AN INVESTIGATION OF THE STRENGTH
OF CONCRETE MASONRY SHEAR WALL STRUCTURES
By
KRISHNAIYER BALACHANDRAN
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1974
ACKNOWLEDGMENTS
The author wishes to express his sincere gratitude to
Dr. M. W. Self for his patience, guidance, and encouragement,
without which this dissertation would not have been possible.
Special thanks are due to Prof. Herbert A. Sawyer, Jr.,
for sparing some of his equipment and literature and, also,
for serving on the supervisory committee. Appreciation is
extended to Dr. C. S. Hartley for serving on his supervisory
committee.
Sincere thanks are due to Dr. Martin A. Eisenberg for
the help he has provided in introducing the author to the
Finite Element Method. Without his professional guidance,
helpful suggestions and long hours of discussion, the
author's task would have been more difficult.
The author wishes to express his gratitude to all
those who assisted him along the way: Graduate students
K. Fuller and M. Chanchalani; and friends M. Krishnamurthy,
S. M. Ulagaraj, J. N. Sharma, A. M. Garde and H. A. Cole, Jr.
Thanks are due to Mr. L. F. Hopkins and W. Whitehead
for their help on the equipment in the Civil Engineering
Laboratory.
iii
Acknowledgment is due to the Concrete Promotion
Council of Florida for their financial support for part of
the experimental program; to the National Concrete Masonry
Association and the National Bureau of Standards for provid
ing the model concrete blocks; and, to the Northeast
Regional Data Center for its support.
Special thanks go to Mrs. C. Combs for her concerned
work when typing the final copy.
Finally, a special note of deep appreciation is due
to his wife, Lalitha, for her encouragement, love and
understanding during the difficult time of being the wife
of a student.
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ......................................... iii
LIST OF TABLES........................................ viii
LIST OF FIGURES....................................... ix
KEY TO SYMBOLS........................................ xv
ABSTRACT.............................................. xxi
CHAPTER
1. INTRODUCTION................................... 1
1.1 History .................................... 1
1.2 General Remarks............................ 2
1.3 Previous Investigations................... 6
1.3.1 Strength of Mortar Joints......... 6
1.3.2 Racking Tests...................... 10
1.3.3 Circular Shear Specimens.......... 12
1.3.4 Square Shear Specimens............ 13
1.3.5 Horizontally and Vertically
Loaded Wall Without Frame........ 16
1.3.6 Test on Small Masonry Assemblages. 17
1.3.7 Reinforced Concrete Masonry
Walls in Shear.................. 20
1.3.8 Effect of Wall Openings........... 22
1.3.9 Shear in Concrete Masonry Piers... 25
1.3.10 Strength of Masonry under
Combined Compression and Shear.. 30
1.4 Objectives and Scope of Present
Investigation............................. 33
2. EQUIPMENT, MATERIALS AND TESTING TECHNIQUES.... 35
2.1 Testing Machines and Other Equipment....... 35
2.2 Concrete Blocks ............................ 36
2.3 Mortar ..................................... 39
2.4 Model Concrete Blocks ..................... 41
2.5 Model Reinforcement....................... 43
2.6 Model Mortar ............................... 43
2.7 Model Grout Mixes.......................... 46
2.8 Mortar Mix for Spandrel................... 51
Table of Contents (Continued)
CHAPTER Page
3. STRENGTH OF MORTAR JOINTS UNDER
COMBINED STRESSES.. ........................... 52
3.1 Scope ...................................... 52
3.2 Test Specimens ............................ 53
3.3 Strength of Mortar Joints under
Compression and Shear.................... 53
3.4 Strength of Mortar Joints under
Compression and Bending................. 63
3.5 Combined Compression, Bending, and Shear.. 69
4. MODEL TESTS OF CONCRETE MASONRY PIERS........... 70
4.1 Selection of Model........................ 70
4.2 Selection of Model Materials............... 83
4.3 Fabrication of Model....................... 86
4.4 Test Setup................................. 89
4.5 Test Parameters............................. 91
4.6 Tests on Grouted Piers..................... 91
4.7 Tests on Nongrouted Piers.................. 101
5. ANALYSIS OF TEST RESULTS....................... 102
5.1 Grouted Piers............................. 102
5.2 Nongrouted Piers ........................ .. 105
5.3 Equations for Predicting the Diagonal
Tensile Strength of Masonry.............. 108
5.3.1 Grouted Piers...................... 108
5.3.2 Nongrouted Piers.................... 111
6. NONLINEAR FINITE ELEMENT ANALYSIS.............. 122
6.1 General Remarks........................... 122
6.2 Finite Element Linear Analysis............ 123
6.3 Finite Element Nonlinear Analysis.......... 125
6.3.1 General Remarks.................... 125
6.3.2 General Physical Approach.......... 126
6.4 Variable Stiffness Methods................ 127
6.5 Initial Stress Method...................... 130
6.6 Initial Strain Method..................... 131
6.7 Previous Investigations.................... 132
6.8 Objective and Scope of Present
Investigation............................ 138
7. DESCRIPTION OF ANALYTICAL MODEL................ 139
7.1 Choice of Finite Elements................. 139
7.2 Formulation of Element Stiffness Matrix... 142
Table of Contents (Continued)
CHAPTER Page
7. Description of Analytical Model (Continued)....
7.3 Material Properties and Failure Criteria.. 147
7.3.1 Uniaxial StressStrain Curves....... 147
7.3.2 Representation of Properties
of Masonry Element............... 147
7.3.3 Plastic Yielding in Compression.... 152
7.3.4 Biaxial Strength of a
Masonry Component................ 153
7.3.5 Crushing of Masonry................ 155
7.3.6 Cracking............................ 155
7.3.7 Bond Failure at the Interface
between Mortar and Block.......... 159
7.3.8 Yielding of Reinforcement.......... 164
8. ANALYSIS AND EXAMPLES.......................... 165
8.1 Method of Solution..... .................... 165
8.2 Computational Procedure................... 167
8.3 Computer Program........................... 172
8.4 Examples of Nonlinear Analysis............ 175
8.4.1 Square Concrete Panel under
Diagonal Compression.............. 175
8.4.2 Hollow Concrete Masonry Panels
under Diagonal Compression....... 182
8.4.3 Grouted Masonry Piers............... 188
8.4.4 Nongrouted Masonry Piers............ 198
9. CONCLUSIONS.................................... 203
9.1 Conclusions. .............................. 203
9.2 Recommendations for Further Study.......... 207
APPENDIX A (ALGORITHM FOR SOLUTION OF EQUATIONS) ...... 208
APPENDIX B (COMPUTER PROGRAM OUTPUT) .................. 213
REFERENCES..... ........ ............................... 221
BIOGRAPHICAL SKETCH................................... 227
vii
LIST OF TABLES
TABLE Page
2.1 PROPERTIES OF MODEL MORTAR AND GROUT............ 48
3.1 PROPERTIES OF MORTAR....... ............... ...... 54
3.2 STRENGTH OF MORTAR JOINTS UNDER
COMPRESSION AND SHEAR......................... 58
3.3 STRENGTH OF 1:1:4.5 MORTAR JOINTS UNDER
COMPRESSION AND SHEAR......................... 59
3.4 STRENGTH OF MORTAR JOINTS UNDER
COMPRESSION AND BENDING....................... 62
3.5 MORTAR JOINTS UNDER COMBINED
COMPRESSION, BENDING, AND SHEAR............... 67
5.1 TEST RESULTS OF GROUTED PIERS................... 103
5.2 TEST RESULTS OF NONGROUTED PIERS................ 109
5.3 ANALYSIS OF RESULTS OF TESTS ON NONGROUTED
PIERS......................................... 115
8.1 MATERIAL PROPERTIES USED IN ANALYSIS OF PR 3.... 190
8.2 MATERIAL PROPERTIES USED IN ANALYSIS OF PR 7.... 195
8.3 MATERIAL PROPERTIES USED IN ANALYSIS OF PR 9.... 197
viii
LIST OF FIGURES
FIGURE Page
1.1 Shear wall with boundary elements............... 5
1.2 Elements of shear wall with openings............ 5
1.3 Type of test specimens used by Zelger.......... 8
1.4 Test specimen adopted by Haller................ 8
1.5 Arrangement of racking test and the force
distribution on the specimen................. 11
1.6 Test for diagonal tensile strength of
brickwork and stress distribution............. 11
1.7 Typical Xcracks in a wall damaged by
an earthquake................................ 14
1.8 Fringe patterns obtained in a photoelastic
analysis of a model of a wall with an
opening and a square panel under
diagonal compression......................... 14
1.9 Diagonal tension test on a square panel......... 15
1.10 Test setup (schematic) adopted by Meli and
Reyes for testing mortar joints under
compression and shear........................ 15
1.11 Types of test specimens adopted by Meli and
Reyes for diagonal compression tests......... 19
1.12 Test panels adopted by Converse................ 19
1.13 Continuous opening in a shear wall............. 23
1.14 Staggered opening in a shear wall............... 23
1.15 Forces acting on a pier element
in a wall with opening....................... 26
1.16 Test setup adopted by Schneider for full scale
test on piers................................ 26
List of Figures (Continued)
FIGURE Page
2.1 Splitting tests on concrete block............... 38
2.2 Sieve analysis of sand for masonry mortar...... 40
2.3 Model concrete block........................... 42
2.4 Model reinforcement (0.147" dia.).............. 42
2.5 Stressstrain curve for model concrete block... 44
2.6 Stressstrain curve for model reinforcement.... 45
2.7 Stressstrain curve for model mortar............ 47
2.8 Stressstrain curve for model grout............. 49
2.9 Stressstrain curve for spandrel mortar......... 50
3.1 Setup for studying the strength of mortar
under pure shear............................. 55
3.2 Test setup for finding the strength of mortar
joints under combined compression and shear.. 56
3.3 Shear failure through mortar joint............. 56
3.4 Effect of precompression on the shearing
strength of mortar joints.................... 60
3.5 Crosssection of a mortar joint................. 64
3.6 Effect of precompression on the flexural
tensile strength of mortar joints............ 65
3.7 Test setups used for obtaining combined
stresses on mortar joints.................... 66
3.8 Interaction of bending and shear
under constant precompression................ 68
4.1 Photoelastic model configurations
chosen by Schneider.......................... 71
4.2 Finite element idealization for a shear wall
with openings.................................. 73
List of Figures (Continued)
FIGURE
Page
4.3 Finite element idealization for a
multiple pier shear wall.....................
