BEHAVIOUR OF BRICK MASONRY COLUMNS WITH FERRO CEMENT OVERLAY .• -. -~ .... -._ ..• THESIS SUBMITTED TO THE DEPARTMENT OF CIVIL ENGINEERING IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY by TohurAhmed 1111111111111111111111111 111111 III #92763# CIVIL ENGINEERING DEPARTMENT BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY (BUET) DECEMBER, 1997
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BEHAVIOUR OF BRICK MASONRY COLUMNS
WITH
FERRO CEMENT OVERLAY
.•-. -~....-._ ..•
THESIS SUBMITTED TO THE DEPARTMENT OF CIVIL ENGINEERING IN
PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
by
TohurAhmed
1111111111111111111111111 111111 III#92763#
CIVIL ENGINEERING DEPARTMENT
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
(BUET)
DECEMBER, 1997
BEHAVIOUR OF BRICK MASONRY COLUMNS WITH FERROCEMENT OVERLAY
Approved a&to &tyleand content by
Dr. Jamilur Reza ChoudhuryProfe&&OrCivil Engineering Dept.Banglade&h Univer&ity ofEngineering and Technology
Dr. Sk. Sekender AliProfe&&OrCivil Engineering Dept.Banglade&h Univer&ity ofEngineering and Technology
Dr. Md Hossain AliProfe&&orand HeadCivil Engineering Dept.Banglade&h Univer&ity ofEngineering and TechnQlogy
Dr. Sohrabuddin AhmadProfe&&OrCivil Engineering Dept.Banglade&h Univer&ity ofEngineering and Tec!m<?logy
Dr. Md Wahhaj UddinProfe&&or --Mechanical EngineeringI?ept.Banglade&h Univer&ity ofEngineering and TechnQlogy
Dr. Md A. MansurM&ociate Profes&OrCivil Engineering Dept.National Univer&ity of SingaporeSingapore
~At.'Member (Co-Supervi&Or)
!Y .it. ~.Member
~-!MMember
.~. ,
Member (Extep1al)
CERTIFICATE
I hereby certify that the work embodied in this thesis is the result of original research
and has not been submitted for a higher degree to any other University or Institute.
Tohur Ahmed
ABSTRACT
This thesis presents a comprehensive finite element study of the composite behaviour
of brick masonry column with ferrocement overlay. The ANSYS package available
at BUET Computer Centre has been used to perform this fmite element analysis. The
model considers the columns as a composite of three types of materials viz. bricks,
mortar matrix and ferrocement.
The nonlinear response of the column is produced by a combination of nonlinear
deformation characteristics and progressive failure of the constituent materials. The
material properties for the analytical model are determined from tests on samples of
ferrocement, bricks, mortar and small brick masonry specimens.
A total of 48 columns were tested in this study. The investigations were carried out
under only concentric and eccentric. short term static loading. The application of
ferrocement overlay on the bare masonry column increases the load carrying
capacity of the column quite significantly. With the increase of cross sectional area
of column by 46% due to addition of ferrocement overlay, the average increase in
strength is found to be 184% for axial loading and 158% for eccentric loading.
The results of the finite element analysis are verified by comparison with the
uniaxial behaviour of masonry column with ferrocement overlay. Several
parameters like type of ferrocement overlay, discontinuity in ferrocement overlay,
mortar proportion and number of layers of wire mesh were varied to produce
variations in behaviour and in failure modes of the specimens. In general, the
agreement between finite element analysis and experiment in case of failure load,
failure pattern and load-deformation characteristics is good.
vii
Sensitivity analyses of various parameters like bed joint thickness, tensile and
compressive strength of mortar, brick and ferrocement, number of layers of wire
mesh and modulus of elasticity and Poisson's ratio of brick and ferrocement, defining
the material model were carried out using the finite element model. The following
parameters were found to be the most significant in the range of values considered in
the study:
i) the compressive strength of ferrocement mortar (range: from 15MPa to 20 MPa)
ii) the tensile strength of brick (range: from 0.5 MPa to 2.25 MPa)
iii) the thickness ratio of bed joint and brick (range: from 0.045 to 0.30).
The finite element program available in ANSYS package has also been used to carry
out a comprehensive parametric study of the composite behaviour of ferrocement-
coated masonry column subjected to axial and eccentric short term static loading.
The parameters related to the strength and deformation characteristics of the
constituent materials of the composite (as listed in the preceding paragraph) were
considered in this study. From the parametric study, empirical equations are derived
to predict the ultimate loads of the ferrocement coated masonry column.
ACKNOWLEDGMENT
The author wishes to express his indebtedness to Dr. J.R. Choudhury, Professor of
Civil Engineering, Bangladesh University of Engineering and Technology, under
whose supervision the work was carried out. The author also expresses his
indebtedness to the Co-supervisor of this work Dr. Sk. Sekender Ali, Professor of
Civil Engineering, Bangladesh University of Engineering and Technology. Without
their constant guidance and invaluable suggestions at every stage, this work could
not have possibly materialized.
The author is grateful to the members of his Doctoral committee for their
suggestions and fruitful discussions at various phases of progress of this research.
The author acknowledges with gratitude the valuable suggestions of Dr.
Sohrabuddin Ahmad, Professor of Civil Engineering, BUET and a member of the
Doctoral Committee during the preparation of the thesis.
The support of the laboratory staff of the Department of Civil Engineering during
the course of experiments is gratefully acknowledged. The author also likes to
acknowledge the suggestions and services received from the Director and other
members of staff at the Computer Centre of BUET. The donation of the software
package ANSYS to BUET by Dr. S.M. Yunus and Dr. Ashraf Ali of ANSYS, USA
is very much appreciated as this software played a key role in the finite element
analyses carried out as part of this thesis.
The author gratefully acknowledges the financial support received during this work
from BUET and BIT, Rajshahi. The author also acknowledges the moral support
and suggestions from the faculty members of BIT, Rajshahi as well as from the
Department of Civil Engineering, BUET.
CONTENTS
Acknowledgment v
Abstract VI
Notation xiii
List of Figures xv
List of Tables xvii
1. INTRODUCTION
1.1 General
1.2 Objective of the Research
1.3 Scope of Work
1
4
5
2. LITERATURE REVIEW
2.1 Introduction 72.2 Material Properties 10
2.2.1 Properties of Ferro cement 102.2.1.1 Strength Properties 102.2.1.2 Deformation Characteristics 12
2.2.2 Properties of Brick 132.2.2.1 Compressive Strength 132.2.2.2 Tensile Strength 142.2.2.3 Other Properties of Brick 15
2.2.3 Properties of Mortar 162.3 Brick Masonry Properties 17
2.3.1 Masonry Compressive Strength 172.3.2 Masonry Tensile Strength 18
•2.3.3 Deformation Characteristics of Masonry 182.4 Experimental Investigations of Columns 192.5 Remarks 22
3. ELASTIC FINITE ELEMENT ANALYSIS
3.1 Introduction23
3.2 Finite Element Method24
3.3 Three-dimensional Linear Elastic Finite Element Model 25
3.4 Cases Analysed25
3.5 Method of Load Application 27
3.6 Comparison Between Homogeneous and Nonhomogeneous Material
Models Used in Analysis 32
3.7 Parametric Study 35
3.7.1 Types of Overlays 35
3.7.2 Thickness of Ferrocement Overlay 35
3.7.3 Number of Mesh Layers in the Overlay 37
3.7.4 Modular Ratio of Ferro cement Overlay and Brick Masonry 40
3.7.5 Thickness of Bed Joint 40
3.7.6 Confinement Effect of Ferro cement Overlay 42
3.7.7 Eccentricity of Loading 44
3.8 Summary 49
4. PROPERTIES OF FERROCEMENT, BRICK, AND MORTAR
4.1 Introduction 51
4.2 Ferrocement Properties 51
4.2.1 Tensile Strength of Ferro cement 51
4.2.2 Compressive Strength of Ferro cement 524.2.3 Stress-strain Characteristics of Ferro cement 53
4.2.4 Poisson's Ratio of Ferro cement 53
4.3 Properties of Brick 564.3.1 Compressive Strength of Brick 57
4.3.2 Tensile Strength of Brick 57
4.3.3 Deformation Characteristics of Brick 58
4.3.4 Poisson's Ratio of Brick 61
4.4 Mortar Properties 62
4.4.1 Compressive Strength of Mortar 62
4.4.2 Tensile Strength of Mortar 62
4.4.3 Stress Strain Characteristics of Mortar 63
4.4.4 Poisson's Ratio of Mortar 66
4.5 Summary69
5. EXPERIMENTAL INVESTIGATION
5.1 Introduction71
5.2 Experimental Study 71
5.2.1 Test Programme 71
5.2.2 Column Details 73
5.2.3 Construction of Column 75
5.2.4 Testing of Columns 80
5.2.5 Failure Load 83
5.2.6 Modes of Failure 83
5.2.7 Stress-strain Characteristics 88
5.3 Confmement Effect of Ferro cement Overlay on Masonry Core 88
5.4 Influence of Overlay on Cost of Columns 91
5.5 Summary 93
6. NONLINEAR FINITE ELEMENT ANALYSIS
6.1 Introduction 95
6.2 Analysis of the Columns 95
6.2.1 Material Deformation Characteristics and Failure Criteria 96
6.3 Method of Load Application 96
6.4 Failure Modes 97
6.5 Failure Load 100
6.6 Confmement Effect of Ferrocement Overlay 102
6.7 Stress-strain Characteristics 103
6.8 Summary 106
7. COMPARlSON OF RESULTS FROM FINITE ELEMENT ANALYSIS ANDEXPERIMENTAL RESULTS
7.1 Introduction 108
7.2 Initial Cracking Load108
7.3 Failure Load111
7.4 Failure Pattern112
7.5 Stress-strain Curves115
7.6 Confmement Effect115
7.7 Summary117
8. SENSITIVITY ANALYSIS OF CRITICAL pARAMETERS
8.1 Introduction119
8.2 Linear Elastic Fracture Analysis 120
8.3 Influence of Various Parameters on the Material Model 124
8.3.1 Elastic Properties of the Constituents Materials 124
8.3.2 Bed Joint Thickness 126
8.3.3 Tensile Strength of Mortar 127
8.3.4 Compressive Strength of Mortar 128
8.3.5 Brick Tensile Strength 129
8.3.6 Brick Compressive Strength 131
8.3.7 Tensile Strength of Ferro cement 131
8.3.8 Compressive Strength of Ferrocement 132
8.3.9 Number of Layers of Wire Mesh 133
8.3.10 Element Size 134
8.3.11 Slenderness Ratio 135
8.3.12 Boundary Conditions 136
8.4 Summary 138
9. RECOMMENDATION OF DESIGN PROCEDURE
9.1 Introduction
9.2 Proposed Design Formulae
9.3 Example Problems
141
141
143
1489,4 Summary
10. SUMMARY AND CONCLUSIONS
10.1 Summary
10.2 Conclusions
149
153
REFERENCES
APPENDIX I
APPENDIX II
APPENDIX III
APPENDIXN
APPENDIX V
APPENDIX VI
APPENDIX VII
APPENDIX vrnAPPENDIX IX
155
Properties of Ferro cement, Brick, Mortar and BrickworkA.l
Quality Control Test Results A.20
Finite Element Formulation A.23
Typical ANSYS Data File A.38
Failure Pattern of Different Columns (Experiment) A,43
Failure Pattern of Different Columns (FEA) A.59
Comparison of Failure Mode and Stress-Strain Curve A.73
Derivation of Proposed Design Formulae A.97
Comparison of Proposed Design Formulae and
Finite Element Analyses A.I06
xiii
NOTATION
Abm Cross-SectionalArea of BrickMasonry
Afrn Cross-SectionalArea of Ferrocement
Al Loaded Area
At Total Cross-SectionalArea
BZA Bare, zero layer ofwire mesh and axial loading
BZE Bare, zero layer ofwire mesh and eccentric loading
DDA Discontinuous,double layer of wire mesh and axial loading
DSA Discontinuous, single layer of wire mesh and axial loading
Eb Modulus of Elasticity of Brick
Ebm Modulus of Elasticity of BrickMasonry
bfrn Modulus of Elasticity of Ferrocement
Em Modulus of Elasticity ofMortar
e Eccentricity
feb Compressive Strengthof Brick
fefrn CompressiveStrengthof FerrocementMortar
ftb Tensile Strengthof BrickGDA Top andbottom gap, double layer of wire mesh and axial loading
GSA Top and bottom gap, single layer of wire mesh and axial loading
h Depth of ColumnHDA Hollow, double layer of wire mesh and axial loading
HSA Hollow, single layer of wire mesh and axial loading
Pexpt Failure Load ofColurnn (Experimental)
Prem Failure Load ofColurnn (Analytical)
PuIe Failure Load ofColurnn (LinearElastic Fracture Analysis)
Pu,nl Failure Load ofColurnn (NonlinearAnalysis)
Pult Failure Load ofColurnn (proposed Design Formula)
tb Thickness of Brick
tm Thickness of MortarNDA Normal, double layer of wire mesh and axial loading
xv
LIST OF FIGURES
3.1 Three-Dimensional Finite Element Idealization(Quarter Column Cross-Section) 26
3.2 Transverse Stress Distribution Along Column Center Line(Top and Bottom Nodes Restrained Laterally) 29
3.3 Transverse Stress Distribution Along Column Center Line in Case ofUniform Displacement 30
3.4 Variation of Top Displacement 31
3.5 Transverse Stress Distribution Along Column Center Line in Case ofPlaster Overlay 33
3.6 Transverse Stress Distribution Along Column Center Line in Case ofFerrocement Overlay 34
3.7 Transverse Stress Distribution Along Column Center Line by VaryingType of Overlay 36
3.8 Transverse Stress Distribution Along Column Center Line forDifferent Thickness of Ferrocement Overlay 38
3.9 Transverse Stress Distribution Along Column Center Line for DifferentNumber of Mesh Layers 39
3.10 Transverse Stress Distribution Along Column Center Line for DifferentModulus of Elasticity of Ferro cement Overlay 41
3.11 Transverse Stress Distribution Along Column Center Line forDifferent Thickness of Bed Joint 43
3.12 Finite Element Mesh for Ferrocement Coated Column with Vertical Groove 45
3.13 Transverse Stress Distribution Along Column Center Line in Case ofDiscontinuous Ferrocement Overlay 46
3.14 Finite Element Mesh for Eccentric Load Case 47
3.15 Transverse Stress Distribution Along Column Center Line in Case ofEccentric Loading 48
4.1 Uniaxial Compression Test on Hollow Ferrocement Block 54
4.2 Average Stress-Strain curve of Ferro cement Loaded in Uniaxial Compression 55
4.3 Lateral vs. Longitudinal Strain for compression Test of Ferro cement 56
4.4 Uniaxial Compression Test on Stack Bonded Prism 59
4.5 Stress-Strain Curve for Brick, Brickwork and Mortar Obtained fromPrism Test 60
xvi
4.6 Lateral vs. Longitudinal Strain of Brick 61
4.7 Uniaxial Compression Test on Mortar Cylinder 64
4.8 Stress-Strain Curve of Mortar (1:5) 64
4.9 Stress-Strain Curve of Mortar (1:2) 65
4.10 Lateral vs. Longitudinal Strain for Mortar (1:5) 67
4.11 Lateral vs. Longitudinal Strain for Mortar (1:2) 67
5.1 Different Types of Column 74
5.2 Column During Construction 78
5.3 Mould for Ferrocement Hollow Column 78
5.4 Column (DDAlDSA) During Construction 79
5.5 Column (DDAlDSA) After Construction 79
5.6 Curing of Column in the Laboratory 81
5.7 The Specimen Before Test 81
5.8 Failure of Column Coated with Ferrocement Series NDA (Axial Loading) 87
5.9 Experimental Stress-Strain Curves of Different Columns 89
6.1 Predicted Failure Mode of Column Series NDA 98
6.2 Predicted Failure Mode of Column Series NSA 99
6.3 Stress-strain Curve of Different Columns with Axial Load Obtained fromFEM Analysis 104
6.4 Load-strain (Compressive Side)Curve for Different Columns withEccentric Load Obtained from FEM Analysis 105
7.1 Failure Mode of Column Series NSA 113
7.2 Stress-Strain Curve of Column Series NDA 114
7.3 Stress-Strain Curve of Column Series NSA 114
8.1 Mode of Failure of Column Series NDA 121
8.2 Mode of Failure of Column Series NSA 122
8.3 Mode of Failure of Column Series NZAW 123
9.1 Comparison of Proposed Design with Finite Element Analysis forAxial Load Case 144
9.2 Comparison of Proposed Design with Finite Element Analysis forEccentric Load Case 145
XVll
LIST OF TABLES
4.1 Summary of Ferro cement Properties 52
4.2 Summary of Brick Properties 61
4.3 Summary of Mortar (1:2) Properties 68
4.4 Summary of Mortar (1:5) Properties 68
5.1 Test Programme 72
5.2 Description of Specimens 76
5.3 Summary of Load Tests 82
5.4 Experimental Cracking and Failure Loads (Axial Loading) 84
5.5 Experimental Cracking and Failure Loads (Eccentric Loading) 85
5.6 Load Increase in Failure Due to Confinement Effect (Derived from
Experiments) 90
5.7 Material Cost of Different Columns 92
6.1 Analytical Cracking and Failure Loads (Axial Loading) 100
6.2 Analytical Cracking and Failure Loads (Eccentric Loading) 101
6.3 Load Increase in Failure Due to Confinement Effect (Derived from Analysis) 103
7.1 Analytical and Experimental Cracking and Failure Load (Axial Loading) 109
7.2 Analytical and Experimental Cracking and Failure Load (Eccentric Loading) 110
7.3 Load Increase in Failure Due to Confinement Effect 116
8.1 Influence of Linear Elastic Fracture Analysis 124
8.2 Parametric Study of Elastic Properties (EmlEnJ and Vfin 125
8.3 Parametric Study of Elastic Properties (EJEm) Vb 125
8.4 Influence of Bed Joint Thickness 127
8.5 Influence of Tensile Strength of Mortar 128
8.6 Influence of Compressive Strength of Mortar 129
8.7 Influence of Tensile Strength of Brick 130
8.8 Influence of Compressive Strength of Brick 131
8.9 Influence of Tensile Strength of Ferro cement 132
8.10 Influence of Compressive Strength of Ferro cement 133
xviii
8.11 Influence of Number of Mesh Layers 1348.12 Influence of Mesh Size in Finite Element Discretization 1358.13 Influence of Slenderness Ratio 1368.14 Influence of Boundary Conditions 1379.1 Failure Load Obtained from Different Methods 147
CHAPTER!
INTRODUCTION
l.1GENERAL
Structures built of stone or stone-like materials are known as masonry structure. In a
primitive form, they were among the earliest types of structures erected by man. The
enduring character of masonry structure, the relative simplicity of the processes
involved, the pleasing outlines usually obtained, together with the almost universal
availability of the materials and the consequent moderate cost, render masonry
construction one of the most important of the civil engineer's activities. Moreover,
the importance of masonry construction is likely to be enhanced in future by the
growing scarcity of other structural materials, notably steel and timber, and the fact
that the ingredients of masonry are almost unlimited in their raw state.
Now-a-days some buildings are used for purposes other than those in the original
design. Sometimes, intermediate floors are added and this involves higher loads on
slabs, beams, columns and foundations. These structures were usually constructed
from bricks or concrete blocks and in older cases stones. These units are tied together
by mortar (e.g. sand-cement mixture) and in some cases, steel or other
reinforcement.
There are several types of masonry structural elements within a building, e.g.
columns and walls. Columns are the primary vertical load carrying members of a
typical multi-storey building. The loads coming on the floors and beams are
transmitted to the foundation through these columns. These columns are also called
upon to resist lateral loads on the building due to wind and/or earthquake. Efforts
have been made in recent years to improve the performance of brick columns in
2
seismic areas by applying ferrocement overlay. The concept has been intuitively
applied for repair of distressed elements as well.
Ferrocement is a type of thin wall reinforced concrete commonly constructed of
hydraulic cement mortar reinforced with closely spaced layers of continuous and
relatively small wire diameter mesh. The mesh may be made of metallic or other
suitable materials. Ferrocement is a versatile construction material and confidence in
the material is building up resulting in its wider applications especially in developing
countries in housing, sanitation, agriculture, fisheries, water resources, water
transportation in freshwater and marine environment, biogas structures, repair and
strengthening of older structures, and others.
Considered to be an extension of reinforced concrete, ferrocement has relatively
better mechanical properties and durability than ordinary reinforced concrete. Within
certain loading limit, it behaves as a homogeneous elastic material and this limit is
wider than those for normal concrete. The uniform distribution and high surface area
to volume ratio of its reinforcement result in better crack arrest mechanism, and
hence better use of its strength.
Although developed more than one hundred and fifty years back, use of ferrocement
composites is comparatively recent and is expanding. Ferrocement overlay is used
now-a-days to increase the ductility of masonry columns and walls. Ferrocement
composite column means a column having a ferrocement casing and a core of
brickwork or concrete (plain or reinforced). The casing may be circular, square or
rectangular depending on the shape of the column. Such columns may have
applications in three situations. Firstly, for prefabricated construction, where the
outer casing will be precast in a factory and concrete is poured into it at the site.
Secondly, for normal construction in which the ferrocement casing is cast in short
heights and filled with concrete. The third application may be for strengthening of
3
existing columns. In the first two cases the need for column formwork is eliminated
but there is a major structural difference between the two. In the first case, the core
shrinks after casting while the casing undergoes shrinkage before casting of the core.
Hence a weak interface may exist between the core and the shell. This is ail
important factor for the confinement effect of the central core.
In formulating design recommendations for axial and eccentric loads on columns,
simplifications are usually made because of the difficulty in obtaining sufficient
experimental data and realistic analysis of column behaviour. The prediction of
failure of such composite columns is difficult due to a large number of parameters
influencing the ultimate behaviour of column, the lack of a suitable material model,
and an efficient numerical technique.
To establish the critical parameters which influence the behaviour of bare masonry
columns and columns with ferrocement overlay, a linear elastic finite element
analysis has been performed using ANSYS package (26). A three-dimensional
analysis is carried out assuming brick masonry to be a homogeneous continuum as
well. as an assemblage of elastic bricks and joints, each with differing material
properties.
To realistically predict failure of such composite column a more sophisticated
material model is required. This model must reflect the inelastic nature of the
constituents as well as the progressive failure that occurs as the applied load is
increased. TIle material model required for such an analysis is microscopic rather
than macroscopic in nature with bricks and joints being modeled separately. The
properties needed to defme this material model available in ANSYS package is
obtained here from various simple tests on sample of bricks, mortar, small brick
masonry specimens and ferrocement specimens thus avoiding the need for more
4
complex testing apparatus. The model consists of elastic and inelastic deformation
characteristics, cracking and crushing of the constituent materials.
Both coated and uncoated brick masonry columns have been analysed in this study
by using finite element technique available in the ANSYS package. Sensitivity
analyses of the various parameters used in the fInite element analyses have also been
carried out. These analyses highlight the importance of the accurate evaluation of
deformation characteristics and strength characteristics of the masonry constituents.
The [mite element analysis is used here to carry out a comprehensive parametric
study of the behaviour of the composite columns. This study illustrates the potential
of the model both as a research tool and as a means of preparing design procedures
for practical use. From the results of the parametric study, design formulae for
predicting the ultimate loads for both axial and eccentric cases of the column have
been proposed.
1.2 OBJECTIVES OF THE RESEARCH
The principal objectives of the study are as follows:
1. The establishment of critical parameters influencing the behaviour of both
coated and uncoated brick columns using three-dimensional finite element
analysis.
2. VerifIcation of the accuracy of the material model used in the [mite element
analysis in predicting the failure loads by conducting experiments on columns
with ferrocement overlay subjected to axial as well as eccentric loading.
3. Investigation of the influence of various parameters involved in the composite
behaviour of brick column and ferrocement overlay.
5
4. The development of a design method for brick columns with ferrocement
overlay.
1.3 SCOPE OF WORK
The study is limited to masonry columns with burnt clay bricks and sand-cement
mortar, subjected to concentric and eccentric short term static loading.
A fInite element computer program (ANSYS) is used to examine the behaviour of
brick masonry column with ferrocement overlay. The nonlinear fInite element
computer program (ANSYS) used in this study will be broadly applied to investigate
its adequacy to:
(i) develop the complete load-deformation response of the columns; and
(ii) predict the ultimate load carrying capacity of the columns.
The effects of the following different parameters will be studied:
(i) Elastic properties of the constituents
(ii) Bed joint thickness
(iii) Tensile strength of mortar
(iv) Compressive strength of mortar
(v) Tensile strength of brick
(vi) Compressive strength of brick
(vii) Tensile strength offerrocement
(viii) Compressive strength offerrocement
(ix) Number oflayers of wire mesh
(x) Element size
6
(xi) Slendernessratio
Themajor parameters in the experimental investigationare
(i) Types of overlay
(ii) Number oflayers of wire mesh in the overlay
(iii) Discontinuities in the ferrocementoverlay
(iv) Types ofloading
CHAPTER 2
LITERATURE REVIEW
2.1 INTRODUCTION
Brick masonry columns are common in low-rise masonry buildings. They may be
reinforced or unreinforced, and commonly of square or rectangular and occasionally
circular cross-section. Although the performance of masonry column under axial
load may be satisfactory, they possess very limited capacity in bending. Encasement
by ferrocement can be a simple way.to increase the axial load carrying as well as
moment resisting capability of brick masonry columns.
This chapter reviews the literature on various aspects of this problem. Since brick
masonry and ferrocement have been used in this investigation, the material properties
of ferroCement and brick masonry are also reviewed. This is followed by a review of
failure mechanism of the constituent materials. Previous finite element models for
the analysis of ferrocement and masonry are then described. Since the number of
investigations made on masonry structural elements coated with ferrocement is very
limited, relevant works on the behaviour of concrete columns are also reviewed
here, because many of the parameters are very similar.
The fIrst large scale modem experimental research on reinforced brickwork (RB) has
been reported by Brebner in 1973 (17). This had established the applicability Of
working stress theory. However, subsequent research justify the use of ultimate
strength theory for the design of RB in flexure. The current British practice is to
design RB on the basis of ultimate strength design for both flexure as well as
compression (37). The Indian practice is similar, but makes use of the limit state
concept for flexure (23). Experiments at University of Roorkee (2, 24, 45, 57) have
shown that Whitney's ultimate stress block is somewhat approximate for RB in
"
8
flexure but, with some modifications, can be applied to it. If a RB column is
subjected to purely axial load, then its ultimate compressive load will be the sum of
the ultimate loads of masonry and reinforcement. However, as loads are commonly
eccentric, the effect of moment has to be considered also. The interaction diagram for
compression and flexure on the basis of ultimate strength has been provided by
Curtin (22).
Ferrocement encasement of a column can considerably increase its capacity to resist
compressive load and moment. This is a new concept of reinforcing a masonry
column and holds out a promise for economy. It can also be applied for repairing
distressed columns. However, the existing load should be removed before using
ferrocement for repairs (74).
The procedure consists of wrapping the layers of wire mesh around the columns
using some suitable arrangement like driving the V-nails through the mesh into the
column (82). A rich mortar having cement:sand ratio of 1:1.5 to 1:3 is then applied
over the mesh and made to penetrate the mesh and adhere to the column surface. On
setting, it forms a casing around the column.
It is well known that in a vertically loaded brick masonry column, cracks always
initiate from the vertical mortar joints and propagate through the bricks. TransverSe
stresses are mainly responsible for influencing the fracture process in this case. To
realistically predict the strength of such column, a numerical model capable of
predicting the ultimate failure of masonry subjected to any general loading is
required.
To develop a representative fmite element model for the analysis and design of
masonry structures with ferrocement overlay, a thorough knowledge of the
deformation and strength characteristics of the materials as weil as the masonry
9
assemblage is needed. Some models of this type have been developed (8), but they
are not necessarily suited to the analysis of brick masonry with ferrocement overlay.
Therefore a three-dimensional modeling is necessary to predict the composite
behaviour of brick masonry with ferrocement overlay.
The existing design rules for masonry columns are empirical and are not applicable
to masonry columns with ferrocement overlay. The design rules vary from country to
country, justifying the need for a comprehensive study in this area.
According to BNBC (97) the allowable axial compressive stress for unreinforced
masonry column is
F. = f~[1-(i-J 3]a 5 42t
where,
F. = allowable average axial compressive stress
f~= specified compressive strength of masonry
h' = effective height of column
t = effective thickness of column
The compressive strength of brickwork varies, roughly, as the square root of the
nominal brick crushing strength, and as the third or fourth root of the mortar cube
strength (37).
10
2.2 MATERIAL PROPERTIES
Brick masonry column with ferrocement overlay is a composite of three materials
and its properties are therefore dependent upon the properties of its constituents- the
ferrocement, the brick and the mortar joint. A brief review of the properties relevant
to the in-plane behaviour of masonry and the behaviour of ferrocement are carried
out in this section.
2.2.1 Properties of Ferrocement
In general, a composite material consists of a matrix and a reinforcement which act
together to form a new material with characteristics superior to either one of its
constituents alone (86). Ferrocement is a composite material which contains a high
percentage of ductile steel wire mesh with a high surface area to volume ratio in a
brittle cemcut-mortar matrix. This enables the matrix to assume the ductile
characteristic of the reinforcement. Usual range of wire diameter from 0.5 mm to 1.5
mm. Provision of reinforcement in excess of about 2 to 2.5% is uneconomical in
ferrocement as the proportional increase in strength is not achieved (86).
2.2.1.1 Strength Properties
The strength of ferrocement, as in ordinary concrete, is commonly considered as the
most valuable property, although in many practical cases other characteristics, such
as durability and permeability may in fact be more important. Nevertheless, strength
always gives an overall picture of the quality of ferrocement, as strength is directly
related with the properties of its hardened cement paste and reinforcement.
11
Tensile Strength
The tensile characteristics of ferrocement have not yet been fully defined and
standardized. In tension, the load-carrying capacity is essentially independent of
specimen thickness because the matrix cracks well before failure and does not
contribute directly to composite strength. The influence of types, sizes and volumes
of wire meshes on elastic cracking and ultimate behaviour offerrocement in uniaxial
tension have been studied by Naaman and Shah (58). They observed that the ultimate
tensile strength of ferrocement is the same as that of mesh alone while its modulus of
elasticity can be predicted from those of mortar and mesh (46, 58, 66, 90). The
specific surface of the reinforcement strongly influences the cracking behaviour of
ferrocement. Some technical information have been released (51, 59), but their
results seem to be specific to certain types of mesh reinforcement. In general, the
optimal choice of reinforcement for ferrocement strength in tension depends on
whether the loading is essentially uniaxial or significantly biaxial. Expanded metal in
its normal orientation is more suitable than other reinforcing meshes for uniaxial
loading because a higher proportion of the total steel is effective in the direction of
applied stress (46). For biaxial loading, square mesh is more effective because the
steel is equally distributed in the two perpendicular directions, although the weakness
in the 45 deg direction may govern in this case.
Compressive Strength
In this mode, unlike tension, the matrix contributes directly to ferrocement strength
in proportion to its cross-sectional area. Compressive strength of ferrocement
(regardless of the amount of mesh reinforcement) seems to be much the same as that
of mortar alone (70). The experimental results showed that under compression the
ultimate compressive strength is lower than that of equivalent pure mortar (66). The
compressive strength at ultimate condition is assumed to be 0.85fc where fc is the
ultimate compressive strength of the mortar. An investigation into the behaviour of
12
ferrocement specimen in direct compression has been discussed by Rao (70).
