PERFORMANCE OF CONCRETE MASONRY SHEAR WALLS
WITH INTEGRAL CONFINED CONCRETE BOUNDARY ELEMENTS
By
WILLIS BRADFORD CYRIER
A thesis submitted in partial fulfillment of
the requirements for the degree of
MASTER OF SCIENCE IN CIVIL ENGINEERING
WASHINGTON STATE UNIVERSITY
Department of Civil and Environmental Engineering
August 2012
To the Faculty of Washington State University:
The members of the Committee appointed to examine the thesis of WILLIS BRADFORD
CYRIER find it satisfactory and recommend that it be accepted.
____________________________________
David I. McLean, Ph.D., P.E., Chair
____________________________________
William F. Cofer, Ph.D., P.E.
____________________________________
J. Daniel Dolan, Ph.D., P.E.
ii
ACKNOWLEDGMENTS
I would like to acknowledge the National Institute of Standards and Technology (NIST) for
providing the financial resources that made this research possible. Recognition is also made to the
Eastern Washington Masonry Promotion Group for the fellowship provided to support my MS studies.
I am incredibly thankful to Dr. David McLean for this opportunity and for serving as my
committee chair. I am thankful for his guidance and support throughout my master’s program at
Washington State University. I express my deepest gratitude to him for sending me to Christchurch,
New Zealand to see, firsthand, the aftermath of two powerful earthquakes. I am grateful for my
committee members, Dr. Cofer and Dr. Dolan, for their advice on this thesis and for their mentorship
these past few years. My sincerest thanks are extended to Dr. Benson Shing, Dr. Richard Klingner, Dr.
Farhad Ahmadai, and my WSU colleagues involved with this joint project, Jacob Sherman and Christina
Kapoi, for their support during wall construction.
Bob Duncan and Scott Lewis have my gratitude for sharing their knowledge and experience with
me during wall construction and testing at the Composite Materials and Engineering Center. My thanks
are also extended to Louis de Fontenay, Tyler Foster, Andrew Kapoi, Alex Kirk, Jake Logar, Ian Scott, and
Ihar Viarenich for their help at various times during specimen construction and testing. I would also like
to recognize individuals who have mentored and encouraged me during my undergraduate and
graduate studies at the university – namely, Renee Petersen, and Dr. David Pollock.
Special thanks go to my parents Brad and Vicki Cyrier, and to my in-laws Mark and Rita Ness.
Thank you for your support, in all areas, during my time at university. Your encouragement has blessed
me and my “little” family. I give thanks to my beautiful wife Amanda. Thank you for your limitless
patience and grace the past five years. I love you. Finally, I owe it all to Jesus Christ who gave me a
foundation on which to build my life (Matthew 7:24-25, Psalm 40:1-2). For me, none of this was
possible without Him.
iii
PERFORMANCE OF CONCRETE MASONRY SHEAR WALLS
WITH INTEGRAL CONFINED CONCRETE BOUNDARY ELEMENTS
Abstract
By Willis Bradford Cyrier, M.S.
Washington State University
August 2012
Chair: David I. McLean
This project was funded by the National Institute of Standards and Technology as part of a joint
study between researchers at the University of California at San Diego, the University of Texas at Austin
and Washington State University to develop improved performance-based design provisions and
methodologies for reinforced concrete masonry shear walls. The objective of research reported herein
is to investigate the behavior of masonry walls incorporating integral confined concrete boundary
elements under lateral loading. Results from this study also provide a basis for establishing prescriptive
detailing requirements for designing masonry walls with integral confined concrete boundary elements.
Four, fully grouted, concrete masonry shear walls with integral confined concrete boundary
elements were designed according to the provisions of the 2011 MSJC and the 2011 ACI-318 codes.
Performance measures investigated included peak load capacities; drifts at three limit states; drift
components from shear, flexure and sliding; displacement and curvature ductilities; plastic hinge
lengths; energy dissipation; and equivalent viscous damping values. The effects of incorporating the
confined concrete boundary elements, axial compressive stress, boundary element geometry, and size
of transverse hoops in the boundary elements were evaluated to determine their influence on wall
performance. Test results in this research were compared to results from tests on two similar masonry
walls without boundary elements performed by Kapoi (2012).
iv
Masonry walls with integral confined concrete boundary elements increased displacement
ductility values by 48% and total energy dissipation was approximately 260% greater compared to
similar masonry walls without boundary elements. Axial compressive stress increased peak load
capacity and total energy dissipation. Peak load, displacement ductility, and total energy dissipated
were greater in the wall with flanged boundary elements compared to the wall with rectangular
boundary elements. These performance benefits were a result of the increased out-of-plane stability
provided by the flanged boundary elements. One flanged wall used No. 3 hoops while the other
employed ¼-in. round wire hoops. Wall responses were nearly identical. Walls with rectangular
boundary elements failed when the boundary element core buckled out-of-plane. Walls with flanged
boundary elements failed due to low-cycle fatigue fracture of the longitudinal reinforcing bars.