4.4 Finite element idealization for a
pier with openings and walls on either side..
4.5 Finite element idealization for the test
specimen adopted by Schneider.................
4.6 Isoshear lines for the pier shaded as shown
above ........................................
4.7 Isoshear lines for the pier shaded as shown
above ........................................
4.8 Isoshear lines for the pier shaded as shown
above ........................................
4.9 Isoshear lines for the pier shaded as shown
above ........................................
4.10 Isoshear lines for the pier shaded as shown
above ........................................
4.11 Isoshear lines for the pier shaded as shown
above.........................................
4.12 Schematic test setup for finding the
shearing strength of a pier..................
4.13 Details of pier model..........................
4.14 Model test on pier .............................
4.15 Failure pattern of PR 4 strong mortar,
weak grout ...................................
4.16 Failure pattern of PR 3 strong mortar,
medium grout .................................
4.17 Failure pattern of PR 5 strong mortar,
strong grout..................................
4.18 Failure pattern of PR 9 weak mortar,
weak grout....................................
4.19 Failure pattern of PR 10 weak mortar,
medium grout..................................
List of Figures (Continued)
FIGURE
xii
Page
4.20 Failure pattern of PR 7 weak mortar,
strong grout.................................
4.21 Typical loaddeflection curves for
grouted piers ............................ ....
4.22 Failure pattern of PR 13 weak mortar,
precompression 50 psi........................
4.23 Failure pattern of PR 23 weak mortar,
precompression 125 psi........................
4.24 Failure pattern of PR 17 weak mortar,
precompression 200 psi.......................
4.25 Failure pattern of PR 19 strong mortar,
precompression 50 psi........................
4.26 Failure pattern of PR 21 strong mortar,
precompression 125 psi.......................
4.27 Failure pattern of PR 20 strong mortar,
precompression 200 psi.......................
4.28 Failure pattern of hollow pier PR 1
(strong mortar) ........................... ..
4.29 Failure pattern of hollow pier PR 6
(weak mortar).............................. ...
5.1 Relation between average shear stress and
square root of prism strength for grouted
piers.........................................
5.2 Comparison of results of grouted piers
with corresponding prism strengths............
5.3 Area used to compute shear stress for
hollow piers .............................. ...
5.4 Effect of precompression on shearing strength
of nongrouted piers..........................
5.5 Idealization for a pier loaded in
diagonal compression..........................
5.6 Test results of nongrouted pier specimens......
5.7 Failure pattern of hollow square panel
subject to diagonal compression..............
94
95
96
96
97
97
98
98
99
100
104
106
107
110
112
113
118
List of Figures (Continued)
FIGURE
5.8 Assumed state of stress at the
center of pier................................
6.1 Effect of nonlinear material properties........
6.2 Iterative solution techniques for
nonlinear analysis............................
6.3 Material idealization and selected results
of analysis of RC panels by
Cervenka and Gerstle.........................
6.4 Failure envelope adopted by Franklin............
6.5 Schematic diagram to illustrate crack
propagation (initial stress method using
variable stiffness within an increment)......
6.6 Schematic diagram to illustrate crack
propagation (initial stress method using
constant stiffness within an increment)......
7.1 Solution of a cantilever beam by elements
with varying degrees of freedom..............
7.2 Quadratic rectangular element..................
7.3 Uniaxial stressstrain curves ..................
7.4 Components of a reinforced grouted element.....
7.5 Rotation of coordinates.......................
7.6 Liu's failure envelope for concrete
under biaxial compression....................
7.7 Assumed failure envelope for block,
mortar, and grout............................
7.8 Cracking at an integration point................
7.9 Bond strength criterion.........................
7.10 Normal stresses acting on interface
of inclined mortar joints....................
8.1 Schematic diagram illustrating the
nonlinear analysis adopted...................
xiii
Page
119
128
128
133
135
137
137
141
141
148
150
150
154
154
157
157
162
166
List of Figures (Continued)
FIGURE
xiv
8.2 General flow chart of the program................
8.3 Flow diagram for the failure criteria............
8.4 Crack pattern of square concrete panel
at 195,000 lbs ................................
8.5 Crack pattern of square concrete panel
at 196,000 lbs ................................
8.6 Crack pattern of square concrete panel
at 197,000 lbs ................................
8.7 Crack pattern of square concrete panel
at 198,000 lbs ................................
8.8 Crack pattern of square concrete panel
at 199,000 lbs ................................
8.9 Experimentally observed failure modes
in hollow concrete masonry panels..............
8.10 Predicted failure pattern for panel SM...........
8.11 Predicted failure pattern for panel MS...........
8.12 Predicted failure pattern for panel MW...........
8.13 Finite element idealization for pier PR 3.......
8.14 Predicted crack pattern for PR 3................
8.15 Analytical and experimental loaddeflection
curves for grouted piers......................
8.16 Predicted failure pattern for PR 7...............
8.17 Predicted failure pattern for PR 9..............
8.18 Predicted failure pattern for PR 6..............
8.19 Predicted failure pattern for PR 19.............
B.1 Finite element idealization for panel SM.........
Page
173
174
176
178
179
180
181
183
184
186
187
189
192
193
196
199
200
201
215
KEY TO SYMBOLS
A sectional area of split in the indirect tension
test on concrete block; area of crosssection
of pier.
A crosssectional area of block.
Sarea of crosssection of go.out.
area of crosssection of steel reinforceIment
a distance from the point of inflection to tht
spandrel restraint; length of a grouted f nit :
element.
a location of integration point j' in the Gci::
quadrature formula.
iBn matrix relating element strains to nolal
displacements.
{R1) matrix of stiffness coefficients which relates the
unknown displacements in (,ol(nun I with those of
column 2.
C initial bond strength between brick and mortar.
{CL, matrix of stiffness coefficients which relates the
the unknown displacements in column 1 with those
of column 3.
c .'hesion between mortar and block.
lI diameter of specimen; overall pier depth.
il ] square matrix of stiffness coefficients whicl reelates
the unknown displacements of column 1 among
themselves.
I' global constitutive matt.ix al thi pu.iit or
occurrence of compressionshear debonding.
[D local constitutive matrix at the point of
occurrence of compressionshear debonding.
xv
Key to Symbols (Continued)
[D cr] rigidity matrix for cracked point in the global
frame of reference.
[D cro material stiffness matrix for cracked ccr:.ie
in the local principal coordinate system.
[) i] lastoplastic matrix.
LDtb] global constitutive matrix at the point of
occurrence of sheartension debonding.
d width of specimen.
E Young's modulus of steel reinforcement.
EB initial tangent modulus of elasticity of block.
EG initial tangent modulus of elasticity of grout.
ES Young's modulus of steel reinforcement.
E equivalent modulus of elasticity of a composite
e element.
F applied load; plasticity factor.
{F} element nodal forces.
{F,} RHS vectors for unknowns in column 1.
f material stresses; function of stress and strain.
f external precompression on mortar joints, psi.
a
fb bending stress on a mortar joint in a state of
combined compression, bending, and shear, psi.
fbo modulus of rupture of mortar joint, psi.
f ultimate uniaxial compressive strength of concrete.
c
fdt diagonal tensile strength of masonry.
fm' prism strength.
f maximum principal stress.
ma x
f normal stress on a crosssection.
n
xvi
Key to Symbols (Continued)
f external precompressive stress on a pier.
S average shear stress on a crosssection.
s
f apparent shear strength of mortar joint under
combined compression and shear, psi.
ft tensile strength of a material.
f
y
fyl precompression applied to brickwork.
fy2
II horizontal component of the ultimate load on pier.
H. weighting coefficients adopted in the Gauss
quadrature formula.
h height of a specimen.
[J] Jacobian matrix used for obtaining strain
transformation matrix for an isoparametric element.
KI,K2 structure stiffnesses.
[K] global stiffness matrix.
[k] element stiffness matrix.
1 length of a specimen.
M spandrel moment.
{N) interpolation functions.
n number of integration points used in the Gauss
quadrature formula.
P applied load on a specimen.
P ultimate load on a specimen.
u
{p} matrix of body forces in an element.
(Q} matrix of equivalent nodal forces corresponding
to "initial stresses".
xvii
Key to Symbols (Continued)
{R} external nodal point forces.
Ri total applied load during 'i'th load increment.
S elastic section modulus.
T applied horizontal load in racking test.
{T } strain transformation matrix.
{T } stress transformation matrix.
t thickness of a specimen; net thickness of a wall.
U. component of nodal force in the direction of
S 'u' displacement.
{u} matrix of displacements in the xdirection.
V base shear; vertical component of applied load.
Vi component of nodal force in the direction of
'v' displacement.
VpI load shared by pipe columns.
vm' shear strength of masonry.
v ultimate shear strength.
w unit weight of concrete, pcf.
X component of body force in an element in the
xdirection.
X1 horizontal distance from center of pier to point
of application of load.
{XI} number of unknowns in column 1.
X xcoordinate of node 'n' of an element.
n
x xccordinate of any point in an element.
Y component of body force in an element in the
ydirection.
y vertical distance of a crosssection of pier from
the point of application of load; ycoordinate of
any point in an element.
xviii
Key to Symbols (Continued)
a ratio of principal stress in orthogonal direction
to principal stress in direction considered;
direction of maximum principal stress at an
integration point; inclination of mortar joints to
global frame of reference.