Conclusions were drawn with respect to the effect of percentage of reinforcement
and the size of reinforcement on the behaviour of ferrocement. Smaller diameter wire
mesh would be preferable to use as this gives higher elasticity and higher ultimate
compressive strengths for the same percentage of reinforcement, all the other factors
remaining essentially the same. When mesh reinforcement is arranged parallel to the
applied load in one plane only, no improvement in strength is observed (66). The
only forms of reinforcement likely to result in significant strength gains in
compression are square mesh reinforcements (86) fabricated in closed box or
cylindrical arrangements which restrain the matrix, thus forcing it to adopt a triaxial
stress condition with associated higher strength.
2.2.1.2 Deformation Characteristics
Following the consideration of ultimate and cracking strengths, it is appropriate t6
examine the overall load-deformation behaviour of ferrocement under various forms
of loading, in particular its modulus of elasticity.
Load Deformation Behaviour in Tension
For square mesh reinforcements, the load-elongation behaviour of ferrocement has
been characterised in three stages (58, 61, 66). In the initial stage, the matrix and
reinforcement act as a continuum having a composite elastic modulus approximately
equal to that predicted from the volumetric law of mixtures of the longitudinal
reinforcement and the matrix (55, 66). The second stage, associated with a fully
cracked matrix, is also linear. Its modulus is somewhat greater than the product of
the volume fraction and the modulus of the longitudinal reinforcement. The mortar
and the lateral reinforcement continue to play an active role after first cracking, either
13
individually or in combination (55,66). In the third stage, the matrix ceases to playa
role. Failure corresponds to the yielding of the reinforcement.
Load Deformation Behaviour in Compression
When the reinforcement is in one plane only, it has a minimal effect on the load-
deformation relationship, and the associated elastic modulus remains virtually the
same as that for the mortar matrix (66). When present in closed peripheral form, the
load-deformation relationship is curvilinear with the initial tangent modulus
increasing gradually with the amount of reinforcement (46). The initial elastic
modulus can be predicted quite accurately and conservatively on the basis of the
volumetric influence of the two material components acting together (71). Values of
the elastic modulus are slightly higher for specimens reinforced with welded mesh
than for their equivalents with expanded metal (46). The experimental results
obtained by various investigators (51, 70) show that the modulus of elasticity in
direct compression increases proportionately with the increase in steel content.
Studies on mechanical properties of ferrocement have been made since the early
1970s but studies on formulation of these properties based on fundamental material
properties has begun only recently. Some of its mechanical properties have not been
sufficiently investigated yet and not enough technical information is available to
suggest acceptable formulae for design.
2.2.2 Properties of Brick
2.2.2.1 Compressive Strength
Compressive strength of brick is one of the most important properties. Compressive
strength tests are easy to perform and give a good indication of the' general quality of
the brick and the compressive capacity of the resulting masonry. For these reasons,
14
the compressive strength test has been traditionally used for brick quality control and
specification.
The standard test for the determination of compressive strength can be influenced by
several factors such as loading rate (35), specimen size (9, 31, 69), perforation
pattern (9, 91, 93) and specimen end conditions (14, 29, 63). However, standard test
provides a basis for quality control and for making relative assessment of the strength
of brick masonry.
The standard test described in the Australian code for concrete masonry units (10)
requires the use of plywood packing on the top and bottom face of the specimen.
Such test results are influenced by the stiffness of the plywood and the frictional
restraint imposed by the solid platen, resulting in an artificial value of compressive
strength. Several investigators have attempted to minimize the effects of platen
restraint by using platens with variable stiffnesses (29, 62) and/or capping materials
(14, 79) on the specimens. Flexible steel brush platens have also been used
successfully for the testing of both concrete (49) and masonry (63, 64). An indication
of the magnitude of this strengthening effect has been given (65) from compression
tests on calcium silicate bricks. Steel brush and solid platens were used in tests on
bricks of varying size and shape. For standard size bricks, the unconfined
compressive strength (with brush platens) was found to be almost half the confined
compressive strength (with solid steel platens). This effect must therefore be
considered when assessing the compressive strength of a material.
2.2.2.2 Tensile Strength
Brick tensile strength has a significant influence on the in-plane behaviour of brick
masonry, as fmal failure usually occurs in some form of biaxial tension, split often
originating in the brick. When brick masonry is loaded in axial compression, for
15
example, lateral expansion of the brick and mortar takes place. Since the mortar
joints are typically more flexible than the bricks, the joint deformation is partially
restrained by the surrounding bricks due to the bond and friction at the brick-mortar
interface. This results in a triaxial compression stress state in the mortar and
compression iUldbilateral tension in the brick. Since the tensile strength of the brick
is low (much lower than its compression strength), failure of brick masonry is
initiated by tensile stresses.
Numerous attempts have been made to determine a convenient relationship between
the brick tensile strength obtained from a simple test and wall strength. Various
tension tests have been investigated, including modulus of rupture tests, splitting
tests (Double Punch or Brazil tests), and various form of shear tests including
indirect tension.
The effect of size, shape and disposition of the perforation on the tensile strength of
brick has been studied (9, 93). Significant reduction in the tensile strength of bricks
was reported in the case of bricks with perforation patterns which produce significant
stress concentration.
Despite the extensive research that has been carried out, no strong relationship
between brick tensile strength and brick masonry strength has emerged. As a result,
. brick compressive strength is still used as the prime indicator of the potential
compressive strength of the assemblage.
2.2.2.3 Other Properties of Brick
There are several other brick properties such as brick growth, pitting, efilorescence,
permeability, dimensional change, etc., which have a significant influence on the
satisfactory performance of masonry structure. However, most of these properties are
16
related to the physical and chemical characteristics of the brick and do not influence
the masonry strength. However the property that does significantly influence brick
masonry strength is the initial rate of absorption (IRA.) or brick suction. Brick
suction plays an important role in the achievement of bond and, as such, significantly
influences both the compressive and tensile strength of the masonry (8).
2.2.3 Properties of Mortar
Mortar in brick masonry has three main functions:
(i) To provide an even bed for the bricks
(ii) To bond the bricks together effectively
(iii) To seal the joint against weather
To perform these functions, mortar should possess suitable properties in both the
elastic and hardened states. These properties are briefly described in the following
section.
In its plastic state, the required properties are its good workability, good water
retentivity and sufficient early stiffening. Mortar workability depends upon the brick
and mortar properties, in particular, water retentivity of the mortar and the initial rate
of absorption of the brick. These two latter properties have also a marked effect on
the bond strength of the resulting brick masonry. Good water retention is required for
several reasons. It is needed to resist brick suction, to prevent bleeding of water from
the mortar, to prevent stiffening of the mortar bed before placement of the brick, and
to ensure retention of sufficient water in the mortar to allow hydration of the cement.
In its hardened state, the required properties are compressive strength, bond strength
and tensile strength. The compressive strength of the mortar is not an important
property since in masonry, the emphasis is on the achievement of adequate bond
17
between mortar and brick. However, it serves as an indicator of quality control. It
may be determined using either cube or prism tests. The compressive strength of
mortar as a function of shape, curing, age, air content and initial flow rate of mortar
(34).
2.3 BRICK MASONRY PROPERTIES
The two strength characteristics which ensure satisfactory performance of masonry
structures (specially for columns) are its compressive and tensile strengths. In
addition, the deformation characteristics of masonry are required for assessing the
stress distributions and relative movements under loads.
2.3.1 Masonry Compressive Strength
Since the majority of masonry structures are used to transmit loads in compression,
the compressive strength of the material is of prime importance.
The compressive strength of brick masonry is determined either from an approximate
relationship between brick strength, mortar type and brick masonry strength or from
compressive tests of prisms. When a more exact estimate of compressive strength is
required, a prism test is used. The strength is typically obtained from compression
tests on a series oftive high stack bonded prisms.
The influence of parameters such as brick and mortar properties, dimensional
variations, slenderness ratio, etc., on the strength of brick masonry have been
extensively reviewed by several investigators (34, 36,38, 39, 52, 56, 63, 75). The
effect of joint thickness on the compressive strength of brick masonry has been
reported (56) and a linear reduction in the compressive strength with the increase in
joint thickness has been suggested, whereas Francis et al (31) imd Chuxian (20)
suggested nonlinear relationS.
18
2.3.2 Masonry Tensile Strength
The tensile strength of brick masonry is inherently low and hence often restricts its
load carrying capacity (for both in-plane and out-of-plane loading). Under in-plane
loading, tensile failure may occur either normal or parallel to the bed joint depending
on the direction of loading. In-plane masonry tensile strength is critically dependent
on the loading direction with relation to the bed joints. This effect was first studied
by Johnson and Thompson (44) using diametrical splitting tests on circular
specimens sawn from a wall. Using this technique, by rotating the orientation of the
bed joint to the splitting force, tensile stress could be applied at varying angles to the
jointing directions.
2.3.3 Deformation Characteristics of Masonry
A knowledge of the deformation characteristics of masonry is needed to calculate the
deflection of masonry structures as well as to estimate differential movements in
buildings composed of masonry and other materials. Deformation characteristics are
also required for the numerical modeling of masonry behaviour in finite element
analysis.
Brick masonry typically exhibits nonlinear stress-strain relations. Most of the
nonlinear deformation occurs in the mortar joints with the bricks often exhibiting
linear stress-strain characteristics. Because of the influence of the bed joints and the
possible anisotropic properties of the bricks, the deformation characteristics of the
masonry are not necessarily isotropic and may vary markedly with loading direction.
Complete stress-strain relations for brick masonry have been experimentally
determined by Powel and Hodgkinson(68) and Scrivener and Williams (79) using
displacement controlled testing machines. Solid as well as perforated bricks were
19
used in their investigation. The shape of the stress-strain relations obtained was
parabolic.
2.4 EXPERIMENTAL INVESTIGATIONS OF COLUMNS
A small number of experimental investigations have been carried out to determine
the failure load of brick masonry column encased in ferrocement. Some tests have
been conducted by Nayak (60) and by Page (63), and it has been found that the
ferrocement helps in increasing the failure load. Tests were conducted by Singh et al
(82) for five different cases (3 specimens for each case) viz. plain, with plaster (1:6
and 1:2) and with two layers of square galvanished wire mesh in mortar with cement
to sand ratio of 1:6 and 1:2. Observations were made for failure loads, cracking load
and strains, and it was concluded that failure load is the lowest for unplastered
columns and highest for columns encased in ferrocement with 1:2 mortar. The failure
load of encased column was more than double the failure load of bare column.
The behaviour of ferrocement composite columns has some similarity with infilled
pipe columns. A number of investigations on R.C. pipe columns (hollow or filled)
and steel or plastic columns filled with concrete have been reported in literature. A
comparison of computer analysis of hollow R.C. spun pipe columns with
experimental results for axial and eccentric loads has been reported by Liu and Chen
(50). Furlong (30) carried out tests on steel pipe columns filled with concrete, for
axial and eccentric loading and found that there is little or no confmement effect of
cOncrete by the pipes. This might be because core concrete undergoes considerable
shrinkage, leaving a gap from the shell. An experimental investigation has been
conducted by Ghosh (33) on concrete filled steel tubes. For axial load, the strength of
concrete increases due to the effect of lateral confmement (33). This may occur as
value of Poisson's ratio of concrete near failure is considerably higher than that of
steel. Thus, under compressive load, both the core and pipe expand laterally due to
20
the Poisson's ratio effect. If the core tends to expand more than the pipe, then it
would be subjected to a lateral compression by the pipe, which in turn would be in,-
tension. An experimental investigation has been conducted by Bertero and Moustofa
(IS) on steel pipes filled with expansive cement concrete. The concrete would
expand instead of shrinking and would thus be subjected to an initial precompression
by the pipe. It is well known that compressive strength of concrete increases
considerably due to the confmement pressure. Tests on square columns with square
hoop steel (85), clearly indicate the strength increase due to lateral confinement.
Experiments on concrete filled plastic tube columns also show some effect of
confmement (48).
From the previous investigations it is clear that the confmement provided by
ferrocement should also contribute to a substantial increase in the axial load carrying
capacity of a masonry ferrocement composite column. For eccentric loads, there can
also be some strength increase. Spun ferrocement pipe columns filled with concrete
and subjected to axial and eccentric loads have been tested (77). The pipes had 0,3,5
and 7 layers of mesh. The most significant conclusion was that ultimate failure load
did not depend on number of mesh layers. In case of column without mesh, the
failure was of brittle type while with mesh it was ductile. The failure load of the
composite was not substantially different from the sum of the individual failure loads
of the core and casing, tested separately. All of these investigations (77) indicate that
the central core may not have confinement effect due to lack of proper bonding
between the core and the outside shell. This is possible due to uneven shrinkage of
these elements which are normally constructed at different times.
Bett et al conducted an experimental investigation and examined the effectiveness of
the different repairing and/Or strengthening techniques in enhancing the lateral load
response of identical reinforced concrete short columns (16). Both the strengthened
and the repaired columns performed better than the original column. Columns
21
strengthened and repaired by jacketing, with or without supplementary crossties,
were much stiffer and stronger laterally than the original unstrengthened columns.
Ersoy et al carried out two series oftests to study the behaviour of jacketed columns
(28). The main objective of the first series (uniaxially loaded) was to study the
effectiveness of repairing and strengthening of columns by jacketing with a new
layer of concrete that is reinforced with both longitudinal and transverse
reinforcement, both under sustained load and after removal of the load from the
column. Specimens repaired and strengthened by jacketing behaved well when
jacketing was introduced after the removal of the load. However, when jacketing was
made under load, the columns exhibited poor behaviour. In the second series,
jacketed columns were tested under combined axial load and bending. Two
monolithic specimens were also tested to serve as reference specimens. The
influence of load history on the behaviour of jacketed columns was also studied and
concluded that repair and strengthening jackets behaved well, both under monotonic
and reversed cyclic loadings.
An experimental investigation into the behaviour of short reinforced concrete
columns was described by Scott et al (78). Results presented include an assessment
of the effect of strain rate, amount and distribution of longitudinal steel, and amount
and distribution of transverse steel. Scott et al concluded that the longitudinal strain
rate influenced both the peak stress and the slope of the falling branch of the stress-
strain curve of the concrete core, an increase in the volume ratio of transverse
reinforcement increased the peak concrete core stress, and an increase in the number
oflongitudinal reinforcing bars resulted in better confmement of the core concrete.
An experimental study was performed by Sandowicz and Grabowski (77) on
columns both under eccentric and axial load. They presented a comparison of the
tests results of columns made of ferrocement pipes and mortar pipes, with or without
22
concrete infill, as well as concrete core alone. Ultimate load carrying capacity of
columns made of ferrocement pipes filled with concrete is higher than that of
reinforced concrete columns having similar diameters and volumetric percentage of
reinforcement. In the authors opinion, these columns are superior to spirally
reinforced concrete columns due to their ability to sustain tensile stresses.
2.5 REMARKS
It is apparcnt from the available literature that a considerable number of researchers
studied thc composite behaviour of masonry columns and reinforced columns
encased in fcrrocement overlay under uniaxial loading. From these studies they made
some conclusions about the overall performance of the composite column but no
empirical rclations of the performance emerged from their investigations. In most of
the caseS the development of these relations are handicapped due to the noninclusion
of all the relevant parameters in their observations. No theoretical investigation is
performed in these areas. A series of studies have, therefore, been initiated in the
Department of Civil Engineering, BUET, to study the behaviour of masonry column
encased in ferracement overlay. The studies include extensive laboratory
investigations and analytical studies using 3-D nonlinear finite element technique.
CHAPTER 3
ELASTIC FINITE ELEMENT ANALYSIS
3.1 INTRODUCTION
The preliminary elastic finite element study outlined in this chapter is aimed at
establishing the important parameters which influence the behaviour of brick
masonry columns with ferrocement overlay subjected to axial loads. In the analysis,
a uniform displacement of all the nodes on the top face of the column is applied to
simulate the effect of axial load. A three-dimensional analysis has been performed in
this study. Since the analysis is based on linear elastic material response, it gives
information about the nature of stress distribution and cannot be used to predict
failure.
Two types of three-dimensional fmite element analyses have been performed. One
aSsumes masonry to be a homogeneous continuum, the other considers masonry to
be an assemblage of elastic bricks and mortar joints, each with differing material
properties. In both the cases, ferrocement overlay has been modeled separately with
two component materials, viz. the mortar and the steel wire mesh as a smeared
equivalent steel thin sheet. The influence of the following parameters on the stress
distribution of ferracement coated masonry colunm is studied using the three-
dimensional fmite element analysis:
(i) Types of overlay
(ii) Thickness of ferrocement overlay
(iii) Number of mesh layers in the overlay
(iv) Modular ratio offerrocement overlay and brick masonry
(v) 111ickness of bed joint
(vi) Confinement effect offerrocement overlay
24
(vii) Eccentricity ofloading
In the comparison, emphasis has been given on the variation of transverse tensile
stresses, as these influence critically the fracture initiation of the composite column.
3.2 FINITEELEMENT METHOD
The present analytical procedure is based on the fmite element method. The
application of this method has become very common and many texts have been
written on the subject (21, 43, 96). It would thus be inappropriate to repeat the
elaborate description of the method here. The finite element method can be thought
as a general method of structural analysis by means of which the solution of a
problem in continuum mechanics may be approximated by analysing a structure
consisting of an assemblage of properly selected finite elements interconnected at a
fmite number of joints or nodal points. Recognized as one of the most versatile
methods of structural analysis, it is capable of analysing plates or solid bodies with
any irregularity in shape and physical properties. Particular advantages of this
method relating to the brickwork with ferrocement overlay are that the size, modulus
of elasticity and Poisson's ratio can be varied from element to element throughout
the composite structural element thus allowing the mortar joints and ferrocement
element to be clearly distinguished from those of bricks.
For the purpose of structural analysis, the continuum is divided by imaginary lines or
surfaces into a number of finite elements. These are assumed to be interconnected at
discrete number of nodes situated on their boundaries. The objective of the analysis,
with specified joint loading, geometry of the structure (location of joints) and
stiffness properties of the structural elements, is to fmd the resulting joint
displacements and the internal stresses in the structural elements. The size of the
elements is one of the major factors influencing the accuracy of the solution. As a
general rule, the size of the elements should be as small as possible.
25
3.3 THREE-DIMENSIONAL LINEAR ELASTIC FINITE ELEMENT MODEL
The analysis of brick columns coated with ferrocement requires three-dimensional
effects to be considered. The particular finite element computer program used for this
analysis is taken from ANSYS package (26). Eight noded three-dimensional solid
elements with three degrees of freedom at each interconnected node and linear
displacement function along their edges have been used with 2x2x2 Gaussian
integration. The details of element formulation are given in Appendix III. The finite
element idealization of the masonry column with overlay is shown in Fig. 3.1. The
computer output includes the nodal displacement, the direct stresses and shear stress
at the Gauss points as well as at the centroid of each element.
3.4 CASES ANALYSED
The Structures Laboratory at BUET is equipped with a 200 ton capacity Universal
Testing Machine. The maximum distance between platens of this machine is 1220
mm. In view of this limitation it was decided to test columns with a height of 1220
mm. The brick columns investigated were of 244 mm x 244 mm cross-section and
were made of244 mm x 116 mm x 70 mm bricks. A 25 mm thickness was used both
for ferrocement overlay and plain mortar plaster applied on the bare columns. lfthe
height of column is considered 3050 mm instead of 1220 mm no change of stress
distribution occurs, since the platen effect is confined within 100 mm to 120 mm
from the ends. This has been verified in Chapter 8 Art 8.3.11. Considering
symmetry, one fourth of the column is considered in the analysis. The typical finite
element mesh with appropriate boundary conditions used in the analysis is shown in
Fig. 3.1. Two types of three-dimensional analyses have been performed in this study.
One considers brickwork as a homogeneous continuum, the other treats bricks and
mortar-joints separately. In each case the overlay (ferro cement or plaster) was
considered separately from the brick column.
26
"..~34.9
6.1$
y
.,,~7.'~. "-
57.9
Bmm Z
cation 1
1220mm
x
FIG. 3.1 TYPICAL THREE DIMENSIONAL FINITE ELEMENT MESH(QUARTER COLUMN CROSS-SECTION)
27
Complete restraint was applied to the nodes at the base of the column while those at
the top were restrained in the horizontal direction only so as to simulate the effect of
applying the load to the column through a beam or slab. All nodes lying on vertical
lines passing through A, B, C and D excepting the top and bottom nodes were
restrained in V-direction and the nodes lying on vertical lines passing through F, G,
H and I excepting the top and bottom nodes were restrained in X-direction (Fig.
3.1). TIle nodes lying on vertical lines passing through E excepting the top and
bottom nodes were restrained both in X and Y direction (Fig. 3.1). In all the analyses,
the load was applied as a uniform displacement of the loading plate, simulating a
rigid loading platen. It would have been possible also to include the distributed
weight of the column. However, the effects of self weight of the small sized columns
were neglected.
3.5 METHOD OF LOAD APPLICATION
The method of load application influences the stress distribution in the column.
Depending on the stiffuess of the loading device, the transverse stress within the
column immediately beneath the load is markedly non-uniform if the loading plate is
flexible, and approximately uniform if the loading plate is stiff (the latter case
corresponds to a prescribed displacement of the loading plate). Furthermore,
depending on the frictional characteristics at the interface between the loading plate
and top of the column, the loaded surface will be either laterally restrained or
unrestrained with relation to the loading plate.
The influence of these parameters was investigated on the column described in
section 3.4. At first the column was loaded by subjecting the plate to a uniform
displacement (rigid loading plate) and then to a uniform load (flexible loading plate).
For each of the loading cases, two different analyses were performed - one with the
28
top and bottom nodes restrained laterally; the other with no restraint against lateral
expansion.
The distribution of transverse stresses, considering top and bottom of the column
restrained against lateral expansion, is shown in Fig. 3.2. It is seen from the figure
that with the application of uniform load instead of uniform displacement (leading to
nodal forces corresponding to same intensity of loading) there is a significant
variation of transverse stress down column centre line at location-2 (Fig. 3.2b) and
also through the centre line of ferrocement overlay (location-I), but only near the top
of the column (Fig. 3.2a).
The transverse stress distributions at centre lines of column (location-l and location-
2) both with and without lateral restraint at top and bottom of the column are shown
in Fig. 3.3. There is a significant variation of transverse stress near top and bottom of
the column at both locations (Figs. 3.3a and 3.3b).
To illustrate the difference between the two load cases (prescribed load and
prescribed displacement), variation of vertical displacement is also presented in Fig.
3.4. Obviously, the vertical displacement at every nodal point of top surface of the
column is same in case of applied uniform displacement. But in case of applied
uniform load (same magnitude as for uniform displacement case) there is a
significant difference in nodal displacements at the top of the column.
It is seen from Figs. 3.2 and 3.3 that there is a significant difference of stress.
distributions at the top and bottom of the column due to different methods of load
application. It is also seen from Fig. 3.4 that significant difference of top
displacement due to different method of load application. However, these differences
are conJined to regions near the ends, having a height approximately equal to the
width of the column.
C. L
Location-2 Ic.L.
tv\!l
----"- "-
\ '\
I
R
- II
II
II~
II
Jj
- II
TI
/I
- II
I'"77
1000
200
800
1200
400
EE~ 600:E.9''"J:
Location-I
QUARTER SECTIONOF COLUMN
~niform Load(10MPA)------1JniformDisplacement
PositivevaluesindicatesTensilestresseso ! ! i , I I ! ! I 0
-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 -1.5 -1.0 -0.5 0.0 0.5
Stress(MPa) Stress(MPa)
a) Transverse Stress Along Column Centre Line b) Transverse Stress Along Column Centre Line(Location-1) (Location-2)
FIG. 3.2 'tRANSVERSE STRESS DISTRIBUTION ALONG COLUMN CENTRE LINE (TOP AND BOTTOM NODES RESTRAINED LATERALLY)
200
1000
1200
800
~ES 600-J::.~J:
400
C. L.
Stress (MPa)
b) Transverse Stress Along Column Centre Line(Location-2)
a-1.5
----- ---'-\
\\f-
1
II
J
II
TI
II
JJ
lJ
III
. 11
-' \
7
wo
0.50.0-0.5-1.0
200
400
800
1000
1200
C.L.
E.s 600
i1:
Positive values indicatesTensile stresses
Location-I'QUARTER SECTIONOF COLUMN
-"-"-'-"Unrestraint--Restraint
Location-2
.
a~ ~ ~
Stress (MPa)
a) Transverse Stress Along Column Centre Line(Location-I)
a
200
1000
1200
800
--EE 600~:E:.9CD1:
400
FIG. 3.3 TRANSVERSE STRESS DISTRIBUTION ALONO COLUMN CENTRE LINE IN CASE OF UNIFORM DISPLACEMENT
31
The difference in stress distributions and displacements at the loaded face indicates
that careful consideration needs to be given to the method of load application during
tests of this type. If thin plates are used between the platen and the loade4 surface,
the stress distribution will approach that for uniform load. As the thickness of the
plate increases, the condition is similar to that of a prescribed displacement of the
loading plate.
Unifonn load case is not considered for the subsequent analyses since the top and
bottom plate of the loading device (universal testing machine) available in Civil
Engineering laboratory is rigid. To simulate the practical situation, restraint against
lateral expansion at top and bottom of the column has been considered for the
subsequent analyses.
-<l.75
--Unifomly DistributedLoad------Unlfonn Displacement
-<l.85 o 61 122
Width (mm)
183 244
FIG. 3.4 VARIAtION OF TOP DISPLACEMENT
32
3.6 COMPARISON BETWEEN HOMOGENEOUS AND NONHOMOGENEOUS
MATERIAL MODELS USED IN ANALYSIS
For the study of factors influencing 'the composite behaviour of columns two
different finite element analyses were performed in this investigation. One assumed
masonry as a homogeneous continuum, the other treated bricks, joints and
ferrocement overlay separately.
In the first series of analyses the homogeneous case was considered by assuming the
same value of modulus of elasticity (Ebm = 12,260 MPa) for all the elements of brick
masonry. Poisson's ratio for the elements was taken to be 0.17. The values of
modulus of elasticity for ferrocement overlay and plaster were taken to be 21,000
MPa and 6,200 MPa respectively. In the analyses Poisson's ratio for ferrocement
overlay was 0.25 and for plaster was 0.2. In the nonhomogeneous case, the columns
were arrangcd to represent the brickwork by assigning to the brick and mortar joints
different values of modulus of elasticity and Poisson's ratio. The values of modulus
of elasticity for bricks and mortar joints in this case were taken to be 17,187 MPa and
2,900 MPa respectively. The values of modulus of elasticity and Poisson's ratio for
plaster and ferrocement overlay were considered to be the same as before. In both
cases the sanle conditions of boundary restraints and loading were applied.
To illustrate the differences between the two analyses, the results of a typical load
case are presented in Figs. 3.5 and 3.6 for the column described in section 3.4 and
shown in Fig. 3.1. From these figures it can be seen that high compressive transverse
stress develops near the ends of the column due to lateral restraint provided at the
boundary nodes. The transverse stress for homogeneous case is quite different from
the non-homogeneous case irrespective of the locations of the column. F6r
homogeneous case, only a small portion of the column (near the top and bottom) is
subjected to transverse compressive stress and the remaining portion at the column
centre line is very lightly stressed as shown in Fig. 3.5b and Fig. 3.6b. Whereas for
non-homogeneous case (Fig. 3.5b and Fig. 3:6b), almost all the vertical joints are
.LLocation.2
C.L.
ww
0.50.0
------..::::,. .....•.
\,-
I
1
- ]
I
J- 1
1
- I
J
1- 1
---- /'---- /,
200
1200
1000Location~l
Positivevalues indicatesTensile stresses
-2.0-2.5o o
-1.5 -1.0 -0.5 0.0 -2.5 -2.0 -1.5 -1.0 -0.5
Stress (MPa) Stress (MPa)
a) Transverse Stress Along Column Centre Line b) Transverse Stress Along Column Centre Line(Location-1) (Location-2)
FIG. 3.5 TRANSVERSE STRESS DISTRIButION ALONG COLUMN CENTRE LINE IN CASE OF PLASTER OVERLAY
200
1200
1000
QUARTER SECTIONOF COLUMN
BOO L -=== I I"I BOO
~ ~E.s- 600 ~ 600- 1:s;; .!ll.!llCD CD
::r: ::r:
400 I --Non-Homogeneous I 400-----Honnogeneous
c. LLocation-2
C.L
Stress (MPa)
b) transverse Stress Along Column Centre Line(Location -2)
w
"'
0.50.0-0.5-1.0.1.5
--- ----~
\. \-
1
-J
- 1
f- J
]
f- /---- /
/o.2.0
400
200
800
1000
1200
ES 600:E.~J:
Location-IQUARTER SECTIONOF COLUMN
Positive values indicatesTensile stresses
--Non-Homogeneous-Homogeneous
oo~ ~ ~ ~ ~ ~
Stress (MPa)
a) Transverse Stress Along Column Centre Line(Location-! )
200
1200
1000
800
~EE 600~-.<:C>'ii)J:
400
FIG. 3.6 TRANSVERSE STRESS DISTRIBUTION ALONG COLUMN CENTRE LINE IN CASE OF FERROCEMENT OVERLAY
35
subjected to high transverse tensile stress which is mainly responsible for the
initiation of the cracks. Hom6geneous representation of brickwork therefore cannot
model the true composite action of the column. Because of this inadequate
representation, analysis based on idealisation of column by homogeneous material,
has not been carried out for the subsequent analyses described below.
3.7 PARAMETRIC STUDY
3.7.1 Types of Overlays
Two types of overlays were studied, viz. ferrocement overlay (with two layers of
mesh) and plain sand-cement mortar plaster overlay.
It is noted that the ferrocement overlay around the column leads to decrease in the
transverse tensile stress quite significantly in the brickwork as seen Fig. 3.7. From
Fig. 3.7b it is seen that the maximum transverse tensile stress at column centre line
(location-2) in the column encased with plaster is 0.365 MPa whereas the maximum
tensile stress at the same location in the column encased in ferrocement of two layers
of wire mesh is 0.254 MPa. It can thus be concluded that the initial cracking of the
column encased in ferrocement is delayed to some extent, and cracking load for
ferrocernent encased columns could be higher 'than those encased in plaster.
3.7.2 Thickness of Ferrocement Overlay
In this Case the area of brick masonry, that is core size of column was held constant
and the thickness of ferrocement was varied. The thickness of ferrocement was 25
mm, 18.75 mm and 12.5 rtlm respectively, while the modulus of elasticity of
ferrocement was kept constant. The intensity of vertical load in all the cases was also
kept constant.
C.L.
W0'\
0.50.0-0.5-1.0-1.5
""'"\ \-
11
I I
- 1I
1 I
11-
I
J
- I I
11
I I
~ J
/"
//o-2.0
200
1000
1200
C.L.Location-2
Location- ,
PositivevaluesindicatesTensilestresses
0.0-0.6.1.0.1.5-2.0-2.5-3.0o-3.5
200
1000
1200
QUARtER SECTIONOF COLUMN
800 800
~ ~E EE 600 E 600- -•• ••..c ..c.2' ClGl 'Qj:l: :l:
400 I ---Plaster I 400--Ferrocement
Stress (MPe) stress (MPe)
a) Transverse Stress Along ColumnCentre Line b) Transverse StressAlong ColumnCentre Line(Location-I) (Location-2)
FIG. 3.7 TRANSVERSE STRESS DISTRlBUTION ALONG COLUMN CENTRER LINE BY VARYING TYPE OF OVERLAY
37
The distribution of the transverse stresses along the columns centre line (location-2)
and also along the vertical centre line offerrocement overlay (location-I) are shown
in Fig. 3.8. It may be seen from Fig. 3.8b that the transverse tensile stress at the
centre line of column increases with an increase in the thickness of ferrocement
overlay. Transverse compressive stress at the centre line of ferrocement overlay
(location-I) decreases with the increase of overlay thickness (Fig. 3.8a). Due to the
variation of overlay area from 845 sq. rom to 1768 sq. rom, the transverse tensile
stress at the column centre line varies from 0.352 MFa to 0.407 MFa (15.6%
increase), and at the centre line of~errocement overlay the transverse compressive
stress varies from 0.99 MFa to 0.9 MPa (9% decrease). From this study it is noted
that for the same intensity of vertical loading, an increase in thickness of
ferrocemcnt overlay leads to an increase in the transverse tensile stress along the
centre line of the column (location-2) and a decrease in the transverse compressive
stress along the centre line of ferrocement overlay (location -1).