v
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ................................................................................................................................ iii
ABSTRACT..................................................................................................................................................... iv
LIST OF TABLES ..............................................................................................................................................ix
LIST OF FIGURES ............................................................................................................................................xi
Dedication ................................................................................................................................................... xiv
CHAPTER 1: INTRODUCTION ......................................................................................................................... 1
1.1
Background ................................................................................................................................... 1
1.2
Scope and Objectives.................................................................................................................... 3
CHAPTER 2: LITERATUE REVIEW ................................................................................................................... 4
2.1
Introduction .................................................................................................................................. 4
2.2
Failure Modes of Masonry Shear Walls ........................................................................................ 4
2.3
Ductility ......................................................................................................................................... 5
2.4
MSJC (2011) .................................................................................................................................. 6
2.5
ACI 318 (2011) ............................................................................................................................ 11
2.6
Research to Increase Strain Capacity and Ductility in Masonry ................................................. 12
2.7
Banting and El-Dakhakhni (2012) ............................................................................................... 18
2.8
Shedid et al. (2010) ..................................................................................................................... 20
2.9
Kapoi (2012)................................................................................................................................ 22
2.10 Summary ..................................................................................................................................... 23
CHAPTER 3: EXPERIMENTAL PROGRAM ..................................................................................................... 25
3.1
Introduction ................................................................................................................................ 25
3.2
Footings ...................................................................................................................................... 25
vi
3.3
Wall Specimens........................................................................................................................... 26
3.4
Loading Beams ............................................................................................................................ 30
3.5
Material Properties..................................................................................................................... 31
3.6
Wall Specimen Construction ...................................................................................................... 32
3.7
Test Setup ................................................................................................................................... 38
3.8
Specimen Instrumentation ......................................................................................................... 39
3.9
System Control & Data Acquisition ............................................................................................ 41
3.10 Test Procedures .......................................................................................................................... 41
CHAPTER 4: TEST RESULTS .......................................................................................................................... 44
4.1
Introduction ................................................................................................................................ 44
4.2
Specimen BE-1 ............................................................................................................................ 44
4.3
Specimen BE-2 ............................................................................................................................ 59
4.4
Specimen BE-3 ............................................................................................................................ 68
4.5
Specimen BE-4 ............................................................................................................................ 76
4.6
Summary ..................................................................................................................................... 84
CHAPTER 5: ANALYSES AND COMPARISONS OF WALL PERFORMANCE ..................................................... 86
5.1
Introduction ................................................................................................................................ 86
5.2
Theoretical Predictions ............................................................................................................... 86
5.3
Drift ............................................................................................................................................. 87
5.4
Displacement Ductility ................................................................................................................ 88
5.5
Height of Plasticity and Equivalent Plastic Hinge Length ........................................................... 89
5.6
Energy Dissipation ...................................................................................................................... 90
5.7
Equivalent Viscous Damping....................................................................................................... 92
5.8
Effects of Wall Parameters on Behavior ..................................................................................... 92
vii
5.9
5.8.1
Axial-Compressive Stress .................................................................................................. 93
5.8.2
Boundary Element Geometry ........................................................................................... 95
5.8.3
Confining Reinforcement .................................................................................................. 97
Summary and Conclusions.......................................................................................................... 99
CHAPTER 6: SUMMARY, CONCLUSIONS, RECOMMENDATIONS AND FUTURE RESEARCH....................... 102
6.1
Summary ................................................................................................................................... 102
6.2
Conclusions ............................................................................................................................... 103
6.3
Recommended Guidelines for Designing Integral Confined Concrete Boundary Elements .... 105
6.4
Future Research ........................................................................................................................ 107
REFERENCES .............................................................................................................................................. 108
viii
LIST OF TABLES
Page
Table 2.1 – Strain Values for Confined Concrete Masonry ......................................................................... 16
Table 2.2 – Test Results (Banting and El-Dakhakhni, 2012) ........................................................................ 19
Table 2.3 – Load, Displacement, and Ultimate Ductility Results (Shedid et al., 2010) ............................... 21
Table 3.1 – Specimen Details ...................................................................................................................... 29
Table 3.2 – Average Material Compressive Strengths, psi.......................................................................... 32
Table 3.3 – Reinforcement Yield Strengths, ksi .......................................................................................... 32
Table 4.1 – Specimen BE-1: Test Observations ........................................................................................... 45
Table 4.2 – Specimen BE-1: Component Percentages of Total Drift .......................................................... 50
Table 4.3 – Specimen BE-1: Displacement Ductility ................................................................................... 55
Table 4.4 – Specimen BE-1: Curvature Ductility ......................................................................................... 56
Table 4.5 – Specimen BE-1: Height of Plasticity.......................................................................................... 56
Table 4.6 – Specimen BE-1: Equivalent Plastic Hinge Length ..................................................................... 57
Table 4.7 – Specimen BE-2: Test Observations ........................................................................................... 60
Table 4.8 – Specimen BE-2: Component Percentages of Total Drift .......................................................... 65
Table 4.9 – Specimen BE-2: Displacement Ductility ................................................................................... 66
Table 4.10 – Specimen BE-2: Curvature Ductility ....................................................................................... 66
Table 4.11 – Specimen BE-2: Height of Plasticity........................................................................................ 67
Table 4.12 – Specimen BE-2: Equivalent Plastic Hinge Length ................................................................... 67
Table 4.13 – Specimen BE-3: Test Observations ......................................................................................... 69
Table 4.14 – Specimen BE-3: Component Percentages of Total Drift ........................................................ 72
Table 4.15 – Specimen BE-3: Displacement Ductility ................................................................................. 75
Table 4.16 – Specimen BE-3: Curvature Ductility ....................................................................................... 75
ix
Table 4.17 – Specimen BE-3: Height of Plasticity........................................................................................ 75
Table 4.18 – Specimen BE-3: Equivalent Plastic Hinge Length ................................................................... 76
Table 4.19 – Specimen BE-4: Test Observations ......................................................................................... 77
Table 4.20 – Specimen BE-4: Component Percentages of Total Drift ........................................................ 80
Table 4.21 – Specimen BE-4: Displacement Ductility ................................................................................. 83
Table 4.22 – Specimen BE-4: Curvature Ductility ....................................................................................... 83
Table 4.23 – Specimen BE-4: Height of Plasticity........................................................................................ 84
Table 4.24 – Specimen BE-4: Equivalent Plastic Hinge Length ................................................................... 84
Table 5.1 – Predicted and Experimental Capacities.................................................................................... 87
Table 5.2 – Total Wall Drift at Three Limit States ....................................................................................... 87
