571E-07

0.23

1:4

LB

300

2.326E-07

-9.334E-04

-1.403E-04

-8.774E-04

2.369E-07

0.23

1:4

LB

400

3.027E-07

-1.217E-03

-1.868E-04

-1.339E-03

3.163E-07

0.23

1:4

LB

500

3.729E-07

-1.493E-03

-2.329E-04

-1.840E-03

3.948E-07

0.23

1:6

MB

100

3.356E-08

-2.824E-04

-3.782E-05

-2.467E-04

8.141E-08

0.23

1:6

MB

200

6.436E-08

-5.544E-04

-7.668E-05

-5.119E-04

1.637E-07

0.23

1:6

MB

300

9.178E-08

-7.972E-04

-1.146E-04

-8.558E-04

2.462E-07

0.23

1:6

MB

400

1.197E-07

-1.027E-03

-1.520E-04

-1.305E-03

3.287E-07

0.23

1:6

MB

500

1.490E-07

-1.236E-03

-1.893E-04

-1.573E-03

4.097E-07

0.23

1:6

LB

100

5.678E-08

-3.361E-04

-4.787E-05

-2.951E-04

9.092E-08

0.23

1:6

LB

200

1.102E-07

-6.690E-04

-9.557E-05

-6.127E-04

1.828E-07

0.23

1:6

LB

300

1.589E-07

-9.583E-04

-1.429E-04

-1.001E-03

2.747E-07

0.23

1:6

LB

400

2.077E-07

-1.232E-03

-1.896E-04

-1.535E-03

3.665E-07

0.23

1:6

LB

500

2.572E-07

-1.485E-03

-2.365E-04

-1.883E-03

4.556E-07

63

Table A-1: ANSYS Results for Span 4.5m Input

Reactions

Displacement (mm)

Thickness (m)

Mortar

Brick

Load (KN)

HzL (N)

HzR (N)

V (N)

ML (N-m)

MR (N-m)