3.7.3 Number of Mesh Layers in the Overlay
In this investigation the effect of volume fraction of reinforcement in ferrocement
overlay was studied by changing the number of mesh layers, keeping all other
parameters constant. The values of volume fraction (volume of wire mesh divided by
volume of ferrocement overlay) cortsidered in this study were 0.000, 0.007, 0.014
and 0.021, Le. zero (corresponding to plain mortar), one, two and three layers of wire
mesh respectively.
The distribution of transverse stress is shown in Fig. 3.9. It can be seen that the
transverse tensile stress at the column centre line i.e., at 10cation-2 decreases (Fig.
3.9b) but the transverse compressive stress at the mid section of ferrocement overlay
(location-I) increases (Fig. 3.9a) with an increase in the volume fraction of
reinforcing wire. For an increase in the volume fraction ofreinforc'ement from 0.7%
to 2.1% (i.e. 200% increase), the decrease in transverse tensile stress is only 9%.
C.L.
LV00
0.60.0.0.6-1.0
- ,- \\
I I
- I
I I
J-
I I
T
- I I
, I
7-./
7o-1.6
800
600
400
200
1200
1000
C.L
I~'"'iii:r
--12.6mm--18.76mm--26mm
QUARTER SECTIONOF COLUMN
Location-2
Location-
PositiVevalues IndicatesTensile stresses
o-2-4-a
400
800
o-a
200
1200
1000
E.E. 600~'"'ii:r
Stress (MPa) Stress (MPIi)
a) transverse StressAlongColumnCentre Line b) Transverse StressAlongColumnCentre Line(Location-I) (Location-2)
FIG. 3.8 TRANSVERSE STRESS DISTRIBUTION ALONG COLUMN CENTRE LINE FOR DIFFERENT THICKNESSES OF FERROCEMENT OVERLAY
C.L.Location-21 C. L.
1200 1200
1000Location-l~
1000
QUARTER SECTIONOF COLUMN
800 800
EE 600-~a>Gi:J:
400 -'-' -1 Layer--2 Layer---3 Layer--QLayer
I:=- 600.t:.2':!
400
(.oJ
\D
200 200
0.50a.26-0.75- -_.o
-1.00 -0.50 -0.25 o.aOStress (MPe)
b) Transverse Stress Along ColUIimCentre Line(Location-2)
Positive values IndicatesTensile stresses
o-2.00 -1.75 -1.50 -1.25 .1.00 -0.75 -0.50 -0.25 0.00 0.25
Stress (MPa)
a) TransverSe Stress Along ColUIimCentre Line(Location-I)
FIG. 3.9 TRANSVERSE STRESS DISTRIBUTION ALONG COLUMN CENTRE LINE FOR DIFFERENT NUMBER OF MESH LAYERS
40
From Fig. 3.9b it is also seen that the transverse tensile stress at the column centre
line (location-2) is the maximum, whereas transverse compressive stress at the mid
section of overlay (location-I) is the minimum when no wire mesh was used in the
overlay.
3.7.4 Modular Ratio of Ferrocement Overlay and Brick Masonry
The effect of varying the strength of ferrocement overlay was studied by varying the
modulus of elasticity of ferrocement (Et1 overlay while holding the modulus of
elasticity constant for brick (Eb) and mortar joint (E.,,).The values ofEr were taken as
21,000,31,500 and 42,000 Mpa.
The transverse stress down column centre line and through the centre line of
ferrocement overlay for different modulus of elasticity is shown in Figure 3.10. From
the figure it is seen that the transverse tensile stress decreases at the column centre
line as modulus of elasticity offerrocement increases (Fig. 3.JOb). But at the centre
line of ferrocement overlay transverse compressive stress is developed (Fig. 3.10a).
For the variation of modulus of elasticity from 21,000 MPa to 42,000 MPa Le. with
100% increase, the transverse tensile stress decreases by 14% at the column centre
line (location-2). It is seen from Fig. 3.10a that the transverse compressive stress at
location-I increases by 18% due to 100% increase in modulus of elasticity of
ferrocement.
3.7.5 Thickness of Bed joint
In this investigation the effect of the thickness of bed joint related to that of the brick
On stress distribution of column with ferrocement overlay was studied by changing
the thickness of bed joint while keeping all other parameters constant. Thickness
ratios (thickness of bed joint /thickness of brick) for this investigation were taken to
be 0.091, 0.2 and 0.33 respectively.
C.L.Location-~ C.L.
1200 1200
'"f-'
0.50.0
~.~
DJ
III
. m
~- III
UI
-III
III
- ~J
.7///
800
1000
E.5. 600.•...c
'"QjJ:
Location-I'
QUARTER SECTIONOF COLUMN
--E =42000 MPa I 400--E =31500 Mpa--E =21000Mpa
Positive values IndicatesTensile stresses
.3.0-3.5o-4.0
200~ ~ I 200
1000
o.2.5 -2.0 -1.5 -1.0 -0.5 -1.5 .1.0 -0.5
stress (MPa) Stress (MPs)
a) Transverse Stress Along ColumnCentre Line b) Transverse StressAlong ColumnCentre Line(Location-I) (Location-2)
FIG. 3.10 TRANSVERSE STRESS DISTRIBUTION ALONG COLUMN CENTRE LINE FOR DIFFERENT MODULuS OF ELASTICITY OF FERROCEMENTOVERLAY
800
~:Ii!!!. 600.•...c
'"'QjJ:400
42
Fig. 3.11 shows the variation of transverse stress down column centre line (location-
1 and location-2) of column coated with ferrocement. It may be seen that there is a
significant change in transverse stresses as the thickness ratio is changed. With the
decrease in thickness ratio (t",/tb) by 73%, transverse tensile stress is decreased by
45% at the centre line of the column (location-2) as shown in Fig. 3.11b. It is seen
from Fig. 3.l1a that there is no transverse tensile stress developed at location-! due
to 73% decrease of thickness ratio (t",/~). From this study it has been found that due
to increase of bed joint thickness (increase of t",/tb) the cracking load of masonry
column with ferrocement overlay is significantly reduced.
3.7.6 Confinement Effect of Ferrocement Overlay
It has been stated earlier (Art 2.4) that the compressive strength and the ductility of
brick column increase due to confinement effect of the ferrocement overlay. lbis
improvement in ductility is very important for structural components especially for
brick masonry elements used in earthquake resistant design. In a typical building,
columns are considered to be the critical load bearing elements, and hence a
considerable amount of research has been done to improve the ductility of columns.
One of the most effective methods to improve the ductility is to confine the elements
with strong overlay.
Attempts have been made to predict the failure load of a ferrocement masonry
composite column by Singh (82). In simple terms its failure load is given by the
following equation by Singh (82).
F= PI + P2 +P3 ---------------- (3.1)
where P is the ultimate load of composite column, PI is failure load of masonry core,
P2 is failure load of ferrocement casing and P3 is strength increase of masonry core
Locallon-2
01>w
~
0.50.0-1.0
.................... "-..\\\
f-ill
IJJ
II I
m]I
III
I I J
mill
ill
/II7
.L/
-0.5
Stress (MPa)
b) Transverse Stress Down Colunm Centre Line(Location-:2 )
o-1.5
400
200
800
1200
1000
E..s 600
~J:
Location-l
--19.05mm--12.1mm--{l.35mm
QUARTER SECTIONOPCOlUMN
Positive values indicatesTensile stress
0.5
~\f-
]
1]
I
]
1]
I
]
\ \
7
i , .. ,o-2.0 -1.5 -1.0 -0.5 0.0
stress (MPa)
a) Transverse Stress Down Column Centre Line(Location-I)
200
1200
1000
800
EE 600~-~.9'"J:
400
FIG. 3. I I TRANSVERSE STRESS DISTRIBUTION DOWN COLUMN CENTRE LINE FOR DIFFERENT THICKNESSES OF BED JOINT
44
due to passive confmement pressure applied on it by the casing. When a column is
subjected to compression, there is a tendency for its lateral expansion due to
Poisson's ratio effect. The ferrocement casing and the brick masonry core will have
different expansion due to different Poisson's ratios. Moreover; the triaxial
compression behaviour of brick masonry has not been explored by Singh (82) and no
attempt has made to quantify P3.
In this study the effect of confmement on the behaviour of brick column due to
ferrocement overlay has been investigated. To see the confinement effect of
ferrocement overlay, a continuous vertical groove was provided at each face of the
coated colunm to eliminate the continuity of the overlay around the column. In this
case the peripheral elements' A' and 'B' throughout the height of column, as shown
in Fig. 3.12, were eliminated to model this discontinuity. Only 0.74% area of
ferrocement overlay has been neglected in this case in comparison with the total
cross-sectional area of the ferrocement encased colunm. Typical transverse stress
distribution is shown in Fig. 3.13. From the figure it is seen that in case of linear
elastic ~Ulalysisthere is no significant change of transverse tensile stress due to the
provision of discontinuity in ferrocement overlay. The effect of confinement has
been discussed in further detail in Chapter 6.
3.7.7 Eccentricity of Loading
In this study the effect of overlay on the stress distribution of eccentrically loaded
masonry column was investigated. Uniformly distributed load was applied within the
zone ABeD as shown in Fig. 3.14 and all other parameters were kept constant in this
analysis. Both ferrocement overlay and plaster overlay were considered. The finite
element idealisation of this study is shown in Fig. 3.14.
Due to the provision of ferrocement overlay around the colunm the transverse tensile
stress decreased as shown in Fig. 3.15. From Fig. 3.15b it is seen that the maximum
45
FIG. 3.12 FINITE ELEMENT MESH FOR FERROCEMENT COATEDCOLUMN WITH VERTICAL GROOVE
. L.
Locaiion-2c. L.
200 I- ;p 7 I 200
Ii'>G'I
0.50.0-0.5-1.0
----~
'\
Jj
I
- 11
1
Jj-
J
1\
-Jj
J- 11
v
/ Io-1.5
800
1000
1200
Eg 600
~'0;J:
Location-!
--Discontinuous I 400--Continuous
QiJARTER SECtiONOF COLUMN
Positive values IndicatesTensile stresses
0.50.0-0.5-1.0"1.5o-2.0
1000
1200
800
EE- 6001:.2'ellJ:
400
Stress (MPa) Stress (MPa)
a) Transverse Stress Along Column Centre Line b) Transverse Stress Along Column Centre Line(Location-l) (Location-2)
FIG. 3.!3 TRANSVERSE STRESS DISTRIBUTION ALONG COLUMN CENTRE LINE IN CASE OF DISCONTINUOUS FERROCEMENT OVE:RLAY
47
y
z
A
B
C.L.
D
CLocation-l
C.L.ABeD:: Loading Zone
Half section of column
x
•
FIG. 3.14 FINITE ELEMENT MESH FOR ECCENTRIC LOAD CASE
• . L.Locatlon-2
C.L
01>00
J \
""'-
"-1
- JJ
11-
JJ
-11
~ 1J
/
. 77
200
1000
1200
Location-I
Positive values IndicatesTensile stresses
o I L --====::=t r=::::: I I 0-1.5 -1.0 -0.5 0.0 0.5 -1.5 -1.0 -0.5 0.0 0.5
Stress (MPa) Stress (NlPa)
a) Transverse StressAlong ColumnCentre Line b) TransverSeStressAlongColumnCentre Line(Location-l) (Location-2)
FIG. 3.15 TRANSVERSE STRESS DISTRIBUTION ALONG COLUMN CENTRE LINE IN CASE OF ECCENTRIC LOADING
200
1200
1000
QUARTER SECTIONOF COLUMN
800 800
~ ~E Eg BOO g
600•.. •..z: z:Dl Dl'CD Gi:r :r
400 I _. _..Ferrocement I 400--Plaster
49
transverse tensile stress at column centre line of the column encased with plaster is
0.16 MPa whereas the maximum transverse tensile stress at the same location of the
column with ferrocement is 0.11 MPa. From this stress variation within the column
due to ferrocement overlay, it can be concluded that the initial cracking of the
column is delayed in case offerrocement overlay.
3.8 SUMMARY
In this chapter a linear elastic fInite element study of the behaviour of composite
action between brick masonry column and ferrocement overlay has been described.
This type of analysis can serve as a useful guideline for comparative study to
establish the most critical parameters influencing the behaviour of brick masonry
column coated with ferrocement. The following conclusions can be drawn from the
study:
1. A three-dimensional linear elastic fInite element analysis which models
bricks, mortar joints and ferrocement overlay separately is more effective
than homogeneous representation of the composite column, since it reflects
the influence of the varying stiffuess of its constituents. This was particularly
important in the study of transverse tensile stresses, where peak stresses are
always greater than those predicted in the homogeneous analysis.
2. SignifIcant variation of transverse stresses takes place near top and bottom of
the column when_uniformly distributed load is applied instead of uniform
displacement.
3. As the ratio of the bed joint thickness to brick thickness is decreased, the
transverse tensile stress decreases in the bricks and the vertical joints.
50
4. There is no significant effect of number of wire mesh layers in ferrocement
overlay on the stress distribution of composite column.
5. The transverse tensile stress (which would initiate cracking) decreases with an
increase in modulus of elasticity and hence the stiffuess of the ferrocement
overlay.
6. TIlcre is no significant effect of confinement on the elastic stress distribution
of composite column.
CHAPTER 4
PROPERTIES OF FERROC:EMENT, BRICK AND MORTAR
4.1 INTRODUCTION
In the finite element analysis considering brick masonry as an assemblage of bricks
set in a mortar matrix, the properties of bricks and mortar must be determined. The
properties of ferrocement also need to be determined when the column is encased by
ferrocement overlay. These are established from various types oftests performed On
representative samples of ferrocement, brick, mortar and brick masonry used in the
investigation. A particular brick-mortar combination was chosen and used
throughout to determine these material properties.
4.2 FERROCEMENT PROPERTIES
Throughout this investigation 25 mID thick ferrocement overlay has been used. The
proportion of cement and sand used in this investigation was 1:2. Water cement ratio
is 0.45 by weight and opening size of woven square wire mesh is 11.3 mID x 11.3
mID made up of 1.2 mID diameter wire. The yield strength of wire is 285 MPa.
Determination of strength and deformation characteristics of ferrocement are
described in the following sections.
4.2.1 Tensile Strength of Ferrocement
The ultimate load in tension is independent of specimen thickness, because the
mortar is cracked long before failure and does not contribute to the ultimate strength
of the composite.
52
The tensile strength was evaluated using the BNBC (97) standard which is based on
ACI committee 549. A total of 6 specimens were tested. The specimens were 25 rom
x 75 rom in cross-section and 300 rom long. Each specimen was fabricated with two
layers of wire mesh of 1.2 rom diameter wire and 11.3 rom x 11.3 rom opening size.
Load was applied using a universal testing machine. The tests were performed on dry
specimens at 28 days after having been moist cured for 7 days. The average tensile
strength of ferrocement is shown in Table 4.1. Complete test results are given in
Appendix I (Table 1- 4).
Table 4.1 Summary of Ferrocement Properties
Compressive 22.3 1.75 7.80 6Strength(MPa)
Tensile Strength 2.75 0.30 11.15 6(MPa)
Initial Modulus of 21,000 1727 8.2 6Elasticity (MPa)
Poisson's Ratio 0.25 .008 3.2 6
S = Standard Deviation, C. ofV. = Coefficient of Variation
4.2.2 Compressive Strength of Ferro cement
In compression, unlike tension, the load carrying capacity of mortar strongly
influences the ferrocement strength in proportion to its cross-sectional area.
Obviously, matrix strength, governed primarily by its water-cement ratio, is a major
factor, as for conventionally reinforced concrete, but the type, orientation and
arrangement of the reinforcement are also important.
53
The behaviour of ferrocement specimens in direct compression was studied by
testing of hollow ferrocement specimen as shown in Fig. 4.1. The size of the
specimen was 15 em x 15 em outside dimension and 10 em x 10 em inside
dimension and the height was 45 em. Load was applied using universal testing
machine. The tests were performed on dry specimens at 28 days after having been
moist cured for 7 days. Each specimen was tested for evaluating the compressive
strength, modulus of elasticity and Poisson's ratio in direct compression. The average
compressive strength of ferrocement are shown in Table 4.1. Detailed experimental
results are given in Appendix 1 (Table 1-4).
4.2.3 Stress-strain Characteristics of Ferro cement
The evaluation of the deformation characteristics of ferrocement was performed by
direct compression test. Compression tests were carried out on hollow specimens
described ill Art. 4.2.2. Deformations were measured using Demec gauges mounted
on opposite sides of the specimen on a central 50 rom gauge length as shown in Fig
4.1. Thc mean stress-strain curve obtained by averaging the strains at successive
stress levels is shown in Fig. 4.2.
4.2.4 Poisson's Ratio of Ferrocement
The Poisson's ratio of ferrocement was determined from the uniaxial compression
tests described in Art. 4.2.2. Deformations were measured on the central position of
the specimen in both vertical and horizontal directions using Demec gauges as
shown in Fig. 4.1. Simultaneous readings of longitudinal and lateral deformation
were recorded during the loading cycle.
A plot of average normal strain against average lateral strain for the ferro cement
specimen is shown in Fig 4.3. It can be seen from the figure that Poisson's ratio is
fairly constant up to approximately 50% of the ultimate strength of ferrocement
54
'.. '
FIG. 4.1 UNIAXIAL COMPRESSION TEST ON HOLLOW FERROCEMENT BLOCK
55
25
14012010080604020
5
oo
20
15mCl.6'"'"l'!ii5(ij
EExperiment0
10 •zBest fit
Normal Slrain (10.5)
FIG. 4.2 AVERAGE STRESS-STRAIN CURVE OF FERRO CEMENTLOADED IN UNIAXIAL COMPRESSION
56
specimen after which the value increases slowly. The mean Poisson's ratio for the
ferrocement specimen is shown in Table 4.1.
• Experiment
40
30of>'b:=-c:
20.~(;j
f!<l>10 10..J
aa 40 60 80
•
100
Longitudinal Strain (10.5)
FIG. 4.3 LATERAL VS.LONGITUDINAL STRAIN FORCOMPRESSION TEST OF FERRO CEMENT
4.3 PROPERTIES OF BRICK
The same type of solid clay bricks were used for all aspects of tills investigation. All
bricks were taken from a local manufacturing plant (Conforce Brick). The bricks
were collected from the same batch and stored in the laboratory after procurement till
their usc in the experimental programme. The nominal brick size was 244 mm x 116
mm X 70 mm having an average weight 01'3.4 kg. Determination of the strength and
deformati(ln characteristics of brick is described in the following sections. The
properties of brick are summarized in Table 4.2.
57
4.3.1 Compressive Strength of Brick
Brick compressive strength is an important property for brick quality control as well
as for strength characteristics. The standard compression test involves loading the
specimen between the solid platen of the testing machine. For typical brick
dimension this results in significant artificial strengthening due to aspect ratio effects.
To obtain true compressive strength, the effect of platen should be accounted for.
However the standard test method of ASTM (C 109) was followed because of
nonavailability of flexible brush platen.
Twelve bricks were selected at random from the stack. From each specimen half of
the brick was cut by a diamond saw. Neat cement paste was used on both faces to fill
frog mark and surface flaws. Thin sulphur capping was used on both surfaces.
Accurate level of the capped surface.s waS maintained using sprit level. Test was
performed between the steel platen of 2,500 kN capacity compression testing
machine. Load was applied at a rate of 150 kN/min. All the specimens failed by
crushing. The mean compressive strength is presented in Table 4.2.
4.3.2 Tensile Strength of Brick
Tensile strength is of great importance in defining the strength of brick masonry as
final failure often occurs in some form of biaxial tension split originating in the brick.
Direct tensile strength test is difficult to perform on brittle materials. Hence indirect
tensile strength was determined from a splitting test.
The indirect tensile strength of a homogeneous prism, suggested by Thomas and
O'Leary (87) as an alternative to the use of cylinders, can be obtained by the
following equation.
58
Tensile strength = 0.648 PIDL
where, P =Applied load
D =Equivalent diameter
L =Length of the specimen
A total of twelve dry bricks randomly selected from the batch were tested. The load
was applied through a steel plate of 11 mm wide and 5 mm high. The plate width
was therefore 10% of the width of the specimen. The load was applied using
universal testing machine. Failure occurred by vertical splitting directly beneath the
loading plate. The mean tensile strength is presented in Table 4.2
4.3.3 Deformation Characteristics of Brick
Brick in a masonry column usually carries load in a direction normal to the bed
plane. The evaluation of deformation characteristics of the brick with the load
applied normal to the bed plane is more difficult, since a brick loaded in this manner
exhibits significant aspect ratio effects. Moreover, the deformation characteristics of
a brick between the machine platen will no doubt differ from that of in-situ
deformation characteristics due to the presence of mortar joints in the brickwork. To
avoid this problem, deformation characteristics of bricks were measured from the
central brick of a 5 bricks high stack bonded prism loaded in uniaxial compression
(Fig. 4.4). lbe prism tests were also used to establish the in-situ properties of the
mortar. The prisms were tested dry at an age of28 days with the load being applied
at a rate of 400 kN/min. Deformations were measured on a central 50 mm gauge
length using Demec gauge. A plot of the average stress-strain curve is shown in Fig.
4.5. The mean initial tangent modulus obtained from the test is given in Table 4.2.
Detailed results are presented in Appendix 1.
59
FIG. 4.4 UNIAXIAL COMPRESSION TEST ON STACK BONDED PRISM
ellell~U5roEoz
10
6
4
2
60
---Brick-0- Brickwork
-- Mortar (derived)
oo 50 100 150
Normal Strain (10-4)
200 250 300
FIG. 4.5 STRESS-STRAIN CURVE FOR BRICK, BRICKWORKAND MORTAR OBTAINED FROM PRISM TEST
61
4.3.4 poisson's Ratio of Brick
The poisson's ratio of brick was estimated from the strain readings obtainedfrom the
compression tests of 5 bricks high stack bonded prisms. A typical plot of the
measured average longitudinal strains versus average lateral strains is shown in Fig.
4.6. Detail results are contained in Appendix I.
f Brick Pr erti s
S = Standard Deviation, C. ofV. = Coefficient of Variation
I~~F~1U¥-'1~r;.~i,2J'•• ',':, ,; ," I (,' " .1 - ' .' ~~~~_' __ -=-____ J ___-"-__ ~ _J .~~ ~-..,":--_.~,,~
Compressive 20.1 1.86 9.00 12
Strength(MPa)
Tensile Strength 2.21 0.19 8.95 12
(MPa)
Initial Modulus of 17,187 1119 6.5 12
Elasticity (MPa)
poisson's Ratio 0.16 .008 5 12
Tabl 42 S mma
101----------------------~"6' 8 • Experiment
:;6l~~:::::;:::Bes::::lfil=:=====JcVi 4;;;~ 2j
o o 10 20 30 40
Longitudinal Strain (10"")
FIG. 4.6 LATERAL VS. LONGITUDINAL STRAIN OF BRICK
62
It is seen thaI Poisson's ratio was approximately constant up to the ultimate strength
of the stack bonded prism. The mean value of Poisson's ratio in the elastic range is
found to be 0.16 (Table 4.2).
4.4 Mortar Properties
The estimate of compressive strength, tensile strength and deformation
characteristics of mortar joints are required for the material model in the finite
element analysis.
Mortar was prepared from normal portland cement and local sand (p.M. = 1.5),
mixed in proportion of 1:5 (cement: sand). For ferrocement specimens, mortar was
prepared using same type of cement and Sylhet sand (p.M. = 2.1) mixed ill
proportion of 1:2 (cement: sand) throughout this experimental programme.
4.4.1 Compressive Strength of Mortar
The compressive strength of mortar was determined from uniaxial compression tests
on 150 mm long cylinders of75 mm diameter. A total of 12 cylinders were cast from
each mix and tests were performed on dry specimens at 28 days after having been
moist cured for 7 days. The mean compressive strength of cement mortar for
different cement: sand ratio are shown in Tables 4.3 and 4.4 respectively.
4.4.2 Tensile Strength of Mortar
The tensile strength of mortar was determined from mortar briquette prepared and
tested according to ASTM (C 109) standard. A total of 12 briquettes were built from
each mix and tests were performed on dry specimens at 28 days after having been
moist cured for 7 days. The mean tensile strength of cement mortar for different
cement: sand proportion are shown in Tables 4.3 and 4.4 respectively.
63
4.4.3 Stress-strain Characteristics of Mortar
The load-deformation characteristics were evaluated using 30 mm and 10 mm
electric strain gauges in longitudinal and transverse direction respectively at the
mid-height of the cylinders used for compression test as shown in Fig 4.7. Stress-
strain curves (using mean values) obtained from cylinders are shown in Figs. 4.8 and
4.9 respectively.
To predict the deformation and strength characteristics of masonry by finite element
analysis, the modulus of elasticity of mortar joint is essential. By loading a stack
bonded prism in uniaxial compression and measuring the deformation in individual
bricks as well as the average deformation on a gauge length encompassing several
bricks and mortar joints, the net deformation characteristics of the mortar joint can be
determined. The readings of brick deformation obtained in Art. 4.3.3 were used in
this case. Longitudinal deformations of brick were measured on a central 50 mm
gauge length bonded prisms of 5 bricks high stack while longitudinal deformations
of masonry were measured in the same manner on a 200 mm gauge length covering
two mortar joints, one full brick and part of two bricks, as shown in Fig. 4.4. Both
the tests were performed under the same condition.
If it is assumed that all the bricks encompassed by the Demec gauge are in a uniform
state of vertical stress. The difference between the total measured deformation and
the deformation of brick can be attributed to the mortar, and the corresponding
mortar strain determined. The mortar strain at any stress level can therefore be
expressed as:
&m=( EtLt - EbLb)/Lm ------------------ (4.1)
5
201510
Normal Strain (104)
5
4
,
. -".
m 3ll..6 I / I 0\
'" """'"tl"iiiE 21. I I • Experiment
:~ IDIIIIJIIlJB ~0 ------ Best fit IZ I ....
--"~~"'-'- 1
FIG. 4.7 UNIAXIAL COMPRESSIONTEST ON MORTAR CYLINDER FIG. 4.8 STRESS-STRAIN CURVE OF MORTAR (1:5)
20
15
r0-o.6'"'" 10f;rJ)
roE0z
5
o
65
• Experiment
----- Best fit
o 5 10 15 20 25 30 35Normal Strain (10-4)
FIG. 4.9 STRESS-STRAIN CURVE OF MORTAR (1 :2)
66
where,
St = total measured strain
Eb = strain in the brick
Lt = total gauge length
Lb = total thickness of brick included within L(, and
Lm = total mortar thickness
Using Eqn. 4.1, the net stress-strain curve for the mortar is derived from the average
measured masonry strain and brick strains for each prism. The average stress-strain
characteristics of brick, brickwork and mortar, acting compositely are derived from
the prism tests, shown in Fig. 4.5. The figure shows the extent of difference of load
deformation response of the constituents of the masonry when the composite action
between them are considered. The stress-strain curve for mortar is nonlinear in nature
as can be seen from Fig. 4.5. The mean initial tangent modulus of elasticity of the
mortar thus obtained, was 2,900 MPa.
4.4.4 Poisson's Ratio of Mortar
The Poisson's ratio of mortar was determined from the uniaxial compression tests of
mortar cylinders, as described in Art. 4.4.2. Deformations were measured on the
central position of the specimen in both vertical and horizontal directions using
electrical strain gauges, as shown in Fig. 4.7. Simultaneous readings oflongitudinal
and lateral deformation were recorded during the loading cycle.
A plot of average normal strain against average lateral strain for two different mortar
types is shown in Figs 4.10 and 4.11. It is seen that Poisson's ratio is fairly constant
up to about 50% of the ultimate strength of mortar after which the value increases
nonlinearly for both the types. 'Ibe mean Poisson's ratio of these mortars is shown in
Tables 4.3 and 4.4.
67
10
• Experiment8 ---- Best fit
"b 6~~c.~-C/) 4~til-l
2
00 5 10 15 20
Longitudinal Strain (10-4)
FIG. 4.10 LATERAL VS. LOGITUDINAL STRAIN FOR MORTAR (1:5)
20
IS
b-~.~ 10l:lC/}
01II!a 5-l
00 10
• Experiment- Bestfil
20 30 40 50
Logitudinal Strain (10-4)
FIG. 4.11 LATERAL STRAIN VS. LONGITUDINAL STRAIN FOR MORTAR (1:2)
68
I[=-~~~~~EJ~-~~__~~ L _.._J L~:~:Compressive 18.5 2.21 11.98 12Strength(MPa)
Tensile Strength 2.5 0.23 9.20 12(MPa)
Initial Modulus of 19,000 994 5.2 12Elasticity (MPa)
Poisson's Ratio 0.17 .008 4.8 12
T
S = Standard Deviation, C. ofV. = Coefficient of Variation
[~~:.]EJ~E]~~~Compressive Strength
(MPa) 4.95 0.62 12.54 12
Tensile Strength(MPa) 0.6 0.05 9.30 12
Initial Modulus ofElasticity (MPa) 6,200 890 14.3 12(Cylinder Test)
Initial Modulus ofElasticity (MPa) 2,900 381 13.1 12(prism Test)
Poisson's Ratio 0.20 .008 4 12
T
S = Standard Deviation, C. ofV. = Coefficient of Variation
69
4.5 SUMMARY
In this chapter small scale experiments have been performed to determine the basic
properties of the ferrocement, brick masonry and the constituents of masonry, used in
this investigation. The following is a brief summary of the important characteristics
of the materials.
Ferrocement
1. In tension , the load carrying capacity of ferrocement is essentially
independent of specimen thickness because of the matrix cracks well before
failure and does not contribute directly to composite strength.
2. The compressive strength offerrocement does not change significantly due to
a change in the number of mesh layers.
3. Poisson's ratio of ferrocement is 0.25 and is fairly constant up to about 50%
of the ultimate strength of ferrocement after which the value increases slowly.
Bricks
1. The compressive strength of brick was found to be 20.1 MPa.
2. The Poisson's ratio is 0.16 and is almost constant up to the ultimate strength.
Mortar
1. Mortar exhibited nonlinear stress-strain characteristics and large deformation
capacity.
2. The Poisson's ratio of mortar used in ferrocement (1:2) is 0.17 and the
Poisson's ratio of mortar used in brickwork (1:5) is 0.20
70
3. The Poisson's ratio was fairly constant to approximately 50% of the ultimate
strength after which it gradually increased.
CHAPTERS
EXPERIMENTAL INVESTIGATION
5.1 INTRODUCTION
A total of 48 columns, including bare masonry columns, masonry columns encased
in different types of ferrocement overlay and hollow ferrocement columns, were
tested in this investigation. They were subjected to both concentric and eccentric
loads to produce a wide range of stress states and failure modes. The objective of the
tests was to verify the adequacy of the idealized material model used in the finite
element analysis in predicting cracking and failure loads, rather than to draw
extensive conclusions about the general behaviour of composite columns. For each
test the cracking load, failure load and deformations were measured and failure
modes were identified.