Table 5.3 – Components of Wall Drifts at Failure ....................................................................................... 88
Table 5.4 – Average Yield, Ultimate Displacement, and Displacement Ductility ....................................... 89
Table 5.5 – Height of Plasticity and Plastic Hinge Length ........................................................................... 90
Table 5.6 – Total Energy Dissipation ........................................................................................................... 90
Table 5.7 – Equivalent Viscous Damping .................................................................................................... 92
Table 5.8 – Axial Compressive Stress Evaluation ........................................................................................ 93
x
LIST OF FIGURES
Page
Figure 2.1 – Masonry Shear Wall Failure Modes (adopted from Eikanas, 2003) ......................................... 5
Figure 2.2 – Yield and Ultimate Displacement Definitions (Priestley et al., 2007) ....................................... 6
Figure 2.3 – Confinement Examples ........................................................................................................... 14
Figure 2.4 – Details of Steel Confinement Plates and Seismic Combs ........................................................ 15
Figure 2.5 – Comparisons of Confinement Techniques by Shing et al. (1993) and Priestley (1981) .......... 16
Figure 2.6 – Load-Displacement Envelopes from Snook (2005) ................................................................. 17
Figure 2.7 – Confining Boundary Element Detail by Banting and El-Dakhakhni (2012) ............................. 18
Figure 2.8 – Wall Details (Shedid et al., 2010) ............................................................................................ 20
Figure 2.9 – Walls C7 and C8 Reinforcement Detail (Kapoi, 2012) ............................................................. 23
Figure 3.1 – Flanged Footing Details ........................................................................................................... 26
Figure 3.2 – Specimen Reinforcement Layout ............................................................................................ 27
Figure 3.3 – Typical Wall Specimen............................................................................................................. 30
Figure 3.4 – Grout Dam Detail .................................................................................................................... 31
Figure 3.5 – Footing Construction............................................................................................................... 33
Figure 3.6 – CMU Construction Sequence .................................................................................................. 34
Figure 3.7 – Construction Prior to Boundary Element Formwork .............................................................. 35
Figure 3.8 – Boundary Element Construction ............................................................................................. 37
Figure 3.9 – Testing Apparatus ................................................................................................................... 39
Figure 3.10 – Specimen Instrumentation ................................................................................................... 40
Figure 3.11 – Load Application & Data Acquisition Flow Chart (adapted from Sherman 2011) ................ 41
Figure 3.12 – Preliminary Test Loading Protocol ........................................................................................ 42
Figure 3.13 – Primary Test Loading Protocol .............................................................................................. 43
xi
Figure 4.1 – Specimen BE-1 Following Testing ........................................................................................... 46
Figure 4.2 – Specimen BE-1 Following Testing: Out-of-Plane Failure ......................................................... 46
Figure 4.3 – Specimen BE-1 Following Testing: South Toe and North Toe ................................................. 46
Figure 4.4 – Specimen BE-1: Load Displacement Hysteresis ...................................................................... 48
Figure 4.5 – Massone and Wallace (2004): Flexure and Shear Deformations ............................................ 49
Figure 4.6 – Specimen BE-1: Displacement Components ........................................................................... 51
Figure 4.7 – Specimen BE-1: Wall Curvature .............................................................................................. 53
Figure 4.8 – Elastoplastic Approximation ................................................................................................... 54
Figure 4.9 – Snook (2005): Energy Dissipation Equation Illustration.......................................................... 58
Figure 4.10 – Priestley et al. (2007): Hysteretic Area for Damping Calculation ......................................... 59
Figure 4.11 – Specimen BE-2 Following Testing ......................................................................................... 61
Figure 4.12 – Specimen BE-2 Following Testing: South Toe and North Toe ............................................... 61
Figure 4.13 – Specimen BE-2: Load Displacement Hysteresis .................................................................... 63
Figure 4.14 – Specimen BE-2: Displacement Components ......................................................................... 64
Figure 4.15 – Specimen BE-2: Wall Curvature ............................................................................................ 65
Figure 4.16 – Specimen BE-3 Following Testing ......................................................................................... 70
Figure 4.17 – Specimen BE-3 Following Testing: South Toe and North Toe ............................................... 70
Figure 4.18 – Specimen BE-3: Load Displacement Hysteresis .................................................................... 71
Figure 4.19 – Specimen BE-3: Displacement Components ......................................................................... 73
Figure 4.20 – Specimen BE-3: Wall Curvature ............................................................................................ 74
Figure 4.21 – Specimen BE-4 Following Testing ......................................................................................... 78
Figure 4.22 – Specimen BE-4 Following Testing: South Toe and North Toe ............................................... 78
Figure 4.23 – Specimen BE-4: Load Displacement Hysteresis .................................................................... 79
Figure 4.24 – Specimen BE-4: Displacement Components ......................................................................... 81
xii
Figure 4.25 – Specimen BE-4: Wall Curvature ............................................................................................ 82
Figure 5.1 – Load-Displacement Hystereses for Specimens BE-1 and C7 ................................................... 91
Figure 5.2 – Load-Displacement Hystereses for Specimens BE-2 and C8 ................................................... 91
Figure 5.3 – Load-Displacement Envelopes for Axial Compressive Stress Comparison ............................. 94
Figure 5.4 – Load-Displacement Envelopes for Boundary Element Geometry Comparison ...................... 96
Figure 5.5 – Load-Displacement Hystereses for Specimens BE-1 and BE-3................................................ 97
Figure 5.6 – Load-Displacement Envelopes for Confining Reinforcement Comparison ............................. 98
Figure 5.7 – Load-Displacement Hysteresis for Specimens BE-3 and BE-4 ................................................. 99
xiii
Dedication
I dedicate this thesis to my amazing wife Amanda, whose love, patience, grace, and support has
sustained and motivated me throughout my undergraduate and graduate education at Washington
State University; to my son Lincoln Bradford, whose genesis was the catalyst to pursue this dream; to my
daughter Evan Elizabeth, whose presence in my life has been a gift beyond measure; and to my newest
son Garrison Byron who brings boundless joy to my life.
My love for you four is infinite
xiv
CHAPTER 1
INTRODUCTION
1.1
Background
Reinforced concrete masonry is an economical building material for low- to mid-rise shear wall
structures when compared to many alternative systems. However, in regions with high seismic risk,
economical elastic response design is difficult to achieve with these types of systems (Shedid et al.,
2010). This situation results in designs that are required to deform inelastically during significant
earthquake events. Because reinforced masonry shear walls will undergo this inelastic response during
severe ground motions, special consideration must be given to detailing of the horizontal and vertical
reinforcement, especially at the ends of such walls where overturning tension and compression forces
are greatest.
During an earthquake, the seismic response of a structure is a function of many factors including
the mass, period, and inherent damping of the structure and its contents. Typical design load
determination procedures, such as the equivalent lateral force method outlined in Section 12.8 of the
2010 ASCE/SEI 7 (ASCE, 2010), place these earthquake forces at the diaphragms (floors and roof), which
then transfer the loads into the elements of the lateral force resisting system. As a result, yielding will
occur in a reinforced masonry shear wall at the bottom and, depending upon support conditions, also at
the top of the wall, often referred to as the hinging regions. Because of this mechanism, attention to
detailing of the hinging regions is important to provide the needed ductility in the wall.
Geometric limitations of concrete masonry units (CMU) prevent the addition of substantial
transverse reinforcement at a spacing less than in the height of the units, typically 8 in. As a result,
confinement of the grouted core and vertical reinforcement in the hinging regions is provided only at
the bed joints between the blocks and by the 180˚ seismic hooks on the horizontal reinforcing steel.
1
While these hooks provide some buckling resistance to the vertical reinforcement, out-of-plane stability
of the element is not enhanced, nor is the masonry compression area adequately confined.
A number of different methods of confinement have been studied for application to masonry,
including providing steel plates and seismic combs in the bed joints, steel rings and spirals around
vertical reinforcing bars within the block cells, and polymer fibers added to the grout in varying
proportions (Priestley and Elder, 1983; Hart et al., 1988; Snook, 2005; Hervillard, 2005). The goal in all of
these studies was to provide confinement to the masonry in order to increase the compressive strain
capacity. While the researchers found strain capacity was enhanced by the various confinement
techniques, the improvements were generally modest. To provide the needed improvements in
ductility, several of the researchers suggested that the vertical spacing of the transverse reinforcement
must be decreased in order to increase the confined core area.
The 2011 Building Code Requirements and Specifications for Masonry Structures (MSJC, 2011)
provides design guidelines for boundary elements in masonry walls. However, these guidelines cover
primarily geometric issues. No guidance is given in the MSJC Code for effective confinement techniques
for application to masonry. As a result, Section 3.3.6.5.5 requires that testing be performed to verify
that the provided detailing is capable of developing a strain capacity in the boundary elements that is in
excess of the imposed strains. In contrast, the ACI 318-11 Building Code Requirements for Structural
Concrete and Commentary (ACI, 2011) provides prescriptive detailing requirements for specially
confined boundary elements in structural concrete walls. The MSJC Commentary states “it is hoped that
reasonably extensive tests will be conducted in the near future, leading to the development of
prescriptive detailing requirements for specially confined boundary elements of intermediate as well as
special reinforced masonry shear walls” (MSJC, 2011).