0.11

1:4

MB

100

-39266

-60734

62023

29192

39202

4.992

0.11

1:4

MB

200

-78893

-121110

123880

58808

78722

10.111

0.11

1:4

MB

300

-119070

-180930

185480

89090

118770

15.378

-240680

247000

119530

158960

20.693

-300430

308420

150250

199380

26.086

0.11

1:4

MB

400

-159320

0.11

1:4

MB

500

-199570

0.11

1:4

LB

100

-39524

-60476

61811

29771

39577

5.130

-120570

123450

59984

79485

10.389

0.11

1:4

LB

200

-79426

0.11

1:4

LB

300

-119920

-180080

184790

90948

119980

15.819

0.11

1:4

LB

400

-160620

-239380

245990

122300

160760

21.347

-298520

307000

154100

201880

26.993

39409

5.070

0.11

1:4

LB

500

-201480

0.11

1:6

MB

100

-39433

-60567

61908

29505

0.11

1:6

MB

200

-79483

-120520

123530

59741

79386

10.331

-180220

184990

90364

119690

15.690

0.11

1:6

MB

300

-119780

0.11

1:6

MB

400

-160170

-239830

246310

121330

160300

21.158

0.11

1:6

MB

500

-205210

-294790

306200

155390

204200

27.917

0.11

1:6

LB

100

-39697

-60303

61683

30120

39805

5.215

-119990

123070

60988

80189

10.627

0.11

1:6

LB

200

-80011

0.11

1:6

LB

300

-120700

-179300

184250

92394

121000

16.170

0.11

1:6

LB

400

-161550

-238450

245200

124350

162240

21.862

-293660

305020

158810

206080

28.566

38110

4.593

0.11

1:6

LB

500

-206340

0.23

1:4

MB

100

-38487

-61513

62642

27504

0.23

1:4

MB

200

-76982

-123020

125280

55015

76225

9.188

-184270

187810

82815

114550

13.878

0.23

1:4

MB

300

-115730

0.23

1:4

MB

400

-154960

-245040

250150

111090

153250

18.686

0.23

1:4

MB

500

-197742

-302257

309158

139892

191614

23.689

-61370

62527

27816

38312

4.667

55645

76633

9.338

0.23

1:4

LB

100

-38630

0.23

1:4

LB

200

-77275

-122730

125050

0.23

1:4

LB

300

-116190

-183810

187450

83784

115180

14.109

-244430

249670

112380

154090

18.992

0.23

1:4

LB

400

-155570

0.23

1:4

LB

500

-195200

-304800

311770

141280

193240

23.927

0.23

1:6

MB

100

-38559

-61441

62591

27642

38199

4.625

0.23

1:6

MB

200

-77258

-122740

125120

55450

76520

9.305

-183490

187420

83819

115280

14.131

0.23

1:6

MB

300

-116510

0.23

1:6

MB

400

-139186

-260813

266527

119077

163891

20.069

0.23

1:6

MB

500

-195620

-304380

311700

141370

193470

23.962

-61287

62466

27982

38419

4.706

56130

76959

9.465

0.23

1:6

LB

100

-38713

0.23

1:6

LB

200

-77563

-122440

124870

0.23

1:6

LB

300

-116980

-183020

187040

84855

115950

14.376

-243340

249080

113920

155210

19.355

-300774

307676

139491

190884

23.639

0.23

1:6

LB

400

-156660

0.23

1:6

LB

500

-199225.1

64

Stress (N/m2)