0 shear retention factor.
y shear strain.
{AR} unbalanced nodal forces
{Ao.} incremental nodal displacements at node 'i'.
{AE'} incremental strains.
{A(} elastic incremental strains in the "initial stress"
method.
{Ac'} incremental stresses; true increment of stress
possible for the given strain in the "initial
stress" method.
{Ao} elastic incremental stresses in the "initial
stress" method.
{An"} initial stresses to be supported by equivalent
nodal forces
{6} nodal displacements.
c uniaxial strain.
{c( vector of strains at a point.
e ultimate uniaxial compressive strain of a material.
cu
{e } vector of initial strains.
ni local ycoordinate of node 'i'.
11 coefficient of friction between brick (block) and
mortar.
v Poisson's ratio of a material.
i. local xcoordinate of node 'i'.
a uniaxial stress at a point.
xix
Key to Symbols (Continued)
} vector of stresses at a point.
0,o uniaxial yield stress.
G normal stress at interface between block and
mortar.
o 0 ultimate strength of concrete plate in uniaxial
compression, psi.
{o } vector of residual stresses.
0 peak stress in biaxial compression, psi.
at tensile strength of a material.
E shear stress; shear stress at the interface between
block and mortar.
lim limiting bond shear strength of mortar.
11m
AbsLiact of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
AN INVESTIGATION OF THE STRENGTH
OF CONCRETE MASONRY SHEAR WALL STRUCTURES
By
Krishnaiyer Balachandran
August, 1974
Chairman: Dr. Morris W. Self
Major Department: Civil Engineering
The main objective of this investigation is to obtain
empirical equations to predict the shear capacity of nonre
inforced concrete masonry elements. An analytical investi
gation using a nonlinear finite element analysis and an ex
perimental investigation were carried out for this purpose.
First, an experimental program was initiated to obtain
equations for predicting the strength of mortar joints under
combined compression, shear, and bending. The test speci
mens were standard threeblock prisms with threeeighthsinch
mortar joints. Precompression up to 300 psi was applied.
Based on test results, a circular interaction curve is pro
posed for predicting the strength of mortar joints under
combined stresses.
xxi
In the second phase of the experimental program, the
shear strength of concrete masonry piers made with one
fourthscale model blocks was investigated. The main vari
ables were the strengths of grout and mortar and the magni
tude of external precompression. A relationship between
the shearing strength of a grouted pier and the correspond
ing prism strength was established. Equations are proposed
for predicting the shearing strength of a nongrouted
concrete masonry pier.
A nonlinear finite element analysis, using the
isoparametric approach and higher order rectangular elements,
was developed to predict the behavior and collapse of con
crete masonry elements. An incremental loading procedure
was adopted and failure was investigated at integration
points due to yielding, cracking, or crushing of the masonry
component. Also, criteria were developed to predict the
debonding of the mortar joints. The "initial stress"
approach was adopted to redistribute the released stresses,
due to cracking, to the surrounding elements. The initial
stiffness was used throughout each iterative cycle as well
as through all the load increments. Predictions of failure
patterns, collapse load, and deformations are compared to
experimental results.
xxii
CHAPTER 1
INTRODUCTION
1.1 History: Masonry construction is perhaps the oldest
building system employed by man as evidenced by the historic
remains of ancient temples in India and Egypt. These early
works evolved more from art than science and are character
ized by their massiveness and quality craftsmanship. This
traditional masonry construction prevailed throughout the
United States in the nineteenth century and was culminated
by the construction of the Monadnock Building in Chicago,
Illinois, completed in 1891. This 16story skyscraper has
exterior bearing walls varying in thickness from 12 inches
at the top story to 6 feet at the base.
Late in the nineteenth century, the concept of the
structural frame in structural steel or reinforced concrete
replaced masonry bearing wall construction. Masonry became
primarily an architectural product used in nonbearing parti
tions and as a facing.
Expanded research in building methods and materials
early in the twentieth century, particularly with respect to
structural concrete, has resulted in renewed interest in
loadbearing masonry. Although a considerable amount of
masonry research has occurred since 1932 (43), there
exists little correlation among the various studies conducted
by governmental, promotional, and university research
agencies. Each study has of economic necessity been con
strained within narrow bounds placed on the variables. For
this reason, recommendations based upon this research have
been purposely conservative. Much reliance has been placed
upon the results of the voluminous research and experience
with concrete and reinforced concrete; and research, design,
and construction procedures for reinforced masonry have ad
vantageously followed those developed for reinforced concrete.
However, there are important differences in the behavior of
masonry and concrete that must be taken into consideration.
1.2 General Remarks: Concrete masonry walls are broadly
classified as either loadbearing or nonloadbearing and
further described in various ways such as either nonreinforced,
solid unit, or hollow unit.
The general behavior of highrise,loadbearing structures
under gravity and lateral loads is the combined action of
floors, bearing walls, and shear walls. Floors transmit hori
zontal forces by diaphragm action from the exterior walls to
the shear walls, which in most cases are also the bearing
walls. The floor system must be sufficiently rigid to serve
as a diaphragm, and connections must be adequate to transfer
these forces to the shear walls which carry them to the
foundation. The height to which the buildings can be
constructed depends upon the strength of the masonry
materials, the spacing of intersecting walls and floors, their
connection to each other,and the shape of the structure.
The design procedure includes an investigation of the
following (41)(20).
1) Bearing capacity: bearing stresses will generally
govern required block strength and wall thicknesses.
2) Stability against overturning: overturning resis
tance to lateral loads depends upon the shape and mass of the
building. Shear walls that are also loadbearing walls are
the most effective structural elements for developing resis
tance to overturning.
3) Shear resistance of walls: lateral load is trans
mitted through the floors to those shear walls parallel to
the assumed direction of the lateral load. The percentage of
total lateral load carried by a shear wall is proportional to
this "relative rigidity" with respect to other participating
shear walls.
4) Flexural resistance of walls: lateral bending of
walls can be produced by wind loads on exterior walls, by
eccentricity of loading, and by insufficiently rigid floor
diaphragms and shear walls.
5) Floorwall connections: finally, because the
strength and stability of the highrise building depend upon
the interaction of the connecting floor and wall elements,
connections must be adequate.
As mentioned previously, shear walls are designed to
resist the effects of lateral forces acting on buildings.
The lateral forces are primarily due to wind or earthquake.
The performance requirements for shear walls under wind
loads are different than that for earthquakes (3). Walls
designed for wind forces have to meet both strength and
stiffness requirements. Walls designed for earthquakes must
also satisfy requirements of ductility and energy absorption,
damping characteristics and damage control, during several
cycles of inelastic deformation (1).
The behavior of shear walls is complicated by the
influence of boundary elements and multiple openings (14)(36).
Figures 1.1 and 1.2 [taken from reference (3)] present some
typical examples. Lateral loads are usually introduced into
shear walls through floor slabs framing into either one side
or both sides of the walls. As a result, the lateral loads
tend to be distributed across the width of the wall. Trans
verse walls or columns are often located at the extreme
edges of the walls. They act with the wall, and usually
contain most of the flexural reinforcement resisting the
moment due to the lateral forces.
When a wall contains large openings, it can be
considered to be made up of a system of piers and spandrels.
Each individual pier or spandrel is, in effect, a shear wall
element, with a shear span approximately equal to onehalf
of its height or length, respectively. In addition to shear,
5
FLOOR BEAMS .
OB SLABS 58>
SHEAS 'AAL'
WALL OR COLUMN 2s
Fig. 1.1. Shear wall with boundary
elements.
SPANDRELS '
PIERS
Fig. 1.2. Elements of shear wall
with openings.
piers will also generally have tension or compression caused
by gravity and overturning forces as well as shrinkage,
creep, and differential settlement.
It is noted by the Joint ASCEACI Task Committee 426
on Shear and Diagonal Tension that the shear strength of a
wall is of interest only for shear span to depth ratios less
than 2, or for walls with a flanged crosssection (3).
1.3 Previous Investigations:
1.3.1 Strength of Mortar Joints: compared with the vast
number of tests reported on concentrically loaded walls with
the load applied vertically, little is known about the
strength of masonry walls with the load applied at different
inclinations to the horizontal joints. However, some test
results are reported. Benjamin and Williams (5) carried out
tests on shear couplets of two bricks bound together with a
mortar joint. Three different mortar types were tested with
watered, stiff mud, sidecut, vacuumtreated clay bricks.
The test results showed little or no influence of brick and
mortar compressive strengths on the couplet bond strengths
in tension and shear. The test results showed that the
relationship between the shear stress, fs (shear force
divided by wall area), and the normal stress, fn' could be
expressed in the form:
(1.1)
f = C + 1 f
s n
where p is the coefficient of friction between mortar and
brick and C is the initial bond strength, a constant.
Benjamin and Williams obtained a value of C = 150 psi and
p= 0.73. They also concluded that, up to a compressive
stress of approximately 650 psi, the shear strength
increases with the compressive stress. For higher compres
sive stresses, the apparent shear stress still increases,
although the joint has already failed in shear. The addi
tional strength is claimed to be due to friction.
Zelger (44) has reported tests on masonry specimens of
the type shown in Figure 1.3. Zelger obtained C = 2 kg/sq cm
and p = 0.5 in his tests. Yorulmaz and Sozen (44) tested
masonry specimens of model bricks 0.53" x 0.86" x 1.87" in
size. The results obtained from test specimens of the type
in Figure 1.3 gave C = 150 psi and p = 0.46.
Haller (22) adopting the test setup shown in Figure 1.4,
arrived at the following empirical relationships:
f = 35/f + 280 540 psi (1.2)
s n
fn < 200 psi
for normal quality masonry consisting of cored bricks (3300
psi to 6500 psi) and cementlimesand mortar (1225 psi).
If the Haller formula is approximated to linear
relationship, the following equation is obtained:
8
Fig. 1.3. Type of test specimens used by
Zelger.