2
1.2
Scope and Objectives
This project was funded by the National Institute of Standards and Technology (NIST) as part of a
joint study between researchers at the University of California at San Diego, the University of Texas at
Austin and Washington State University to develop improved performance-based design provisions and
methodologies for reinforced concrete masonry shear walls. The objective of research reported in this
thesis is to investigate the behavior of masonry walls incorporating integral confined concrete boundary
elements at each end under lateral loading. Results from this study provide a basis for establishing
prescriptive detailing requirements for designing masonry walls with integral confined concrete
boundary elements.
Four, fully grouted, concrete masonry shear walls with integral confined concrete boundary
elements were designed according to the provisions of the 2011 MSJC and the 2011 ACI-318 codes. The
walls were subjected to a prescribed cyclic, in-plane lateral displacement sequence. Performance
measures evaluated include peak load capacities; drifts at various limit states; decoupled drift
components from shear, flexure and sliding; displacement and curvature ductilities; plastic hinge
lengths; total energy dissipation; and equivalent viscous damping values. The effects of incorporating
the confined concrete boundary elements, axial compressive stress, boundary element geometry, and
size of transverse hoops in the boundary elements were evaluated to determine their influence on wall
performance. Test results in this research were compared to results from tests on two similar masonry
walls without boundary elements performed by Kapoi (2012). Recommendations were provided for the
design of integral confined concrete boundary elements for application in masonry walls.
3
CHAPTER 2
LITERATURE REVIEW
2.1
Introduction
A review of current literature pertinent to this study is presented in this chapter. Gaining an
improved understanding of the seismic response of masonry structures has been the focus of recent
research efforts, particularly associated with the development of performance-based design procedures.
The behavior of reinforced masonry shear walls under seismic loading is discussed, and issues relating to
ductility are reviewed. Current code provisions for reinforced masonry shear wall design and for
confined concrete boundary elements are summarized. Reviews of several recent studies on the seismic
performance of reinforced masonry shear walls are also provided.
2.2
Failure Modes of Masonry Shear Walls
Research since the 1970s has demonstrated that reinforced masonry walls subjected to cyclic,
in-plane loading have four commonly recognized forms of response. The type of response is important
because it can determine a wall’s performance under seismic loading. Various design parameters affect
a wall’s response including the applied axial load, wall aspect ratio, longitudinal and horizontal
reinforcing ratios, and anchorage detailing.
Paulay and Priestley (1992) found that four common response modes for masonry shear walls
are associated with flexure, rocking, shear, and sliding deformations. These deformations are illustrated
in Figure 2.1. Adequate anchorage of the wall to the foundation will allow the shear and flexure modes
to dominate wall response. A ductile failure typically results from a flexural response, while a brittle
failure often results from a shear response. Ductile failures are preferred because the structure
possesses the ability to deform inelasticity without sudden fracture. Energy dissipation is also greatly
4
improved in a ductile structure. Brittle failures are generally violent and provide little notice for
occupant egress. Therefore, a flexural response and associated ductile failure is a more desirable
reaction to seismic impacts.
Figure 2.1 – Masonry Shear Wall Deformation Modes (adopted from Eikanas, 2003)
Flexure failure is typically characterized by yielding of the extreme vertical reinforcement,
vertical separation at the mortar bed joints in the tension zone, plastic hinge formation, and eventual
crushing of the compressive toe regions of the wall (Shedid et al., 2008; Shing et al., 1989). Large
compressive strains in the masonry cause vertical splitting in the toe regions. Subsequent face shell
spalling occurs, followed by crushing of the grouted core and buckling of the vertical reinforcement. As
this happens, the available compressive area is reduced along with the wall’s strength, and load
resistance is significantly diminished (Shedid et al., 2008).
Eikanas (2003) and Sherman (2011) found that increased vertical reinforcing ratios negatively
affect flexural performance resulting in lower drift capacity, reduced ductility, and a brittle response to
lateral loading. Thus, in walls where a flexure response will control, the longitudinal reinforcing ratio
should be limited to insure ductile, inelastic behavior (Eikanas, 2003).
2.3
Ductility
Ductility is a measure of inelastic deformations such as displacement, curvature and strain. It is
defined as the ratio of maximum to effective yield deformations (Priestley et al., 2007). However,
differences in reported ductility values often arise as a result of different definitions for the yield and
5
ultimate deformations. The point of initial yielding has been defined as: (1) the intersection of the line
through the origin with initial stiffness, and the nominal strength; (2) the displacement at first yield; (3)
and the intersection of the line through the origin with secant stiffness through first yield and the
nominal strength. The ultimate deformation has been defined as: (4) displacement at peak strength; (5)
displacement corresponding to 20% or 50% degradation from peak strength; and (6) displacement at
initial fracture of the transverse reinforcement (Priestley et al., 2007). Figure 2.2 illustrates a forcedisplacement curve with points corresponding to the above definitions for yield and maximum
displacement. The value for the ductility factor is highly dependent upon which points are chosen for
the yield and ultimate deformations. Priestley et al. (2007) define the yield displacement at point 3 and
the ultimate displacement at point 5.
Figure 2.2 - Yield and Ultimate Displacement Definitions (from Priestley et al., 2007)
2.4
MSJC (2011)
Seismic design requirements for masonry shear walls are provided in Section 1.18 of the 2011
Building Code Requirements and Specification of Masonry Structures developed by the Masonry
Standards Joint Committee (MSJC). The MSJC establishes three classifications of reinforced masonry
6
shear walls: ordinary, intermediate, and special. The seismic design category determines which type of
shear wall is permitted. Requirements for special reinforced masonry shear walls, which are applicable
to the wall specimens of this study, are given in Section 1.18.3.2.6 of the MSJC code. Additionally, the
walls must comply with the requirements for either allowable stress design or strength design given in
Sections 2.3 or 3.3, respectively.
Reinforcement requirements for special reinforced masonry shear walls are presented in
Section 1.18.3.2.6. The maximum spacing of vertical and horizontal reinforcement is limited to the
smallest of one-third the length of the shear wall, one-third the height of the shear wall, and 48 in.
Horizontal reinforcement must be evenly distributed over the height of the wall and embedded in grout.
The minimum area of vertical and horizontal reinforcement shall not be less than 0.2 in2 or 0.0007
multiplied by the gross cross-sectional area of the wall. The sum of the cross-sectional area of
horizontal and vertical reinforcement shall be at least 0.002 multiplied by the gross cross-sectional area
of the wall. Additionally, the minimum cross-sectional area of the vertical reinforcement shall be onethird of that required for shear reinforcement. Shear reinforcement must be anchored around vertical
reinforcing bars with a standard hook.
Section 1.18.3.2.6.1.1 provides a shear design requirement when using strength design that
decreases the likelihood of a shear failure prior to a flexural failure. It requires that the factored
nominal shear strength shall exceed the shear corresponding to the development of 1.25 times the
nominal moment strength. However, the nominal shear strength need not exceed 2.5 times the
required shear strength (MSJC, 2011).