Input Thickness (m) 0.11 0.11

σLB

σLU

σC

σRB

σRU

MB

Load (KN) 100

3.025E+03

-1.271E+06

-2.533E+05

-1.079E+06

2.552E+03

Mortar

Brick

1:4 1:4

MB

200

6.100E+03

-2.480E+06

-5.056E+05

-2.175E+06

5.107E+03

0.11

1:4

MB

300

9.216E+03

-3.614E+06

-7.556E+05

-3.342E+06

7.632E+03

0.11

1:4

MB

400

1.238E+04

-4.705E+06

-1.006E+06

-4.592E+06

1.016E+04

0.11

1:4

MB

500

1.561E+04

-5.787E+06

-1.256E+06

-5.947E+06

1.269E+04

0.11

1:4

LB

100

2.894E+03

-1.195E+06

-2.423E+05

-1.018E+06

2.447E+03

0.11

1:4

LB

200

5.849E+03

-2.332E+06

-4.839E+05

-2.061E+06

4.886E+03

0.11

1:4

LB

300

8.894E+03

-3.396E+06

-7.254E+05

-3.122E+06

7.323E+03

0.11

1:4

LB

400

1.213E+04

-4.439E+06

-9.515E+05

-4.260E+06

9.608E+03

0.11

1:4

LB

500

1.554E+04

-5.503E+06

-1.179E+06

-5.529E+06

1.190E+04

0.11

1:6

MB

100

3.066E+03

-1.303E+06

-2.545E+05

-1.118E+06

2.578E+03

0.11

1:6

MB

200

6.185E+03

-2.484E+06

-5.060E+05

-2.273E+06

5.117E+03

0.11

1:6

MB

300

9.365E+03

-3.589E+06

-7.543E+05

-3.549E+06

7.619E+03

0.11

1:6

MB

400

1.260E+04

-4.587E+06

-1.001E+06

-4.854E+06

1.011E+04

0.11

1:6

MB

500

1.587E+04

-4.457E+06

-1.229E+06

-5.914E+06

1.241E+04

0.11

1:6

LB

100

2.959E+03

-1.242E+06

-2.470E+05

-1.066E+06

2.499E+03

0.11

1:6

LB

200

5.985E+03

-2.366E+06

-4.913E+05

-2.168E+06

4.966E+03

0.11

1:6

LB

300

9.114E+03

-3.413E+06

-7.351E+05

-3.324E+06

7.422E+03

0.11

1:6

LB

400

1.244E+04

-4.404E+06

-9.641E+05

-4.619E+06

9.736E+03

0.11

1:6

LB

500

1.580E+04

-4.385E+06

-1.180E+06

-5.714E+06

1.192E+04

0.23

1:4

MB

100

1.535E+03

-6.443E+05

-1.290E+05

-5.503E+05

1.304E+03

0.23

1:4

MB

200

3.070E+03

-1.294E+06

-2.566E+05

-1.088E+06

2.588E+03

0.23

1:4

MB

300

4.625E+03

-1.918E+06

-3.844E+05

-1.638E+06

3.883E+03

0.23

1:4

MB

400

6.195E+03

-2.506E+06

-5.121E+05

-2.199E+06

5.187E+03

0.23

1:4

MB

500

7.799E+03

-3.043E+06

-6.338E+05

-2.877E+06

6.402E+03

0.23

1:4

LB

100

1.483E+03

-6.106E+05

-1.263E+05

-5.171E+05

1.274E+03

0.23

1:4

LB

200

2.968E+03

-1.231E+06

-2.479E+05

-1.037E+06

2.505E+03

0.23

1:4

LB

300

4.478E+03

-1.829E+06

-3.716E+05

-1.568E+06

3.753E+03

0.23

1:4

LB

400

6.007E+03

-2.379E+06

-4.953E+05

-2.103E+06

5.002E+03

0.23

1:4

LB

500

7.561E+03

-2.939E+06

-6.188E+05

-2.658E+06

6.248E+03

0.23

1:6

MB

100

1.558E+03

-6.712E+05

-1.277E+05

-5.742E+05

1.304E+03

0.23

1:6

MB

200

3.126E+03

-1.325E+06

-2.588E+05

-1.131E+06

2.607E+03

0.23

1:6

MB

300

4.709E+03

-1.931E+06

-3.875E+05

-1.715E+06

3.912E+03

0.23

1:6

MB

400

6.604E+03

-2.637E+06

-5.434E+05

-2.372E+06

5.486E+03

0.23

1:6

MB

500

7.926E+03

-3.087E+06

-6.416E+05

-2.999E+06

6.484E+03

0.23

1:6

LB

100

1.521E+03

-6.430E+05

-1.271E+05

-5.433E+05

1.288E+03

0.23

1:6

LB

200

3.053E+03

-1.277E+06

-2.539E+05

-1.090E+06

2.574E+03

0.23

1:6

LB

300

4.605E+03

-1.864E+06

-3.803E+05

-1.658E+06

3.842E+03

0.23

1:6

LB

400

6.180E+03

-2.426E+06

-5.054E+05

-2.245E+06

5.105E+03

0.23

1:6

LB

500

7.691E+03

-2.985E+06

-6.265E+05

-2.762E+06

6.331E+03

65

Input Thickness (m) 0.11 0.11

Strain

Mortar

Brick

1:4

MB

Load (KN) 100

εLB