Averoge J
thickness
ot bd .
joints: 0.47nch
Wh.ernorc 1
gouges o
gougonh I  I
gauges length :
20 inch
6J 4 rt,
Fig. 1.4. Test specimen adopted by Haller.
f = 50 + 0.88 f (1.3)
s n
f < 200 psi
n 
The tests of the type shown in Figure 1.3 give the
most representative values for shear strengths of the mortar
joints in masonry, since disturbances caused by the testing
machine platens, etc., are much less likely to occur in
this type of test compared with the couplet type tests.
From the limited number of tests mentioned, it seems
reasonable to assume that the bond or shear failure of a
mortar joint in brick masonry follows Equation (1.1) in a
range of approximately 2% to 15% of the compressive strength
of the masonry. C is of the order of 2% to 3% of the com
pressive strength of masonry. However, since the couplet
tests indicate that the compressive strength of the mortar
has no influence on the bond strength, the shear strength
should be tested when high stresses are employed.
For compressive stresses lower than approximately 2%
of the compressive strength of the masonry, and for pure
tensile stresses, the shear strength falls below that calcu
lated from Equation (1.1), as revealed by couplet tests and
model masonry tests. The pure tensile bond strength is
greatly influenced by workmanship and wetness of the bricks.
A suction rate of 20 g/min or less seems to give maximum
bond, although saturated bricks produce close to maximum bond.
For high compressive stresses, the apparent shear strength
again is lower than calculated from Equation (1.1).
Hedstrom (24) reports load tests of concrete masonry
walls with constant wall dimensions but with mortar bed
joints in 90, 45, and 0 inclination to the axial load,
which was applied parallel to the longer side of the walls.
The tensile bond strength obtained with the two types of
mortar was tested on masonry prisms of two blocks in
bending. A plot of bond shear strength vs. compressive
strength yielded C = 48.5 psi and p = 0.84 for Mtype
mortar and C = 24 psi and p = 0.92 for Stype mortar. The
figures are supported by too few tests to be conclusive.
1.3.2 Racking Tests: the present standard racking test
described in ASTM E 7268, Method of Conducting Strength
Tests of Panels for Building Construction, provides only a
relative measure of the shearing or diagonal tensile
resistance of a wall. Results of this test are consequently
valid only for comparison purposes and are not suggested for
determination of design values.
In this method of test (Figure 1.5), horizontal
movement of the wall specimen (8' x 8'),due to the horizon
tal racking load at the top of one end, is prevented by a
stop block at the bottom of the other end. To counteract
rotation of the specimen due to this overturning couple,
tie rods are used near the loaded edge of the wall specimen.
Under racking load these rods superimpose an indeterminate
h
3 F4 IF  L = h = 8fl
3 FIF Floor or
foundation
Fig. 1.5. Arrangement of racking test and the force
distribution on the specimen.
Jul
//<\
TE SION COMPRESSION
Fig. 1.6. Test for diagonal tensile strength of
brickwork and stress distribution.
brickwork and stress tlistrihut ion.
compressive force which suppresses the critical diagonal
tensile stresses and increases the load required to rack
the specimen. A typical mode of failure is indicated.
The obtained apparent shear strength as calculated from
f = T/ld is usually of the order of 25 psi to 300 psi
s
under laboratory conditions.
For concrete masonry walls, the racking strength was
reported by Fishburn (18) to be 25 psi to 50 psi for
masonry walls having a compressive strength of 390 psi to
470 psi giving a racking strength of about 7% to 10% of
compressive strength.
1.3.3 Circular Shear Specimens (28): in these tests
(Figure 1.6), a 15" diameter specimen is tested in compres
sion with the line of load at 450 to the bed joints. As
shown in Figure 1.6, the diametrical stresses are largely
tensile over the central 80% of the specimen. The tensile
stress is approximately constant for about 60% of the dia
meter and may be calculated by the following equation:
S 2P (1.4)
t = Dt
where P equals load at rupture, in pounds, D equals the
diameter of the specimen, in inches, and t equals the thick
ness of the specimen, in inches.
1.3.4 Square Shear Specimens (6)(16): in examining the
damage done during earthquakes, it was noted that cracks in
shear walls were frequently of a diagonal nature, so fre
quently that they were called typical "X cracks" (Figure 1.7).
With this as a starting point, the theory was early recog
nized that the force of quake working against the static
resistance of a building would produce a racking effect;
this in turn would be resisted by the diagonal strength of
the wall member. It was found that the "X" cracking devel
oped in a diagonal tension test.
Photoelastic analysis through the use of polarized
stress panels was used to demonstrate the validity of this
theory (Figure 1.8). The stress distribution in the wall
panel was shown to be the same as in the diagonal test
panel. It was then decided that the proper test would
consist of breaking, by diagonal loading, 4' x 4' panels
incorporating desired variables (Figure 1.9). In this
method, the test results are susceptible to stress analysis.
In addition, they are more reproducible and thus more
reliable for comparison and design data purposes.
The square specimen is placed in the testing frame so
as to be loaded in compression along a diagonal, thus pro
ducing a diagonal tension failure with the specimen split
ting apart along the loaded diagonal. The shear strength,
Fig. 1.7. Typical Xcracks in a wall damaged
by an earthquake.
Fig. 1.8. Fringe patterns obtained in a photoelastic
analysis of a model of a wall with an
opening and a square panel under diagonal
compression.
Fig. 1.9. Diagonal tension test on a
square panel.
Loading Jacks
Loading Frame
Bearing Plates
Gap
Fig. 1.10. Test setup (schematic) adopted
by Meli and Reyes for testing
mortar joints under
compression and shear.
v ', is determined from the equation (6)(27):
0.707 F (1.5)
m tl
where F equals the diagonal compressive force or load, in
pounds, t equals the thickness of wall specimen, in inches,
and 1 equals the length of a side of a square specimen, in
inches.
1.3.5 Horizontally and Vertically Loaded Wall Without Frame:
the load carrying capacity of a wall subjected to a horizon
tal load at one of the upper corners is governed mainly by
the shear and tensile strength of the bedjoints at the
foundation of the wall (44). By precompression, for example,
by dead load from slabs and walls above, the strength is in
creased in a manner similar to that described for masonry
specimens loaded with an inclined load.
Murthy and Hendry (44) report "1/6modal" tests on
three bay, onestory, shear walls, 0.669" thick, about 16"
in height and length. The bricks had an average strength
of 4421 psi and the cementlimesand mortar about 1200 psi.
The horizontal shear strength was tested for various addi
tional loads up to 180 psi, and the following relationship
was established:
f = 30 + 0.5 f (1.6)
s n
f < 180 psi
n 
Benjamin and Williams (5) tested model walls, without
frames and without vertical loads, and found apparent shear
strengths of 15 psi to 30 psi.
1.3.6 Test on Small Masonry Assemblages: at the University
of Mexico, Meli and Reyes (39) conducted tests on small
assemblages for investigating the mechanical properties of
masonry. Three tests were found to be the most useful: a
small prism subjected to axial compression, a wallette under
diagonal compression, and a three unit assemblage subjected
to shearing of the joints. Results of the prism test were
related with the behavior of masonry walls under vertical
loads. The remaining two tests were related with the
behavior of walls under lateral loads. Tests were performed
on a large number of specimens built with commonly used
types of masonry units and mortars.
Based on test results, it was found that the prism with
height/thickness ratio of 4.0 gave satisfactory and uniform
index to the resistance to axial load of masonry.
Figure 1.10 shows the schematic test setup adopted for
the shearing tests on joints with precompression. The
results were expressed in the form of Equation (1.1) with
C = 1.8 kg/sq cm and p = 0.8 for concrete blocks with dif
ferent types of mortar whose strengths varied from 151 kg/
sq cm to 43 kg/sq cm. Coefficient of friction was found to
be a very uniform property for the different types of bricks
and concrete blocks adopted. The values were approximately
0.7 in all the cases. However, the value of adhesion varied
depending on the type of brick and mortar. At low levels of
confinement, the results varied; however, uniformity in re
sults was obtained with high level of precompression.
Figure 1.11 shows the different types of specimens
adopted for the diagonal compression tests. For each series
of specimens shown in Figure 1.11, four different types of
mortars and seven types of masonry units were used. For
each combination of materials, there were three specimens
of each type. The object of the series of the tests was to
study the effect of the variation of the height/width ratio
(h/l) of the panel and number of joints in the specimen on
the resistance of the assemblage. The results showed that
each type of specimen had a definite mode of failure inde
pendent of the type of mortar used. In general, the failure
occurred by shearing along the joints for long specimens and
by diagonal tension for specimens with high h/l ratio. The
type of failure was not always perfectly defined. In many
cases, the crack crossed the joints and the blocks partially.
Qualitatively, it could be said that when the failure was by
diagonal tension, the resistance was relatively uniform for
similar specimens and did not depend much on the type of
mortar used. On the contrary, when the failure was by shear,
the dispersion of results was very high. It was found that
the resistance increased with increase in h/l ratio.
N C j~!
I :, 1
:, 4j
__ ___r
r L
o ' ]
L" ___ ,  f
IHHI E LIh
LIEc
E IL P
~ 11
\ ,, ,,
07"
OK
d e
50'L
00
S
z o~ 
I I
c
z
C
C.
C:
7,J
ED'
D
i '
cJ
m
En
LL HLI. 7
.0
4.1
0
0
o
ln
4
41
a) 0
(U. 0
C4
a o
4
aJm
UC
M
6 co
m 0 0
r l
ml
il
S w
o
O '
1^
However, the effect of this increment was of very little
influence when the failure was by diagonal tension and
very much noticeable when the failure was by shearing along
the joints. It might be due to the fact that the h/l ratio
controls the value of compression normal to the joints that
causes the effect of friction to be developed.
All the specimens considered in this investigation
were nongrouted. It was found that the strength in diagonal
tension was equal to the square root of the compressive
strength of the prism when the stresses were expressed in
kg/sq cm.