Reinforcement requirements when using strength design are given in Section 3.3.3 of the MSJC
Code. Provisions for the maximum area of flexural tensile reinforcement are given in Section 3.3.3.5 and
are intended to ensure that the tensile reinforcement develops a specified level of inelastic strains prior
7
to crushing of the masonry in the compression zone. Equation 2.1 provides the maximum
reinforcement ratio for fully grouted walls with only concentrated tension reinforcement.
(
)
Where:
ρ
= the maximum reinforcement ratio;
As
= the area of steel (in2);
b
= the net thickness of the wall (in.);
d
= the distance between the centroid of the tension reinforcement and the
extreme compression fiber (in.);
f’m
= the masonry compressive stress (psi);
εmu
= the maximum compressive masonry strain;
α
= the tension reinforcement strain factor (4 for special reinforced shear walls);
εy
= the longitudinal steel yield strain;
P
= the axial load demand (lbs); and
fy
= the steel yield stress (psi).
MSJC Section 3.3.6.5 provides an alternative approach to ensure adequate ductility in masonry
shear walls by means of special confined boundary elements. For walls complying with Section 3.3.6.5,
the maximum reinforcement requirements of Section 3.3.3 do not apply. When using this alternative
approach, Section 3.3.6.5.1 provides “screens” to determine if specially confined boundary elements are
necessary. The MSJC Commentary states that shear walls meeting these screens will not develop
sufficiently high compressive strains in the masonry to warrant special confinement. If a wall meets the
following requirements, then special boundary elements are not required:
8
1.
Pu ≤ 0.10Agf’m
for geometrically symmetrical wall sections
Pu ≤ 0.05Agf’m
for geometrically unsymmetrical wall sections; and either
2.
or
√
3.
Where:
PU
= the factored axial load (lbs);
Ag
= the gross cross-sectional area of the wall (in2);
Mu
= the factored moment (in.-lb);
dv
= length of the wall in the direction of the applied shear (in.);
Vu
= the factored shear force (lbs); and
An
= the net cross-sectional area of the wall (in2).
The expectation is that many shear walls will pass through the screens, therefore negating the
requirement for special confining boundary elements. This will be the case for shear walls with small
axial loads, short or moderate in height, and subject to only moderate shear stresses. If an element
does not pass the screens, then a designer utilizes Sections 3.3.6.5.2 through 3.3.6.5.5 to design the
boundary elements.
Section 3.3.6.5.3 states that special boundary elements shall be provided over portions of the
compression zones where:
⁄
Where:
c
= the distance from the neutral axis to the fiber of maximum compressive strain;
lw
= the length of the shear wall (in.);
9
Cd
= the deflection amplification factor from ASCE/SEI 7;
δne
= the displacement computed using code-prescribed seismic forces assuming
elastic behavior (in.); and
hw
= the height of the shear wall (in.).
If a boundary element is required by Equation 2.2, then the height of the element shall extend vertically
from the critical section a distance not less than the larger of lw or Mu/4Vu.
Alternatively, Section 3.3.6.5.4 can be used for designing the length of the boundary element. A
boundary element is required where the maximum extreme fiber compressive stress corresponding to
factored forces including earthquake effects exceeds 0.2f’m and is permitted to be discontinued where
the compressive stress is less than 0.15f’m. The MSJC Code requires that factored stresses shall be used
in the computation using a linearly elastic model and gross section properties.
Additional design provisions for boundary elements are given in Section 3.3.6.5.5. The length of
the special boundary elements shall have a length of not less than the larger of (c – 0.1lw) and c/2
extending from the extreme compression fiber. If a flanged section is utilized, the effective flange width
in compression and a 12-in. minimum extension into the web shall be included in the element. The
transverse reinforcement at the wall base shall extend into the support structure to a minimum depth of
the development length of the largest longitudinal reinforcement, unless the element ends on a footing
or mat where the transverse reinforcement shall extend at least 12 in. into the foundation. The
horizontal shear reinforcement in the wall web shall be anchored to develop the specified yield strength
within the confined core of the boundary element.
No guidance is given in the MSJC for effective confinement techniques for application to
masonry. As a result, Section 3.3.6.5.5 requires that testing be performed to verify that the detailing
provided is capable of developing a strain capacity in the boundary elements that is in excess of the
imposed strains. In contrast, the ACI 318-11 Building Code Requirements for Structural Concrete and
10
Commentary (ACI, 2011) provides prescriptive detailing requirements for specially confined boundary
elements in concrete structural walls. The MSJC Commentary states “it is hoped that reasonably
extensive tests will be conducted in the near future, leading to the development of prescriptive detailing
requirements for specially confined boundary elements of intermediate as well as special reinforced
masonry shear walls” (MSJC, 2011).
2.5
ACI 318-11 (2011)
Provisions for the design of boundary elements in special reinforced concrete walls are given in
Section 21.9.6 of ACI 318-11 (2011). The ACI requirements for the geometry of special confining
boundary elements are similar to those in the MSJC. However, unlike the MSJC, the ACI Code provides
prescriptive reinforcement detailing requirements in Sections 21.9.6.4(c) and 21.9.6.5.
Transverse reinforcement in the boundary elements must satisfy the requirements of Section
21.6.4.2, which specifies that the transverse reinforcement shall be provided by either single or
overlapping spirals, circular hoops, or rectilinear hoops with or without crossties. Spacing limits for the
transverse reinforcement are given in Section 21.6.4.3. Provision (a) in this section is modified to be
one-third of the minimum member dimension because tests have shown that acceptable performance
can be achieved using a larger hoop spacing for walls (Thomsen and Wallace, 2004). Provision (b) limits
the transverse spacing to six times the diameter of the smallest longitudinal bar in the boundary
element. Provision (c) limits the transverse reinforcement spacing to that determined by Equation 2.3.
The spacing determined by Equation 2.3 shall not exceed 6 in. and need not be taken less than 4 in. The
spacing of the transverse reinforcement cannot exceed the smallest of provisions (a) through (c) to
guarantee sufficient core confinement.
(
Where:
11
)
so
= the center-to-center spacing of transverse reinforcement with length lo (in.);
and
hx
= maximum center-to-center horizontal spacing of crossties or hoop legs on all
faces of the column or boundary element (in.).
When using rectangular hoop reinforcement for the transverse reinforcement in the boundary
elements, the total cross-sectional area of the hoop reinforcement shall not be less than that
determined by Equation 2.4.
This required area of transverse reinforcement, determined with Equation 2.4, is “intended to
ensure adequate flexural curvature capacity in yielding regions” (ACI 318-11, 2011).
Where:
Ash
= the total cross-sectional area of transverse reinforcement (including crossties)
within spacing s and perpendicular to dimension bc;
s
= the center-to-center spacing of transverse reinforcement (in.);
bc
= the cross-sectional dimension of the boundary element core measured to the
outside edges of the transverse reinforcement composing area Ash (in.);
2.6
f’c
= the specified concrete compressive strength (psi); and
fyt
= the specified yield strength of transverse reinforcement (psi).