εLU

εC

εRB

εRU

9.112E-07

-3.993E-04

-8.054E-05

-3.308E-04

8.153E-07

1:4

MB

200

1.837E-06

-7.766E-04

-1.608E-04

-6.661E-04

1.629E-06

0.11

1:4

MB

300

2.776E-06

-1.129E-03

-2.404E-04

-1.020E-03

2.454E-06

0.11

1:4

MB

400

3.729E-06

-1.468E-03

-3.203E-04

-1.398E-03

3.284E-06

0.11

1:4

MB

500

4.702E-06

-1.807E-03

-4.002E-04

-1.809E-03

4.119E-06

0.11

1:4

LB

100

1.103E-06

-4.750E-04

-9.751E-05

-3.950E-04

9.964E-07

0.11

1:4

LB

200

2.230E-06

-9.239E-04

-1.948E-04

-7.989E-04

1.992E-06

0.11

1:4

LB

300

3.391E-06

-1.343E-03

-2.924E-04

-1.208E-03

3.001E-06

0.11

1:4

LB

400

4.624E-06

-1.754E-03

-3.841E-04

-1.645E-03

4.049E-06

0.11

1:4

LB

500

5.925E-06

-2.176E-03

-4.764E-04

-2.135E-03

5.137E-06

0.11

1:6

MB

100

9.234E-07

-4.093E-04

-8.089E-05

-3.425E-04

8.157E-07

0.11

1:6

MB

200

1.863E-06

-7.766E-04

-1.609E-04

-6.938E-04

1.635E-06

0.11

1:6

MB

300

2.821E-06

-1.120E-03

-2.400E-04

-1.080E-03

2.468E-06

0.11

1:6

MB

400

3.796E-06

-1.431E-03

-3.188E-04

-1.477E-03

3.304E-06

0.11

1:6

MB

500

4.778E-06

-1.373E-03

-3.924E-04

-1.809E-03

3.953E-06

0.11

1:6

LB

100

1.128E-06

-4.935E-04

-9.940E-05

-4.135E-04

1.004E-06

0.11

1:6

LB

200

2.282E-06

-9.357E-04

-1.979E-04

-8.387E-04

2.013E-06

0.11

1:6

LB

300

3.475E-06

-1.347E-03

-2.964E-04

-1.283E-03

3.039E-06

0.11

1:6

LB

400

4.745E-06

-1.739E-03

-3.894E-04

-1.780E-03

4.104E-06

0.11

1:6

LB

500

6.025E-06

-1.712E-03

-4.780E-04

-2.207E-03

5.025E-06

0.23

1:4

MB

100

4.623E-07

-2.026E-04

-4.103E-05

-1.690E-04

4.129E-07

0.23

1:4

MB

200

9.246E-07

-4.069E-04

-8.157E-05

-3.338E-04

8.258E-07

0.23

1:4

MB

300

1.393E-06

-6.019E-04

-1.222E-04

-5.023E-04

1.238E-06

0.23

1:4

MB

400

1.866E-06

-7.850E-04

-1.628E-04

-6.718E-04

1.651E-06

0.23

1:4

MB

500

2.392E-06

-9.676E-04

-2.046E-04

-9.066E-04

2.093E-06

0.23

1:4

LB

100

5.656E-07

-2.428E-04

-5.090E-05

-2.008E-04

5.098E-07

0.23

1:4

LB

200

1.132E-06

-4.896E-04

-9.977E-05

-4.027E-04

1.020E-06

0.23

1:4

LB

300

1.707E-06

-7.264E-04

-1.495E-04

-6.087E-04

1.529E-06

0.23

1:4

LB

400

2.290E-06

-9.427E-04

-1.994E-04

-8.138E-04

2.040E-06

0.23

1:4

LB

500

2.883E-06

-1.164E-03

-2.493E-04

-1.026E-03

2.557E-06

0.23

1:6

MB

100

4.692E-07

-2.112E-04

-4.057E-05

-1.762E-04

4.149E-07

0.23

1:6

MB

200

9.415E-07

-4.163E-04

-8.224E-05

-3.468E-04

8.293E-07

0.23

1:6

MB

300

1.419E-06

-6.050E-04

-1.232E-04

-5.235E-04

1.244E-06

0.23

1:6

MB

400

1.920E-06

-7.996E-04

-1.663E-04

-7.108E-04

1.688E-06

0.23

1:6

MB

500

2.388E-06

-9.644E-04

-2.041E-04

-9.108E-04

2.088E-06

0.23

1:6

LB

100

5.798E-07

-2.559E-04

-5.115E-05

-2.110E-04

5.165E-07

0.23

1:6

LB

200

1.164E-06

-5.076E-04

-1.022E-04

-4.233E-04

1.033E-06

0.23

1:6

LB

300

1.756E-06

-7.387E-04

-1.531E-04

-6.412E-04

1.550E-06

0.23

1:6

LB

400

2.356E-06

-9.597E-04

-2.036E-04

-8.657E-04

2.074E-06

0.23

1:6

LB

500

2.803E-06

-1.130E-03

-2.421E-04

-1.006E-03

2.484E-06

66

Table A-1: ANSYS Results for Span 5m Input

Reactions

Displacement (mm)

Thickness (m)

Mortar

Brick

Load (KN)

HzL (N)

HzR (N)

V (N)

ML (N-m)

MR (N-m)