5.2 EXPERIMENTAL StUDY
5.2.1 Test Programme
The experiments were performed to determine the load carrying capacity and
deformation characteristics of short columns under axial and eccentric loads of short
duration. The main parameters of the study were the effect of ferrocement overlay,
plaster, and number of mesh layers in overlay. A summary of test program is given
in Table 5.1.
The columns were divided into five groups, according to their appearance. A
designation system with four to five characters is used to identify the specimen type.
The first character indicates the type of specimen - N for normal i.e. without any
discontinui ty in overlay, B for bare, D for discontinuous overlay, G for gap at the top
MORTAR1:2
72
TABLE 5.1 TEST PROGRAMME
COLUMN
COATED FERROCEMENTSHELL
PLASTER FERROCEMENT
MORTAR1:5
SINGLELAYEROFWlREMESH
DOUBLELAYER 0WlREMESH
73
and bottom and H for hollow. The different types are shown in Fig. 5.1. The second
character indicates the number of mesh layers - S for single layer, D for double layer
and Z for zero (i.e ordinary plaster). Two types of loading were considered in the
present investigation. The third character of the designation system indicates the
loading type - A for axial load and E for eccentric. fourth character indicates the
serial number. Fifth character, W, ifpresertt, indicates weak mortar (only for plaster).
Graphical representation of designation is given below.
Appearance Loading type Weak mortar
1slLetter
2nd 3rdLetter Letter
4th 5thLetter Letter
5.2.2 Column Details
Number of mesh layer Serial number
IJI
Attempts were made to select column dimensions similar to those used in actual;
buildings. While it was possible to keep the cross-sectional dimension same as actual
columns, limitations in testing facilities did not permit full-height columns to be
tested. TIle maximum height of column which could be accommodated within the
Universal Testing Machine was selected.
The aspect ratio (height: least dimension) of all the columns was between 4.16 and
5.0. This aspect ratio was considered to be satisfactory to avoid the effects of
restraint at the base of the column and thus can be considered to be representative Of
storey height columns. The c;olumns were 16 courses high and 2 bricks wide. This
provides 16 potential vertical joints of weakness, (in line with the vertical mortar
joints) in two vertical planes along the centre line of the cross-section, which were
75
considered to be sufficient to represent the storey height of brick columns. The bed
joint thickness was 6.35 rnm and vertical joint thickness was 12.5 rnm. The resulting
column was 1220 rnm in height and 244 rnm x 244 rnm in cross-section The
thickness of overlay was 25 rnm. In this investigation sixteen sets of brick columns
with 1:5 cement mortar were tested in the laboratory. The description of specimens is
given in Table 5.2.
5.2.3 Construction of Columns
To minimize effects of workman ship and to be consistent with the procedure used for
the small brick masonry specimens, the columns were constructed in the
conventional manner by a professional bricklayer. The columns were constructed in
sixteen batches, each of 3 columns. A typical column under construction is shown in
Fig. 5.2. Three 150 rnm high and 75 rnm diameter mortar cylinders were prepared
from each batch for quality control. The results of these quality control tests of
different batches are given in Appendix II.
For each specimen, the ferrocement overlay or plaster was applied two days after the
construction of the columns. In case of ferrocement overlay containing single layer
of wire mesh, a 12.5 rnm thick layer of mortar was applied around the column on
which one layer of wire mesh was wrapped around the column and the vertical edges
were tied with GI wire. Another 12.5 rnm thick layer of mortar was then applied to
make a 25 rnm thick ferrocement overlay for series NSA and NSE. In case of
ferrocement overlay containing double layers of wire mesh, an 8 rnm thick layer of
mortar was applied around the column on which first layer of wire mesh was
wrapped around the column and the vertical edges were tied. Then, another 9 rnm
thick layer of mortar was applied. On this mortar layer, a second layer of wire mesh
was wrapped on which an additional 8 rnm mortar layer was applied to make 25 mm
thick ferrocement overlay for series NDA and NDE. For GDA and GSA series, a 25
rnm thick ferrocement overlay containing double layers and single layer of wire
76
Table 5.2 Description of Specimens
Height of column ~1220 mm and core size = 244 mm x 244 mm for all column
l'J)i\ 1:5
NDE 1:5
HDi\
DDi\ 1:5
GDi\ 1:5
NSi\ 1:5
NSE 1:5
HSi\
DSi\ 1:5
GSi\ 1:5
NZi\ 1:5 1:2
NZE 1:5 1:2
NZi\-W 1:5 1:5
NZE-W 1:5 1:5
BZi\ 1:5
llZE 1:5
~
1:2 25 II
1:2 25 2 Layers(1.2 rnm
1:2 25 dia. [email protected]
1:2 25 c/c)I
1:2 25 I
1:2 25 II
1:2 25 1 Layer(1.2 rnm
1:2 25 dia. [email protected]
1:2 25 c/c)I
1:2 25 I
25 II
25 IZero Layer
25 II
25 I
IZero Layer
I
NDA ,..Normal. double layer a/wire mesh and axial loadingNSA. =- Normal, single layer a/wire mesh and axial/aDdingNZA =- Norma!, zero layer a/wire mesh and axial loadingNZ4. rv "'"Normal, zero layer a/wire mesh, axial loading and weak mortarDDA ,. Discontinuous, double layer a/wire mesh and axial/aDdingDSA :0 Discontinuous, single layer a/wire mesh and axial loadingHDA = Hollow, double layer a/wire mesh and axial/aodingHSA ""Hollow, single layer a/wire mesh and axial/aDdingGDA ~ Top and bottom gop. double layer a/wire mesh and axial loadingGSA = Top and hallam gap. single layer a/wire mesh and axial loadingBM = Bare, zero layer a/wire mesh and axial loadingNDE = Normal, double layer a/wire mesh and eccentric loadingNSE = Normal, single layer a/wire mesh and eccentric loadingNZE =Normal, zerO layer a/wire mesh and eccentric loadingNZEW =Normal, zero layer a/wire mesh, eccentric loading and weak mortarBZE = Bare, zero layer a/wire mesh and eccentric loading
77
mesh respectively, was applied around the masonry column with a 25 mm gap at the
top and bottom of the masonry column. For NZA, NZE, NZA-W and NZE-W series,
plain mortar plaster was applied. For construction of hollow ferrocement column
(series HDA and HSA), a mould was fabricated using 1/16 inch thick mild steel
plates (Fig. 5.3). The mould was covered by polythene paper and the ferrocement
shell was constructed by similar procedure as of the ferrocement overlay for bare
masonry column. On the second day, the mould was taken out and the hollow
ferrocement column was available for curing.
For construction of ferrocement overlay with a longitudinal groove along the column
axis (series DDA and DSA), a steel plate of 2 mm thick, 25 mm wide and 1300 mm
long was placed vertically at the mid point of each of the four faces of the specimen.
An 8 mm thick layer of mortar was applied around the column on which one layer of
discontinuous wire mesh was wrapped on the column as shown in Fig. 5.4 and tied
it. Then another 9 mm thick layer of mortar was applied. On this mortar layer,
another layer of discontinuous wire mesh was wrapped as before, on which
additional 8 mm mortar was applied to make a 25 mm thick ferrocement overlay for
series DDA. All steel plates were removed just after the construction of ferrocement
overlay. The same procedure was adopted for single layer of wire mesh for series
DSA. In this case the wire mesh was wrapped on the column after the application of
12.5 mm thick layer of mortar as shown in Fig. 5.4. Then another 12.5 mm thick
layer of mortar was applied to make a 25 mm thick ferrocement overlay. The
specimens of series DDAIDSA are shown in Fig. 5.5.
After construction, the columns were moist cured for 14 days by wrapping all the
faces with gunny bags and air cured in the laboratory for 14 days before testing (Fig.
5.6). Demec targets were attached at mid height to monitor longitudinal strains
before testing.
78
FIG. 5.3 MOULD FOR FERROCEMENT FIG. 5.2 COLUMN DURING CONSTRUCTIONHOLLOW COLUMN
79
FIG. 5.4 COLUMN (DDAlDSA) FIG. 5.5 COLUMN (DDAfDSA)DURING CONSTRUCTION AFTER CONSTRUCTION
80
5.2.4 Testing of Columns,
All the specimens were tested with a monotonically increasing vertical load upto
failure, A typical test arrangement is shown in Fig. 5.7. A summary of the tests
performed is schematically presented in Table 5.3.
The specimens were tested using universal testing machine of 1,800 kN capacity.
The vertical load was applied through a rigid steel bearing plate located on the top of
the specimen. Plywood sheets (2x1l4" thick) were placed at the top and bottom of
the column to absorb any local irregularities at the contact surfaces. After placing the
specimen in the testing machine, vertical alignment was adjusted to eliminate any
eccentricity.
At the start of each test, a small load (20 kN) was applied and then released. The zero
readings of the Demec Gauges were then recorded. The load was then applied in
increments. Different load increments were used for different types of columns.
Loads were recorded using machine dial gauge. Deformations were measured on a
central 200 rom gauge length on opposite faces of the columns using a Demec gauge.
The readings were averaged to eliminate the bending effects. The load was applied
incrementally until the final failure occurred. The total duration of loading was about
20 minutes. The cracking load, failure load, failure pattern and stress-strain
characteristics were recorded for every specimen during testing. A summary of the
observations is contained in Tables 5.4, and 5.5 and Fig. 5.8 and Appendix V. In case
of columns subjected to eccentric loading, a steel plate (12 rom x 12 rom x 300 rom)
was placed at the top of the column. The plate was placed at a distance 'e' (e = 77
rom for coated masonry columns and e = 64 rom for bare masonry columns) from the
centroidal axis of the columns as shown in the Table 5.3. The load was then applied
on the plate.
•
81
FIG. 5.6 CURING OF COLUMN IN FIG. 5.7 THE SPECIMEN BEFORE TESTTHE LABORATORY
ConcentricLoad
(NDA,NSA, 21 1 0.0NZA,NZAW,
BZA) ,~
Concentric 6 0.75 0.0Load
(GDA,GSA)
ConcentricLoad
(HDA,HSA)
EccentricLoad
(NDE,NSE,NZE,NZEW)
EccentricLoad
(BZE)
6
12
3
1
S2
0.0
0.26
0.26
AI=Loaded area = Shaded areaAt = Total areah = total width of column
NDA =Normal, double layer of wire mesh and tuia/loadingNSA ""Normal, single layer of wire mesh and ax/a/loadingNZA ""Normal, zero layer a/wire mesh and axial loadingNZA.W '" Normal, zero layer of wire mesh, axial loading and week mortarDDA ""Discontinuous, double layer a/wire mesh and ax/alloadingDSA ""Discontinuous, single layer a/wire mesh and axial loadingHDA ""Hol/ow, double layer a/wire mesh and axial loadingHSA = Hollow, single layer a/wire mesh and axfa/loadingGDA ""Top and bottom gap. double layer a/wire mesh and axial loadingGSA ""Top and bottom gap, single fayer a/wire mesh and axiaJloadingBZ4. == Bare. zero layer of wire mesh and ax/a/loadingNDE ""Normal. double layer of wire mesh and eccentric loadingNSE '" Nonnal, single layer a/wire mesh and eccentric loadingNZE ""Normal, zero layer of •••.lrt mesh and eccentric loadingNZEW ""Normal. zero layer o/wlre mesh, eccentric loading and week morlarBZE ""Bare. zero layer 0/ wire mesh and eccentric loading
83
5.2.5 Failure Load
The failure loads of different columns are shown in Tables 5.4 and 5.5. As expected,
failure load was minimum for bare column and maximum for column with
ferrocement overlay. It may be seen from Table 5.4 that in case of axial loading the
nominal stress at ultimate load of column with ferrocement overlay is 1.94 times of
that of the bare column and 1.89 times of that of the column with plaster. This
indicates that ferrocement has a good potential to be used as an overlay for
strengthening brittle structural elements like brick columns. It may be seen from
Table 5.5 that for eccentric loads the nominal stress at failure of masonry column
with ferroccment overlay is 2.54 times of that of the masonry column with plaster. It
is also interesting to note that the effect of number of layers of wire mesh is not
significant both for axial and eccentric loading. From Table 5.4 it is seen that the
load carrying capacity of axially loaded brick columns coated with rich mortar
(cement : sand = 1:2) is 1.07 times that of the columns coated with weak mortar
(cement: sand = 1:5).
5.2.6 Modes Of Failure
The failure pattern for axially loaded ferrocement coated columns (NDA series) has
been shown in Fig. 5.8 and the failure pattern for other series of axially loaded and
eccentrically loaded columns are given in Appendix V. It may be seen from the
figures that failure modes are different even for the same type of specimen and
loading, although they are usually of the same general form. This variation is due to
the variability in the properties of the joints, the bricks, the ferrocement and the
plaster.
In case of bare masonry columns, cracks were initiated in the vertical joints in the
region near mid-height of the columns as shown in Fig. A.V.1. In.most of the cases
local failure occurred near the ends of the specimens due to platen effect. The failure
84
Table 5.4 Experimental Cracking and Failure Loads(Axial Loading)
NDA2 652 689 7.91 765 769 8.83 HDA2 480 457 16.62
NDA3 675 752 HDA3 454
NSAI 652 762 HSAI 437
NSA2 585 7.31 764 769 8.83 HSA2 450 436 15.80637
NSA3 675 781 HSA3 423
NZAI 270 445 GDAI 360 621
NZA2 306 297 3.41 427 437 5.02 GDA2 427 382 4.38 648 622 7.14
NZA2 315 441 GDA3 360 598
180 387 GSAI 360 574
202 190 2.18 427 406 4.66 GSA2 382 375 4.30 628 603 6.92
190 405 GSA3 382 607
DDAI 708 BZAI 176 275
DDA2 648 653 7.50 BZA2 158 156 2.62 279 270 4.53
DDA3 603 BZA3 135 257
DSAI 686
DSA2 585 635 7.29
DSA3 634
NDA ~ Nonnal, double layer a/wire mesh and axial loadingNSA ~ Nonnal, J:inglelayer a/wire mesh and axial loadingNZ4 ~ Nonnal. zero layer a/wire mesh and axial loading, i.e. plain mortarNZ4 W ~ Nonnal. zero layer a/wire mesh, axial loading and weak mortarDDA ~ Discontinuous, double layer a/wire mesh and axial loadingDSA = DiscontinUl1us,single layer a/wire mesh and axial loadingHDA = Hal/ow, double layer a/wire mesh and axial loadingHSA ~ Hal/ow, .ufI1(lelayer 0/wire mesh and axial loadingGDA .. Top and hoI/om Rap, douhle layer 0/ wire mesh and axialloadingGSA ~ Top and hot/om gap, .ungle layer o/wire mesh and axial loadingBZA ~ Bare, zero layer a/wire mesh and axial loading
85
Table 5.5 Experimental Cracking and Failure Loads(Eccentric Loading)
Specimen Cracking ~,-::i. FailureLoad Tensile. Compcssiw' Load ."Mean Mean. (kN) load(kN)
, IIllIllinal IIllIllinal . (leN) JOiId(kN)-"'- ~-slress 'f' ~-;- -
NOEl 495 540 77 0.26NOE2 486 477 3.06 \4.02 553 522 3.35 15.35 77 0.26NOE3 450 473 77 0.26NSEI 405 486 77 0.26NSE2 405 427 2.74 \2.55 495 5\7 3.32 \5.20 77 0.26NSE3 472 572 77 0.26NZEI 270 405 77 0.26NZE2 315 300 1.93 8.82 432 417 2.68 12.26 77 0.26NZE3 315 414 77 0.26NZEIW 93 180 77 0.26NZE2W 100 97 0.62 2.85 203 205 1.31 6.03 77 0.26NZE3W 106 234 77 0.26BZEI 130 223 64 0.268ZE2 122 122 1.14 5.24 209 218 2.05 9.37 64 0.26BZE3 113 223 64 0.26
h = total width of columnNDE Normal, double layer of wire mesh and eccentric loadingNSE Normal, single layer of wire mesh and eccentric loadingNZE = Normal, zero layer of wire mesh and eccentric loadingNZEW = Normal, zero layer of wire mesh, eccentric loading and weak mortarBZE = Bare. zero layer of wire mesh and eccentric loading
86
of columns with ferrocement overlay occurred slowly, whereas failure of the bare
column or columns coated with plaster took place suddenly. The ultimate failure of
ferrocement coated masonry columns occurred mainly due to the formation and
propagation of a few dominant vertical cracks at the centre of the column, (Figs. 5.8
andA.V.2).
In case of columns with plaster the crack propagation was very rapid. In most of the
cases the cracks widened very quickly after their formation and spalling occurred
very rapidly near the ultimate load (Figs. A.V,3 and A.VA). In case of ferrocement
hollow columns, the fracture process was mainly confined at the ends of the
specimen. This can be attributed to the restraint provided by the platens. The spalling
failure normally occurred in this case due to high out-of-plane tensile stress, (Figs.
A.V.5 and A.v.6). The failure pattern for columns with discontinuous ferrocement
overlay (series DDA and DSA), which were tested mainly to see the confinement
effect of ferrocement overlay, is shown in Figs. A.V.7 and A.v.8. In most of the
cases the gap at the discontinuity widened gradually and the ferrocement overlay
separated totally from the masonry column near the ultimate load. No cracks were
found in the four separate pieces of the ferrocement overlay. The failure pattern of
columns from series GDA and GSA are the same as that of columns from series,
NDA and NSA (Figs. A.V.9 and A.V.lO).
The failure patterns of each column subjected to eccentric loading are shown in Fig.
A.V.l1 to Fig. A.V.15. The type of failure for the compression face of all the
specimens is the same as that for the concentric load case. No major crack appeared
at the tension face of the specimens.
87
,Y-"
I!\ 3
3 £ ,- .; . ,
I'~ I3 . ',~( , n• ~~~ u,. ~~ n
\
u.~. u.
8~ f
/i
,0° I i'rt: \ ' ',
,
.: ';.•'! I I " . , ,. !~:<'I. ' ..
FIG, 5.8 FAlLURE OF COLUMN COATED WITH FERRO CEMENT SERJES NDA(AXIAL LOADING)
88
5.2.7 Stress-strain Characteristics
The stress-strain curves for all the columns are shown in Fig. 5.9. Due to the nature
of the testing machine the falling branch (unloading portion) of the stress-strain
curves in these cases could not be obtained. From Fig. 5.9 it can be seen that all the
columns, with or without overlay, show a distinct non-linear stress-strain response
over almost the entire loading range, while the hollow ferrocement columns
maintains almost a linear behaviour upto the ultimate load. From the figure it can be
seen that the stiffuess of the columns with ferrocement overlay is higher than the
bare column. The columns with different wire mesh layers showed similar stress7
strain behaviour as can be seen from the figure. It may also be seen that the stiffuess
of masonry column coated with rich mortar (cement: sand = 1:2) is higher than the
masonry columns coated with normal mortar (cement: sand = 1:5).
5.3 CONFINEMENT EFFECT OF FERRO CEMENT OVERLAY ON MASONRY CORE
The behaviour of masonry in direct compression is improved if it is subjected to
compressive stresses in the transverse direction, resulting from confmement. When a
column is subjected to an axial load it is compressed in the vertical direction and
tends to expand in the lateral direction due to Poisson's effect. However, the
ferrocement overlay opposes the lateral expansion and imposes compressive stress
on the core. The structural behaviour of the column changes due to this confIDing
effect.
To obtain the strength increase of masonry column due to confinement effect of
ferrocement overlay, two types of investigations have been performed. In the first
case a vertical groove in the ferrocement overlay at each face of the column was
provided to discontinue the ferrocement overlay (Fig. 3.12) and hence to eliminate
the confmement effect of overlay. The difference in load carrying capacity of the
ferrocement encased masonry column and the column with discontinuous, ~- '~
"-./
89
14
1600140012001000800600400200oo
12
10
.•...•• -----.IIIa. 8 •:2:'-'IIIIII[!!•...C/)tii -.-NDAl:: 6 _-NSA"e -.-NZA0Z -,,-NZAW
-+-DDA-+-DSA
4 -X-HDA-Q-HSA-A-GDA-v-GSA--BZA
2
Strain (10-6)
FIG. 5.9 EXPERIMENTAL STRESS-STRAIN CURVES FOR DIFFERENT COLUMNS
90
ferrocement overlay was considered to be the increase of load due to confinement
effect in this case. In the second case the constituent members of the composite
system (ferrocement hollow column and bare masonry column) were tested
individually to failure. The difference in load carrying capacity of the ferrocement
encased masonry column and the total capacity of the individual members was
considered to be the increase ofload due to confinement effect in this case.
Table 5.6 Load Increase in Failure Due to Confinement Effect(Derived from Experiment)
NDA 769
DDA 653NSA 769
DSA 635NDA 769
BZA+HDA 727NSA 769
BZA+HSA 706
116
134
42
63
18
21
6
9
NDA = Normal, double layer of wire mesh and axial loadingNSA =Normal, single layer of wire mesh and axial loadingDDA =Discontinuous, double layer of wire mesh and axial loadingDSA = Discontinuous, single layer of wire mesh and axial loadingHDA = Hollow, double layer of wire mesh and axial loadingHSA =Hollow, single layer of wire mesh and axial loadingBZA = Bare, zero layer of wire mesh and axial loading
From the test results (Table 5.6) it can be seen that the failure load of ferrocement
encased column (specimen series NDA) is 18% higher than that of column encased
91
with discontinuous ferrocement overlay (specimen series DDA). Failure load of
ferrocement encased column (specimen series NSA) is 21% higher than that of
column encased in discontinuous ferrocement overlay (specimen series DSA). It can
also be seen from Table 5.6 that the failure load of column encased in ferracement
(specimen series NDA) is 6% higher than that of the sum of failure load of bare
column (specimen series BZA) and hollow ferrocement shell (specimen series
HDA). Failure load of column encased in ferrocement (specimen series NSA) is 9%
higher than that of the sum offailure load of bare column (specimen series BZA) and
hollow ferrocement shell (specimen series HSA). From this study it can be
conCluded that there is a confmement effect on the masonry column due to the
provision offerrocement overlay.
It is found that introduction of vertical grooves separating the overlay along the
centre line of the four faces of the columns represents a case where the overlay
consists of four separate angle sections with no transfer of stresses from one angle to
the other; this does not represent a hollow ferrocement section where there would be
sOmedirect stresses in the lateral direction. Although the failure pattern of the hollow
sections are different from those in the composite column, it appears that the second
case gives a better indication of the confinement effect.
5.4 INFLUENCE OF OVERLAY ON COST OF COLUMNS
The material cost of columns with different types of overlay has been shown in Table
5.7. It can be seen from the table that with the increase of 46% cross-sectional area of
bare masonry column (BZA/BZE) due to the application of different types of
overlay, the material cost increases by 233% for column with ferrocement overlay
containing double layer of wire mesh (NDA/NDE), 164% for column with
ferrocement overlay containing single layer of wire mesh (NSAlNSE), 48% for
column with plaster (I :5) (NZAWINZEW), and 95% for column.with plaster (1:2)
(NZAlNZE). The results of Table 5.7 show that, the material cost increases 124%
92
due to ferrocement overlay containing double layer of wire mesh (NDAlNDE)
instead of plaster (l :5) (NZA W/NZEW).
Table 5.7 Material Cost of Different Columns
Specimen NDA/NDE NSAINSE NZAW/NZEW NZAINZE BZAlBZEseries
Cost per 3mheight of Tk.l,065 Tk. 845 Tk.475 Tk.625 Tk. 320column
Percentage ofarea increasesover bare 46 46 46 46masonrycolumn
Cost differencewith bare +Tk.745 + Tk. 525 +Tk. ISS + Tk. 305 -masonry
column(BZA)Cost differencewith masonrycolumn with + Tk. 590 + Tk. 370 - + Tk. ISO - Tk. ISSplaster (I :5)(NZAW)Percentage
increase of cost 233 164 48 95 -overbaremasoI1l)'column(BZA)Percentage
increase of costover masonry 124 78 - 32 - 32column withplaster (l :5)(NZAW)
The procurement costs have been calculated on the basis of prices of bricks, sand, cementand wire mesh used in the test specimen.
NDA = Normal, double layer a/wire mesh and axial loadingNSA = Normal, single layer a/wire mesh and axial loadingNZA = Normal, zero layer a/wire mesh and axial loading, i.e. piane morfarNZAW = Normal, zero layer a/wire mesh, axial loading and weak morfarBZA = Bare, zero layer a/wire mesh and axial loadingNDE = Normal, double layer 0/wire mesh and eccentric loadingNSE = Normal, single layer 0/wire mesh and eccentric loadingNZE = Normal, zero layer a/wire mesh and eccentric loadingNZEW = Normal, zero layer 0/wire mesh, eccentric loading and weak morfarBZE = Bare, zero layer 0/wire mesh and eccentric loading
93
It is also seen from Table 5.7 that, the material cost increases 78% due to
ferrocement overlay containing single layer of wire mesh (NSAlNSE) instead of
plaster (1:5) (NZAWINZEW). From Table 5.7 it is seen that, the material cost of
column series NDAlNDE, series NSAlNSE, series NZAWINZEW and series
(NZAlNZE) increases in Tk. 745, Tk. 525, Tk. 155 and Tk. 305 over bare masonry
column (BZNBZE). It is also seen from table that, the material cost of column series
NDAlNDE, series NSAlNSE, and series (NZAlNZE) increases in Tk. 590, Tk. 370,
and Tk. 150 over masonry column with plaster (1:5) (series NZAWINZEW).
5.5 SUMMARY
The experimental investigation of columns subjected to axial and eccentric loading
has been described in this chapter. The types of ferrocement overlay were changed to
observe the variations in the behaviour and failure modes. The following conclusions
can be drawn from this experimental study.
1. The application of fetrocement overlay on bare brick masonry column
enhances the load carrying capacity both for axial and eccentric loadings.,With the increase of 46% croSs sectional area of column due to application of
ferrocement overlay, the average increase in failure load is found to be 184%
for axial loading and 158% for eccentric loading. The average increase in
failure nominal stress is found to be 95% for axial loading
2. With the increase of 46% cross-sectional area of bare masonry column due
the application of ferrocement overlay, the material cost increases by 233%
for column with ferrocement overlay containing double layers of wire mesh
and 164% for column with ferrocement overlay containing single layer of
wire mesh.h.
94
3. The application of plaster with a weak mortar (1:5) over bare masonry
column increases the failure load by 50% and increases the nominal stress at
failure only by 2.8%.
4. The use of plaster with rich mortar (1:2) instead of weak mortar (1:5) for
brick columns does not increase the load carrying capacity significantly. The
increase in strength (compared to a column encased in weak mortar) was
approximately 7%.
5. The cracking resistance of bare columns is improved due to the provision of
ferrocement overlay. The average increase in cracking nominal stress is found
to be about 200% for axial loading
6. The failure of bare column and column coated with plaster is sudden and
crack widths increase very rapidly after their formation, leading to brittle
failure for the system, whereas the failure of columns with ferrocement
overlay Occurred slowly.
7. There is a confmement effect on bare column due to the provision of
ferrocement overlay and the effect of confinement varies from 6% to 9%.
CHAPTER 6
NONLINEAR FINITE ELEMENT ANALYSIS
6.1 INTRODUCTION
With the advent of sophisticated numerical tools for analysis like the finite element
method (FEM), it has become possible to model the complex behaviour of brick
masonry column encased in ferrocement and plaster with appropriate constitutive
relationships. In this study all the columns were analysed using the finite element
method (FEM) available in ANSYS package. The objective of this chapter is to carry
out the fInite element analysis of the columns in order to obtain a better understanding of
the stress redistribution and progressive cracking of the ferrocement and the masonry.
6.2 ANALYSIS OF THE COLUMNS
In order to simulate the actual behaviour of columns, it is essential that the three-
dimensional nature of stress distribution is recognized. A three dimensional fInite
element analysis has, therefore, been performed for the columns mentioned in the
previous chapter. As mentioned earlier the finite element computer program used for
this analysis is taken from ANSYS package.
The constituent materials were assumed to be isotropic and a perfect bond is assumed at
the interface between the brick and the mortar joint, the ferrocement and the brick. In
case of ferrocement, the wire meshes were assumed to be smeared throughout the
element. The brickwork has been considered as nonhomogeneous continuum Le. bricks
and mortar joints were treated separately.
In the analyses the prescribed displacement has been applied at the nodes of the interface
between the machine platen and the specimen to simulate the load applied from bearing
96
plate of the machine. To simulate the friction between column and the rigid plate the
nodes were restrained along the horizontal directions (X and Y). The nodes at the base
of the column were restrained along X, Y and Z directions and the nodes at the plane of
symmetry were assigned appropriate restraint as shown in Figs. 3.1 and 3.12 for the
axial loading case. In case of eccentric loading the nodes at the base of the column were
restrained in X, Y and Z directions whereas the nodes at the plane of symmetry were
restrained in X direction only as shown in Fig. 3.14.
6.2.1 Material Deformation Characteristics and Failure Criteria
The nonlinear behaviour of brick masonry is caused mainly due to plasticity, cracking
and crushing type of fracturing. For modeling plasticity the Besseling model, also called
the sublayer or overlay model has been adopted in this analysis. Fig. A.III.3 and Table
A.III.l illustrates typical stress-strain curve and data input is demonstrated by an
example. The material model can predict elastoplastic behaviour through to fracture of
the constituent materia!. To predict cracking or crushing type of failure the stress-strain
matrix is adjusted as discussed in Appendix III. The failure criterion of William and
Warnke (97) has been used in this analysis and is discussed in Appendix III.
6.3 METHOD OF LOAD APPLICATION
The load was applied in the form ofincrementai prescribed displacements of the loading
plate for axial load case only. For the eccentric loading case, distributed load was
applied. The corresponding displacement/load increment varied from test to test. The
displacement/load increment was maintained constant until the cracks initiated after
which a smaller increment of displacement/load was considered. This procedure of
applying small increment of displacement/load after the initiation of fracture, allows
faster convergence Ofthe solution and more cracks to propagate in a narrow band.
97
6.4 FAILURE MODES
It is well known that in a vertically loaded masonry column tensile cracking type of
fracture dominates the whole fracture process. Transverse stresses are mainly
responsible for influencing the ultimate failure load of the column. The crack in this case
will start from the vertical mortar joints and then propagate through the bed joints, other
header joints and the bricks. The failure pattern for each case of axial loading has been
shown in figures 6.1, 6.2 and Appendix VI. It should be pointed out that in case of
ferrocement coated columns (series NDA and NSA) crack initiated from the vertical
joints but the propagation of cracks was delayed to some extent. All the columns
continued to sustain further load until the crack or cracks propagated through a
substantial portion of the column. The failure pattern of columns NDA and NSA are
shown in Figs. 6.1 and 6.2. In case of columns with plaster (series NZA and NZA W) the
crack propagation was very rapid. In these cases the cracks propagated very quickly
after their formation and failure occurred shortly afterwards. The failure patterns are
shown in Figs. A.VI.I and A.VI.2 respectively. In case of masonry columns coated with
discontinuous ferrocement overlay (series DDA and DSA) cracks initiated from the
vertical joints and then propagated through the bed joints and the bricks. In this case no
crack appeared in the ferrocement overlay as shown in Figs. A.VI.3 and A.VIA. In case
of ferrocement hollow column (series HDA and HSA) the fracture process is mainly
confmed at the ends of the column. This is due to the friction developed at the interface
between the specimen and the machine platen. The failure patterns at ultimate load for
column series HDA and HSA are shown in Figs. A.VI.5 and A.VI.6 respectively. The
failure patterns for columns series GDA and GSA (Figs. A.VI.7 and A.VI.8) are very
similar to the failure patterns of column series NDA and NSA. In case of bare masonry
columns (series BZA) the cracks initiated in the vertical joints near the top of the column
and then propagated through the bed joints and the bricks. The failure pattern for this
case is shown in Fig. A.VI.9. The failure patterns for each case of eccentric loading have
been shown in Figs. A.VI.!O, A.VI.!I, A.VI.12, A.VI.13 and A.VI.14. For eccentrically
98 ,
•
.,
Outer Ferrocement Shell Centra! Masonry Core
• Cracked Blement
Mortar Joint
FIG. 6.1 PREDICTED FAll.URE MODE OF COLUMN SERIES NDA
99
Outer Ferrocement Shell Central Masonry Core
• Cracked Element
••••
Mortar Joint
FIG. 6.2 PREDICTED FAILURE MODE OF COLUMN SERIES NSA
100
loaded columns failure occurs near the top of the column as shown in figures from
A.VI.I0 to A.VI.14.