Research to Increase Strain Capacity and Ductility in Masonry
Numerous studies have been conducted to investigate methods for providing confinement in
masonry with the goal of increasing the compressive strain capacity and ductility. Priestley and Elder
(1983) looked at the compressive stress-strain characteristics of reinforced concrete masonry containing
12
steel confinement plates placed in the mortar bed joints. Figure 2.3 (a) shows this detail. Masonry
prisms were tested in a testing machine operated under displacement control. The researchers
concluded that the confinement plates produced a more gradual failure and improved the ductility of
the concrete masonry prisms.
Hart et al. (1988) studied confinement reinforcement in concrete masonry prisms using seven
different types of steel confinement reinforcement including Priestley plates, No. 3 ties, closed wire
mesh, seismic combs, steel ring cages, spirals, and spiral cages. These details are illustrated in Figure
2.3. Displacement-controlled compression testing was conducted to obtain the stress-strain behavior of
each masonry prism. The researchers concluded that all prisms with confinement, when compared to
prisms without confinement, had greater displacement ductility and a decreased slope of the post-peak
portion of the compressive stress-strain curve.
Malmquist (2004) investigated the use of confinement plates and seismic reinforcement combs
in concrete block and hollow clay brick masonry prisms (see Figure 2.4). The prisms were loaded to
failure in compression under a controlled rate of displacement. Results showed that the use of
confinement reinforcement in the mortar bed joints of masonry increased the strain capacity above that
of unconfined masonry. Strains at 50% of peak stress were 30% and 50% greater for clay brick and
concrete block masonry, respectively, when confinement reinforcement was provided. Improvements
from the two types of confinement reinforcement were approximately the same.
13
Figure 2.3 - Confinement Examples – Priestley Plate (a), No. 3 Ties (b), Closed Wire Mesh (c), Seismic
Combs (d), Steel Ring Cages (e), Spiral Cages (f), Fiber Reinforced Grout (g)
14
Figure 2.4 - Details of Steel Confinement Plates and Seismic Combs (dimensions in in.)
Hervillard (2005) studied the effects of incorporating polymer fibers into the grout in masonry
prisms. Polypropylene fibers were mixed into the grout prior to grout placement in the masonry cells.
Fifteen specimens were constructed with CMUs, and an additional fifteen specimens were constructed
with hollow clay brick masonry. Two different fiber concentrations were utilized: 5 lbs/yd3 and 8
lbs/yd3. The prisms were tested under displacement control. It was found that strain-capacity
improvements from the addition of the fibers were comparable to results from previous studies using
other confinement methods. Strains at peak stress were 0.0019 for both concentrations of fibers in the
CMU prisms. This coincided well with the 0.0019 and 0.0020 strain values at peak stress for the
Priestley plates from previous studies. Strains at 50% peak stress were 0.0039 and 0.0047 for the 5- and
8-lb/yd3 fiber concentrations, respectively.
Strain values for confined concrete masonry at the three limit states of peak stress, 50% of peak
stress and 20% of peak stress from some of these previous studies are given in Table 2.1.
15
Table 2.1 – Strain Values for Confined Concrete Masonry
Peak stress
50% peak stress
20% peak stress
Concrete Masonry w/ Plates
Priestley and Elder
0.0020
0.0074
0.0120
Hart et al
0.0019
0.0065
0.0135
Malmquist
0.0023
0.0055
0.0122
Concrete Masonry w/ Combs
Hart et al
0.0016
0.0055
0.0140
Malmquist
0.0019
0.0060
0.0112
Concrete Masonry w/ Fibers in Grout - Hervillard
No fibers
0.0016
0.0032
0.0043
3
Fibers @ 5 lbs/yd
0.0019
0.0039
0.0071
Fibers @ 8 lbs/yd3
0.0019
0.0047
0.0073
Shing et al. (1993) compared the performance of masonry shear walls with seismic combs in the
toe regions to walls without any confinement. Differences in performance were small, with slight
increases observed in the peak load value and ultimate displacement, as seen in Figure 2.5. Priestley
(1981) tested reinforced masonry shear walls with confinement plates (Priestley plates) and compared
the results with similar walls without confinement. As illustrated in Figure 2.5, a slight improvement in
peak load was obtained along with a more substantial increase in the ultimate displacement for walls
with confinement.
Figure 2.5 – Comparisons of Confinement Techniques by Shing et al. (1993) and Priestley (1981)
16
Snook (2005) investigated various masonry confinement techniques in nine fully-grouted,
reinforced concrete masonry walls. Three confinement methods were used: Priestley plates, seismic
combs, and fibers added to the grout at 5-lb/yd3 and 8-lb/yd3 concentrations. Load-displacement
envelopes for Snook’s wall specimens are illustrated in Figure 2.6 where Walls 1 and 5 were unconfined,
Walls 2 and 6 utilized Priestley plates, Walls 3 and 7 had seismic combs, Walls 4 and 8 used polymer
fibers in the grout at the lower concentration, and Walls 5 and 9 contained polymer fibers in the grout at
the higher concentration.
Figure 2.6 – Load-Displacement Envelopes from Snook (2005)
Snook found that displacement ductilities varied from 4.1 for walls with no confinement to 7.3
for walls with fibers in the grout at 8 lbs/yd3. Snook concluded that confinement produced modest but
positive effects on seismic performance of the specimens. Performance improvements included
increased energy dissipation and enhanced displacement ductility. Seismic combs, when compared to
the Priestley plates, produced more consistent results through increased drift, ductility, and energy
dissipation. Walls that contained fiber reinforcement had the best overall seismic performance.
While these studies all show improvements in wall performance when the toe regions are
confined, the extent of the improvements varied and were, in most of the studies, relatively modest.
17
2.7
Banting and El-Dakhakhni (2012)
Four half-scale masonry walls with confined boundary elements were constructed and tested at
McMaster University’s Applied Dynamics Laboratory. Results were compared to an earlier study by
Shedid et al. (2010). The goal of the study was to evaluate existing and new reinforced masonry
construction techniques to advance a performance-based seismic design approach in the next cycle of
North American seismic design codes. Each wall specimen had overall dimensions of 1.8 m x 4.0 m (70.8
in. x 157 in.) resulting in an aspect ratio of 2.2. Variations between specimens included the intensity of
applied axial load, the presence of inter-story reinforced concrete floor slabs, and the presence of
confining boundary elements above the first story. The boundary elements were constructed with two
concrete masonry units (CMU) to enable the placement of four vertical reinforcing bars in two rows.
Confinement was provided by closed hoops at each course with employment of full grouting. This detail
is illustrated in Figure 2.7.
Figure 2.7 – Confining Boundary Element Detail by Banting and El-Dakhakhni (2012)
The provided confinement delayed buckling of the vertical reinforcement and reduced the rate
of strength degradation after the onset of toe crushing. Specimen W1 incorporated the boundary
element detail over the height of the wall, had an axial stress of 0.45 MPa (65.3 psi), a vertical
18
reinforcing ratio equal to 0.56%, and a horizontal reinforcing ratio of 0.30%. Specimen W2 had identical
parameters to Specimen W1 except the boundary element detail shown in Figure 2.7 terminated at the
first-story slab and transitioned to a single-block, flanged element with two vertical reinforcing bars.