0.11

1:4

MB

100

-38574

-61426

55649

29068

40188

4.923

0.11

1:4

MB

200

-77472

-122530

111160

58528

80685

9.961

0.11

1:4

MB

300

-116980

-183020

166410

88705

121770

15.161

-243350

221590

119050

163000

20.412

-303400

276650

149720

204530

25.761

0.11

1:4

MB

400

-156650

0.11

1:4

MB

500

-196600

0.11

1:4

LB

100

-38848

-61152

55434

29722

40610

5.074

-121940

110720

59866

81551

10.269

0.11

1:4

LB

200

-78056

0.11

1:4

LB

300

-117910

-182090

165700

90836

123150

15.652

0.11

1:4

LB

400

-158110

-241890

220520

122280

165120

21.155

-301350

275170

154190

207440

26.776

40380

4.989

0.11

1:4

LB

500

-198650

0.11

1:6

MB

100

-38711

-61289

55551

29363

0.11

1:6

MB

200

-78088

-121910

110810

59534

81409

10.195

-182190

165930

90088

122770

15.495

0.11

1:6

MB

300

-117810

0.11

1:6

MB

400

-158550

-241450

220770

121270

164900

21.087

0.11

1:6

MB

500

-203820

-296180

274110

156130

210800

28.048

0.11

1:6

LB

100

-39007

-60993

55318

30072

40838

5.153

-121320

110340

60971

82330

10.525

0.11

1:6

LB

200

-78677

0.11

1:6

LB

300

-118820

-181180

165150

92447

124300

16.036

0.11

1:6

LB

400

-159390

-240610

219760

124470

166740

21.713

-295010

272850

160190

213060

28.813

38951

4.482

0.11

1:6

LB

500

-204990

0.23

1:4

MB

100

-37731

-62269

56280

27151

0.23

1:4

MB

200

-75471

-124530

112560

54311

77909

8.966

-186570

168750

81711

117060

13.532

0.23

1:4

MB

300

-113430

0.23

1:4

MB

400

-151850

-248150

224770

109570

156580

18.214

0.23

1:4

MB

500

-190560

-309440

280660

137800

196410

22.964

-62115

56163

27506

39180

4.564

55025

78372

9.132

0.23

1:4

LB

100

-37885

0.23

1:4

LB

200

-75787

-124210

112320

0.23

1:4

LB

300

-113920

-186080

168390

82795

117760

13.781

-247490

224280

111050

157540

18.553

0.23

1:4

LB

400

-152510

0.23

1:4

LB

500

-191430

-308570

280040

139670

197620

23.392

0.23

1:6

MB

100

-37808

-62192

56228

27307

39053

4.517

0.23

1:6

MB

200

-75727

-124270

112410

54739

78203

9.076

-185820

168390

82725

117810

13.787

0.23

1:6

MB

300

-114180

0.23

1:6

MB

400

-152980

-247020

224230

111110

157740

18.573

0.23

1:6

MB

500

-191930

-308070

280010

139630

197810

23.404

-62026

56100

27695

39303

4.607

55418

78627

9.220

0.23

1:6

LB

100

-37974

0.23

1:6

LB

200

-75976

-124020

112190

0.23

1:6

LB

300

-114670

-185330

168010

83893

118550

14.052

-246320

223700

112720

158780

18.940

-307180

279320

141720

199160

23.883

0.23

1:6

LB

400

-153680

0.23

1:6

LB

500

-192820

67

Stress (N/m2)