6.5 FAILURE LOAD
In this analysis complete failure of the columns is assumed when the solution failed to
converge. The failure load of columns (both axial and eccentric loading) with different
types of overlay has been shown in Table 6.1 and 6.2.
o~~SJ[.~'~.@-;~~~~~..- ..~[_.=~Table 6.1 Analytical Cracking and Failure LoadAxi
Load(kN) Nominal Load(kN) Nominalstress a stress a
NDA 354 4.07 788 9.06
NSA 346 3.98 725 8.34
NZA 343 3.94 525 6.04
NZAW 314 3.61 468 5.38
DDA 318 3.65 639 7.35
DSA 314 3.61 617 7.01
HDA 301 10.99 396 14.46
HSA 279 10.19 365 13.33
GDA 256 2.94 550 6.32
GSA 255 2.93 528 6.07
BZA 250 4.19 324 5.44
NDA ~ Normal, double layer a/wire mesh and axiallaadingNSA = Normal, single layer a/wire mesh and axial loadingNZA =Normal, zero layer a/wire mesh and axial loadingNZA W =: Normal, zero layer of wire mesh, axial loading and week mortarDDA = Discontinuous, double layer a/wire mesh and axial loadingDSA = Discontinuous, single layer a/wire mesh and axial/oatlingHDA = Hollow, double layer a/wire mesh and axiallaadingHSA = Hollow, single layer a/wire mesh and axial loadingGDA = Top and hollom gap, double layero/wire mesh and axiallaadingGSA ~ Top and bollom gap, single layer o/wire mesh and axial loadingBZ4. = Bare, zero layer a/wire mesh and axial loading
101
As expected the failure load was minimum for unplastered masonry column and
maximum for column coated with ferrocement overlay. From Table 6.1 it can be seen
that in case of axial loading the ultimate load carrying capacity of masonry column with
ferrocement overlay (series NDA) is about 1.6 times than the corresponding column
coated with plaster (series NZAW). This indicates that the ferrocement overlay can be
used to strengthen the brittle structural element like brick columns. In case of eccentric
loading it can be seen from Table 6.2 that the ultimate load carrying capacity of masonry
column with ferrocement overlay (series NZE) is about 1.9 times the masonry column
coated with plaster. From Tables 6.1 and 6.2 it can be also seen that there is no
appreciable increase of ultimate load due to the provision of double layers of mesh
instead of single layer of wire mesh in ferrocement overlay for both axial and eccentric
load cases. This has also been observed experimentally as mentioned in Chapter 5.
Table 6.2 Analytical Cracking and Failure Loads(Eccentric Loading)
NDE 335 2.15 9.85 481 3.09 14.14 77 0.26
NSE 335 2.15 9.85 454 2.92 13.35 77 0.26
NZE 252 1.62 7.41 434 2.78 12.76 77 0.26
NZEW 125 .80 3.67 250 1.60 7.35 77 0.26
BZE 71 .66 3.05 185 1.72 7.95 64 0.26
h = total width of columnNDE =Normal, double layer of wire mesh and eccentric loadingNSE =Normal, single layer of wire mesh and eccentric loadingNZE =Normal, zero layer of wire mesh and eccentric loadingNZEW =Normal, zero layer of wire mesh, eccentric loading and weak mortarBZE =Bare, zero layer of wire mesh and eccentric loading
102
6.6 CONFINEMENT EFFECT OF FERROCEMENT OVERLAY
A nonlinear fInite element analysis has been performed to see the confInement effect of
ferrocement overlay on masonry column. In this case the lateral continuity of the overlay
has been disrupted by providing longitudinal groove of 6.35 mm wide through the
height of the column. It is assumed that the difference in load carrying capacity of this
composite column and the laterally confIned composite column is mainly due to the
confInement effect of ferrocement overlay. From the results shown in Table 6.3, the
failure load of masonry columns with ferrocement overlay (series NDA and NSA) is
higher than that of masonry columns with discontinuous ferrocement overlay (series
DDA and DSA). It can also be seen from Table 6.3 that the sum of the failure load of
bare masonry column (series BZA) and hollow ferrocement shells (series HDA and
HSA) is lower than that of ferrocement encased masonry columns (series NDA and
NSA).
From the results (Table 6.3) it can be seen that the failure load of ferrocement encased
column (specimen series NDA) is 23% higher than that of column encased with
discontinuous ferrocement overlay (series DDA). Failure load of ferrocement encased
column (series NSA) is 17% higher than that of column encased in discontinuous
ferrocement overlay (series DSA). It can also be seen from Table 6.3 that the failure
load of column encased in ferrocement overlay (series NDA) is 9% higher than that of
the sum of failure load of bare column (series BZA) and hollow ferrocement shell (series
HDA). Failure load of column encased in ferrocement overlay (series NSA) is 5%
higher than that of the sum of failure load of bare column (series BZA) and hollow
ferrocement shell (series HSA). From this study it can be concluded that there is a
confInement effect on the masonry column due to the provision of ferrocement overlay;
however, this is not very signifIcant and varies from 5% to 9%.
103
Table 6.3 Load Increase in Failure Due to Confinement Effecterived from Anal sis
NDA 788
DDA 639
NSA 725
DSA 617
NDA 788
BZA+HDA 720
NSA 725
BZA+HSA 689
149
108
68
36
23
17
9
5
NDA =Normal, double layer a/wire mesh cind axial loadingNSA =Normal, single layer a/wire mesh and axial loadingDDA = Discontinuous, double layer o/wire mesh and axial loadingDSA =Discontinuous, single layer a/wire mesh and axial loadingHDA =Hollow, double layer a/wire mesh and axial loadingHSA = Hollow, single layer o/wire mesh and axial loadingBZA = Bare, zero layer o/wire mesh and axial loading
6.7 STRESS-STRAIN CHARACTERISTICS
The stress-strain curves for axial and eccentric loading cases have been provided in Figs.
6.3 and 6.4 respectively. From these figures, it can be seen that all the columns (with or
without overlay) show a distinct nonlinear stress-strain curve over almost the entire
loading range. The nominal E value of hollow ferrocement columns is higher than all
other columns. The stiffness of the columns with ferrocement overlay is higher than that
of the bare columns and columns coated with plaster. From Figs ..6.3 and 6.4 it can be
104
14
12
10
en~enro.~ 6Eoz
4
2
oo 400 800 1200
Strain (10-0)
•
-----NDA-NSA-a-NZA-.-NZAW-DDA-+-DSA-x-HDA-o-HSA-o-GDA-L>-GSA--BZA
1600 2000
FIG. 6.3 STRESS-STRAIN CURVE FOR DIFFERENT COLUMNS wrrnAXIAL LOAD OBTAINED FROM FEM ANALYSIS
105
600P,
800
-.-NDE_-NSE-A-NZE-~-NZEW--BZE
600
P,=Total eccentric loadA ~ C.G. of the loade = eccentricityL = gauge length 200mmAverage strain calculatedbetween B and C
400
Strain (10~
,,
,----- -- ---~~-----
-/{'
200
L
oo
100
200
500
400
Ze. 300"C01
.3
FIG. 6.4 LOAO-S1RAIN(COMPRESSIVE SIDE) CURVE FOR DIFFERENT COLUMNSWITH ECCENTRIC LOAD OBTAINED FROM FEM ANALYSIS
106
also seen that the stiffuess of masonry column coated with rich mortar (cement: sand =
1:2) is higher than the masonry column coated with normal mortar (cement: sand = 1:5).
6.8 SUMMARY
In this chapter a nonlinear finite element analysis has been performed on the composite
behaviour of masonry column encased in ferrocement overlay. In the analyses both axial
and eccentric loading have been considered. The following conclusions can be made
from this study.
1. The application of ferrocement overlay on bare masonry column instead of
plaster (1:5) overlay enhances the load carrying capacity quite significantly both
for axial and eccentric loadings. The increase in strength for axial loading is
found to be 68% and 55% in case of double and single layer of wire mesh
respectively. In case of eccentric loading the increase in strength has been found
to be 92% and 82% for double and single layer of wire mesh respectively.
2. With the increase of 46% cross-sectional area of bare masonry column due the
application of ferrocement overlay, the material cost increases by 233% for
column with ferrocement overlay containing double layers of wire mesh and
164% for column with ferrocement overlay containing single layer of wire mesh.
3. The cracking resistance of bare masonry columns is improved quite significantly
due to the provision of ferrocement overlay. The increase in cracking nominal
stress is found to be about 220% for eccentric loading.
4. The strength increase of bare masonry column due to the passive confinement of
ferrocement overlay is between 5% to 9%.
5. The crack propagation in a ferrocement encased masonry column is slower than
the columns without ferrocement overlay.
107
6. The nominal E value of columns with ferrocement overlay is 63% and 38%
higher than bare masonry columns and masonry columns with plaster
respectively.
CHAPTER 7
COMPARISON OF RESULTS FROM FINITE ELEMENT ANALYSIS AND
EXPERIMENTAL RESULTS
7.1 INTRODUCTION
Experimental investigation performed on different types of columns and the results
obtained have been presented in Chapter 5. Nonlinear ftnite element analyses have
been performed and the results presented in Chapter 6. In this chapter a comparison
has been made between nonlinear ftnite element analysis and experiments performed
on bare masonry columns, masonry columns with ferrocement overlay and hollow
ferrocement columns. The initial cracking load, the ultimate load, the failure pattern,
the stress-strain curves and confmement effect for each case are compared.
7.2 INITIAL CRACKING LOAD
The analytical initial cracking loads for different cases are compared with the
experimental values presented in Tables 7.1 and 7.2. It can be seen from Table 7.1
that the experimental cracking loads were 1.94 and 1.84 times the analytical cracking
loads in case of column encased in ferrocement overlay containing double and single
layer of wire mesh respectively. From Table 7.1 it can be seen that the experimental
cracking loads of all other columns encased in ferrocement overlay (specimen series
GDA and GSA) were 1.49 and 1.47 times the analytical cracking loads. It can also
be seen from Table 7.1 that the experimental cracking loads in case of bare columns
and columns encased in plaster were 0.62, 0.86 and 0.60 times the analytical
cracking loads (specimen series BZA, NZA and NZAW). In case of eccentrically
loaded column it can be seen from Table 7.2 that the experimental cracking loads
were 1.42, 1.27, 1.19, 0.77 and 1.71 times the analytical cracking loads (specimen
series NDE, NSE, NZE, NZEW and BZE). The variation of experimental cracking
109
Table 7.1 Analytical and Experimental Cracking and Failure Load(Axial Loading)
.SpeGUne . CraGldng Load (pcrY Por{E~t)/.' Failure Lqad (PJ Pu~t)Type (kN) PettFEM) '" (kN) Pu(FEA)
J
" ~xperiment Finite' E~.erlment Finite.,";. (Avg.Qf Element, ! V\v~.(jf Element'. ,; tb,ree) " A:u.aJ,ysis • three) ,Analysis"Pcr{Ex;pt) P~, Pu{E;Ij(pt) Pu(FBA)
NDA 689 354 1.94 769 788 0.97NSA 637 346 1.84 769 725 1.06NZA 297 343 0.86 437 525 0.83NZAW 190 314 0.60 406 468 0.87DDA --- 318 --- 653 639 1.02DSA --- 314 --- 635 617 1.03HDA --- 301 --- 457 396 1.15HSA --- 279 --- 436 365 1.19GDA 382 256 1.49 622 550 1.13GSA 375 255 1.47 603 528 1.13BZA 156 250 0.62 270 324 0.83
NDA = Normal, double layer o/wire mesh and axialloodingNSA '" Normal, single layer o/wire mesh and axialloodingNZA = Normal, zero layer o/wire mesh and axialloodingNZAW = Normal, zero layer o/wire mesh, axiallooding and weak mortarDDA = Discontinuous, double layer o/wire mesh and axialloodingDSA = Discontinuous, single layer o/wire mesh and axialloodingHDA = Hollow, double layer 0/wire mesh and axialloodingHSA = Hollow, single layer o/wire mesh and axialloodingGDA = Top and bottom gap, double layer o/wire mesh and axialloodingGSA = Top and bottom gap, single layer o/wire mesh and axiallooding1JZA = Bare, zero layer o/wire mesh and axiallooding
110
load is from -40% to 94% in comparison with the analytical cracking load in case of
axial loading and the variation of experimental cracking load is from -23% to 42% in
comparison with the analytical cracking load in case of eccentric loading. It appears
from the above discussion that the analytical results do not agree with the
experimental results. This is because the analytical cracking loads are directly related
to the strength of the vertical mortar joints, since the fIrst crack always formed in
these elements.
Table 7.2 Analytical and Experimental Cracking and Failure Loads(Eccentric Loading)
NDE 477 335 1.42 522 481 1.08
NSE 427 335 1.27 517 454 1.13
NZE 300 252 1.19 417 434 0.96
NZEW 97 125 0.77 205 250 0.82
BZE 122 71 1.71 218 185 1.17
NDE = Normal, double layer o/wire mesh and eccentric loodingNSE =Normal, single layer o/wire mesh and eccentric IOodingNZE =Normal, zerO layer o/wire mesh and eccentric loodingNZEW =Normal, zero layer o/wire mesh, eccentric looding and weak mortarBZE ""Bare, zero layer o/wire mesh and eccentric loading
The fIrst cracking in the analytical investigation always occurs in the vertical mortar
joints inside the columns. Obviously these cracks are not visible from the outside.
The experimental cracking load represents the load at which the fIrst crack is visible
on the exterior surface of the column. The exact experimental iIiitial cracking load
111
corresponding to the failure of the vertical joints could not be observed due to the
presence of plaster or ferrocement overlay. In the analytical investigation, cracks
occurred in the vertical joints long before the cracks were detected experimentally in
the plaster or ferrocement overlay by naked eyes. In the experimental investigation
local cracks appeared in the surface of the columns (series NZA, NZAW, BZA and
NZEW) long before the cracks were occurred analytically in the vertical joints.
Analytical model assumes uniform properties of the constituent materials throughout
the whole column. However, the material properties may vary within the actual
column. The fIrst initial crack may be in a location which has the weakest mortar.
For the columns encased in discontinuous ferrocement overlay (series DDA and
DSA) and for the hollow ferrocement column (series HDA and HSA), the initial
cracking load could not be measured experimentally because of sudden failure.
7.3 FAILURE LOAD
The analytical failure load of the columns was obtained from fInite element analysis.
Tables 7.1 and 7.2 show the comparisons between the analytical results and the
experimental results for axial and eccentric loading respectively.
It can be seen from Table 7.1 that the experimental failure loads were 0.97 and 1.06
times the analytical failure loads in case of column coated with ferrocement overlay
containing double and single layer Ofwire mesh respectively. From Table 7.1 it can
be seen that the experimental failure loads of all other columns coated with
ferrocement overlay (specimen series DDA, DSA, GDA and GSA) were 1.02, 1.03,
1.13 and 1.13 times the analytical failure loads. It is noted from these comparisons
that analytical results compare reasonably well with the experiment. It can also be
seen from Table 7.1 that the experimental failure loads in case of bare columns and
columns coated with plaster were 0.83, 0.83 and 0.87 times the analytical failure
loads (specimen series BZA, NZA and NZAW). These variations occur due to
inadequacy of the bond failure criterion of the material model available in ANSYS
112
package. In case of eccentrically loaded ferrocement encased masonry column it can
be seen from Table 7.2 that the experimental failure loads were 1.08 and 1.13 times
the analytical failure loads (specimen series NDE and NSE). It can also be seen from
Table 7.2 that the experimental failure loads in case of columns coated with plaster
were 0.96 and 0.82 times the analytical failure loads (specimen series NZE and
NZEW). From Table 7.2 it can be seen that the experimental load in case of bare
masonry column was 1.17 times the analytical failure load (specimen series BZE).
This variation may occur due to non-inclusion of bond failure criterion in the model
used in FEA. However, further investigation is required incorporating the appropriate
bond failure criterion in the ANSYS package. Overall the variation of failure loads in
case of eccentric load is almost similar to that of axial load. The variation of
experimental failure load is from -17% to 19% in comparison with the analytical
failure load in case of axial loading and the variation of experimental failure load is
from -18% to 17% in comparison with the analytical failure load in case of eccentric
loading. From the comparison of experimental loads with finite element prediction,
it is concluded here that the agreement between the finite element analysis and
experiment is reasonable.
7.4 FAILuRE PATTERN
Final cracking patterns rather than the sequence of cracking are compared in this
study, since it was not possible to record the experimental cracking sequence in
many cases. Comparisons between experimental and analytical failure patterns are
presented for different cases (Fig. 7.1 and Appendix Vll). Only failure pattern of
peripheral elements are presented. From these figures it can be seen that there is
reasonably a good agreement between the experimental failure patterns and the
failure patterns predicted by the finite element analysis.
I,
113
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. 7.1 FAILURE MODE OF COLUMN SERIES NSA
10 10
16001200800400
8
200016001200800400oo
8
~Ol 6a.~
f-'
/ ~1/1
I f-'
~
1/1
~
Ol 6
Q)
a.
17>
//
~
I J
~
(ij
1/11/1
c:
l!1
'E
Ci5
(I 0Z
~
(ij
.. -FEM
c: 4
J 1/ . ---EXPT.
'E0z
I . FEM I---EXPT.2 ~ I,
Strain (10")FIG. 7.2 STRESS-STRAIN CURVE OF COLUMN SERIES NDA
Strain (1(y')
FIG. 7.3 STRESS-StRAIN CURVE OF COLUMN SERIES NSA
115
7.5 STRESS-STRAIN CURVES
Comparisons are made between the stress-strain curves of different columns obtained
from experiment and those obtained from finite element analysis. The comparison
for NDA and NSA series is shown in Figs. 7.2 and 7.3 and the comparison for other
cases is shown in the Appendix vn. It is seen from Figs. 7.2, 7.3 and Appendix vnthat the value of "modulus of elasticity" for the composite column derived from
analytical curves are higher than those obtained from the experimental curves for
almost all the columns. This is due to the fact that the stiffuess of the elements in the
finite element model is higher than the actual stiffuess of the structure. In case of
columns NZAW and BZA (Fig. A.Vll.17 and Fig. A.Vll.24) there is a considerable
difference between the two curves. This variation occurs due to the non-
incorporation of bond failure criterion in the finite element analyses. However, from
the comparison of experimental and analytical stress-strain curves, it can be
concluded that in general, the agreement between fmite element analyses and
experiment is reasonably good.
7.6 CONFINEMENT EFFECT
To examine the confmement effect of ferrocement overlay, both experimental and
analytical investigations have been made in this study. Two different cases were
considered to eliminate the confinement effect of ferrocement overlay on masonry
column as mentioned in Chapter 5. As outlined in Art. 5.3, in the fIrst case a vertical
groove in the ferrocement overlay at each face of the column was provided to
discontinue the ferrocement overlay (Fig. 3.12) and hence to totally eliminate the
capability of overlay to resist direct stresses in the lateral direction. The difference in
load carrying capacity of the ferrocement encased masonry column and the column
with discontinuous ferrocement overlay was considered to be the increase of load
due to confmement effect. In the second case the constituent members of the
116
composite system (ferrocement hollow column and bare masonry column) were
tested individually to failure. The difference in load carrying capacity of the
ferrocement encased masonry column and the total capacity of the individual
members was considered to be the increase of load due to confinement effect in this
case. The results for the cases are presented in Table 7.3.
Table 7.3 Load Increase in Failure Due to Confinement Effect
NDA 769 788116 149
DDA 653 (17%) 639 (23%)NSA 769 725
134 108DSA 635 (21%) 617 (17%)NDA 769 788
42 68BZA+HDA 727 (6%) 720 (9%)NSA 769 725
63 36BZA+HSA 706 (9%) 689 (5%)NDA =Normal, double layer o/wire mesh and axial loadingNSA =Normal, single layer o/wire mesh and axial loadingDDA =Discontinuous, double layer o/wire mesh and axial loadingDSA =Discontinuous, single layer o/wire mesh and axial loadingHDA =Hollow, double layer o/wire mesh and axial loadingHSA =Hollow, single layer o/wire mesh and axial loadingBZA = Bare, zero layer o/wire mesh and axial loading
From the table it is seen that the strength increase of masonry column encased in
ferrocement overlay due to the confinement effect is between 17% to 23% for the
first case (composite column with grooves in ferrocement overlay). It is also seen
117
from Table 7.3 that the strength increase of masonry column encased in ferrocement
overlay due to the effect of confinement is between 5% to 9% for the second case
(masonry column and ferrocement hollow column). As discussed in Art. 5.3, the
confinement effect determined from bare masonry column and hollow ferrocement
column has been considered to be more representative in this study.
7.7 SUMMARY
A comparison between the experiment and the finite element analysis of composite
behaviour of masonry column coated with ferrocement overlay has been presented in
this chapter. The cracking load determined from tests is usually higher since it is not
possible to observe cracks (which are usually initiated inside the columns) during
tests; cracking loads determined from tests represent the values when cracks appear
on the surface of the column. However, in case of failure loads, the agreement
between finite element analysis and experiment is good. The finite element model
available in the ANSYS package will, therefore, be used onwards for predicting
failure loads. The following conclusions can be drawn from this study.
1. The variation of experimental cracking load IS from -40% to 94% in
comparison with the analytical cracking load.
2. The variation of experimental failure load is from -17% to 19% in comparison
with the analytical failure load.
3. The experimental failure patterns and the failure patterns predicted by the
finite element analysis are almost similar.
4. The value of modulus of elasticity for the composite column derived from
analytical curves are higher than those obtained from. the experimental
curves for almost all the columns
118
5. The strength increase of masonry column encased in ferrocement overlay due
to the confmement effect is between 5% to 9% analytically and the strength
increase of masonry column encased in ferrocement overlay due to the effect
of confmement is between 6% to 9% experimentally.
CHAPTER 8
SENSITIVITY ANALYSIS OF CRITICAL PARAMETERS
8.1 INTRODUCTION
The material properties determined from experiment on individual components and
small brick masonry specimens have been incorporated in the three-dimensional
finite element analysis. The appropriateness of the material model adopted in the
analysis have already been verified by carrying out experiments on masonry columns
coated with ferrocement. Although, the results of the experiments agreed well with
the prediction of the fmite element analyses, it is also important to determine which
parameters of the material model and the fmite element analysis are particularly
significant. In this chapter a study of the parameters affecting the fracture behaviour
of column is performed by analysing the behaviour of a ferrocement coated column
subjected to axial load, distributed uniformly over the cross-section. Individual
parameters are changed in turn and the influence of each change is investigated. In
the analysis a colunm encased in ferrocement, containing double layers of wire mesh,
is investigated (column series NDA).
Two groups of parameters are considered for this sensitivity analysis, one which
affects the material model and the other which relates directly to the finite element
analysis. The parameters which directly affect the material model are,
(i) Elastic properties (viz. modulus of elasticity and Poisson's ratio) of the
constituents
(ii) Bed joint thickness
(iii) Tensile strength of the constituent materials
(iv) Compressive strength ofthe constituent materials
120
(v) Number oflayers of wire mesh
The parameters which do not affect the material model directly but affect the finite
element analysis are:
(i) Finite element size
(ii) Slenderness ratio of the column
8.2 LINEAR ELASTIC FRACTURE ANALYSIS
This study was carried out to test the possibility of assuming linear elastic properties
for the brick, the mortar and the ferrocement in the finite element analyses using
ANSYS package. This has significant advantages in reducing computer time. Bricks,
mortar and ferrocement were assumed to remain linearly elastic; therefore
progressive cracking was the only source of nonlinearity. The columns encased in
ferrocement, containing double, single and zero layer(s) of wire mesh and bare
masonry columns were considered in this investigation. The original material
properties of the constituents were kept constant. The ultimate loads for both the
linear and nonlinear elastic properties are compared in Table 8.1. The failure pattern
for both the cases are shown in Figs. 8.1,8.2 and 8.3.
From the results of this study, it is seen that the assumption of elastic behaviour has
small influence on both the ultimate load and the fmal failure pattern of the colurrm.
In case of linear elastic fracture analysis, the ultimate load is 3.4% to 9.8% higher in
comparison to the nonlinear analysis. Previous investigations (8) showed that a linear
elastic fracture analysis is reasonably adequate to predict the behaviour of masonry
panels under concentrated loading. However, the behaviour of other types of
masonry structures could be influenced by the nature of relations between stress and
plastic strain.
121
• Cracked Element
Non-Linear Fracture Analysis Elastic Fracture Analysis
FIG.8.1 MODE OF FAILURE OF COLUMN SERIES NDA
122
• Cracked Element
Non-Linear Fracture Analysis Elastic Fracture Analysis
FIG.8.2 MODE OF FAILURE OF COLUMN SERIES NSA
123
• Cracked Element
Non-Linear FraclIJre Analysis Elastic FracllJre Analysis
FIG.S.3 MODE OF FAILURE OF COLUMN SERIES NZAW
124
Table 8.1 Influence of Linear Elastic Fracture Analysis
NDA
NSA
NZAW
BZA
788
725
468
324
831
795
484
356
1.054
1.096
1.034
1.098
15,086
14,879
6,304
1,257
1,869
1,831
724
186
From this study, it can therefore be concluded that nonlinear analysis may not be
necessary to predict the behaviour of masonry columns coated with ferrocement, and
that a linear elastic fracture analysis could be adequate. Moreover, it takes less
computing time (using RS6000). For these reasons linear elastic fracture model has
been used for the sensitivity analysis in the subsequent sections.
8.3 INFLUENCE OF VARIOUS PARAMETERS ON THE MATERIAL MODEL
\
8.3.1 Elastic Properties of the Constituent Materials
The influence of the elastic properties was studied by varying both the modulus of
elasticity and Poisson's ratio of the ferrocement mortar, holding the brick properties
constant at their original value (Eb = 17,187 MPa, Vb= 0.16). Only one parameter
was varied at a time. A summary of the values used is given in Table 8.2.
125
Table 8.2 Parametric Study of Elastic Properties, (EtlErnJ and Vrm-~------':--'--~r-'-".--r- .-,-'r---- -_.."~, I ~ ' 1<',,-r. I" __ ;!!t'l" J)I l,.. . ",. '..".,. -,,.. 'I , .• V' •...,l (O~.ll1;JD I; j : IJ{i)jX!! • ,". ;
..... ,. 1'. . .l i[ ,O.~~rD _ : ' _ . i-
19,000 0.25 0.90 859 1.033
19,000 0.20 0.90 858 1.032
19,000* 0.17* 0.90* 831* 1.00
15,000 0.17 1.15 811 0.97
20,000 0.17 0.86 836 1.005
*Indicates the values for the original material model
Table 8.3 Parametric Study of Elastic Properties, (E.,IEnJ and Vb
1;;;;--- .;.-r'e.r~:~r,JIt;;..,'~-r;'~~..:-:" d I IW~~l~~;\» I : ~ta!J I ,
!i 1'i~!iJ.l::f)) I_~ __ ...JL_ __ ,t " -' ~~__ _ ____ ____ _ __ ._
17,187* 0.16* 2.77* 831* 1.00
17,187 0.20 2.77 809 0.97
15,000 0.16 2.41 798 0.96
20,000 0.16 3.21 834 1.003
22,000 0.16 3.54 835 1.005
*Indicates the values for the original material model
The ultimate load of the column was influenced by changes in the value of Erm (or
EtlEfin). However, the mode of failure was not significantly affected in this case. The
ultimate load for each case are shown in Table 8.2. Although the EJE1m ratio has
126
some influence, it is not considered a sensitive factor. For example, a 28% increase
in the value of Et/Efin only resulted in a decrease of 3% of the ultimate load. With a
47% increase of Poisson's ratio of ferrocement mortar, the failure load is increased
by only 3.3%. The influence of modulus of elasticity and Poisson's ratio of brick was
also studied by changing the original values of the bricks and keeping all other
parameters constant. The results are summarized in Table 8.3.
In this case a 28% increase in Et!Em resulted in an increase of 0.5% ultimate strength
and a 13% decrease in Et!Em resulted in a decrease of 4% ultimate strength. With a
25% increase of Poisson's ratio of brick, the failure load was decreased by only 3%.
It may therefore be considered that, in general, the elastic parameters are not
particularly significant for this type of loading. The simplifications introduced in the
standard procedures for evaluation of the elastic material properties as discribed in
Chapter 4, therefore, seem justified.
8.3.2 Bed Joint Thickness
The influence of joint thickness ratio (bed joint thickness I brick thickness t,,/tb) is
studied by changing the original thickness and bed joints, keeping all other
parameters constant. The joint thickness considered were 3.18 mm, 6.35 mm 12.7
mm, 15.87 and 19.05 mm, resulting in a thickness ratio of the mortar and the brick
(t,,/tb) of 0.04, 0.091, 0.2, 0.26 and 0.33, respectively. The original joint thickness
was 6.35 mm. The ultimate load of the columns for different joint thickness is given
in Table 8.4.
The results of Table 8.4 show that the ultimate strength of the column decreases
with the increase of joint thickness. An increase in joint thickness from 6.35 mm to
19.05 mm (t,,/tb = 0.33) resulted in a decrease of ultimate strength by 16%, and a
100% increase in the bed joint thickness (t",= 12.7 mm or t,,/tb = 0.2) resulted in a
127
decrease of ultimate strength by 8%. This is due to the fact that with the increase of
mortar bed joint thickness the ratio of mortar and brick thickness (Vtt, ) increases
and as a result the transverse tensile stress in the materials increases as can be seen
from Fig. 3.11 of chapter 3. From this parametric study it is concluded that the
variation of bed joint thickness is an important parameter for the evaluation of
ultimate strength of brick column coated with ferrocement. This investigation agrees
with the previous experimental investigation on different masonry structures (20, 31,
56).
Table 8.4 Influence of Bed Joint Thickness
3.18 0.04 862 1.04
6.35* 0.091* 831* 1.00
12.7 0.2 765 0.92
15.87 0.26 730 0.88
19.05 0.33 698 0.84
* Indicates the values for the original material model
8.3.3 Tensile Strength of Mortar
The influence of tensile strength of mortar used in brick masonry on the behaviour of
ferrocement coated column is studied by changing the tensile strength of the mortar,
keeping all other parameters constant. The values of the tensile strength used were
0.40 MPa, 0.8 MPa, 1.0 MPa and 1.20 MPa. The original tensile strength of the
128
mortar was 0.60 MFa. The failure loads of the columns for different tensile strengths
6fmortar are given in Table 8.5.
Increasing the tensile strength of the mortar did not significantly increase the ultimate
strength of the composite column. Table 8.5 shows that there is no change of column
strength due to decrease or increase of tensile strength of mortar. From this
parametric study it is concluded that within the range of values studied the ultimate
strength of brick column encased in ferrocement is not sensitive to the variation in
the tensile strength of mortar.