For the shear failure along the joints, a relation
similar to that of Polyakov (42) was proposed:
f = 0.8/(1 0.9 p h/1) (1.7)
1.3.7 Reinforced Concrete Masonry Walls in Shear: Figure
1.12 shows the steel arrangement of reinforced concrete
masonry walls tested by Converse (12). The basic mode of
failure was one of diagonal tension. Walls under group 'B'
showed an increase in strength of 38% over group 'A'. It
suggested that the increase in strength was nearly propor
tional to the areas of additional steel, irrespective of
position. Due to the difference in number of bars, no
direct comparison could be made of the relative effect of
vertical and horizontal steel, but indications were that
they were equally effective.
Scrivener (48) confirmed the previous findings in his
tests. The objectives of his tests were to determine:
1) the pattern of behavior as the percentage of reinforcing
was increased, 2) the relative effectiveness of vertical
and horizontal reinforcing, and 3) the difference between
the behavior of walls where the vertical steel was periph
eral and where the steel was distributed over the length of
the wall. The following conclusions were drawn from these
series of tests:
1) Vertical and horizontal reinforcing are equally
effective in producing satisfactory crack behavior and
failure loads.
2) Walls with evenly distributed reinforcing have a
later onset of severe cracking than walls where the rein
forcement is concentrated in the wall periphery.
3) With a low percentage of reinforcing, failure
occurs soon after the onset of severe cracking. With higher
percentages of reinforcing, the failure load is much greater
than the load causing severe cracking.
4) Higher failure loads were obtained with walls with
higher percentages of reinforcing up to 0.3% of the gross
crosssectional area of the wall. Above this percentage,
additional reinforcing had little effect on the failure
load. From the walls with the optimum (0.3%) or higher per
centage of reinforcing, the ultimate horizontal shear stress
(ultimate load divided by the gross crosssectional area
of the wall) was found to be 170 psi.
Confirmation of the last conclusion can be had from
the test results of Schneider (45), who found a maximum
effective quantity of reinforcement of 0.2%. In his tests,
a racking load only was applied, but sufficient peripheral
vertical reinforcement was placed in the walls to prevent
this steel being stressed beyond its yield point when sub
jected to the tensile forces induced by the maximum over
turning moment. Schneider's walls failed in shear with
the typical diagonal cracking. The difference between
Schneider's and Scrivener's test walls lies in the boundary
conditions on the vertical sides. Schneider also found
that, workmanship and reinforcement remaining the same, the
shear resistance of stack and running bond and stack bond
masonry block walls was about the same.
1.3.8 Effect of Wall Openings: openings in shear walls
are mainly due to doors, corridors and mechanical duct
space. When the opening is relatively small and spaced, at
least a distance equal to the size of the opening in each
direction, its influence on the behavior of the structure
is negligible (29). Figure 1.13 shows an elevation of a
typical shear wall in an apartment building using an 8"
concrete, flat plate slab construction. The opening shown
at the center indicates the corridor at each floor. In
Fig. 1.13, Continuous opening in a
shear wall.
Fig. 1.14. Staggered opening in a
shear wall.
apartment buildings, the opening would normally be from
top of the floor to bottom of the floor above. In apart
ment buildings where the architectural planning frequently
permits the shear wall to extend from one face of the
building to the other, openings such as shown in Figure
1.13 limit the full utilization of the entire shear wall as
a unit. The connecting slab at each opening is relatively
very flexible. As a result, the shear wall acts as two
individual shear walls on either side of the corridor
opening. Although for medium height buildings, this inef
ficiency does not seriously affect the economy of the
entire structure, for heights above 40 stories, its effect
on overall economy becomes significant. As a solution to
this problem, Khan (29) proposes staggering of such open
ings at alternate floors in order to maintain the struc
tural continuity of the entire shear wall. Figure 1.14
illustrates the proposed arrangement.
In office buildings the requirement for mechanical
duct space under the floor slab makes the problem of open
ings different from that in the apartment buildings. A
hung ceiling is almost always necessary. The door opening
size generally allows a 2 ft to 5 ft connecting beam over
each opening. The proper analysis and design of the con
necting beam is important because the beam not only con
nects the adjacent parts of a shear wall for monolithic
action, but also redistributes loads in different parts of
the shear wall. Girijavallabhan (21), on the basis of an
analysis using the Finite Element Method, found that one
of the most influencing factors on the distribution of
stresses and deformations in the shear wall was the stiff
ness of the lintel beam. He varied the depth of the lin
tel beam and studied the influence of the variation on the
overall behavior of the shear wall.
Kokinopoulos (30) conducted a photoelastic analysis on
models of single story walls with openings to study the
effect of size of opening on the stress distribution in
walls. Schneider (46) conducted full scale tests on piers
in a shear wall with openings. This is the only experi
mental investigation on this problem which utilized full
scale tests. This investigation is described in the next
subsection.
1.3.9 Shear in Concrete Masonry Piers: this investigation
was carried out to estimate the capacity of concrete masonry
piers, functioning within the confines of a shear wall in a
building, to resist lateral load effects. To simulate as
nearly as possible conditions that occur in an actual wall,
such as degree of restraint, amount of reinforcing, manner
of vertical load imposition, and magnitude of secondary
stresses, the pier was considered along with the wall around
it (Figure 1.15)'. The fully restrained configuration was
either 10' 8" or 11' 4" high. The cantilever pier was either
I ti
I,
PANEL 'FREEBODY"
SHEAR TLS!
Fig. 1.15. Forces acting on a pier
element in a wall with
opening.
DIACOIGAt LOAD FRAME
(PIER DITAILS VARY)
Fig. 1.16. Test setup adopted by
Schneider for full scale
tests on piers.
LJL
6

7' 4" high and 8' 0" wide or 10' 0" high and 10' 8" wide.
Also tested was a set of 48" square concrete masonry assem
blies. A diagonal loading frame was used to apply the
loading (Figure 1.16). Pipe columns were used to maintain
the geometry of the openings.
The important variables considered were:
1) a/D ratio, where a is the distance from the point
of inflection to the spandrel restraint, and D, the overall
pier depth.
2) Amount of web reinforcement (both horizontal and
vertical).
3) Amount of jamb reinforcement.
4) External axial compressive stress.
5) Nongrouted panel behavior.
The average strength of blocks used varied from 1338
psi to 2962 psi. The 28day mortar strength varied from
2487 psi to 5116 psi. The strength of grout prisms varied
from 1789 psi to 3414 psi. Reinforcing steel conforming
to ASTM A 15, had a yield strength of 55,000 psi and ulti
mate tensile strength of 80,000 psi.
The following are the main findings of this investigation:
1) The shear strength increased with a decrease in the
a/D ratio, and this rate of increase jumped sharply below an
a/D ratio of 0.5:1.
The very consistency of the test results throughout the
range of a/D ratios selected for analysis suggested the
following relationships for average ultimate shear stress
of a pier contained within a shear wall, where web rein
forcement is not provided:
M/VD (a/D)
Fixed Pier Elements:
0.10:1 < M/VD < 0.50:1
0.50:1 < M/VD < 1.50:1
1.50:1 < M/VD
Cantilever Pier Elements:
1.0:1 < M/VD < 3:1
3.0:1 < M/VD
ULTIMATE MASONRY SHEAR STRESS,
Vu, psi
V/tD = 310 350 M/VD
V/tD = 152.5 35 M/VD
V/tD = 100 psi
V/tD = 95 15 M/VD
V/tD = 50 psi
where M equals spandrel moment, V equals base shear, D
equals overall pier depth, a equals distance from the point
of inflection in the span of the pier to the fixed end, and
t equals net thickness of wall.
2) The presence of adequate horizontal web
reinforcement materially increased the shear resistance of
the pier.
The following relationships between the M/VD ratio and
ultimate shear stress were proposed for piers with horizontal
web reinforcement.
ULTIMATE MASONRY SHEAR STRESS
WITH ADEQUATE WEB REINFORCEMENT,
M/VD (a/D) vu, psi
Fixed Pier Elements:
0.10:1 < M/VD < 0.50:1 V/tD = 347.5 225 M/VD
0.50:1 < M/VD < 1.50:1 V/tD = 290 110 M/VD
1.50:1 < M/VD < 2.00:1 V/tD = 200 50 M/VD
2.00:1 < M/VD V/tD = 100 psi
3) Vertical steel did not seem to function effectively
as web reinforcement.
4) Assuming that enough jamb steel was present to
resist the end moments, any further increase did not alter
the pier resistance appreciably.
5) The existence of a bedjoint fracture at a foundation
did not seem to impair the ability of the panel to resist
lateral loads. However, if a bedjoint crack occurred at the
center of a square panel, where tensile stresses are maximum,
its shear resistance was drastically reduced.
6) The energy absorbing ability of an adequately rein
forced masonry pier was well demonstrated. As the shape of
the load deflection curves indicated, these piers were able
to absorb a great deal of inelastic strain energy without
collapsing or even spelling seriously.
7) Concrete masonry, if properly reinforced, exhibits
a tendency toward a ductile behavior throughout the loading
sequence. It can sustain significant proportions of the
ultimate load well into the inelastic regions (beyond the
first significant crack) while undergoing rather large
lateral deflections. It also exhibits effective dampening
characteristics, especially after cracking.
8) On the basis of defining ductility as the ratio
of the total deflection experienced to the deflection at
the first shear crack, which was assumed to be the incep
tion of inelastic deformation, the ductility factor
exceeded two, which is considered a desirable level.
1.3.10 Strength of Masonry under Combined Compression and
Shear: Sinha and Hendry (50) propose that brickwork sub
jected to combined compression and shear exhibits two dis
tinct types of failure:
1) Shear failure at the brick/mortar interface. The
shear strength consists of initial bond shear and the resis
tance, proportional to the normal stress, due to friction
between brick and mortar.
2) Diagonal tensile cracking through bricks and mortar
governed by constant maximum tensile stress or strain.