Input Thickness (m) 0.11 0.11

σLB

σLU

σC

σRB

σRU

MB

Load (KN) 100

2.184E+03

-1.318E+06

-2.553E+05

-1.126E+06

2.579E+03

Mortar

Brick

1:4 1:4

MB

200

4.376E+03

-2.568E+06

-5.100E+05

-2.311E+06

5.152E+03

0.11

1:4

MB

300

6.588E+03

-3.719E+06

-7.662E+05

-3.863E+06

7.739E+03

0.11

1:4

MB

400

8.839E+03

-4.828E+06

-1.026E+06

-5.596E+06

1.036E+04

0.11

1:4

MB

500

1.114E+04

-5.855E+06

-1.288E+06

-7.585E+06

1.301E+04

0.11

1:4

LB

100

2.286E+03

-1.239E+06

-2.349E+05

-1.055E+06

2.371E+03

0.11

1:4

LB

200

4.600E+03

-2.409E+06

-4.696E+05

-2.169E+06

4.743E+03

0.11

1:4

LB

300

6.973E+03

-3.500E+06

-7.086E+05

-3.473E+06

7.157E+03

0.11

1:4

LB

400

9.478E+03

-4.553E+06

-9.362E+05

-5.012E+06

9.459E+03

0.11

1:4

LB

500

1.211E+04

-5.634E+06

-1.162E+06

-6.822E+06

1.174E+04

0.11

1:6

MB

100

2.291E+03

-1.365E+06

-2.706E+05

-1.190E+06

2.738E+03

0.11

1:6

MB

200

4.593E+03

-2.561E+06

-5.392E+05

-2.576E+06

5.443E+03

0.11

1:6

MB

300

6.949E+03

-3.669E+06

-8.107E+05

-4.352E+06

8.191E+03

0.11

1:6

MB

400

9.448E+03

-4.291E+06

-1.081E+06

-6.099E+06

1.091E+04

0.11

1:6

MB

500

1.236E+04

-4.289E+06

-1.329E+06

-7.943E+06

1.343E+04

0.11

1:6

LB

100

2.419E+03

-1.297E+06

-2.528E+05

-1.119E+06

2.548E+03

0.11

1:6

LB

200

4.874E+03

-2.435E+06

-5.048E+05

-2.389E+06

5.091E+03

0.11

1:6

LB

300

7.414E+03

-3.490E+06

-7.618E+05

-3.920E+06

7.687E+03

0.11

1:6

LB

400

1.011E+04

-4.397E+06

-1.006E+06

-5.696E+06

1.017E+04

0.11

1:6

LB

500

1.310E+04

-4.200E+06

-1.229E+06

-7.613E+06

1.241E+04

0.23

1:4

MB

100

1.166E+03

-6.692E+05

-1.296E+05

-5.672E+05

1.310E+03

0.23

1:4

MB

200

2.219E+03

-1.345E+06

-2.591E+05

-1.139E+06

2.619E+03

0.23

1:4

MB

300

3.332E+03

-1.992E+06

-3.884E+05

-1.725E+06

3.926E+03

0.23

1:4

MB

400

4.448E+03

-2.599E+06

-5.176E+05

-2.443E+06

5.231E+03

0.23

1:4

MB

500

5.569E+03

-3.202E+06

-6.472E+05

-3.308E+06

6.537E+03

0.23

1:4

LB

100

1.174E+03

-6.335E+05

-1.178E+05

-5.360E+05

1.190E+03

0.23

1:4

LB

200

2.349E+03

-1.279E+06

-2.409E+05

-1.078E+06

2.434E+03

0.23

1:4

LB

300

3.533E+03

-1.896E+06

-3.613E+05

-1.642E+06

3.650E+03

0.23

1:4

LB

400

4.731E+03

-2.465E+06

-4.818E+05

-2.296E+06

4.862E+03

0.23

1:4

LB

500

5.945E+03

-3.036E+06

-6.044E+05

-3.072E+06

6.103E+03

0.23

1:6

MB

100

1.245E+03

-6.976E+05

-1.379E+05

-6.001E+05

1.390E+03

0.23

1:6

MB

200

2.338E+03

-1.380E+06

-2.756E+05

-1.210E+06

2.790E+03

0.23

1:6

MB

300

3.511E+03

-1.999E+06

-4.129E+05

-1.933E+06

4.178E+03

0.23

1:6

MB

400

4.693E+03

-2.602E+06

-5.499E+05

-2.768E+06

5.562E+03

0.23

1:6

MB

500

5.893E+03

-3.175E+06

-6.883E+05

-3.686E+06

6.960E+03

0.23

1:6

LB

100

1.248E+03

-6.677E+05

-1.300E+05

-5.695E+05

1.313E+03

0.23

1:6

LB

200

2.498E+03

-1.347E+06

-2.606E+05

-1.151E+06

2.629E+03

0.23

1:6

LB

300

3.763E+03

-1.929E+06

-3.903E+05

-1.835E+06

3.943E+03

0.23