Table 8.5 Influence of Tensile Strength of Mortar
~'I~;;i%_~1~~¥!~)-lr~;~'J;iJ~~~i~~,~[}~~o--"1~".__..., .. ".' J. ". , , .' ... . \ ••.~._..A_'" . . J
0.4 831 1.000.6* 831* 1.000.8 831 1.001.0 831 1.001.2 832 1.001
* Indicates the values for the original material model
8.3.4 Compressive Strength of Mortar
The influence of compressive strength of mortar used in brick masonry was studied
by increasing and decreasing the original compressive strength of the mortar, holding
all other parameters constant. Five different strengths were considered, as
summarized in Table 8.6. It is seen from the table that the strength of the column did
not change due to the changes of compressive strength of mortar. The failure patterns
129
for all the cases also remain unchanged. This is due to the type of fracture
experienced by the mortar joint. For this type of composite system and loading the
transverse tensile stress mainly controls the fracture process of the columns and in
that case the mortar joints will experience bond failure rather than crushing failure.
However, some of the bed joints may experience crushing type of failure at its
crushing strain which normally happens after the load attains the maximum value.
From this parametric study it is concluded that within the range of values studied the
ultimate strength of brick column encased in ferrocement is not sensitive to changes
in the compressive strength of mortar.
Table 8.6 Influence of Compressive Strength of Mortar[.~--"":~-'~l[=~=~.- ~,.."mp~. ~~ t\i]\~r'l.u~ iPI\l~t1(i)I!.~'c, i
~~:jl~:.'!~~~~i9),J . (O]~~~.._J ..:..:..~,..~.'_ J4.00 830 1.001
4.95* 831* 1.00
6.00 831 1.00
8.00 831 1.00
10.00 831 1.00
* Indicates the values for the original material model
8.3.5 Brick Tensile Strength
The influence of tensile strength of the brick was investigated by increasing and
decreasing the original tensile strength of the brick, keeping all other parameters
constant. Four different strengths plus the strength obtained from the experiment
were considered in this case. The results are summarized in Table 8.7.
, .
}
130
As would be expected, changes to the tensile strength of the brick affected the
ultimate strength of the column as for this type of loading, failw::einvolves tensile
failure of both brick and mortar joint. The!esults of Table 8.7 show that a,77%
decrease in brick tensile strength from the experimental value, resulted in a decrease
bf 17% in the ultimate strength, but there is no significant effect.on ultimate strength
Ofcolumn due to increase of tensile st;rengthof brick from the 'original value. Thi~ is
due to the fact that with the ~crease of tensile str(mgth of brick the propagation of
cracks through the bricks will be delayed to some extent and eventually the system
will abSorb more energy. Henceit will carry more load before the fracture propagates
through the ferrocement .overlay and as a result most of the ferrocement elements
will be stressed nearly to their tensile capacity. As a result after the cracking of
these strong bricks many feliocement elements will be cracked at a time leading to
immediate failure. This phenomenon may not be observed in 'case of bricks with
lower tensile strength. From the resu!ts, it is concluded that the tensile strength of
brick is an important parameter for the evaluation of ultimate strength of brick. .
column coated with ferrocertltmt.
Table 8.7 Influence of Tensile Strength of Brick
I ~lll'!li". ".''. .
_' i ~ .
3.00 831 1.00
2.2~* 831* 1.00
1.50 788 0.94
1.00 752 0.90
0.50 684 0.85
'" Indicates the values for the original material Il10del.f. ) •.. • .
133
19% decrease of compressive strength of ferrocement mortar results in a decrease of
23%, of the ultimate strength and 8.1% increase results in an increase of 7%. But
the ultimate strength of column did not increase significantly with further increase of
compressive strength of ferrocement mortar. From Table 8.10, it is seen that due to
increase of compressive strength of ferrocement mortar from 20 MPa to 25 MPa
(25% increase) the ultimate strength of column increases by only 0.1%. These results
agree well with the previous experimental investigation reported by Singh (84). From
the Table 8.10, it is seen that the model is less sensitive to increase in the
compressive strength of ferrocement from the original value of 18.5 MPa but it is
sensitive to decrease in the compressive strength of ferrocement. From the result, it is
concluded that the compressive strength of ferrocement is an the important parameter
for the evaluation of ultimate strength of brick column coated with ferrocement.
Table 8.10 Influence of Compressive Strength of Ferro cement
n£1?iiuw~i;;~J:~~)"'rmmlliilli' ~ r~~~~:/~~:,::;"ll ~:lJlJ'~il1jl~ll."'J.ItlI,\-j!W'!a!lIi \Ql.(~J i1.., Il'...0 •• _ \9.~m.(!) Ii 1 J
15.0 644 0.77
18.5* 831* 1.00
20.0 886 1.07
22.5 887 1.07
25.0 887 1.07
* Indicates the values for the original material model
8.3.9 Nurn ber of Layers of Wire Mesh
In this study the effect of volume fraction of reinforcement was investigated by
changing the number of wire mesh layers, keeping all other parameters constant. The
values of volume fraction used in this study were 0.007, 0.014 ,0.021 and 0.028,
134
equivalent to one, two, three and four layers of wire mesh, respectively. The failure
loads of the columns for different number of layers of wire mesh is given in Table
8.11.
It is seen from the table that the variation of volume fraction of wire mesh in
ferrocement overlay did not increase the ultimate strength of column significantly.
The results of Table 8.11 show that a 100% increase of wire mesh (from two layers
to four layers) resulted in only 1.6% increase of column strength. These results agree
well with the previous investigation reported by Sandowicz and Grabowski (77).
From this parametric study it can therefore be concluded that the number oflayers of
wire mesh is not a sensitive parameter for the evaluation of ultimate strength of
column encased in ferrocement.
Table 8.11 Influence of Number of Mesh Layers
1
2
3
4
0.71.4
2.1
2.8
795
831842
845
0.95
1.00
1.013
1.016
*Indicates the values for the original material model
8.3.10 Element size
All the analyses carried out as part of the study and reported in Chapters 3 and 6 and
in Arts. 8.3.1, 8.3.2, 8.3.3, 8.3.4, 8.3.5, 8.3.6, 8.3.7, 8.3.8 and 8.3.9 in these chapters
and arts. used the finite element idealisation shown in Fig. 3.1. Each brick was
135
represented by two layers of elements each having one half the height of a brick. The
influence of the element size on the nonlinear fracture analysis was studied by
changing the number of elements in the column. For the analysis one and three
elements through the brick height were provided instead of two elements in the
original model. There is no difference in the prediction of ultimate load as shown in
Table 8.12.
Table 8.12 Influence of Mesh Size in Finite Element Discretization
1
2*
3
832
831*
830
1.001
1.00
0.99
*Indicates the values for the original material model
8.3.11 Slenderness Ratio
In this study the effect of slenderness ratio was investigated by changing the height
of the column, keeping all other parameters constant. The maximum height was
equal to the typical floor height in a building (viz. 3.05 m) and the minimum was
taken to be one fourth the original height of 1.22 m. The values of slenderness ratio
used in this study were 3.58,7.16,10.74,14.32,21,48,28.64 and 35.8.
The results are shown in Table 8.13. It can be seen from the table that the column
strength decreases with the increase of column height up to a certain height after
which the change in strength is very negligible.
136
The high strength of low height column is mainly due to the boundary restraints used
in the finite element idealisation which effect the stress distribution throughout the
height of the column. The effect decreases with the increase of column height (as can
be seen from the table). Therefore, the column height (1220 mm) chosen in this study
is quite adequate from. the consideration of this effect of restraints in the boundary
conditions. l1le results of table 8.13 show that ultimate strength increases by 15%,
when the column height changes from 1220 mm to 305 mm.
Table 8.13 Influence of Slenderness Ratio
[(;~';T,,~~;;;';~T~;[-lliP:;Ii'",' ,. J;J~t", I; !:.9l1illiJ. I. J.;.W.l(O"~~D)i.~~~ ....Ii.. It.. . J •.... ' J
305** 3.58 957 1.15
610** 7.16 855 1.03
915** 10.74 833 1.002
1220* 14.32* 831* 1.00
1830 21,48 830 0.998
2440 28.64 830 0.998
3050 35.8 829 0.997
* Indicates the values for the original material model** The behaviour is more like short compression block
8.3.12 Boundary Conditions
The linear elastic finite element investigation of the effects of the assunled boundary
conditions at the top and bottom of the column has already been described in Chapter
3. It is assumed that all the nodes at top and bottom are restrained. against horizontal
movements. This is referred to in Table 8.14 as Case 1. In this article, the effects of
137
variation in the boundary conditions on the ultimate behaviour of the column has
been investigated. The same column and the material model as described in Art. 8.2
has been adopted for this study.
Three additional analyses have been performed. The first analysis (Case II) assumed
the nodes at the interface of the bottom platen of the machine and the base of the
column restrained horizontally, and the nodes at the interface of the loading plate and
the column top were unrestrained against horizontal movement. The second analysis
(Case III) assumed both the base of the column and the nodes at the interface of the
loading plate and the column top to be unrestrained horizontally. In the third analysis
(Case N) the nodes at the base of the column were unrestrained horizontally, while
the nodes at the interface of the loading plate and the column top were restrained
against horizontal movement. In all the cases the continuity effect due to quarter
symmetry of the columns remain the same as explained in Art. 3.4 and as shown in
Fig. 3.1. The ultimate loads are shown in Table 8.14. For Case II, there is no
variation in the ultimate load from the Case I, whereas for the third and fourth cases
the loads were reduced by 16%.
Table 8.14 Influence of Boundary Conditions
Case No. Restraint conditions Ultimate LoadPu,le IPu,le *
(kN)
I Top and bottom 831* 1.00restrained
II Top unrestrained and 830 0.99bottom restrained
ill Top and bottom 696 0.84unrestrained
N Top restrained and 696 0.84bottom unrestrained
* Indicates the values for the original material model
The ultimate load for Cases II and N should be equal but there.is a difference of
16%. No explanation was apparent for this difference. One possible reason could be
138
the stress concentration which occurs near the top due to existence of additional
stress produced due to horizontal restraint. The crack propagation for Cases ill and
IV was rapid in comparison to Case n. In these cases, horizontal tensile stress rather
than compressive stress was developed at the base of the column. These results
therefore indicate that the values of ultimate load are sensitive to the manner of
modelling of the boundary conditions. However, further investigation considering
various types of boundary conditions is required.
a.4 SUMMARY
The results of finite element analyses carried out to study the relative importance of
the various parameters have been presented in this Chapter. Two groups of
parameters were considered for this investigation. The first group were the
parameters which are directly related to the material model used in ANSYS package
and the second group were the parameters which are not directly related to the
material model but sensitive to the finite element analysis. The following conclusions
can be drawn from this sensitivity analysis of the parameters related to the finite
element model.
1. The influence of material nonlinearity on the ultimate behaviour of the
composite column is not significant. The nonlinearity due to progressive
fracture of the constituent materials is rather more significant. For analysing
this type of problem a linear elastic-fracture material model would therefore
be sufficient.
2. The modular ratio of the brick and the ferrocement overlay influenced the
ultimate strength of the column but not to a significant extent. Poisson's ratio
of ferrocement is also not very sensitive to the ultimate strength of the
column.
139
3. The modular ratio of bricks and mortar joints influenced the ultimate strength
of the column but not to a significant extent. Poisson's ratio of bricks has also
been found to be insensitive parameter.
4. The effect of joint thickness (and hence the ratio of the joint height to brick
height) on the ultimate strength of ferrocement coated columns has been
found to be significant.
5. For values of tensile strength of brick lower than 2.21 MPa, the lower the
tensile strength of the bricks, the lower the ultimate load of the column.
However, for values larger than 2.21 MPa, the ultimate load is not sensitive to
the increase in tensile strength of brick.
6. The influence of compressive. strength of brick, with the range of values
studied, on the ultimate strength of composite column is found to be
insignificant.
7. The tensile strength of ferrocement overlay influenced the ultimate strength of
column but not to a significant extent.
8. nle compressive strength offerrocement overlay influenced the load carrying
capacity of the column.
9. The influence of number of layers of mesh on the ultimate strength of
composite column is found to be insignificant.
10. The fmite element idealization used in analysis by dividing each brick into
two horizontal layers produces the desired level of accuracy. The use of fmer
140
mesh is not therefore necessary in the finite element analysis of composite
behaviour of brick masonry column coated with ferrocement overlay.
11. The influence of the boundary conditions on the ultimate strength of
composite column is found to be significant.
CHAPTER 9
RECOMMENDATION OF DESIGN PROCEDURE
9.1 INTRODUCTION
A study of previous research reveals that a significant number of experiments have
been carried out, but analytical investigation in this area is lacking. The analytical
prediction of failure of ferrocement encased masonry column is complex because of
the large number of influencing parameters involved, lack of suitable material
models, and absence of efficient numerical techniques. As mentioned earlier the
finite element method of analysis with a linear fracture material model has been
used to investigate this complex behaviour of masonry column coated with
ferrocement overlay. At present, no design procedure exists to provide guidelines in
the design of brick masonry columns with ferrocement overlay. A comparison of the
failure loads of the 48 columns obtained experimentally with those obtained form
analysis shows that the finite element method with the material model used is
capable of predicting the failure loads with reasonable accuracy. An attempt has,
therefore, been made to develop design formulae for brick columns with
ferrocement overlay subjected to axial as well as eccentric loads.
9.2 PROPOSED DESIGN FORMULAE
The fOlIDulation of a design procedure for ferrocement encased masonry column is
difficult due to the interaction of a large number of variables which influence the
composite behaviour of these columns. However, a review of the parametric study
discussed in Chapter 8 shows that not all the parameters have significant influence on
the failure load. The important variables are:
142
(i) tensile strength of brick,
(ii) compressive strength of ferrocement mortar, and
(iii) thickness of bed joint.
The design formulae developed here are based on the linear elastic fracture analysis
of these columns subjected to static axial and eccentric loading. For practical
purposes design formula should be as simple as possible. Considering this important
point, the following two formulae are proposed for two different loading cases. A
detailed description of the procedure adopted for the derivation of these simplified
design formulae is presented in Appendix. VIII. All those expressions are based on
the linear elastic fracture analysis. From Chapter 8 it is seen that the linear elastic
fracture analysis gives higher load than the nonlinear analysis (exact analysis). To
account for this overestimation of failure load and to make the equation
conservative, a reduction factor 0.80 has been used.
For axial load, the ultimate column load, Pult> is taken as,
Pull= 0.80 (PI + P2) (9.1)
where:
PI =Axial load carrying capacity of the masonry core in Newton (N),
and is given by the formula
PI =Abm {2.3 +3.16 t;b - 0.74 (t;b)2 - 6.85 1m + 7.9 (1m i} (9.2)Ib Ib
for
0.5 MPa ::;;t;b ::;; 2.2 MPa and 0.04::;; !E.. ::;; 0.33Ib
and
P2 = Axial load carrying capacity of ferrocement overlay including the confinement
effect in Newton (N),
P2 = Af (2.2 fcfin - 19.2) (9.3)
143
for
15 MPa ~ fcfm ~ 20 MPa
For eccentric loading, the column capacity,
Pe,ull = Pull (I - 1.5 e/h) (9.4)
where:
tb = Thickness of brick (rnm)
1m = Thickness of bed joint (rnm)
Abm = Cross-sectional area of brick masonry (rnm2)
Af = Cross-sectional area offerrocement (rnm2)
f,b = Tensile strength of brick (MPa)
fcfin = Compressive strength offerrocement mortar (MPa)
e = Eccentricity (rnm)
h =Depth of column (rnm)
The proposed formulae involve seven important parameters, namely, the tensile
strength of brick, compressive strength offerrocement mortar, thickness ratio of bed
joint and brick, cross-sectional area of brick masonry, cross-sectional area of
ferrocement, eccentricity and depth of column. The agreement between the proposed
formulae and the finite element analysis for different column sizes is shown in Figs.
9.1, 9.2 and Appendix IX.
9.3 EXAMPLE PROBLEMS
To check the adequacy of the proposed design formulae, four example problems are
considered in this section. The problems have already been investigated both
analytically and experimentally before (Chapter 6 and Chapter 5). In this section only
the results are compared with those from the proposed design formulae.
144
3500
3000
381 mm x 381 mm column
25.4 mm overlay
2500
Z 20006"C
'"0..J
1500
•
508 mm x 508 mm column38.1 mm overlay
Proposed Design Fonnula
Proposed Design Formula
1000
Finite Element Analysis ---_..-500 •. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=~~~~~-:~-=:=:=~-~p~ro~p:os:e~d~o:eS:ig~n~F:ormUla
~ 244 mm x 244 mm column19.05 mm overlay
15 16 17 18 19Compressive Strength of Ferrocement Mortar (MPa)
20
FIG.9.1 COMPARISON OF PROPOSED DESIGN FORMULA WITnFINITE I~LEMENT ANALYSIS FOR AXIAL LOAD CASE
1.0
0.9
0.8
0.7
0.6
0.5
145
-Prop05ed Design Formula-e- 381mm x 381mm column, overlay =25,<lmmn
t",tt,,=O.273-A-244m x 244 mm column, overlay:38.1mm
t,A=O.273
-O-244mm x 244mm column, overlay=19.05mm'm,"15MPa
-.- 244mm x 244mm column, overlay:19.OSmmt,A"'O.091
0.00 0.05 0.10 0.15
e/h
0.20 0.25 0.30 0.35
FIG. 9.2 COMPARISON OF PROPOSED DESIGN FORMULA WITHFOOTE ELEMENT ANALYSIS FOR ECCENTRIC LOAD CASE
146
Problem 1
A 295 nun X 295 nun column cross section is chosen as an example problem for this
case. The overlay thickness is 25.4 nun. Two layers of woven square wire mesh of
1.2 nun diameter wire and opening size 11.3 nun X 11.3 nun are used, Le. volume
fraction Vf becomes 0.014 in this case. Thickness of bricks and bed joints is 70 mm
and 6.35 mm respectively. Tensile strength of brick, compressive strength of
ferrocement mortar and yield strength of wire are 2.21 MPa, 18.5 MPa and 285 MPa
respectively. A uniformly distributed load at the top of the column is applied in this
case.
Problem 2
A 295 mm X 295 nun column with 25.4 nun thick ferrocement overlay is analysed.
One layer of woven square wire mesh of 1.2 nun diameter wire and opening size
11.3 mm X 11.3 nun is used, Le. volume fraction Vf becomes 0.007 in this case.
Thickness of bricks and bed joints was kept constant as problem NO.1. There were
no changes in the values of the parameters like tensile strength of brick, compressive
strength of ferrocement and yield strength of wire. A uniformly distributed load at
the top of the column is applied.
Problem 3
In this case the column of problem No. 1 has been considered. All the parameters
related with the strength characteristics and the deformation characteristics of the
component materials were kept constant. Only the loading type has been varied. In
this case an eccentric load with an eccentricity of 77 nun at the top of the column is
applied.
Problem 4
In this case the column of problem NO.2 has been considered. The values of all the
parameters were kept constant. Only the loading type has been varied. In this case an
eccentric load with an eccentricity of77 nun at the top of the column is applied.
'~/'.
\ \
147
From Table 9.1 it is seen that the results obtained from the proposed formulae are
. very close to the experimental and the analytical values. The failure load obtained
from experiments are on an average 7% and 20% higher than the failure loads
obtained from proposed design formulae for axial and eccentric loading
respectively. The failure load obtained from fmite element analyses are on an
average 1% and 10% higher than the failure loads obtained from proposed design
formulae for both axial and eccentric loading respectively. This indicates the
suitability of the proposed design formulae for the uniaxial compressive strength of
masonry colunm coated with ferrocement.
454
1.18
1.04
481
435 435
1.20
1.10
725
1.01
1.07
788
714 714
1.10
1.07
Table 9.1 Failure Load Obtained from Different Methods
2 3 4
59536 59536 59536 59536
27489 27489 27489 27489
1.4 0.7 1.4 0.7
0.091 0.091 0.091 0.091
2.21 2.21 2.21 2.21
18.5 18.5 18.5 18.5
0.0 0.0 77 77
769 769 522 517
148
9.4 SUMMARY
The formulation of a design procedure for ferrocement encased masonry column is
difficult due to the interaction of a large number of variables which influence the
composite behaviour of these columns. However, a review of the parametric study
discussed in Chapter 8 shows that not all the parameters have significant influence on
the failure load. The important variables are tensile strength of brick, compressive
strength of ferrocement mortar and thickness of bed joint. Considering these
important parameters two formulae have been proposed for two different loading
cases. The following conclusions can be drawn from this study.
1. For axial loading the failure load obtained from experiment is on an average
7% higher than the failure load obtained from proposed design formula.
2. For eccentric loading the failure load obtained from experiment is on an
average 20% higher than the failure load obtained from proposed design
formula.
3. For axial loading the failure load obtained from finite element analysis is 1%
higher than the failure load obtained from proposed design formula.
4. For eccentric loading the failure load obtained from finite element analysis is
10% higher than the failure load obtained from proposed design formula.
CHAPTER 10
SUMMARY AND CONCLUSIONS
10.1 SUMMARY
Linear elastic finite element analysis has been performed to establish the important
parameters which influence the behaviour of ferrocement encased columns,.subjected to vertical loads. A three-dimensional analysis was used for various types
ofloading. Two types of finite element analyses were used - one assumes masonry to
be a homogeneous continuum and the other considers masonry to be an assemblage
of bricks and joints. Two loading types were considered in this investigation - one of
uniformly distributed load at the top and the other of uniform displacement at the top.
In order to defme the material model of the fmite element analysis an extensive
investigation into the properties of brick, mortar, brick masonry and ferrocement has
been carried out. The model is microscopic in nature and considers the bricks and the
mortar joints separately. The material parameters were established from various
types of tests performed on representative samples of bricks, mortar, mortar joints,
brick masonry and ferrocement. These involve compression tests on bricks, mortar
cylinders, stack bonded prisms, hollow ferrocement block, splitting tests on brick and
tensile test on ferrocement plate.
A total of 48 columns were tested in the investigation. These included six bare
masonry columns (244 mm x 244 mm x 1220 mm), 24 bare masonry columns coated
with 25 mm thick ferrocement overlay and 12 bare masonry columns coated with
25 mm thick plaster. Six hollow columns, 1220 mm in height with ferrocement shell
thickness 25 mm and 244 mm x 244 mm inside dimension were also investigated.
The number of layers of wire mesh in ferrocement overlay, type of loading and type
of specimen were varied to produce variations in strength characteristics and'
150
deformation characteristics of the composite column. With the increase of 46% cross
sectional area of column due to addition of ferrocement overlay, the increase in
strenith is found to be 184% for axial loading and 158% for eccentric loading (with
e/h = 0.26). With the increase of 46% cross-sectional area of bare masonry column
due to the application of ferrocement overlay, the material cost increases by 233%
for column with ferrocement overlay containing double layer of wire mesh and 164%
for column with ferrocement overlay containing single layer of wire mesh. The
increase of number of layers of wire mesh in the ferrocement overlay does not
produce significant change in the failure load for axial loading. The influence Of
number of mesh layers in ferrocement overlay on the load carrying capacity of
eccentrically loaded column has also been found to be negligible.
In order to determine the increase in strength of masonry column due to confinement
effect of ferrocement overlay two series of tests were performed. In the first series a
vertical groove in the ferrocement overlay at each face of the column was provided
to discontinue the ferrocement overlay (Fig. 3.12) and hence to eliminate the
confinement effect of overlay. The difference in load carrying capacity of the
ferrocement encased masonry column and the column with discontinuous
ferrocement overlay was considered to be the increase of load due to confinement
effect in this case. In the second Series the constituent members of the composite
system (ferrocement hollow column and bare masonry column) were tested
individually to failure. The difference in load carrying capacity of the ferrocement
encased masonry column and the total capacity of the individual members was
considered to be the increase of load due to confinement effect in this case. A more
realistic assessment of the confmement effect can be made by testing the bare
masonry column and hollow ferrocement shell. The strength increase of bare
masonry column due to the confinement of ferrocement overlay is fOund to be
around 5% to 9%.
151
A comparative study of the experimental and analytical results has been carried out.
In general, the agreement between finite element analysis and experiment is good,
thus indicating that the material model used in the finite element package (viz.
ANSYS as outlined in Appendix A Ill) is suitable for the analysis of composite
behaviour of masonry column coated with ferrocement overlay. The finite element
analysis is capable of predicting the failure load and the failure pattern with
reasonable accuracy and thus considered appropriate for a comprehensive parametric
study for the design recommendation.
A sensitivity analysis of the parameters which influence the nonlinear behaviour of
the column has been carried out. This study revealed that the tensile strength of
brick, the ratio of joint thickness and brick (tm/tb) and compressive strength of
ferrocement mortar are of prime importance. The model is found to be less sensitive
to modulus of elasticity, Poisson's ratio, compressive strength of brick, the tensile
strength of mortar and number of layers of wire mesh.
From linear elastic fracture analyses of ferrocement coated columns subjected to
static axial and eccentric loading the following two formulae have been developed.
For axial load, the ultimate column load, Pult> is taken as,
Pult = 0.80 (PI + P2) ••••••••••••••••• (l0.1)
where:
PI = Axiillioad carrying capacity of the masonry core in Newton (N),
and is given by the formula
PI = Abm{2.3 +3.16 ftb- 0.74 (ftbi-6.85 tm + 7.9 (~)2} (10.2)tb t,
for
0.5 MPa ~ ftb ~ 2.2 MPa and 0.04 ~ tm~ 0.33
tb
and
152
P2 '= Axial load carrying capacity of ferrocement overlay including the confinement
effect in Newton (N),
P2 = Ar(2.2 fcfin - 19.2) (10.3)
for
IS :MFa:S; fcfin :s; 20:MFa
For eccentric loading, the column capacity,
Pe.u!l = Pult (1 - 1.5 e/h) (lOA)
where:
tb = Thickness of brick (mm)
1m = Thickness of bed joint (mm)
Abm = Cross-sectional area of brick masonry (mm2)
Ar = Cross-sectional area offerrocement (mm2)
f.b = Tensile strength of brick (:MFa)
fefin = Compressive strength Offerrocement mortar (:MFa)
e = Eccentricity (mm)
h = Depth of column (mm)
A comparison of the failure loads obtained from experiments, fInite element analyses
using ANSYS package and proposed design formulae has been carried out. The
failure load obtained from experiments are 7% and 20% higher than the failure loads
obtained from proposed design formulae for both axial and eccentric loading
respectively. The failure load obtained from fInite element analyses are 1% and 10%
higher than the failure loads obtained from proposed design formulae for both axial
and eccentric loading respectively.
Even though the validity and potential of the proposed design formulae have been
demonstrated, the limitations of the formulae should be recognized. The proposed
design formulae are only applicable to ferrocement encased masonry columns
subjected to short term static loading. These formulae are valid for the compressive
153
strength of ferrocement mortar ranging from 15 MPa to 20 MPa, tensile strength of
brick ranging from 0.5 MPa to 2.2 MPa and thickness ratio of bed joint to brick
height ranging from 0.04 to 0.33.
10.2 CONCLUSIONS
Based on fmite element analyses and compression tests carried out on 244 mm x 244
mm brick masonry columns encased with 25 mm thick ferrocement overlay and 25
mm thick sand-cement plaster, the following conclusions may be drawn:
1. In case of axial loading the nominal stress at cracking load obtained from tests
on ferrocement encased masonry column is 262% higher than the column
encased in plaster, whereas for fmite element analysis the nominal stress at
cracking load offerrocement encased masonry column is 13% higher than the
column encased in plaster.
2. In case of axial loading the nominal stress at ultimate load obtained from tests
on ferrocement encased masonry column is 89% higher than the column
encased in plaster, whereas for finite element analysis the nominal stress at
ultimate load of ferrocement encased masonry column is 68% higher than the
column encased in plaster.
3. In case of eccentric loading the nominal stress at ultimate load obtained from
tests on ferrocement encased masonry column is 154% higher than that of the
column encased in plaster, whereas for finite analysis the nominal stress at
ultimate load of ferrocement encased masonry column is 92% higher than that
of the column encased in plaster.
4. The increase in strength of cOmposite column due to confmement effect of
ferrocement overlay obtained from tests is within 6% to 9% and for finite
154
element analysis the increase in strength of composite column due to
confmement effect of ferrocement overlay is within 5% to 9%.
From parametric study, it is found that within the range of values used in this study,
the tensile strength of brick, compressive strength of ferrocement mortar and
thickness of bed joint have significant influence on the failure load. The tensile
strength of mortar, compressive strength of brick, number of layers of wire mesh in
ferrocement do not appear to influence the failure load significantly. The finite
element idealization used in analysis by dividing each brick into two horizontal layers
produces the desired level of accuracy. The use of fmer mesh is not therefore
necessary in the finite element analysis of composite behaviour of brick masonry
column coated with ferrocement overlay. Although the tests have been carried out on
1220 mm high columns, increase in height upto 3050 mm does not lead to any
decrease in strength.
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APPENDIX I
PROPERTIES OF FERRO CEMENT, BRICK, MORTAR ANDBRICKWORK\
A.2
Contents
Table 1.1 Compressive and Tensile Strength of Brick A.3
Table 1.2 Compressive and Tensile Strength of Mortar (Cement: Sand = 1:2) A.4
Table 1.3 Compressive and Tensile Strength of Mortar (Cement: Sand = 1:5) A.5
Table 1.4 Compressive and Tensile Strength of Ferro cement A,6
Table 1.5 Compression Test on Brick A.7
Table 1.6 Compression Test on Mortar (Cement: Sand = 1:5) A.8
Table 1.7 Compression Test on Mortar (Cement: Sand = 1:2) A.9
Table 1.8 Compression Test on Ferrocement A.10
Table 1.9 Average Lateral Strain vs. Longitudinal Strain of Brick A.ll
Table 1.10 Average Lateral Strain vs. Longitudinal Strain of Mortar
(Cement: Sand = 1:5) A.12
Table 1.11 Average Lateral Strain vs. Longitudinal Strain of Mortar
(Cement: Sand = 1:2) A, 13
Table 1.12 Average Lateral Strain vs. Longitudinal Strain of Ferro cement A.14
Table 1.13 Initial Modulus of Elasticity of Brick A.15
Table 1.14 Initial Modulus of Elasticity of Mortar (Cement: Sand = 1:5) A.l6
Table 1.15 Initial Modulus of Elasticity of Mortar (Cement: Sand = 1:2) A.17
Table 1.16 Initial Modulus of Elasticity of Ferro cement A,18
Table 1.17 Compression Test on Stack Bonded Prism A.l9
A.3
TABLEI.1
COMPRESSIVE AND TENSILE STRENGTH OF BRICK
Compressive Strength Tensile Strength
Specimen Compo Strength Specimen Tensile StrengthNo. (MPa) No. (MPa)
1 18.27 1 2.35
2 18.55 2 2.50
3 22.07 3 2.10
4 18.8 4 2.30
5 24.6 5 1.85
6 22.62 6 1.93
7 21.50 7 2.15
8 19.50 8 2.45
9 20.82 9 2.27
10 20.68 10 2.05
11 18.50 11 2.15
12 20.60 12 2.42
X 20.50 2.21
S 1.86 0.19
C.ofV. 9.00 8.95(%)
Note: X = Mean, S = Standard Oeviation andC. ofV. = Coefficient of Variation
A.4
TABLE 1.2
COMPRESSIVE AND TENSILE STRENGTH OF MORTAR
(Cement:Sand = 1:2)
Compressive Strength Tensile Strength.