Specimen W3 was similar to Specimen W1 except inter-story slabs were not incorporated. Specimen
W4 was identical to Specimen W1 but the axial stress was increased to 1.34 MPa (194 psi). Vertical
reinforcement was continuous up the height of each wall except in Specimen W2 where the two interior
bars of the boundary element were curtailed with 90 degree hooks into the first story slab. Table 2.2
summarizes test results for the four walls.
Specimen
Table 2.2 – Test Results (Banting and El-Dakhakhni, 2012)
Δy,test (mm, in.)
Δ%,y
Qpeak (kN, kip) Δu (mm, in.)*
Δ%,u
μΔu
W1
10.1, 0.40
0.25
143, 32.1
135, 5.31
3.38
12.0
W2
13.2, 0.52
0.33
125, 28.2
103, 4.05
2.58
8.1
W3
9.8, 0.39
0.25
141, 31.7
128, 5.04
3.21
15.2
W4
11.0, 0.43
0.28
203, 45.1
86, 3.39
2.16
6.6
* Average of values gathered visually from Figure 12 (Banting and El-Dakhakhni, 2012)
The researchers concluded that the confined boundary elements provided resistance against
buckling of the vertical reinforcement and that the appearance of face-shell spalling did not indicate
imminent failure. Significant drifts at failure were obtained as a result. The chosen hoop spacing
offered minimal resistance to lateral buckling of the vertical reinforcement and suggested that increased
resilience in the compression toes could be obtained by decreasing the hoop spacing.
Compared to Wall W3, the floor slabs in Wall W1 hindered the propagation of shear cracking
above the first-story slab and inhibited the extent of inelastic curvature (Banting and El-Dakhakhni,
2012). In Specimen W2, a second hinge formed above the first-story slab and allowed further crack
propagation above the first-story slab elevation. As a result, lateral load resistance diminished but
ultimate drifts still reached 2.7%. Axial stress caused Wall W4 to experience shear cracking through the
first-story slab and into the second-story wall panel.
19
The authors concluded that the cracking pattern in a wall is influenced by the presence and
detailing of inter-story slabs, loading conditions on the wall, and the height of plasticity. Furthermore,
all walls showed that plastic hinging extended to a height lower than flexural cracking and, in-turn, a
height lower than shear cracking. Maximum plastic hinge lengths ranged from 77.5% of the wall length
in Wall W4 to 123.3% in Wall W2.
As intended by the researchers, walls in the study were governed mostly by flexural
deformations; however, shear contributions indicated that it should be considered during analysis.
Sliding displacements were small relative to the shear and flexure displacements.
2.8
Shedid et al. (2010)
Shedid, El-Dakhakhni, and Drysdale (2010) designed and tested seven two- and three-story
reinforced masonry shear walls. The researchers employed half-scale units. Varied parameters included
the aspect ratio which ranged between 2.2 and 1.5, vertical and horizontal reinforcing ratios, the
amount of applied axial stress, and the reinforcement detailing illustrated in Figure 2.8. All walls had a
length of 180 cm (70.9 in.).
Figure 2.8 – Wall Details (Shedid et al., 2010)
The walls were built in two phases. Phase I included the three-story-high walls, and Phase II
included the two-story-high walls. Walls in each phase had identical axial load and were designed to
20
have the same lateral load resistance at the point of reaching the critical masonry strain. Flanged walls
with boundary elements were designed to have the same lateral resistance as the rectangular walls. In
doing so, the amount of vertical reinforcement was reduced by 43%. The three-story walls in Phase I
employed three 100-mm thick (3.94-in.) reinforced concrete slabs and the two-story walls in Phase II
had two reinforced concrete slabs.
The specimens were loaded cyclically at the top level to produce cantilever shear wall action.
Vertical reinforcement was welded directly to the stiff steel loading beam to simulate diaphragm action.
Axial load was applied by two hydraulic jacks attached to high-strength prestressing rods. These rods
were anchored to a steel beam that spanned over the top of the wall, orthogonal to the lateral loading
direction. Potentiometers measured local displacements at the surface of each specimen. Electronic
strain gages were epoxied to reinforcing steel before construction.
Load resistance and the corresponding displacement for initial yield, peak load, and 20% peakload degradation are presented in Table 2.3. Displacement ductility at 20% peak-load degradation is
also provided in Table 2.3. The researchers found that the experimental results corresponded well with
predicted values obtained using the 2008 MSJC. Material and strength reduction factors were not
employed in the calculations. Also, compression reinforcement was utilized because a previous study by
Shedid et al. (2008) showed that the inclusion of compression reinforcement in capacity predictions
provided better correlation with experimental results.
Table 2.3 – Load, Displacement, and Ultimate Ductility Results (Shedid et al., 2010)
Qy (kN, kip)
Δy (mm, in.)
Qu (kN, kip)
Δu (mm, in.)
W1
105 23.6
8.5 0.33
179 40.2
25.2 0.99
144 32.3
46.5 1.83
5.5
W2
122 27.4
10.5 0.41
153 34.4
31.5 1.24
125 28.1
69.0 2.72
6.6
W3
108 24.3
9.2 0.36
150 33.7
36.0 1.42
122 27.4
94.0 3.70
10.2
W4
161 36.2
3.5 0.14
266 59.8
13.3 0.52
214 48.1
27.5 1.08
7.9
W5
184 41.4
5.0 0.20
242 54.4
19.9 0.78
195 43.7
43.5 1.71
8.7
W6
171 38.4
4.0 0.16
238 53.5
24.1 0.95
192 43.2
54.5 2.15
13.7
W7
179 40.2
5.0 0.20
241 54.2
20.1 0.79
195 43.7
64.5 2.54
12.9
Phase II
Phase I
Specimen
21
Q0.8u (kN, kip) Δ0.8u (mm, in.)
μΔ0.8u
Wall drifts in each phase were very similar up to first yield and indicated end-wall confinement
had little effect on the initial stiffness. However, ductility at 20% load degradation from peak load was
augmented by the confinement. The increase in ductility is significant because elements that employ
similar detailing could be designed for a lower seismic force (via an increase in the seismic force
reduction factor). The researchers found that for walls W1 and W4 the idealized displacement ductility
at 80% of peak load produced a response modification factor that was 50% greater than the value
assumed in the Canadian code. Minimum idealized displacement ductility values at 20% load
degradation of 3.0 and 4.6 were reported for Walls W1 and W4, respectively.
Aspect ratio was investigated by normalizing the wall displacements for walls with identical
cross-sectional properties. The researchers found that the normalized load-displacement relationships
were nearly identical despite a difference in aspect ratio of 0.7. They concluded that the cross-sectional
properties may significantly affect wall response more than wall height and that the plastic hinge length
is more a function of the wall length than wall height.