1:6

LB

400

5.043E+03

-2.503E+06

-5.210E+05

-2.617E+06

5.266E+03

0.23

1:6

LB

500

6.351E+03

-3.053E+06

-6.537E+05

-3.483E+06

6.603E+03

68

Input Thickness (m) 0.11 0.11

Strain

Mortar

Brick

1:4

MB

Load (KN) 100

εLB

εLU

εC

εRB

εRU

6.930E-07

-4.183E-04

-8.236E-05

-3.453E-04

4.077E-07

1:4

MB

200

1.388E-06

-8.126E-04

-1.646E-04

-7.060E-04

6.935E-07

0.11

1:4

MB

300

2.089E-06

-1.174E-03

-2.475E-04

-1.169E-03

1.046E-06

0.11

1:4

MB

400

2.803E-06

-1.524E-03

-3.316E-04

-1.692E-03

1.401E-06

0.11

1:4

MB

500

3.533E-06

-1.848E-03

-4.167E-04

-2.296E-03

1.761E-06

0.11

1:4

LB

100

9.259E-07

-4.972E-04

-9.575E-05

-4.089E-04

4.887E-07

0.11

1:4

LB

200

1.862E-06

-9.642E-04

-1.916E-04

-8.375E-04

9.782E-07

0.11

1:4

LB

300

2.822E-06

-1.399E-03

-2.895E-04

-1.332E-03

1.481E-06

0.11

1:4

LB

400

3.835E-06

-1.817E-03

-3.832E-04

-1.919E-03

2.009E-06

0.11

1:4

LB

500

4.898E-06

-2.252E-03

-4.763E-04

-2.616E-03

2.562E-06

0.11

1:6

MB

100

7.261E-07

-4.337E-04

-8.744E-05

-3.651E-04

3.582E-07

0.11

1:6

MB

200

1.455E-06

-8.098E-04

-1.744E-04

-7.821E-04

7.180E-07

0.11

1:6

MB

300

2.202E-06

-1.158E-03

-2.624E-04

-1.317E-03

1.085E-06

0.11

1:6

MB

400

2.995E-06

-1.348E-03

-3.501E-04

-1.856E-03

1.443E-06

0.11

1:6

MB

500

3.925E-06

-1.336E-03

-4.311E-04

-2.464E-03

1.746E-06

0.11

1:6

LB

100

9.767E-07

-5.209E-04

-1.033E-04

-4.344E-04

5.052E-07

0.11

1:6

LB

200

1.967E-06

-9.736E-04

-2.065E-04

-9.190E-04

1.013E-06

0.11

1:6

LB

300

2.992E-06

-1.392E-03

-3.120E-04

-1.503E-03

1.538E-06

0.11

1:6

LB

400

4.078E-06

-1.754E-03

-4.128E-04

-2.187E-03

2.088E-06

0.11

1:6

LB

500

5.295E-06

-1.657E-03

-5.052E-04

-2.971E-03

2.599E-06

0.23

1:4

MB

100

3.713E-07

-2.125E-04

-4.179E-05

-1.742E-04

2.071E-07

0.23

1:4

MB

200

7.041E-07

-4.272E-04

-8.359E-05

-3.495E-04

4.143E-07

0.23

1:4

MB

300

1.057E-06

-6.318E-04

-1.253E-04

-5.288E-04

5.280E-07

0.23

1:4

MB

400

1.411E-06

-8.228E-04

-1.670E-04

-7.413E-04

7.043E-07

0.23

1:4

MB

500

1.766E-06

-1.013E-03

-2.090E-04

-9.991E-04

8.830E-07

0.23

1:4

LB

100

4.755E-07

-2.544E-04

-4.803E-05

-2.080E-04

2.509E-07

0.23

1:4

LB

200

9.513E-07

-5.137E-04

-9.821E-05

-4.180E-04

5.020E-07

0.23

1:4

LB

300

1.431E-06

-7.607E-04

-1.473E-04

-6.361E-04

7.527E-07

0.23

1:4

LB

400

1.915E-06

-9.871E-04

-1.965E-04

-8.818E-04

1.005E-06

0.23

1:4

LB

500

2.406E-06

-1.214E-03

-2.468E-04

-1.174E-03

1.262E-06

0.23

1:6

MB

100

3.959E-07

-2.218E-04

-4.457E-05

-1.845E-04

2.129E-07

0.23

1:6

MB

200

7.411E-07

-4.382E-04

-8.908E-05

-3.715E-04

3.649E-07

0.23

1:6

MB

300

1.112E-06

-6.329E-04

-1.335E-04

-5.866E-04

5.473E-07

0.23

1:6

MB

400

1.487E-06

-8.231E-04

-1.779E-04

-8.367E-04

7.326E-07

0.23

1:6

MB

500

1.867E-06

-1.003E-03

-2.227E-04

-1.114E-03

9.196E-07

0.23

1:6

LB

100

5.040E-07

-2.684E-04

-5.313E-05

-2.214E-04

2.607E-07