Specimen Compo Specimen No. Tensile StrengthNo. Strength (MPa)
(MPa)
1 20.90 1 2.4
2 17.94 2 2.3
3 15.70 3 2.6
4 21.67 4 2.8
5 17.90 5 2.5
6 19.80 6 2.9
7 14.50 7 2.6
8 20.95 8 2.4
9 19.00 9 2.3
10 18.50 10 2.2
11 15.45 11 2.8
12 19.70 12 2.2
X 18.50 2.50
S 2.21 0.23
C.ofV. 11.98 9.20(%)
Note: X =Mean, S = Standard Deviation andC. ofV. = Coefficient of Variation
A.5
TABLE 1.3
COMPRESSIVE AND TENSILE STRENGTH OF MORTAR
(Cement:Sand = 1:5)
Compressive Strength Tensile Strength
Specimen Compo Strength Specimen No. Tensile StrengthNo. (MPa) (MPa)
1 5.40 1 0.70
2 3.95 2 0.60
3 5.10 3 0.65
4 5.60 4 0.62
5 3.90 5 0.50
6 4.95 6 0.63
7 5.30 7 0.53
8 4.80 8 0.65
9 5.80 9 0.53
10 4.20 10 0.57
11 4.80 11 0.62
12 5.60 12 0.60
X 4.95 0.60
S 0.62 0.05
C.ofY. 12.54 9.30(%)
Note: X = Mean, S = Standard Deviation andC. ofY. = Coefficient ofYariation
A.6
TABLEI.4
COMPRESSIVE AND TENSILE STRENGTH OF FERRO CEMENT
Compressive Strength Tensile Strength
Specimen Compo Strength Specimen No. TensileNo. (MPa) Strength
(MPa)
I 25.4 I 2.25
2 21.5 2 3.10
3 20.6 3 3.05
4 22.6 4 2.95
5 23.4 5 2.60
6 20.3 6 2.55
X 22.3 2.75
S 1.75 0.30
C.ofV. 7.8 11.15(%)
Note: X = Mean, S = Standard Deviation andC. ofV. = Coefficient of Variation
A.7
TABLEI.5
COMPRESSION TEST ON BRICK
Strain Readings for Bricks (XI0'~
Stress Specimen No. C.ofV.(MPa) X S
1 2 3 4 5 6 7 8 90.79 5 5 4 5 4 4 5 5 4 4.6 .49 10.9
1.58 9 10 9 9 9 8 10 10 9 9.2 .62 6.8
2.37 14 15 14 13 13 13 16 14 13 13.8 .99 7.1
3.16 20 19 21 17 18 17 21 20 18 19.0 1.5 7.8
3.95 25 26 26 23 23 22 25 24 23 24.1 1.3 5.6
4.74 28 30 30 28 27 26 29 27 27 28.0 1.3 4.7
5.53 34 35 36 33 32 30 33 32 33 33.1 1.6 5.0
6.32 39 43 37 36 35 38 38 38.0 2.4 6.2
7.11 47 44 41 45 43 44.0 2.0 4.5
7.90 60 50 55.0 5.0 9.0
Note: X =Mean; S = Standard Deviation andC. of V. = Coefficient of Variation.
A.8
TABLE 1.6
COMPRESSION TEST ON MORTAR
(Cement:Sand = 1:5)Strain Readings for Mortar (XI0-4)
Stress Specimen No. C.ofV(MPa) X S
1 2 3 4 5 6 7 8 90.5 .6 .9 .7 .8 .7 .9 .9 .8 .9 0.8 .10 13.1
1.0 1.2 1.7 J.5 J.5 1.4 1.8 1.9 1.6 1.8 1.6 .21 13.1.
J.5 1.9 2.6 2.0 2.4 2.3 2.7 2.9 2.4 2.9 2.46 .33 13.7
2.0 3.1 3.7 3.4 3.8 3.8 3.9 4.2 3.8 4.3 3.8 .34 9.1
2.5 4.9 5.1 5.0 5.2 5.2 5.3 5.5 5.3 5.6 5.23 .21 4.0
3.0 6.8 6.7 7.1 7.2 7.3 7.4 7.2 7.4 7.14 .24 3.4
3.5 8.5 8.3 9.8 9.6 J.O 10 11 11 9.78 .93 9.5
4.0 12 13 13 14 14 15 13.5 .95 7.1
4.5 17 18 19 21 20 21 19.4 1.5 7.7
Note: X =Mean; S = Standard Deviation andC. ofV. = Coefficient of Variation
A.9
TABLE!.7
COMPRESSION TEST ON MORTAR(Cement:Sand = 1:2)
Strain Readings for Mortar (XIO-4)
Stress Specimen No. C.ofV.(MPa) X S
1 2 3 4 5 6 7 8 9
2 1 l.l l.l .97 .98 l.l l.l 1 l.l 1.05 .05 4.90
4 2.2 2.3 2.4 2.2 2.2 2.3 2.3 2.3 2.4 2.29 .07 3.05
6 4.3 4.7 4.6 4.2 4.4 4.7 4.9 4.6 4.8 4.58 .22 4.90
8 7.7 7.8 7.7 7.6 7.3 7.9 8.1 7.7 8.0 7.75 .22 2.80
10 11 12 12 12 11 12 12 12 12 11.8 .47 4.00
12 15 16 16 16 15 18 18 17 18 16.6 1.0 6.10
14 21 22 22 23 25 23 24 22.8 1.2 5.40
16 28 29 30 32 31 32 30.4 1.5 4.90
18 38 43 39 45 41.3 2.8 6.90
Note: X =Mean; S = Standard Deviation andC. ofV. = Coefficient of Variation
A.l0
TABLE 1.8
COMPRESSION TEST ON FERROCEMENT
Strain Readings for Ferrocement (XI0'~
Stress Specimen No. C.ofV.(MPa) X S
1 2 3 4 5 62 10 11 8 9 10 9 9.5 0.9 10.0
4 20 22 17 18 20 18 19.1 1.6 8.7
6 30 34 25 27 30 26 28.6 3.0 10.5
8 39 43 34 37 40 36 38.2 2.9 7.6
10 49 54 42 46 51 43 47.5 4.3 9.0
12 58 63 52 57 62 52 57.3 4.3 7.5
14 71 76 67 70 75 68 71.1 3.3 4.6
16 86 92 81 85 90 78 85.3 4.8 5.6
18 97 108 96 101 104 101 4.4 4.4
20 114 124 117 122 119 3.9 3.3
22 130 136 146 137 6.6 4.8
Note: X =Mean; S = Standard beviation andC. ofV. = Coefficient of Variation
A.ll
TABLE 1.9
AVERAGE LATERAL STRAIN VS. LONGITUDINAL STRAINOF BRICK
Lateral Strain Longitudinal Strain
(X10.5) (XI 0.5)
3.71 23.2
4.65 29.0
9.30 58.0
10.58 66.0
19.50 122.0
27.80 174.0
41.80 261.0
63.11 394.0
A.12
TABLE 1.10
AVERAGE LATERAL STRAIN VS. LONGITUDINAL STRAINOF MORTAR
(Cement:Sand = 1:5)
Lateral Strain Longitudinal Strain
(X 10'5) (X 10,5)
1.6 8.1
3.2 16.1
4.9 24.7
7.6 38.0
11.1 52.7
15.7 71.5
24.1 98.6
35.2 135.5
56.8 196.0
A.13
TABLE I. 11
AVERAGE LATERAL STRAIN VS. LONGITUDINAL STRAINOF MORTAR
(Cement:Sand = 1:2)
Lateral Strain Longitudinal Strain
(XIO's) (X10's)
1.8 10.5
3.9 23.0
8.0 46.0
13.9 78.0
23.5 118.0
36.6 166.0
57.0 228.0
88.2 304.0
136.3 413.0
A.14
TABLE 1.12
AVERAGE LATERAL STRAIN VS. LONGITUDINAL STRAINOF FERRO CEMENT
Lateral Strain Longitudinal Strain
(XIO's) (XIO's)
2.38 9.5
4.76 19.05
7.14 28.57
7.52 30.1
11.9 47.6
14.28 57.14
20.1 70.7
27.2 84.85
A.15
TABLE 1.13
INITIAL MODULUS OF ELASTICITY OF BRICK
Specimen No. Eb(MPa)
1 18110
2 15890
3 17230
4 17600
5 16820
6 19750
7 16310
8 16260
9 16710
X 17187
S 1119
C. ofV. (%) 6.5
Note: X =Mean, S = Standard Deviation andC. ofV. '" Coefficient of VariationEb= Initial Modulus of Elasticity of Brick
A.16
TABLE 1.14
INITIAL MODULUS OF ELASTICITY OF MORTAR(Cement:Sand = 1:5)
Specimen No. En,(MPa)
1 7890
2 5760
3 7500
4 6250
5 6520
6 5550
7 5200
8 5400
9 5730
X 6200
S 890
C. ofV. (%) 14.3
Note: X = Mean, S = Standard Deviation;C. ofV. = Coefficient of Variation andEm= Initial Modulus of Elasticity of Mortar
A.17
TABLE 1.15
INITIAL MODULUS OF ELASTICITY OF MORTAR
(Cement:Sand = 1:2)
Specimen No. Erm(MPa)
1 20000
2 18100
3 18200
4 20600
5 20400
6 18700
7 17800
8 18800
9 18400
X 19000
S 994
C. ofV. (%) 5.2
Note: X = Mean, S = Standard Deviation;C. ofV. = Coefficient of Variation andErm= Initial Modulus of Elasticity of Ferro cement Mortar
A.18
TABLE 1.16
INITIAL MODULUS OF ELASTICITY OFFERRO CEMENT
Specimen No. Er(MPa)
1 20400
2 18500
3 23800
4 21700
5 19600
6 22000X 21000
S 1727
C. ofV. (%) 8.2
Note: X =Mean, S = Standard Deviation;C. ofV. ""Coefficient of Variation andEr = Initial Modulus of Elasticity of Ferrocement
A.19
TABLE 1.17
COMPRESSION TEST ON STACK BONDED PRISM
Derived Stress-Strain Readings for Mortar Joint (XIO.3)
Stress Specimen No. .ofV(MPa) X S
1 2 ..3 4 5 6 7 8 90.79 .3 .3 .3 .2 .3 .2 .2 .3 .3 .27 .05 17.01.58 .6 .5 .5 .5 .6 .5 .5 .5 .6 .54 .05 8.8'2.37 25 24 20 23 26 18 19 22 21 22 2.5 11.03.16 34 38 33 34 38 32 33 34 30 34 2.4 7.2
3.95 56 58 55 59 57 54 56 51 53 55 2.4 4.5
4.74 65 74 70 71 66 63 63 60 62 66 4.4 6.75.53 90 95 100 94 99 89 90 89 82 92 5.2 5.76.32 123 130 140 145 liD 120 135 129 II. 8.77.11 192 200 188 194 201 195 4.9 2.57.90 252 268 260 8.0 3.0Eo 2.6 3.1 3 3.2 2.7 3.3 3.1 2.6 2.5 2.9 .28 9.7
(OPa)
Note: X '" Mean; S = Standard Deviation; C. ofV. = Coefficient of Variation; andEo = Initial Tangent Modulus of Masomy Mortar
Contents
Table II.!
Table II.2
APPENDIX. II
QUALITY CONTROL TEST RESULTS
Compressive and Tensile Strength of Mortar (I :2)
Compressive and Tensile Strength of Mortar (l :5)
A.21
A.22
A.21
TABLE 11.1
Compressive and Tensile Strength of Mortar (1:2)
Specimen Sl. No. :ompressive Tensile StrengthStrength
1 19.90 2.62NDA 2 17.50 2.32
3 18.10 2.53
1 17.00 2.40NDE 2 20.10 2.43
3 18.80 2.70
1 16.85 2.66NSA 2 18.40 2.48
3 20.50 2.33
1 19.80 2.27NSE 2 17.80 2.50
3 18.00 2.68
1 18.10 2.53NZA 2 20.00 2.62
3 17.3 2.37
1 20.30 2.66NZE 2 18.50 2.31
3 16.90 2.51
1 17.00 2.30DDA 2 18.90 2.48
3 19.80 2.70
1 16.90 2.66DSA 2 18.20 2.49
3 20.30 2.34
1 19.90 2.61HDA 2 17.80 2.33
3 17.90 2.51
1 18.00 2.31HSA 2 17.5 2.52
3 20.10 2.63
1 16.90 2.41GDA 2 20.00 2.43
3 18.50 2.64
1 18.80 2.50GSA 2 18.40 2.62
3 18.20 2.40
X 18.52 2.49S 1.15 0.13
:::.ofY.% 6.3 5.20
Note: the mean and Stai1dard deviation for the complete sample have been calculatedusing individual values and not the mean value for each batch.
X =Mean, S = Stai1dardDeviation and C. ofY. =Coefficient ofYariation
A.22
TABLEII.2
Compressive and Tensile Strength ofMortar (1:5)
Specimen SI. No. Compressive Tensile StrengthStrength
1 4.70 0.64NZAW 2 5.20 0.61
3 5.00 0.56
1 4.90 0.62NZEW 2 5.10 0.61
3 4.85 0.58
1 4.73 0.59BZA 2 4.98 0.62
3 5.10 0.58
1 5.15 0.60BZE 2 4.85 0.62
3 4.95 0.57
X 4.96 0.60S 0.15 0.023
C.ofV.% 3.0 3.80
Note: TIle mean and Standard deviation for the complete sample have beencalculated using individual values and not the mean value for each batch.
X = Mean, S = Standard Deviation and C. ofV. = Coefficient of Variation
A.ID.!
A.ID.2
AID.3
AIDA
A.ill.5
APPENDIX ill
FINITE ELEMENT FORMULATION
List of Figures
Solid 65 3-D Reinforced Concrete Solid
Reinforcement Orientation
Uniaxial Behaviour for MKIN'
Full Newton-Raphson Iterative Solution (2 Load Increment)
3-D Failure Surface in Principal Stress Space
A.25
A.29
A.3!
A.35
A.37
A.24
3-D REINFORCED CONCRETE SOLID (SOLID65)
The following discussion regarding the finite element adopted in this study is taken
from ANSYS manual.
SOLID65 is used for the three-dimensional modelling of solids with or without
reinforcing bars (rebars). The solid is capable of cracking in tension and crushing in
compression. In concrete applications, for example, the solid capability of the
element may be used to model the concrete while the rebar capability is available for
modelling reinforcing behaviour. Other cases for which the element is also
applicable would be reinforced composites (such as fiberglass), and geological
materials (such as rock). The element (shown in Fig. A.III.I) is defined by eight
nodes having three degrees of freedom at each node: translations in the nodal x, y
and z directions. Up to three different rebar specifications may be defined.
The most important aspect of this element is the treatment of nonlinear material
properties. The concrete is capable cracking (in three orthogonal directions),
crushing, plastic deformation and creep. The rebars are capable of plastic
deformation and creep.
Assumptions and Restrictions
1. Cracking is permitted in three orthogonal direction at each integration point.
2. If cracking occurs at an integration point, the cracking is modelled through an
adjustment of material properties which effectively treats the cracking as a
"smeared band" of cracks, rather than discrete cracks.
3. The concrete material is assumed to be isotropic.
A.25
z
I'-'
Q}
x-- y
2x2,,2 J
o l
/
-_.5
!lIlcJ:"nfioll Poilll LocatiOlls
FIG. A.III.1 SOLID65 3-D REINFORCED CONCRETE SOLID
A.26
4. Whenever the reinforcement capability of the element is used, the
reinforcement is assumed to be "smeared" throughout the element.
Description
SOLID65 allows the presence of four different materials within each element; one
matrix material (e.g. concrete) and the maximum of three independent reinforcing
materials. The concrete material is capable of directional integration point cracking
and crushing besides incorporating plastic and creep behaviour. The reinforcement
(which also incorporates creep and plasticity) has uniaxial stiffness only and is
assumed to be smeared throughout the element. The shape functions for 8 noded
brick element are:
u = t (uI(1-s)(1-t)(I-r) + u](1+s)(1-t)(1-r)
+ uK(I+s)(1+t)(I-r) + uL(1-s)(1+t)(I-r)
+ uM(1-s)(l-t)(1+r) + UN(1+S)(1-t)(1+r)
+ uo(l +s)(1 +t)(1+r) + up(1-s)(1+t)(1 +r» A-I
v = t (VI(1-S) (analogous to u) A-2
w = t (WI(1-S) (analogous to u) A-3
The element stiffuess matrix for reinforcing bar is:
1 0 0 -1 0 0
0 0 0 0 0 0
[Ktl = ALB0 0 0 0 0 0
0...................... A-4
-1 0 1 0 0
0 0 0 0 0 0
0 0 0 0 0 0
A.27
where:
A = Cross-sectional area of the element
E = E, Young's modulus of elasticity
= ET, tangent modulus if plasticity is present
L = Length of the element
Linear Behaviour
1. General
The stress-strain matrix [D] used for this element is defmed as:
where:
[Nr RJ Nr R
[D] = I - LV [DC]+ LV. [Dr]i1=1 1 1=1 1
.................. A-S
N, = number of reinforcing materials (maximum of three)
ViR = ratio of the volume of reinforcing material 'i' to the total
volume of the element
[DC] = stress-strain matrix for concrete, defmed by equation (A-6)
[D']i = stress-strain matrix for reinforcement 'i' defmed by equation (A-7)
2. Concrete
The matrix [DC] for concrete is defmed by:
(1- v) v v 0 0 0v (1- v) 0 0 0v v (1- v) 0 0 0[DC] ~ E 0 0 0 (1-2v) 0 0 .....A-6- (l-v)(1~2v)
2
0 0 0 0 (1-2v) 02
0 0 0 0 0 (1-2v)2
A.28
where: E == Young's modulus for concrete
V = Poisson's ratio for concrete
3. Reinforcement
The orientation of the reinforcement 'i' within an element is shown in Fig.A.m.2.
The element coordinate system is denoted by (X, Y, Z) and (x{, y{, z{) describes
the coordinate system for reinforcement type 'i'. The stress-strain matrix with
respect to each coordinate system (x{, y{, z{) defmed by equation (A-?).
crt e 0 0 0 0 0 £' £xxxx 1 xxcrt 0 0 0 0 0 0 £' £yyyy yycrt 0 0 0 0 0 0 £'
= [D'l £zzzz = zz ........... A-?,0 0 0 0 0 0
,£xycrxy £xy,
0 0 0 0 0 0 ' . £yzcryz £yz, 0 0 0 0 0 0 £' £xzcrxz xz
where: E f = Young's modulus of elasticity of reinforcement type 'i'
It may be seen that the only nonzero stress component is cr~, the axial stress in
the x f direction of reinforcement type i. The reinforcement direction x f is related
to element coordinates X, Y, Z through
.jX) jCOSSi
Y = s~nSiZ smSi
COS<l>i) jlr)cos<l>ixf = :~ xf A-8
.X
A.29
z
riI
II
II
II
II
x!I
y
FIG. A.m.2 REINFORCEMENT ORIENTATION
A.30
where: 8i= angle between the projection of the xfaxis on XY plane and the X
axis
l/li = angle between the x faxis and the XY plane
1J= direction cosines between xfaxis and element X, Y, Z axes
Nonlinear Behaviour
As mentioned previously, the matrix material (e.g. concrete) experiences
deformation due to creep, plasticity, cracking and crushing type of fracturing. For
modelling plasticity the Besseling model, also called the sublayer or overlay model
has been adopted in the [mite element analysis. This option is not recommended
for large-strain analyses. Fig. A-IIU illustrates typical stress-strain curve and data
input is demonstrated by an example. The material model can predict elastplastic
behaviour through to fracture of the constituent materia!. To predict elastic
behaviour the concrete is treated as a linear elastic material. To predict cracking or
crushing type of failure the stress-strain matrix is adjusted as discussed below for
each failure mode.
Modelling of Cracking Type of Failure
The presence of a crack at an integration point is represented through modification
of the stress-strain relations by introducing a plane of weakness in a direction
normal to the crack face. Also, a shear transfer coefficient ~t is introduced which
represents a shear strength reduction factor for those subsequent loads which
induce sliding (shear) across the crack face. The stress-strain relation for a material
that has cracked in one direction only becomes:
A.31
cr .
as .
0'4 -- .
0'2 .
e, e
FIG. A.III.3 UNIAXIAL SERA VIOUR FOR MKIN
Table A.m.l Stress and Corresponding Strain of Different Materials
Material Brick Ferrocement Plain Mortar MasonryMortar Mortar
O't (MPa) 2 3 I 2101 LIM x10'4 1.579 x10'4 1.613 x10.4 3.45 xlO-4
0'2 (MPa) 4 7 2 4102 2.38xI0.4 6.028 xlO-4 3.795 x10-4 21.85 xl0-4
0'3 (MPa) 5 11 3 5103 2.99 xlO-4 14.06 xlO-4 7.1535 x10.4 55.2 xl0-4
0'4 (MPa) 6 15 4 6104 3.61 xlO '" 26.12xl0~ 13.55 xl0.4 121.9 x10.4
O's (MPa) 8 18 4.5 8
lOs 5.8 xlO:<l 38.4 xlO:<I 19.578 x10.4 266 xlO-4
A.32
0 0 0 0 0 00 1-2v v(1-2v) 0 0 0I-v I-v
0 v(I-2v) 1-2v 0 0 0[DCk]_ E I-v I-v ..A-9P (l-2v)c - (1+v)(1-2v) 0 0 0 t 2 0 0
0 0 0 0 1-2v 020 0 0 0 0 P (1-2v)
t 2
where the superscript ck signifies that the stress strain relations refer to coordinate
system parallel to principal stress directions with the xck axis perpendicular to the
crack face. If the crack closes, then all compressive stresses normal to the crack
plane are transmitted across the crack and only a shear strength reduction factor Pcfor a closed crack is introduced. Then [D~k]can be expressed as
(1- v) v v 0 0 0v (1- v) v. 0 0 0
[D"] - EV v (1- v) 0 0 0
.........A-IOc - (IH'XI-2v) 0 0 0 {3 (1-2v) 0 0, 2
0 0 0 0 1-2v 0-2-
0 0 0 0 0 {3 (I-2v), 2
The stress strain relations for concrete that has cracked in two directions are:
0 0 0 0 0 00 0 0 0 0 00 0 I 0 0 0
[D~k]=E 0 0 0 ~, 0 0 ................................... A-II2(1+v)
0 0 0 0 ~, 02(I+v)
0 0 0 0 0 ~,2(I+v)
A.33
If both directions rec1ose, the stress-strain relation for concrete is
(1- v) v v 0 0 0v (1- v) v 0 0 0
[Dok] _ E V v (I-v) 0 0 0f3 (1-2v) ......A-12c - (1+vXI-2v) 0 0 0 0 0o 2
0 0 0 0 f3 (1-2v) 0o 2
0 0 0 0 0 f3 (1-2v)o 2
The stress-strain relations for concrete that has cracked in all three directions are:
0 0 0 0 0 00 0 0 0 0 00 0 1 0 0 0[D~k]= E 0 0 0 P, 0 0 ...................... A-13
2(l+v)
0 0 0 0 P, 02(1+v)
0 0 0 0 0 P,2(l+v)
If all three cracks rec1ose, equation (A-12) is followed.
Modelling of Crushing Type of Failure
If the material at an integration point fails in uniaxial, biaxial, or triaxial
compression, the material is assumed to crush at that point. In SOLID65, crushing
is defmed as the complete deterioration of the structural integrity of the material
(e.g. material spalling). Under conditions where crushing has occurred, material
strength is assumed to have degraded to an extent such that the contribution to the
stiffuess of an element at the integration point in question can be ignored.
A.34
Equilibrium Iterations
The ANSYS program uses Newton-Raphson equilibrium iterations, which derive the
solution to equilibrium convergence (within some tolerance limit) at the end of each,
increment. Fig. A.III.4 illustrates the use ofNewton-Raphson equilibrium iteration in
a single DOF nonlinear analysis. Before each solution, the Newton-Raphson method
evaluates the out-of-balance load vector, which is the difference between the
restoring forces (the load corresponding to the element stress) and the applied loads.
The program then performs a linear solution, using the out-of-balance loads, and
checks for convergence. If convergence criteria are not satisfied, the out-of-balance
load vector is re-evaluated, the stiffuess matrix is updated, and a new solution is
obtained. This iteration procedure continues until the program converges. If
convergence cannot be achieved, then the program either proceeds to the next load
increment Orterminates (according to instructions).
By default, the program will check for convergence by comparing the square root
sum of the squares (SRSS) of the force imbalance against the product of VALUE x
TOLER. The default value of VALUE is the SRSS of the applied loads (or, for
applied displacements, of the Newton-Raphson restoring forces), The default value
ofTOLER is 0.001.
William and Warnke Failure Criterion
The concrete material model predicts the failure of brittle materials. Both cracking
and crushing failure modes are accounted for. The criterion for failure of concrete
due to multiaxial stress state can be expressed in the form
A.35
"
u
FIG. A.m.4 FULL NEWTON-RAPHSON ITERATIVE
SOLUTION (2 LOAD INCREMENTS)
F--S~O!,
A.36
_________________A.l4
where,
F = a function of the principal stress state (axp, ayp, azp)
S = failure surface expressed in terms of principal stresses and five input
parameters ft>fe, feb,fl and f2
:fc= ultimate uniaxial compressive strength
axp, ayp, azp = principal stresses in principal directions xp, yp, zp
ft = ultimate uniaxial tensile strength
:fcb= ultimate biaxial compressive strength = 1.2 fe
f1
= ultimate compressive strength for a state of biaxial compression
superimposed on hydrostatic stress state = 1.45 :fc
f2 '" ultimate compressive strength for a state of uniaxial compression
superimposed on hydrostatic stress state = 1.725 fe
Both the function F and the failure surface S are expressed in terms of principal
stresses denoted as ah a2, and a3 where:
al =max (axp, ayp, azp)
a3 =min (axp, ayp, azp)
and at ~ a2 ~ a3. The failure of concrete is categorized into four domains:
7 1. o ~ 0'1 ~ a2 ~ a3 (compression - compression - compression)
2. at ~ 0 <: a2 ~ a3 (tensile - compression - compression)
3. at ~ a2 ~O ~ a3 (tensile - tensile - compression)
4. al ~ a;, ~ a3 ~ 0 (tensile - tensile - tensile)
The failure surface is shown in figure A.Ill.5
~~-~ ..---- ..~~ ---
APPENDIX. IV
TYPICAL ANSYS DATA FILE
A.39
TYPICAL DATA FOR COLUMN SERIES NDA
/BATCHIFILNAME,file/PREP7mTLE, BEHAVIOUR OF BRICK MASONRY COLUMNS WITHFERROCEMENT OVERLAYET,1,65KEYOPT, 1,6.3MP,EX,I,17187 *BRICKMP,NUXY,I,0.16 *BRICKMP,EX,2,2900 *MORTARMP,NUXY,2,O.2 *MORTARMP,EX,3,19000 *FERROCEMENTMP,NUXY,3,0.17 *FERROCEMENTMP,EX,4,206896 *WIREMP,NUXY,4,0.3 *WIRE/COM*************************************************************VR=0.007 *DOUBLE LAYERS OF WIRE MESH/COM VR=0.007/2 *SINGLE LAYER OF WIRE MESH/COM VR=O.O *ZERO LAYER OF WIRE MESHR,2,4,VR,90,O,4,VRRMORE,0,90R,3,4,VR,90,0,4,VRRMORE,0,90,4,VR,0,0R,4,4,VR,0,0,4,VRRMORE,O,90/COM*************************************************************TB,CONCR,lTBDATA,1,.5,.5,2.21,20.5TB,CONCR,2TBDATA,1,.5,.5,.6,4.95TB,CONCR,3TBDATA,1,.5,.5,3.75,18.5 *2.5,18.5/COM*************************************************************TB,BKIN,4TBDATA,1,285,O/COM*************************************************************TB,MKIN,lTBTEMP" STRAIN
*NUMBER OF BRICK LAYER*NUMBER OF LAYER PER BRICK*NU11BER OF LAYER PER 110RTAR LAYER*NU11BER OF ELE11ENT PER ROW*FERROCE11ENT THICKNESS*VERTICAL 110RTAR THICKNESS*BED JOINT THICKNESS
A.40
TBDATA,1,1.164E-4,2.38E-4,2.99E-4,3.61E-4,5.8E-4TBTEMP,TBDATA,1,2,4,5,6,8/C011*************************************************************TB,l\1KIN,2TBTEMP "STRAINTBDATA,l ,3045E-4,21.85E-4,55.2E-4, 121.9E-4,266E-4TBTE11P,TBDATA,1,1,2.5,4,6,8/C011*************************************************************TB,l\1KIN,3TBTE11P"STRAINTBDATA,I, 1.579E-4,6.028E-4, 1o406E-3,2.612E-3,3.84E-3/C011 TBDATA, I, 1.613E-4,3.795E-4,7.1535E-4, 13.55E-4, 19.578E-4TBTE11P,TBDATA,I,3,7,11,15,18/C011 TBDATA, 1,1,2,3,4,4.5/C011*************************************************************NL=16BL=211L=1NE=4FT=250411TV=6.3511T=6.35T11L=11TI11LLB=9.625*2504/2 *LENGTH OF BRICK/2BT=3*2504.11T *THICKNESS OF BRICKNE1 =NE+ 1 *NUMBER OF NODE PER ROWNN=NEI *NE 1 *NUMBER OF NODE PER LAYERTNN=NN*«ML+BL)*NL+ I) *TOTAL NUMBER OF NODENEL=NE*NE *NUMBER OF ELE11ENT PER LAYERTNE=NL *(BL+11L)*NEL *TOTAL NUMBER OF ELE11ENTN,lN,2"FTN,NE"FT+LB-11TVFILL,2,NEN,NE1"FT+LBNGEN,2,NEI,1 ,NEI, 1,FTNGEN,NE-I ,NE1,NEI +1,2*NEI ,1,(LB-11TV)/(NE-2)NGEN ,2,NE 1,NE 1*NE.NE,NE 1*NE, 1,11TV
A.41
NGEN,ML+ 1,NN, 1,NN, l",TMLNGEN,BL+ 1,NN,NN*ML+ l,NN*(ML+ l),l",BT/BLNGEN,NL,NN*(BL+ML),NN+ l,NN*(BL+ML+ l), 1",BT+MTMAT,3 *lSTLAYERE,l,2,NEl +2,NEl + l,NN+ l,NN+2,NN+NEl +2,NN+NE 1+ 1EGEN,NE,l,-lEGEN,2,NEl,-NEEMODIF,NE+2,MAT,2RP3,lEGEN,NE-l ,NEI ,-NE/COM*************************************************************EMODIF,I,REAL,3EMODIF ,2,REAL,2RP3,1EMODIF ,5,REAL,4RP3,NE/COM*************************************************************EGEN,2,NN,-NEL *2ND LAYEREMODIF,NEL+NE+2,MA T, IRP3,1EMODIF,NEL+NE*2+2,MA T,IRP3,1EGEN,2,NN,-NEL *3RD LAYEREGEN,2,NN*3,-NEL *3 *4TH+5TH+6TH LAYEREMODIF ,(2*ML+BL)*NEL+NE*2,MA T,2RP2,NEEMODIF,(2*ML+BL+ I)*NEL+NE*2,MA T,2RP2,NEEMODIF ,(2*ML+BL+ I)*NEL-NE+2,MA T, IRP2,1EMODIF,(2*ML+BL+ I+ I)*NEL-NE +2,MA T, IRP2,1EGEN,NL/2,2*(ML+BL)*NN,-2*(BL+ML)*NNSAVEFINISH/SOLUD,I,ALL,O"NN,l *BOTTOM SUPPORTD,TNN-NN+I,UX,O"TNN,I *TOP SUPPORTD,TNN-NN+ I,UY,O"TNN,ID,NEI,UY,O"TNN,NN *SIDE SUPPORTRP5,NEI
A.42
D,NN-NE,UX, O"TNN,NNRP5,1/CO~*************************************************************D,TNN-NN+ 1,UZ,-.65"TNN, 1SAVESOLVED,TNN-NN+ 1,UZ,-.7"TNN,1SAVESOLVED,TNN-NN+ I ,UZ,-.75"TNN,1SAVESOLVED,TNN-NN+ 1,UZ,-. 775"TNN, 1SAVESOLVEFINISH/POST!*DO,m,I,14,1SET,m,1NSEL,S,NOD E,,5,TNN ,NNPRDISP*ENDDOFINISH/POST!*DO,m, 1,4,1SET,m,1NSEL,S,NODE"l ,25, 1PRRSOL*ENDDOFINISHIEOFIEOF
APPENDIX V
FAILURE PATTERN OF DIFFERENT COLUMNS (EXPERIMENT)
A.50
A.44
A.45
A.46
A.47
A.48
A.49
List of Figures
Failure of Bare Masonry Column Series BZA (Axial Loading)
Failure of Column Coated with Ferrocement Series NSA (Axial Loading)
Failure of Column Coated with Plaster (I :2) Series NZA (Axial Loading)
Failure of Column Coated with Plaster (I :5) Series NZAW (Axial Loading)
Failure of Hollow Ferrocement Column Series HDA (Axial Loading)
Failure of Hollow Ferrocement Column Series HSA (Axial Loading)
Failure of Column Coated with Discontinuous Ferrocement Overlay
Series DDA (Axial Loading)
A,V.8 Failure of Column Coated with Discontinuous Ferrocement Overlay Series
DSA (Axial Loading) A.51
A.V.9 Failure of Column Series GDA (Axial Loading) A.52
A.V.lO Failure of Column Series GSA (Axial Loading) A.53
A.V.llFailure of Column Coated with Ferrocement Series NOE (Eccentric Loading) A.54
A,V.l2 Failure of Column Coated with Ferrocement Series NSE (Eccentric Loading) A.55
A.V.l3 Failure of Column Coated with Plaster (I :2) Series NZA (Eccentric Loading) A,56
A.V.l4 Failure of Column Coated with Plaster (1 :5) Series NZAW (EccentricLoading) A.57 .