On the basis of tests on circular shear specimens,
Sinha and Hendry found the diagonal tensile strength of
brickwork to be:
f = 2.0 f
t m
(1.8)
Let f equal precompression applied to brickwork and
fs equal shear stress. If it is assumed that failure is
determined at a certain stage by the criterion of maximum
tensile stress, then:
f
ft = /f 2/4 + f 2 = constant (1.9)
y s
For failure:
f > f
fs y
It is assumed that the above condition will be fulfilled by
two values of f : f y and fy2. Between the precompressive
stresses f y and f 2 failure of the structure will occur by
attaining maximum tensile strength. Below and above this
range, failure will be governed by shear at the brick/mortar
interface. Precompression above f 2 will suppress the
inherent failure due to diagonal tension and modify its
value. At very high precompression values, the failure of
the brickwork will take place in compression.
Since fs = C + P fy, where C is the initial bond shear
strength between brick and mortar,
ft = fy2/4 + (C + 11 fy )2 fy/2 (1.10)
When fs = P fy2,
S= f2/4 + ( f 2)2 f2/2 (1.11)
Knowing ft, C and V, f y and f 2 can be calculated. Thus,
the ultimate shear strength may be calculated from the
following formulae:
f = C + p f (1.12)
for p fy < f 1, and,
ft = f 2/4 + f 2 fy/2 (1.13)
for f f < f 2 and,
f = I f (1.14)
for f 2 < f < compressive strength of brickwork.
However, in a recent study, Smith et al. (51) have
concluded that the diagonal tensile strength of brickwork
is approximately equal to the tensile strength of brickwork
or mortar, whichever is weaker. This conclusion was based
on an analysis of a masonry circular shear specimen using
the Finite Element Method supported by experimental data.
1.4 Objectives and Scope of Present Investigation: A
survey of the available literature revealed a need for more
elaborate research on shear strength of concrete masonry
walls with openings. To meet this objective, an experimen
tal and an analytical investigation is attempted in this
dissertation. In the experimental investigation, it was
decided to adopt the test specimen proposed by Schneider (46).
Thus, the main objective of the experimental investigation
was to obtain empirical equations to predict the shear capa
city of grouted and nongrouted piers without reinforcement.
Since the effect of various types of configurations and
reinforcement had already been established, it was decided
to restrict the investigation to one particular configuration.
The main variables considered for grouted piers were the
grout and mortar strengths; for the nongrouted piers, the
effect of external precompression normal to bedjoints was
treated as the main test parameter for different types of
mortar adopted.
Since the strength of mortar joints is a main factor
determining the behavior of a nongrouted masonry element,
an extensive study was initiated to obtain equations for
predicting the strength of mortar joints under combined
compression, bending and shear. This investigation is
described in Chapter 3.
A fullscale testing of piers was not possible
because of limitations of capacity of testing machines,
space, and cost. The present investigation on piers was
restricted to 1/4size models. Chapters 4 and 5 describe
the model tests on piers.
While investigating a complex phenomenon such as the
behavior of masonry, if a suitable analytical model could
be proposed, it would facilitate understanding the stress
distribution in the structure more thoroughly. Such a
model was attempted using the Finite Element Method. The
model chosen was capable of predicting the different failure
modes associated with masonry and a nonlinear finite element
analysis was adopted accordingly to determine the ultimate
load and failure pattern. The analytical results were com
pared with experimental ones. The analytical investigation
is described in Chapters 6 through 8.
CHAPTER 2
EQUIPMENT, MATERIALS AND TESTING TECHNIQUES
2.1 Testing Machines and Other Equipment: The Civil
Engineering Laboratory is equipped with a hydraulic press
of 300,000 lb capacity and a mechanical press of 160,000
lb capacity. The clearance of these two machines allowed
good observations of all sides of the specimen being
tested. For testing the model reinforcement, the 10,000
lb capacity, Instron Machine, Model TTC, in the department
of Metallurgical Engineering was used. The machine was
provided with suitable gripping devices for clamping small
test specimens and an automatic recorder for plotting the
loadextension curves.
The investigation on the strength of mortar joints
was carried out in the 300,000 lb hydraulic press. The
higher clearance and lower load ranges required for the
model tests determined the use of the 160,000 lb mechanical
press for testing model piers.
Sieves, mechanical shakers, and balances were available
for analysis of sand.
An electric rotary mixer of 5 cu ft capacity was used
in mixing mortars for building 3block prisms used for deter
mining the strength of mortar joints under combined stresses.
The same mixer was also used for mixing cementsand mortar
for making spandrels for piers. A standard flow table,
standard molds for mortar cubes, paper molds for mortar
cylinders, and different size rods were used for mortar and
grout control.
A large moist room was used for storage of mortar
cubes and cylinders, and sufficient storage room was avail
able for the masonry prisms and model specimens.
A 6" diameter brass disc (normally used for capping
concrete cylinders), together with four 1/4" x 1/4" brass
bars, formed a mold for the sulfur caps of the model con
crete blocks and prisms.
Dial gages with a least count of 0.001" were used for
measuring deflection. They were mounted on magnetic stands
for easy removal.
The electrical strain gages used were BLH's SR4 fixed
on the test surface with Duco cement. The strain indicator
was a portable Baldwin Type N. The strain gages were wired
to the indicator through a switch selector.
2.2 Concrete Blocks: The concrete blocks used for the first
investigation had nominal dimensions of 8" x 8" x 16". The
net area of a block based on the average of five specimens
was 61.4 sq in. Selected blocks were capped with sulfur and
tested according to ASTM C90 and C140. The average com
pressive strength based on net area was 6500 psi. The ini
tial rate of absorption (IRA) of the block, according to
ASTM C67, is measured as the amount of water initially
absorbed by a dry unit when it is partially immersed in
water to a depth of 1/8" for a period of one minute. IRA
is measured in grams per minute per 30 square inches. The
test was conducted in the following manner.
Four steel bars, 1/4" x 1/4" in crosssection and 4"
long, were provided with needles 1/8" high. A steel pan,
which area was much larger than the gross area of the con
crete block, was chosen and placed on a level surface. The
steel bars were positioned on the pan in such a manner that
the concrete block could rest on them. Water was allowed
to stand in the pan till the needle points were just
immersed. The previously weighed block was placed in posi
tion over the steel bars, and the water supply was continued
to cope with the absorption of the block. After one minute,
the block was removed, the immersed surface wiped, and the
block reweighed. The initial rate of absorption of the
blocks varied between 12 g to 17 g/min/30 sq in.
An indirect tension test was conducted to find the
tensile strength of the block (49). Two test methods were
devised for splitting hollow concrete block. The first
method, shown in Figures 2.1(a) and 2.1(b), was arranged so
that the block could be split twice. The load was applied
through hexagonal bars with 3/4" flats, first through one
cell and then through the other cell of the block. The
second method, shown in Figure 2.1(c), was arranged to load
asf
both cells simultaneously. Round bars of 13/8" diameter
were used to distribute the load in this test. Usually
only one split occurred as is shown in Figure 2.1(d). The
results of the tests are given in reference (49). The
indirect tensile strength of the block was calculated using
the relation:
2P
f (2.1)
t TA
where P is the splitting load and A the sectional area of
split. In the range of the block strengths tested, it
appears that the split tensile strength is approximately
five times the square root of the compressive strength as
determined by the standard block compression test. For
the blocks used in this investigation, the indirect tensile
strength was found to be 405 psi.
2.3 Mortar: The cements and sand were provided by local
suppliers in Gainesville, Florida. The cements were manu
factured by Florida Portland Cement. Portland Cement Type
I and Masonry Cement were used in the mortar mixes in
accordance with ASTM C27068. The granulometry of the
sand is shown in Figure 2.2. For the first investigation,
two types of mortars were used. The following are their
proportions by volume.
40
100
80
60
\
40
20
16 30 50 60 80 100 140 200
(l.O~n) (0. LTm)
SIEVE No.(OPENING SIZE)
Fig. 2.2. Sieve analysis of sand for masonry mortar.
PC MC Sand
Type I 1 1 4.5
Type II 1 1 6
An initial rate of flow of about 100% was adopted. Two
inch cubes were molded and tested according to ASTM C270.
The average compressive strength of Type I mortar was 1948
psi and that of Type II 917 psi.
2.4 Model Concrete Blocks: The model concrete blocks were
provided by the National Concrete Masonry Association,
Arlington, Virginia. They were modelled to be onefourth
the size of the full block of nominal dimensions 8" x 8"
x 16". Thus, the model block had nominal dimensions of 2"
x 2" x 4". A typical block is shown in Figure 2.3. The
average length of the block was 3.9", width 1.9", and
height 1.85". The net area, based on an average of six
specimens, was 4.16 sq in. The model blocks, capped with
0.15" thick sulfur capping, were tested in axial compression.
The average of thirteen tests yielded a compressive strength
of 2688 psi based on net area. The coefficient of variation
was 20.15%.
The absorption of the model block was 11.98%. It was
difficult to measure the initial rate of absorption for the
model blocks because 1) their rate of absorption was quite
high, and 2) a suitable depth of immersion of surface could
not be defined for models.
1
Fig. 2.3. Model concrete block
Fig. 2.4. Model reinforcement (0.147" dia.).
The tensile strength of the block could not be
determined by an indirect tension test because of the un
certainties involved in choosing the size of splitting
bars for models. Also, a suitable testing machine was not
available. A value equal to five times the square root of
the compressive strength of the block was assumed.
In order to obtain the stressstrain curve in
compression, two SR4 gages were mounted centrally, one on
each longitudinal side. The gage length was 0.2". The
stressstrain curve obtained is shown in Figure 2.5.
2.5 Model Reinforcement: Number 2 bars of 40 ksi grade
steel were used for main reinforcement in spandrel beams of
model piers. For vertical and shear reinforcements, 0.147"
diameter, high strength DuroWall bars were used. A typical
bar is shown in Figure 2.4. The bar had minute depressions
0.3" long and alternate projections 0.1" long. The yield
and ultimate strengths of the bar were, respectively, 68 ksi
and 75 ksi. A typical stressstrain curve is shown in
Figure 2.6.