0.23

1:6

LB

200

1.009E-06

-5.417E-04

-1.065E-04

-4.469E-04

5.217E-07

0.23

1:6

LB

300

1.519E-06

-7.728E-04

-1.596E-04

-7.056E-04

7.816E-07

0.23

1:6

LB

400

2.036E-06

-1.001E-03

-2.132E-04

-1.001E-03

1.047E-06

0.23

1:6

LB

500

2.563E-06

-1.220E-03

-2.676E-04

-1.332E-03

1.317E-06

69

REFERENCES Arulselvan, S. and K.Subramanian, K., Experimental Investigation on Three

Dimensional RC Infilled Frame - RC Plane Frame Interactions With Slab for Seismic Resistance, American Journal of Applied Sciences, ISSN 1546-9239 2008 Asteris,P.G., Finite Element Micro-Modeling of Infilled Frames, Electronic Journal of Structural Engineering (8) 2008 Bryan Stafford Smith and C. Carter, A Method of Analysis for Infilled Frames, University of Southampton, Southampton College of Technology, February 1970 FEMA 306, Evaluation Of Earthquake Damaged Concrete And Masonry Wall Buildings, Basic Procedures Manual, Prepared by: Applied Technology Council (ATC-43 Project) 555 Twin Dolphin Drive, Suite 550, Redwood City, California 94065, Prepared for: The Partnership for Response and Recovery, Washington, D.C., Funded by: Federal Emergency Management Agency, 1998 FEMA 356, Prestandard and commentary for the seismic rehabilitation of the buildings, Prepared by: American society of Civil Engineers(ASCE), Reston, Virginia, Prepared for: Federal Emergency Management Agency, Washington, D.C., 1998

Ghassan Al-Chaar, Mohsen Issa, and Steve Sweeney, Behavior of Masonry-Infilled Nonductile Rein forced Concrete Frame, Journal of Structural Engineering, Vol. 128, No. 8, ©ASCE, ISSN 0733- 9445/2002/8-1055–1063, August 1, 2002 Moghaddam,H.A. and Karimian, M.R., Prediction of Cracking pattern and shear strength of masonry infilled frames,2007 Ng’andu, B.M., Bracing Steel Frames with Calcium Silicate Element Walls, Eindhoven University of Technology, the Netherlands, 2006

Paulay, T. and Priestley, M.J.N., Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley & Sons, U.S.A., 1992 70

Polyakov, S.V., Masonry in framed buildings (Godsudarstvenoe Isdatel’ stvo Literatury Po Stroidal stvui Architecture. Moscow, 1956). Translated by G. L. Cairns in 1963. National Lending Library for Science and Technology, Boston Spa, Yorkshire, U.K.

Pradhan, P.L., Composite Actions of Brick Infill Wall In RC Frame under In-Plane Lateral Load, Institute of Engineering, Tribhuvan University, Ph. D. Thesis, 2009 Rai, D.C., Masonary infills in Framed Buildings, Indian Institute of Technology, Kanpur(India), 2009 Rooij, A., Steel frames with precast reinforced concrete infill panels, January 2005.

Shakya, A., Application of Artificial Neural Network in the Analysis of In-filled Frame., Institute of Engineering, Tribhuvan University, M. Sc. Thesis,2003 Smyrou, E., Implementation and Verification of a masonry panel model for nonlinear dynamic analysis of infilled RC frames, 2006 Thiruvengadam, V., On The Natural Frequencies fo In-filled Frames, Earthquake Engineering and Structural Dynamics, Vol. 13, pp.401-419, 1985

71