A.V.15 Failure of Bare Masonry Column Series BZA (Eccentric Loading) A.58
A.V.l
A.V.2
A.V.3
A.V.4
A.V.5
A.V.6
A.V.7
A.44"
FIG. A.V.l FAILURE OF BARE MASONRY COLUMN SBRlES BZA(AXIAL LOADING)
.~•••
A.45
I' IIi ,
II )\1
~ 1ft
~
~ ~.i!
J
\•, , .
- ~~I n
. 5 n ~~.•, ~:-5~S~.
,f~~-
FIG. A.V.2 FAlLURE OF COLUMN COATED WITH FERROCEMENT SERJES NSA(AXlAL LOADING)
" ::- ": -.,. '.. -.~- .'
Q,- ',,,-. '\....).
A.46
... ,
'., ".
, .
1
,,
~
~.
; , ~ I,~~
; S•~S ~~g" iii~
,.
FIG. A.V.3 FAJLURE OF COLUMN COATED WITH PLASTER (1 :2) SERJES NZA(AXJAL LOADING)
AA7
",\'
FIG, AVA FAILuRE OF COLUMN COATED WITH PLASTER (l :5) SERIES NZAW(AXIAL LOADING)
A.48
FIG. AV.5 FAILURE OF HOLLOW FERROCEMENT COLUMN SERIES HDA(AXIAL LOADING)
A.49
':I •• ~., r"
, .
~
' .
, .
~'"-n~~ "
,•l:!£,
,
'".": ~
..'L
, .II
j(' I'i.
:' '. "?,", "- ,
,,,",-:"" i.~~.
". ~"j,,
> ">
~~
n i!,"~ ';#~~
~.~~
,.~,.e ~~....•.~!£
.• •..... ,;~-~
<.>
, <
:,. -. '.
.
,"'.>i~+;~t:.'....•. ", :',.1.'9
,.
FIG. A.V.6 FAILURE OF HOLLOW FERRO CEMENT COLUMN SERIES HSA(AXIAL LOADING)
A.50
FIG. A.V.? FAILURE OF COLUMN COATED WITH DISCONTINUOUS FERROCEMENTOVERLAY SERIES DDA (AXIAL LOADING)
A.51
; ...-'
1"'--I
I._, ,".
I
I.! ~~ !
\ '~I
!.~ ~']L -. ' .~~s ' - I~; 5 ' ..! .
Ul ,t
:~~nnIS. ~ I
.' ~I
{o'
"
\,\ - .
, 1\'
: '-~1J:,:"
FIG. A.V.8 FAILURE OF COLUMN COATED WITH DISCONTINUOUS FERROCEMENT OVERLAY SERIES DSA(AXIAL LOADING)
, \
r
I
A.52
\ Ii 1 '/ I \ II.. \! ,'I
I I I
r I III .. " n, r', E
~'
.1.I
( rn!{ I U II Ii
!)1
FIG. AV.9 FAILURE OF COLUMN SERIES GDA(AXIAL LOADING)
A.53
FIG. A.V.IO FAILURE OF COLUMN SERlES GSA(AXIAL LOADING)
A.54
.... "" .•... ,.,.. ~
"'I. ,.,'
FIG. A.V.11 FAILURE OF COLUMN COATED WITH FERROCEMENT SERlES NDE(ECCENTRlC LOADING)
A.55
r ~\.• i,,.
I\ \
I ,I , , ;
I ~II
;1 ,n!, ,~;I
'HIi,
II
, ,
,I
,
:,
FIG. A.V.12 FAILURE OF COLUMN COATED WITH FERROCEMENT SERJES NSE(ECCENTRIC LOADING)
A.56
;....•
'{f'.. },'. ~.. ';' .1..:: '
•••••.• '1-.. '.r....": ...,:.' "
., ),
1 .
I., :
c--11¥•~~u. l,;,;.
t '.•! r, '.'
I' .
. "'.<.'..<*. '. ,; , ,
f ., •
FIG. A.V.J3 FAILURE OF COLUMN COATED WITH PLASTER (1 :2) SERIES NZE(ECCENTRIC LOADING)
A.57
FIG. A.V.14 FAILURE OF COLUMN COATED WITH PLASTER (l:5) SERlES NZEW(ECCENTRIC LOADING)
~I"t \\. I '-"';
A.58
FIG. A.V.l5 FAILURE OF BARE MASONRY COLUMN SERIES BZE(ECCENTRIC LOADING)
•
APPENDIX VI
FAILURE PATTERN OF DIFFERENT COLUMNS (FEA)
List of Figures
A.VI.I Predicted Failure Mode of Column Series NZA
A.VI.2 Predicted Failure Mode of Column Series NZAW
A.VI.3 Predicted Failure Mode of Column Series DDA
A.VIA Predicted Failure Mode of Column Series DSA
A.VI.5 Predicted Failure Mode of Column Series HDA
A.VI.6 Predicted Failure Mode of Column Series HSA
A.VI.7 Predicted Failure Mode ofColuinn Series GDA
A.VI.8 Predicted Failure Mode of Column Series GSA
A.VI.9 Predicted Failure Mode of Column Series BZA
A.VI.lO Predicted Failure Mode of Column Series NDE
A.VI.II Predicted Failure Mode of Column Series NSE
A.VI.12 Predicted Failure Mode of Column Series NZE
A.VI.13 Predicted Failure Mode of Column Series NZEW
A.VI.14 Predicted Failure Mode of Column Series BZE
A.60
A.61
A.62
A.63
A.64
A.64
A.65
A.66
A.67
A.68
A.69
A.70
A.71
A.72
A.60
Outer Ferrocement Shell Central Masonry Core
• Cracked Element
Mortar Joint
FIG. A.VI.l PREDICTED FAILURE MODE OF COLUMN SERIES NZA
A.61
•
•
Outer Ferrocement Shell Central Masonry Core
• Cracked Element
Mortar Joint
FIG. A.VI.2 PREDICTED FAILURE MODE OF COLUMN SERIES NZAW
•..:- "'.It':: '- . '"...0
A.62
Outer Ferrocement Shell Central Masonry Core
• Cracked Element
Mortar Joint
FIG. A.VI.3 PREDICTED FAILURE MODE OF COLUMN SERIES DDA
A.63
Outer Ferrocement Shell Central Masonry Core
• Cracked Element
. Mortar Joint
FIG. A.VIA PREDICTED FAILURE MODE OF COLUMN SERIES DSA
A.64
• Cracked Element
FIG. A.VI.S PREDICTED FAILUREMODE OF COLUMN SERlliSHDA
FIG. A.V1.6 PREDICTED FAILUREMODE OF COLUMN SERlliS HSA
A.65
•
Outer Ferrocement Shell Central Masonry Core
• Cracked Element
Mortar Joint
FIG. A.VI.7 PREDICTED FAILURE MODE OF COLUMN SERIES GDA
"
A,66
•
Outer Ferrocement Shell Centra! Masonry Core
• Cracked Element
Mortar Joint
FIG, A,VI,8 PREDICTED FAILURE MODE OF COLUMN SERIES GSA
..
A.67
Masonry Core
• Cracked Element
Mortar Joint
FIG. A.VI.9 PREDICTED FArr.,URE MODE OF COLUMN SERIES BZA
•,,4,
A.68
Outer Ferrocemerit Shell Central Masonry Core
• Cracked Element
Mortar Joint
FIG. A.VI.lO PREDICTED FAILURE MODE OF COLUMN SERIES NDE
A.69
Outer Ferrocement Shell Central Masonry Core
• Cracked Element
Mortar Joint
FIG. A.VI.II PREDICTED FAILURE MODE OF COLUMN SERIES NSE
A.70
Outer Ferrocement Shell Central Masonry Core
• Cracked Element
Mortar Joint
FIG. A.VI.12 PREDICTED FAll..URE MODE OF COLUMN SERIES NZE
A.71
Outer Ferracement Shell Central Masonry Core
• Cracked Element
Mortar Joint
FIG. A.VI.13 PREDICTED FAILURE MODE OF COLUMN SERIES NZEW
A.72
Masonry Core
• Cracked Element
Mortar Joint
FIG. A.VI.14 PREDICTED FAILURE MODE OF COLUMN SERIES BZE
A.74
A.75
A.76
A.77
A.7S
A.79
A.SO
A.SI
A.S2
A.S3
A.S4
A.S5
A.S6
A.87
A.88
A.89
A.89
A.90
A.90
A.91
A.91
A.92
A.92
A.93
A.94
A.94
A.95
A.95
A.96
APPENDIX vnCOMPARISON OF FAILURE MODE AND STRESS-STRAlN CURVE
List of Figures
A.VIT.I Failure Mode of Column Series NDA
A.VIT.2 Failure Mode of Column Series NZA
A.VIT.3 Failure Mode of Column Series NZAW
A.VITA Failure Mode of Column Series DDA
A.VIT.s Failure Mode of Column Series DSA
A.VIT.6 Failure Mode of Column Series HDA
A.VIT.7 Failure Mode of Column Series HSA
A.VIT.S Failure Mode of Column Series GDA
A.VIT.9 Failure Mode of Column Series DSA
A.VIT.lO Failure Mode of Column Series BZA
A.VIT.II Failure Mode of Column Series NDE
A.VIT.l2 Failure Mode of Column Series NSE
A.vn.13 Failure Mode of Column Series NZE
A.vn.l4 Failure Mode of Column Series NZEW
A.vn.l5 Failure Mode of Column Series BZE
A.vn.l6 Stress-Strain Curve of Column Series NZA
A.vn.17 Stress-Strain Curve of Column Series NZAW
A.vn.IS Stress-Strain Curve of Column Series DDA
A.vn.19 Stress-Strain Curve of Column Series DSA
A.vn.20 Stress-Strain Curve of Column Series HDA
A.vn.2l Stress-Strain Curve of Column Series HSA
A.VIT.22 Stress-Strain Curve of Column Series GDA
A.vn.23 Stress-Strain Curve of Column Series GSA
A.vn.24 Stress-Strain Curve of Column Series BZA
A.vn.25 Stress-Strain Curve of Column Series NDE
A.vn.26 Stress-Strain Curve of Column Series NSE
A.vn.27 Stress-Strain Curve of Column Series NZE
A.vn.2S Stress-Strain Curve of Column Series NZEW
A.vn.29 Stress-Strain Curve of Column Series BZE
<l: '.
A.74
o Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.Vll.1 FAILURE MODE OF COLUMN SERIES NDA
A.75
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.YII.2 FAILURE MODE OF COLUMN SERIES NZA
A.76
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.VII.3 FAILURE MODE OF COLUMN SERIES NZAW
A.77
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.YIlA FAILURE MODE OF COLUMN SERIES DDA
A.78
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.VII.5 FAILURE MODE OF COLUMN SERIES DSA
A.79
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.VII.6 FAILURE MODE OF COLUMN SERIES HDA
A.80
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.VII.7 FAILURE MODE OF COLUMN SERIES HSA
A.8l
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.Vll.8 FAILURE MODE OF COLUMN SERIES GDA
A.82
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.VII.9 FAILURE MODE OF COLUMN SERIES GSA
A.83
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.Vll.lO FAILURE MODE OF COLUMN SERIES BZA
A.84
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.VII.!! FAILURE MODE OF COLUMN SERIES NDE
A.85
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.VII.l2 FAILURE MODE OF COLUMN SERIES NSE
A.86
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.VIl.13 FAILURE MODE OF COLUMN SERlES NZE
A.S?
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.Vll.l4 FAILURE MODE OF COLUMN SERIES NZEW
A.88
• Cracked ElementAnalytical Failure Pattern Experimental Failure Pattern
FIG. A.VII.15 FAILURE MODE OF COLUMN SERIES BZE
7 6
~CDv:>
800600
I~:EM I---+---£XPT.
200
5
oo 400
Strain (10-6)
FIG. A.Vll.17 STRESS-STRAIN CURVE OF COLUMN SERIES NZAW
700600400 . 500300Strain (10-6)
200100oo
1
6
FIG. A.VII.16 STRESS-STRAIN CURVE OF COLUMN SERIES NZA/'-, \
!
5I / I
4
i 4
~'"0..~
en~
en en
1len
3
""'Q)~
OJ-
3 fC/)
.~ 0;c
0.E
z 0I . :EM Iz 2
21- /.1' ---+---£XPT.
8
800600400Strain (10-<)
200
FIG. A.VII.19 STRESS-STRAIN CURVE OF COLUMN SERIS DSA
oo800600400200
Strain (10.6)
FIG. A.VII.18 STRESS-STRAIN CURVE OF COLUMN SERIS DDA
8
6
8
';0'
/~ ~~'"'",g
~
<Zl
'"
til 4
'",g 4
.~ j/g 1 l //0z---+-EXPT.
~
I-:-~EM I.\.0
---+-EXPT.0
22
200015001000Strain (10-6)
500
2
200015001000Strain (10-6)
500
2
161 I
14I •
14 I- -' I 12 ~ /12 l- I / I
10l /•/10 ro-r0- o.
0. e.e. rnrn rn
B Q)rn ~~ - ~- rnrn m 6m c \i)
c .E I-'.E 6 00 I . ~EMI Z I~EM IZ ---+-EXPT. ---+-EXPT.4
I /I4
FIG. A.Vll.20 STRESS-STRAIN CURVE OF COLUMN SERIES HDAFIG. A.Vll.21 STRESS-STRAIN CURVE OF COLUMN SERIES HSA
7 7
800600400Strain (10~
200oo
1
6
1000800400 600Strain (10-6)
200o o
1
6
5 5
~ ~'" '"~ 4 ~ 4~ ~
'"on
'"on
" "b bCZl
~ 3~ I :t-O! 3
..~ .03 \D
e 10
0 0
Z Z
~2~ f ~2r J/ --EXPT.
--EXPT.
FIG. A.VII.22 STRESS-STRAIN CURVE OF COLUMN SERIES GDA FIG. A.VII.23 STRESS-STRAIN CURVE OF COLUMN SERIES GSA
A.93
6
5
12001000600400200
4
'2'
~'"'"" 3
/~C/l
10Z 2 /~--EXPT.
fIG. A.VII.24 STRESS-STRAIN CURVE OF COLUMN SERIES BZA
.-'\. , ....-l
1000800600400200o
o1000800600400200o
o
500500
/•/ 400400 I- //
/.300300 l- I/
•IJ J/ z /~;J:I"0
'" I0\0...J 200ol'>
I 1-"" 1 ! g/ -.-EXPT -.-EXPT
/I. 100 (I100 I-
Strain (10.6) Strain (10.6)
FIG. A.VII.25 LOAD-STRAIN CURVE OF COLUMN SERIES NDEFIG. A.VII.26 LOAD-STRAIN CURVE OF COLUMN SERIES NSE
500 300
700600500400300
Strain (10.6)
200100oo100 200 300 400 500 600 700 800
Strain (10.6)
400 f- / I '~I /
e/ = j/~300f- / /
e
~,~ ~~l /o e ~
-' 200 /
S"O I g ID
/e ~lJ1
-e-EXPT -e-EXPT
'00' ;; / ~I(/e e
FIG. A.YII.27 LOAD-STRAIN CURVE OF COLUMN SERIES NZE FIG. A.VII.28 LOAD-STRAIN CURVE OF COLUMN SERIES NZEW
A.96
200
~Z"'" 100~"0co0...J
I rEM I-.-EXPT
50
700
FIGAVI1.29 LOAD-STRAIN CURVE OF COLUMN SERIES BZE
APPENDIX. vmDERIVATION OF PROPOSED DESIGN F'ORMULA
List Of Figures
A.VIII.I Tensile Strengthof Brick vs. Column StressCurve A.l02
A.VIII.2 ThicknessRatio VS. Column StressCurve A,103
A.VIII.3Nominal Stress in Overlay at Failure vs. Strengthof Ferrocement
Mortar Curve 4.104
A.VIIIA InteractionDiagram A.IOS
A.98
The total load carrying capacity of masonry column with ferrocement overlay is
the summation of load carrying capacity of bare masonry column and load carrying
capacity of ferrocement overlay including confinement effect. Therefore, the
following formula for the masonry column encased in ferrocement overlay is
obtained:
Pull = PI + P2 ••••••••••••••• (A.VIII.I)
where:
PI =Ultimate load for bare masonry column (N)
P2 = Load carrying capacity of ferrocement overlay including the effect of
confinement in Newton (N)
A review of the parametric study discussed in Art. 8.3 shows that all the parameters
have not significant influence on the failure load. The important parameters are:
(i) tensile strength of brick,
(ii) compressive strength of ferrocement mortar; and
(iii) thickness ratio of bed joint and brick.
A total of 99 column have been analysed by changing the values of the important
parameters, cross-sectional dimension of bare masonry, cross-section of ferrocement
overlay and eccentricity. Linear fracture analysis have been adopted to predict the
failure loads of the columns. The results are presented in Appendix IX.
Bare Masonry Column
To develop the design formula of PI> fifteen bare masonry columns of three
different cross-sectional area, have been analysed by changing the values of tensile
strength of brick and thickness ratio of bed joint and brick Two best fit curves are
drawn using least square method - one nominal failure stress of bare column vs.
A.99
tensile strength of brick and the other nominal failure stress of bare column vs.
thickness ratio of bed joint and brick as shown in Figs. A.VIII.1 and A.VIII.2.
From the curves shown in Figs. A.VIII. 1 and A.VIII.2 the following expressions are
obtained:
PI/Abm = 2.05 + 3.16 ftb - 0.74 (ftb)2
PI/Abm = 5.98 - 6.85 :m + 7.9 (:m i• •
.................. (A.VIII.2)
.................. (A.VIII.3)
Keeping the coefficient of ftb , (ftb i ,.s,. and (11m i the same as in the above twoI. •
equations and using trial and error method to achieve the best fit,. the following
simplified formula for bare masonry column is obtained:
PI =Abm {2.3 + 3.16 ftb - 0.74 (ftb i -6.85 :m + 7.9 (:m )2} (A.VIIIA)b b
where:
PI =Ultimate load for bare masonry column (N)
Abm = Cross-sectional area of bare masonry column (mm2)
ftb = Tensile strength of brick (MPa)
.s,. = Thickness ratio of bed joint and brickIb
Masonry Column with Ferrocement Overlay (Axial Loading)
To develop the design formula of P2, twenty nine masonry columns with
ferrocement overlay of nine different cross-sectional area, have been analysed by
changing the value of compressive strength of ferrocement mortar. The value of P2
is obtain by subtracting the failure load of masonry column from failure load of
masonry column (same cross-sectional area) with ferro cement overlay. A best fit
curve of nominal failure stress of ferrocement overlay vs. compressive strength of
A.lOO
ferrocement mortar have been plotted using least square method as shown in Fig.
A.VIII.3. (package- Origin version 3.5)
The equation shown in Fig. A.VIII.3 can be written as
P2/Af= 2.2 fcfin - 19.2 (A.VIII.S)
or
P2 = Af (2.2 fcfin - 19.2) (A.VIII.6)
where,
P2 = Load carrying capacity of ferrocement overlay including the effect of
confinement in Newton (N)
A{= Cross-sectional area of ferrocement in mm2
fcfin = Compressive strength of ferrocement mortar in MPa
All these above expressions are based on the linear elastic fracture analysis. From
chapter 8 it is seen that the linear elastic fracture analysis gives higher load than
the nonlinear analysis (exact analysis). To account for this overestimation of failure
load and to make the equation conservative, equation A.VIII.l can be modified as,
Pult = 0.80 (PI + P2) ••••••••••••• (A.VIII.7)
where:
Pult =Ultimate load (N)
PI =Ultimate load for bare masonry column (N)
P2 = Load carrying capacity of ferrocement overlay including the effect of
confmement in Newton (N)
A.10l
Masonry Column with Ferrocement Overlay (Eccentric Loading)
To develop a design formula for eccentric loading, fifty four masonry column with
ferro cement overlay, of nine different cross-sectional area have been analysed by
changing the values of eccentricity, compressive strength of ferro cement mortar
and thickness ratio of bed joint and brick. A best fit curve of Pe,ult!Pult vs. e/h (h =
depth of column) have been plotted as shown in Fig. A.VIlIA.
The expression shown in Fig. A.VIlIA for eccentric load can be written as,
Pe, ultPult
(0.9996-1.51208 h) (A.VIII.8)
In order to simplify the procedure the above expression may be written as,
Pe•u1t= PU!t(l-1.5*) (A.VIII.9)
/ ,
A.102
6.0
•5.5
roQ.
~'"'" 5.0Q)~-(/)roc'E0z
4.5
4.0
•
y=2.05+3.16x-O.74x2
•
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Tensile Strength of Brick fib (MPa)
FIG. A.VIII. I TENSILE STRENGTH OF BRICK VS. COLUMN STRESS CURVE
A.l03
6,0
•5,5
roIl.
~<Il<Il 5,0Cll.:-(/)
roc'E0z
4,5 •
4,0
0,0 0,1 0,2 0,3 0.4Thickness Ratio of Bed Joint and Brick (tm/tbl
~IG, A,VIII.2 THICKNESS RATIO VS, COLUMN STRESS CURVE
A.104
FIG. A.VIII.3 NOMINAL STRESS IN OVERLAY AT FAILUREVS. STRENGTH OF FERROCEMENT MORTAR CURVE
A.10S
y=O.99966-1.5120B X0.9
1.0
0.8
'50---'5
<Ii •0- 0.7
••••
0.6
•,•-.
0.5
0.00 0.05 0.10 0.15
e/h0.20 0.25 0.30
FIG. AVillA INTERACTION DIAGRAM
APPENDIX IX
COMPARISON OF PROPOSED DESIGN FORMULAE AND FINITEELEMENT ANALYSIS
AXIAL LOAD CASE (MASONRY COLUMN WITH FERROCEMENT OVERLAY)
I-'o-J
:J:'
Variable Problem number
1 2 3 4 5 6 7 8 9 10 11 12 13 14Thickness ratio of bedjoint and brick 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.273 .273
(t"/t,, )X-Sectional area of 244 244 244 244 244 244 244 244 244 381 381 381 381 244brick masonry (At,.,) x x x x x x x x x x x x x x
(mmx~) 244 244 244 244 244 244 244 244 244 381 381 381 381 244Thickness of"errocement overlay 19.05 19.05 19.05 25.4 25.4 25.4 38.1 38.1 38.1 19.05 19.05 19.05 25.4 38.1
(mm)Compressive strength offerrocement mortar (fm.) 15 18.5 20 15 18.5 20 15 18.5 20 15 18.5 20 18.5 18.5
IMPa)Tensile strength ofbrick (fd,) 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21
rMPa)
Pt(kN) 304 304 304 304 304 304 304 304 304 742 742 742 636 261
P2(kN) 277 431 497 378 588 679 593 924 1066 420 654 756 888 924
Pull=~,+P2) 465 588 641 546 714 786 718 982 1096 930 1118 1198 1219 984
P,=(kN) 565 711 792 643 831 886 816 1060 1144 1300 1580 1780 1384 1018
P,oJPull 1.21 1.20 1.23 1.17 1.16 1.12 1.13 1.07 1.04 1.39 1.41 1.48 1.13 1.07
/' "\
AXIAL LOAD CASE (MASONRY COLUMN WITH FERRO CEMENT OVERLAY)
VariableProblem number
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29Thickness ratio of bedjoint and brick .091 .091 .091 .091 0.091 .091 0.Q91 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091
(t,,/!,,)X-Sectional area of 381 381 381 381 381 381 508 508 508 508 508 508 508 508 508brick masonry (A"",) x x x x x x x x x x x x x x x(mm x mm) 381 381 381 381 381 381 508 508 508 508 508 508 508 508 508
Thickness ofCerrocement overlay 25.4 25.4 25.4 38.1 38.1 38.1 25.4 25.4 25.4 38.1 38.1 38.1 19.05 19.05 19.05
(mm)Compressive strength of""errocement mortar 15 18.5 20 15 18.5 20 15 18.5 20 15 18.5 20 15 18.5 201(1;, •• ) IMPa)Tensile strength ofbrick (f",) 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21
IMP~)
P,(kN) 742 742 742 742 742 742 1319 1319 1319 1319 1319 1319 1319 1319 1319
P,(kN) 570 888 1024 881 1373 1584 748 1165 1344 1148 1789 2064 554 863 996
Pull = 0.8O(P,+ 1', ) 1050 1304 1413 1298 1692 1861 1654 1987 2130 1974 2486 2706 1498 1796 1852(kN)
p, ••••(kN) 1400 1696 1902 1557 1870 2103 2350 2722 3111 2555 2939 3322 2200 2500 2822
I',OJP u11 1.33 1.30 1.34 1.19 1.10 1.13 1.42 1.36 1.46 1.29 1.18 1.22 1.46 1.43 1.52
~f-'o00
AXIAL LOAD CASE (BARE COLUMN)
VariableProblem
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44Thickness ratio of bed joint and
brick 0.091 0.182 0.273 0.091 0.091 0.091 0.182 0.273 0.091 0.091 0.091 0.182 0.273 0.091 0.091(t,,/t,,)
X-Sectional area of 244 244 244 244 244 381 381 381 381 381 508 508 508 508 508brick masorny (A"",) x x x x x x x x x x x x x x x(mrnxmm) 244 244 244 244 244 381 381 381 381 381 508 508 508 508 508
Tensile strength ofibrick (fib) (MPa) 2.21 2.21 2.21 1.5 1.0 2.21 2.21 2.21 1.5 1.0 2.21 2.21 2.21 1.5 1.0
P,(kN) 304 279 261 286 247 742 680 635 697 602 1319 1209 1130 1240 1071
Pr"" (kN) 324 298 268 304 263 798 740 672 751 650 1437 1332 1187 1345 1172
Pron/P, 1.06 1.06 1.03 1.06 1.06 1.07 1.08 1.06 1.07 1.08 1.09 1.10 1.05 1.08 1.09
~t-'o\0
1
ECCENTRIC LOAD CASE
Variable Problem number
1 2 3 4 5 6 7 8 9 10 Il 12 13 14 15 16 17 18 19Thickness ratio of bed joint
and brick 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091(t",It,,)
X-Sectional area of 244 244 244 244 244 244 244 244 244 381 381 381 381 381 381 381 381 381 508brick masonry (Am.) x x x x x x x x x x x x x x x x x x x(mmxmnl) 244 244 244 244 244 244 244 244 244 381 381 381 381 381 381 381 381 381 508
Thickness of ferrocementoverlay (mm) 19.05 19.05 19.05 25.4 25.4 25.4 38.1 38.1 38.1 19.05 19.05 19.05 25.4 25.4 25.4 38.1 38.1 38.1 19.05
Compressive strength offerrocemenl mortar (f..,,) 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5
(MPa)Tensile strength of brick (1;,,)
(MPa) 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.21
Eccenlrcity I Depth (e/b) 0.0337 0.136 0.2612 0.043 0.141 0.2607 0.0594 0.1497 0.259 0.0227 0.132 0.257 0.0294 0.136 0.257 0.0416 0.1423 0.257 0.0174
PI (kN) 304 304 304 304 304 304 304 304 304 742 742 742 742 742 742 742 742 742 1319
P, (kN) 431 431 431 588 588 588 924 924 924 654 654 654 888 888 888 1373 1373 1373 863
eP,,,,,9l.80(P. -P,X1-1.5 11) 558 468 358 668 563 435 895 761 600 1080 897 692 1247 1038 801 1586 1331 1040 1700
(kN)
P••• (kN) 661 533 419 765 640 483 977 755 615 1470 Il03 764 1534 Il87 837 1770 1419 1042 2300
PremlPe,uft 1.18 1.13 1.17 1.14 1.13 1.11 1.09 0.99 1.02 1.36 1.23 1.10 1.23 1.14 1.04 I.Il 1.06 1.00 1.35
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ECCENTRIC LOAD CASE
Variable Problem nwnber
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Thickness ratioof bedjoint
andbrick 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.2731t,Jt,,)
X-Sectionalareaof 508 508 508 508 508 508 508 508 244 244 244 244 244 244 381 381 381 244 244 244brickmasomy(AtmJ x x x x x x x x x x x x x x x x x x x x_x~ _ _ _ _ _ _ _ _ ~ ~ ~ ~ ~ ~ ~I ~I ill ~ ~ ~
Thickness of ferrocementoverlay (mm) 19.05 19.05 25.4 25.4 25.4 38.1 38.1 38.1 19.05 19.05 19.05 25.4 25.4 25.4 25.4 25.4 25.4 38.1 38.1 38.1
Compressive strength offerroccmen~m;"'" (t..) 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 IS IS IS 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5
Tensilestreogtbof brick(f••)~ UI UI UI UI UI UI UI Ul UI UI UI UI UI ~ UI UI ~ ~ UI ~
Eccentreity/Depth(cIh) 0.13 0.255 0.0227 0.133 0.2556 0.0326 0.1385 0.2554 0..0337 0.136 0.2612 0.043 0.141 0.2607 0.0416 0.136 0.257 0.0594 0.1497 0.259
P, (kN) 1319 1319 1319 1319 1319 1319 1319 1319 304 304 304 261 261 261 637 637 637 261 261 261
P, (kN) 863 863 1165 1165 1165 1789 1789 1789 277 277 277 588 588 588 888 888 888 924 924 924
eP,...=O.80(P,• PV(I.1.5h) 1406 1078 1914 1591 1225 2364 1969 1534 442 370 283 635 533 414 1143 970 749 896 763 600
IkNl
1tl~ (kN) 1935 1357 2599 2118 1450 2792 2219 1542 542 446 367 686 586 429 1301 1107 858 822 733 580
I .~. "" 1.37 1.25 1.35 1.33 1.18 1.18 1.12 1.00 1.22 1.20 1.29 1.08 1.09 1.03 1.13 1.14 1.14 0.92 0.96 0.96J ,
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