2.6 Model Mortar: Based on trial mixes, the proper grade
of sand for modelling Type I and Type II mortars was arrived
at. The sand, of gradation shown in Figure 2.2, was sieved
through a set of sieves (nos. 8, 16, 30, 50, 100, and 200,
in that order). Trial mixes were made with the sands re
tained on sieves nos. 50, 100, and 200. It was found
3600.
3000
a2400
z
w
1800
1200
600
0 300 600 900 1200 1500
STRAIN ( x 10"6 IN./IN. )
Fig. 2.5. Stressstrain curve for model concrete block.
fu = 75.78
48.32
Diameter of bar: 0.147"
Gage Length: 3.25"
0.04
0.06
0.08
STRAIN ( IN./IN. )
Fig. 2.6. Stressstrain curve for model reinforcement.
fy = 68.35
0.02
that for the same watercement ratio and proportions of
ingredients, the strengths of mortar obtained, using the
sand retained in no. 100 sieve, compared favorably with
those of Type I or Type II, as the case may be. Hence,
this grade was chosen as the model sand. No attempt was
made to model cements. An initial flow of 120% was adopted.
Compressive strength of the mortar was determined by testing
standard 2" cubes. The tensile strength was obtained by
splitting cylinders 3" in diameter and 6" long. The model
mortar properties are summarized in Table 2.1. Plates,
5.75" x 5.75" x 0.625", made of the different types of
mortar and cured in air, were tested in uniaxial compression.
The plate compression strength was used in the analytical
investigation described in Chapter 8. The stressstrain
curves for the two types of mortars obtained on the basis of
tests on 3" x 6" cylinders are given in Figure 2.7.
2.7 Model Grout Mixes: No gravel could be used in model
grout because of difficulties in obtaining proper compaction
due to the small size of the cells. Hence, the model grout
consisted of only cement and sand. Standard 2" cubes molded
in standard molds and cured in air were used for measuring
the compressive strength of the grout. Due to the uneven
surfaces obtained for cubes molded by using the concrete
blocks as molds, the test results on those cubes were not
satisfactory. Plates, 5.75" x 5.75" x 0.625", were tested
in uniaxial compression. Their compressive strengths were
2800 
MS
2400 
2000
1600
z
MW
LI
S1200
LIn
800 
400
0 800 1600 2400 3200
STRAIN ( x .0 6 IN./IN. )
Fig. 2.7. Stressstrain curve for model mortar.
TABLE 2.1
PROPERTIES OF MODEL MORTAR AND GROUT
Proportions by
Volume
Initial
Rate of
Flow
28day Strength
Cube Split
Plate Comp. Cylr.
Type PC MC Sand % psi psi psi
Mortar: MS 1 1 4.5* 120 656 1695 200
MW 1 1 6 120 485 905 135
Grout: GW 1 5 +450 570 75
GM 1 4 +760 800 205
GS 1 3 ** 1000 1850 322
Note: Gradation of sand: passing through sieve no. 50 but
retained on sieve no. 100.
+ Gradation of sand: passing through sieve no. 30 but
retained on sieve no. 50.
** Gradation of sand: as shown in Figure 2.2.
49
2100
GS
1800
10 GM
1500
//
S1200
900
/
600 GW
300 /
0 300 600 900 1200 1500
STRAIN ( 106 IN/IN. )
Fig. 2.8. Stressstrain curve for model grout.
3600
3000
2400
n 1800
0n
Q /
Fig. 2.9. Stressstrain curve for spandrel mortar.
required for use in analysis later. The indirect tensile
strength was obtained by splitting cylinders 3" in diameter
and 6" long. The properties of grout mixes adopted are
summarized in Table 2.1. For grout types GW and GM, the
sand used was of such a grade it passed through sieve no.
30, but was retained on sieve no. 50. For type GS, the
sand used for mortars Type I and Type II was adopted.
Initially, the required amount of water was determined by
trial for each type so that the grout could easily be poured
in the cells without separation of its components. The
stressstrain curves obtained using 3" x 6" cylinders are
shown in Figure 2.8.
2.8 Mortar Mix for Spandrel: A mortar mix of the following
proportions by weight was used in forming the spandrel of
the pier specimen used in model tests described in Chapter 4:
Portland Cement:Sand (river sand used in concrete mixes) = 1:3.
A watercement ratio of 0.55 by weight was adopted. The
compressive strength of the mix was 3830 psi and the tensile
strength 400 psi. Compression tests on a plate of 5.75" x
5.75" x 0.625" yielded 2300 psi. The stressstrain curve
obtained by testing 3" x 6" cylinders under uniaxial com
pression is shown in Figure 2.9.
CHAPTER 3
STRENGTH OF MORTAR JOINTS UNDER COMBINED STRESSES
3.1 Scope: This study was designed to investigate the
influence of precompression upon the shear and flexural
tensile strengths of mortar joints in concrete block
walls. First, the strength of the joint is studied under
a state of pure shear. Secondly, this is followed by a
study of pure bending. In the third phase, the strength
of the joint is studied under combined bending and shear
for a known amount of precompression. Combining the
above, the study is directed toward obtaining interaction
diagrams that can be used to predict behavior under com
bined loading.
The structural bond between mortar and units is an
important factor in the structural behavior of masonry
walls where the masonry is subjected to forces which pro
duce tensile and/or shearing stresses in the joints.
Factors which seem to influence the bond of masonry mor
tars are (13)(25): 1) composition, 2) suction rate (IRA),
3) initial moisture content of the block, 4) compressive
strength, 5) air content, 6) initial flow of mortar, and
7) curing of specimens. Shear bond may be considerably
increased by the presence of compressive stress normal to
the shearing force.
In the present investigation, only the mortar
composition and strength were considered as variables.
Other factors such as suction rate, initial flow, block
characteristics and curing procedures were standardized
and held constant.
3.2 Test Specimens: Test specimens were standard 3block
prisms with 3/8" mortar joints. All specimens were air
cured under laboratory conditions. The initial rate of
absorption of the blocks varied between 12g to 17 g/min/
30 sq in. The net area of a block, based on the average
of five specimens, was 61.4 sq in. Since the blocks were
fully bedded, this value was taken as the area of a mor
tar joint. Type M mortar was used with two compositions
The properties of mortars used are summarized in Table 3.1.
3.3 Strength of Mortar Joints under Compression and Shear:
A simple method was developed for applying shear to the
joints while a constant uniform compressive stress was
maintained across the joints. The specimens were supported
and loaded in such a way that the joints were at the points
of contraflexure. The testing arrangement adopted by Base
(4) was used with certain modifications. The test setup
adopted is shown schematically in Figure 3.1 and positioned
in the hydraulic press in Figure 3.2. The axial force
across the section was applied through steel rods and was
varied by tightening nuts at the threaded ends. The amount
TABLE 3.1
PROPERTIES OF MORTAR
Proportion by
Mortar Volume
Initial
Rate of
Flow
28day Strength
Cube Split
Comp. Cylr.
Specimens Type PC MC Sand % psi psi
PSM 112 II 1 1 6 90 864 172
PSM 1325 II 1 1 6 103 932 198
PSM 2637 I 1 1 4.5 96 2138 290
PSM 3941 II 1 1 6 110 956
PSM 4244 I 1 1 4.5 100 1758
1"thick bearing plate
3/4" threaded rods
Celotex Board
points of contrMa A
flexure at joints
\ + / BENDI NG MOMENT DIAGRAM
Fig. 3.1. Setup for studying the strength of
mortar under pure shear.
Test Specimen
Fig. 3.2. Test setup for finding the strength of mortar joints
under combined compression and shear.
IIT' A~bh&~d~red~1I
Fig. 3.3. Shear failure through mortar joint.
of prestress developed in the rods is found by measuring
the strains with electrical strain gages. On each rod,
two strain gages were mounted diametrically opposite to
each other and connected in series to compensate for
bending effects.
Table 3.2 presents the summary of test results for
the low strength mortar and Table 3.3 for the high strength
mortar. For the low strength mortar, at precompressions
up to 220 psi, bond failures were observed; but at a pre
compression of 300 psi, shear failure through the mortar
frequently occurred. Figure 3.3 shows an example of shear
failure through the joint. However, for the high strength
mortar (within the range of precompression adopted), the
failure pattern was always one of bond. Testing beyond
the range of precompression (300 psi for the high strength
mortar) was not possible due to flexural failure of the
concrete block.
Figure 3.4 shows the plot between precompression and
the shearing strength of mortar joints. It is evident
that the effect of precompression is to increase the
shearing strength of the joint considerably. It can also
be observed that a higher strength mortar does not appre
ciably increase the shear strength. This statement cannot
be generalized because, within the range of precompression
applied thus far in this investigation, bond failures were
usually observed. It is quite possible to have an increased
o> in
N01'
Lfl.
0n
11
N Cl
000
000
Ltn Ln o
cmo \
mY r rI
r r4 (,i
9
0000
* * *
00000
0r00 C 00
0000
Nmn n
m4 r4 u
r rA H C0
1 (\] (N (N
0000oooo
0000
00
00
N I
o o
S00
 O H H H O (
00 01% On mrrrnin ro m LO C) mm
0o 0000D C NO00 a>U0 m COOalC0 C) 0 lm
+++ ++
0 000 00000 0000
000 CCN CNI\ 0000
iHH cMNNNcN mmmm
00
nm
ON m
Ln r coo
a as
VI CO O
(ll (1< (< (
HHrJ
EEEEE
namen E~
PIAttAt
0) Uri CM
amaam
CO CO CO
0
14 4
cO
40
q d
U r1 dPo
H '
O'
UO
0 n
U 0
a 
,C:
4
.w .
Q)
 0 M
"40H
4
C
4J 
WU
Ci
0
*CJ2
bU)
D>
< r0
0
O
,
EQ
,.
OO
,.
r
0 U
(d 0
4Ufr
CJ2C
0
 .,4
OH
af
1O
0)
)>
0
0 rI
: (0
Om
+ X
.0 0o0 r)
H
4J 0
)4J
44 (U
) Hl o\O
o4
Uo
0 4
IJco
C 0
3(1) 0
S
U)
I
O 
i o
0 r
14
Sa) U)
i)nn 000
N 000
0CO 4 0L r
N. ,Q\On
c m 
000
000
000
C0 0
0 CO r1
Soo
00
00
0 0
m m
0:)11
mm cmm mmm mm
rlrl r l H H rlq r 1 rl r
C(0 C0)0)0) C)NC) C 00H
00 000 000 00
000 00NN 00
r rHr C04i C mm
000 cOOrH 0OOr 00
CoCC cmym mmm mm
oN coo \a k
U)U) U) In U)
PL4 C14 P II PL
S,H r
ma mm
c04an
&ti di
cY) m
mm
aU
0 CN CN Ln
\.D in Un
o.\U) rNeJ U)C'cJ m
*cr" m(nCN oCNoo 4 nm
r N ro rq H ri (N 0N 01
0
A /
A
280
240
200
+ 54
S/
A
/ 0
A /
o= 0.606 fo + 54
0 /
A MEAN VALUES
/0
/ A 1 :1 :1MOR T AR
0 1:1:6 MORIAR
PERMISSIBLE SHEAR STRESS
PRECOMPRESSION, PSI
Fig. 3.4. Effect of precompression on the shearing
strength of mortar joints.
fo = 0.6641
I
shear strength due to increase in strength of mortar at
higher precompressions, because the failure would likely
be due to shear failure of the mortar.
Using the method of least squares, the bestfit curve
for the observed data was found to plot as straight lines
with the following equations:
f = 0.606 f + 34 (3.1)
so a
for 1:1:6 mortar, and,
f = 0.641 f + 54 (3.2)
so a
for 1:1:4.5 mortar.
The above equations may be used for predicting the
shearing strength of mortar joints with a precompression
up to 300 psi for Type M mortar when blocks having an IRA
of 12 g to 17 g/min/30 sq in are used.
The specifications (2) limit the allowable shearing
stress to 34 psi for Type M mortar, irrespective of the
strength of mortar or level of precompression. Test re
sults to date indicate clearly that the specifications are
conservative.
0)
00
SI H
rm
a 0
1.4
H
SH
04
5
0
U)
C) >i
N> co (m mL o
0 0 00 0
n o o o o
, L o o o0
o t n .
a l m ) l Ol
co nc oo
,A N (i M
mam me IIC
N iH
(N LA
co o
0 0 0
) 0
a0 0
m m
00 CO 00
m mm
(Ni r4 r'
cfi
min c
 'In Ln
ft m m
x x x~
(f) U) U
3.4 Strength of Mortar Joints under Compression and
Bending: The test setup shown in Figure 3.1 was modified
to produce bending in the specimen with flexural stresses
acting normal to the bedjoints. The load corresponding
to the first crack was taken as the failure load since
beyond the initial failure, the load could have been shared
by the prestressing rods. Table 3.4 presents the results
of the tests. The maximum bending moment corresponding
to the failure load, when divided by the section modulus
of the joint, yielded the value of modulus of rupture
shown in Table 3.4. Adopting the crosssection of mortar
joint shown in Figure 3.5, the value of section modulus
corresponding to the extreme fiber was obtained as 117 cu in.
The results are plotted in Figure 3.6. Failure at the joint
was precipitated by a break in bond between the mortar and
the blocks.
The modulus of rupture appears to increase linearly
with precompression. In addition, the influence of precom
pression upon the modulus of rupture is significant with
high strength mortar. The following empirical relations
are proposed:
fbo = 1.250 f + 27 (3.3)
bo a
for 1:1:6 mortar, and,
1 .25"
1.25" 1 .25"
HO L LOW
15.6" T1
Fig. 3.5. Crosssection of a mortar joint.
560
480
00oo
/
//\
/ f
o fbo 1.25a + 27
o 1:1:6 MORTAR
A 1:1: 4 MORTAR
150
PRECOMPRESSION, PSI
Fig. 3.6. Effect of precompression on the flexural
tensile strength of mortar joints.
f o = 1.725
520
240
16o
80
4 )
r
0
*I
ca
41
0
o
0
on
4J
u
C6
'4
(0
ro
o
CO
C)
Q)
r L r r r t
m n m CV) iv Ln Lf
o o o a0 I I
o o o o v<
N N N N 'N CN4 N
rn <3< a) CN r m) CN
CN Lfn C I n (n CN (1)
e m cc 0 o oD r m
o i O m m m
Ur)
H
z
o
O
U
H
E z
0
H
0
E
CQ
a:
O *
O H
0 
1fnU)
4a 0
44 124
04
04) %
UE )
4J
4J 
U)
al( Q) *H
X 4J 0
(n
IT %D D D 00
%D in) in in) in
a) a a a r^'
ri
0 0 0 0 0 0 0
0 0 0 0 0 0 0
c' m 14 m CN
H H H
H H
H
> H H
H H H
H
S 1:1:6 MORTAR
A 1:1:1 MORTAR
fb / fo
Fig. 3.8. Interaction of bending and shear
under constant precompression.
2
<
bo = 1.725 f + 42 (3.4)
for 1:1:4.5 mortar.
Here, also, the specifications are conservative in
limiting the allowable stress to 23 psi.
3.5 Combined Compression, Bending, and Shear: Various
test arrangements were devised to produce several combina
tions of bending and shear under a constant precompression
of 300 psi. These testing arrangements are shown schemat
ically in Figure 3.7, and the results are summarized in
Table 3.5. Knowing the mean value of modulus of rupture
at a precompression of 300 psi (fbo), also the shear strength
(fso) without flexure, and the combined bending and shearing
stresses (fb and fs), the values of fb/fbo and fs /fso can be
calculated and plotted to provide the unit interaction curve
shown in Figure 3.8. It is anticipated that this curve is
one from a family of curves that will be generated by vary
ing the precompression in an expanded program of testing.
Thus, the flexural and shearing stresses in a mortar joint
under combined loading can be assumed to follow the equation:
+ ( = 1 (3.5)
so bo
CHAPTER 4
MODEL TESTS OF CONCRETE MASONRY PIERS
4.1 Selection of Model: The problem under investigation
consists of determining the stress distribution in a con
crete masonry shear wall, particularly in the region be
tween openings called piers. Even if models were used,
it is not economical to fabricate a model for a multiple
story wall with a large number of openings. Schneider (46)
conducted a photoelastic analysis on plastic models with
configurations as shown in Figure 4.1. The loads were
applied either diagonally or horizontally for all config
urations except in the case of multiple pier models where
the load was applied in a manner simulating the way in
which a roof diaphragm would load a shear wall. A simi
larity in fringe patterns was found to exist between the
model walls containing several piers and a diagonally
loaded single pier. Accordingly, the test specimen was
chosen as described in subsection 1.3.9 of Chapter 1.
In this investigation, a linear plane stress finite
element analysis is adopted in lieu of a photoelastic
analysis to verify the above findings and also to check
the effect of pipe columns that have been used to maintain
the geometry of the openings. The configurations chosen
o/r) * 1.1
S!1 ', :l'. I0 "i' 1n.P
cDi [1]
11Ed [:I
7.1] L:]
IF
o/D  .i
N a/D .2=
I'U.LIl.TIF i'5l'S  SlN: L. S'I*' Y
,..II' IPLE f'!. 'S  ; t .i ; h." '
Fig. 4.1. Photoelastic model configurations
chosen by Schneider.
for analysis and the finite element idealization are
shown in Figures 4.2 through 4.5. Figure 4.4 shows the
pier in a story with openings and walls on either side of
it, but loaded diagonally; Figure 4.5 shows the configu
ration adopted by Schneider. In this case, the pipe
columns are idealized as an equivalent rectangular element.
The equivalent modulus of elasticity of the element is
calculated by equating the axial rigidities of the actual
pipe column with that of the idealized element. In a
photoelastic analysis, the fringe patterns represent the
lines joining the points of constant maximum shear stress,
also called isoshear lines. In the analysis, maximum
shear stresses are computed at centroids of all elements.
The contour lines for these values represent the isoshear
lines. The isoshear lines are plotted for all the piers
investigated and these are shown in Figures 4.6 through
4.11. It is evident that the fringe patterns in all the
above cases are very similar and this confirms the method
of loading adopted in a single pier to simulate the actual
loading conditions a pier in a wall is subjected to.
To check the effect of substituting pipe columns for
end piers (Figure 4.4), the modulus of elasticity of the
pipe column elements was arbitrarily increased by 100%.
However, the corresponding changes in the maximum stresses
in the pier were less than 1% of the previous values.
I
0.5P
I I
I I
I I
Fig. 4.2. Finite element idealization for a
shear wall with openings.
0.5P
P
P
I " 1 12" I 12" I 12" 6"1 I
0.5P
Ckj
7t,7 ,f7
i~, I 3 1 23'
I 12" I 1 2"
I_ 12"_ I 6"'
' I. I PH 11 1
Fig. 4.3. Finite element idealization for a
multiple pier shear wall.
O.5P
P
I 1
!
11[ 9 11 L 9
t) o
a v
a)
Q)
04i .
0 0
H 0H
4J
ca
o c
4i
~Jw
co
4) to
il c0
0)

4.J
4C4
e c
rI
(U 0
&,
6" 6 
Fig. 4.5. Finite element idealization for the test
specimen adopted by Schneider.
12"11P I 6" 10
\\"
Fig. 4.6. Isoshear lines for the pier shaded as shown above.
D D
Fig. 4.7. [sosheat lines for the pier shaded as shown above.