2.9
Kapoi (2012)
Kapoi (2012) tested eight, full-scale, unconfined reinforced concrete masonry shear walls at the
Composite Materials Engineering Laboratory at Washington State University. Two of these walls were
similar to two walls in the current study (Walls C7 and C8) and are briefly discussed here. Results from
these walls will be used in later comparisons. Walls C7 and C8, shown in Figure 2.9, had No. 6 vertical
reinforcing bars concentrated at the ends in addition to a single No. 4 vertical reinforcing bar at midlength. The concentrated reinforcement at the ends is commonly referred to as jamb reinforcement.
Vertical bars were oriented in two rows with each row containing two bars. Both walls had an aspect
ratio of 2.0 and contained two No. 3 horizontal reinforcing bars spaced 8 in. vertically. The horizontal
reinforcing bars had 180-degree hooks on both ends that fully engaged the extreme vertical steel. Wall
22
C7 had zero axial stress and Wall C8 had an axial stress of 0.0625f’m. Lateral load was applied at a rate of
0.03 in./min by a 220-kip hydraulic actuator operated under displacement control. The axial load on
Wall C8 was applied by three identical hydraulic jacks operated under pressure control. Kapoi also
tested a wall with evenly distributed vertical reinforcement (Wall C6) to compare with Wall C7 with the
jamb reinforcement.
Figure 2.9 - Walls C7 and C8 Reinforcement Detail (Kapoi, 2012)
Kapoi concluded that the performance of the Wall C7 was very similar when compared to Wall
C6. Similar displacement ductilities were observed between the two walls; however, Wall C7 dissipated
50% more energy than Wall C6. This increased energy dissipation in Wall C7 was attributed to the
location of the vertical steel and to a slightly larger vertical reinforcing ratio. The applied axial load on
Wall C8 improved the peak load resistance by 10- to 15-kips when compared to that for Wall C7. The
ultimate drifts at 20% load degradation were similar for the two specimens.
2.10
Summary
This chapter provided a review of current literature pertaining to masonry walls and confined
boundary elements. Different masonry shear wall failure modes were discussed. To ensure a ductile
response, walls should generally be designed to produce a flexural failure. A discussion of issues relating
to ductility was given. Provisions in the 2011 MSJC and 2011 ACI 318-11 Codes for shear walls and
boundary element design were presented. Previous investigations of confinement methods in masonry
to improved strain capacity and ductility were discussed. Current studies of half- and full-scale CMU
23
shear walls with boundary elements and special jamb steel were reviewed. Finally, a previous study that
investigated the behavior of masonry walls that were similar to some of the walls in this study, but
without confined boundary elements, was briefly discussed.
24
CHAPTER 3
EXPERIMENTAL PROGRAM
3.1
Introduction
The following chapter provides information on the design, construction, instrumentation and
testing protocol for the four wall specimens of this study.
3.2
Footings
Two types of heavily reinforced concrete footings were constructed to secure each specimen to
a laboratory strong floor via high-strength threaded rods. These rods passed through 2-in. diameter PVC
tubes, cast into each footing, which acted to prevent sliding and rocking of the specimens during testing.
Each footing had a length of 86 in. and a height of 18 in. Two footings were rectangular in form and had
a width of 24 in. The other two footings incorporated flanges on each end when viewed from the top.
The width of the footing web was 26 in. and the width of the flange portions was 40 in. All footings
contained twelve No. 7 bars for longitudinal reinforcement that ran the length of the footing. These
longitudinal bars were confined by No. 4 closed hoops and crossties spaced at 4 in. on center. The
footings with flanges had an additional rebar cage on each end that ran transverse through the
longitudinal cage to reinforce the flanged portions of the footing. These cages utilized twelve No. 7 bars
for longitudinal reinforcement and No. 4 closed hoops and crossties spaced at 8 in. on center. Four No.
4 U-shaped bars were embedded as lifting hooks in the footings, one in each corner. All reinforcement
was Grade 60. An illustration of a flanged footing is provided in Figure 3.1.
25
Figure 3.1 – Flanged Footing Details
3.3
Wall Specimens
Each wall specimen included a middle section that was constructed of 8x8x16-in. concrete
masonry units (CMUs). The units were placed in running bond and were fully grouted. The walls also
included a reinforced concrete boundary element at each end. The boundary elements were integrally
connected to the masonry wall section using two No. 3 horizontal reinforcing bars spaced at 8 in. on
center over the wall height. Two specimens had rectangular boundary elements, and two specimens had
boundary elements with wall returns. Cross sections of the two wall configurations investigated in this
study are presented in Figure 3.2.
All specimens had the same height to the point of horizontal load application (HLA) and wall
length (LW) of 112 in. and 56 in., respectively. This provided an approximate wall aspect ratio of 2.0 for
all specimens. Specimen BE-2 was the only specimen with axial stress, which was equal to 0.0625*f’m.
The vertical reinforcement was the same in each specimen, consisting of four No. 6 bars at each end and
26
a single No. 4 bar placed in the middle of the wall. All vertical reinforcement was continuous from the
footing to the loading beam thereby eliminating the need for lap splices in these bars.
Figure 3.2 – Specimen Reinforcement Layout: Rectangular Boundary Element for Specimens BE-1 and
BE-2 (top) and Boundary Element with Return for Specimens BE-3 and BE-4 (bottom)
Specimens BE-3 and BE-4 had boundary elements with wall returns. Therefore, in addition to
the four No. 6 flexural reinforcing bars, four No. 3 bars were provided at each wall end. Horizontal
reinforcement was provided using No. 3 bars spaced 8 in. on center over the wall height. The horizontal
bars had 180-degree hooks at each end that engaged the two extreme No. 6 vertical reinforcing bars.
This arrangement of horizontal reinforcement was determined to provide sufficient shear capacity to
produce a flexural response in the specimens.
27
The potential for sliding between the masonry wall section and the concrete boundary elements
was evaluated using ACI 318-11 (2011) Section 17.5 for horizontal shear strength of composite
members. Two cases were checked to determine an envelope of available shear strength. The actual
value of the shear capacity across the interface will be somewhere between the lower and upper
bounds. The upper bound was calculated assuming an intentionally roughened surface of
approximately ¼ in. The capacity-to-demand ratio for this scenario was 11.0 to 1. The lower bound was
determined assuming clean surfaces without intentional roughening. This scenario resulted in a
capacity-to-demand ratio of approximately 1.25. Thus, it was determined that the two No. 3 horizontal
bars would be adequate to prevent sliding at the interface.
The reinforcement and dimensions of the boundary elements were chosen to allow
comparisons of these masonry walls with integral concrete boundary elements with the masonry walls
tested in a previous study by Kapoi (2012) and to be consistent with the CMU thickness used in the
masonry sections of the walls.
The MSJC Code (2011) does not provide prescriptive detailing provisions for the design of
masonry boundary elements. Therefore, the provisions given in Section 21.9.6 of the ACI 318-11 Code
(2011) for boundary elements in concrete structural walls were utilized to design the boundary elements
in this study. Transverse reinforcement requirements were based on ACI Section 21.9.6.4(c). The
transverse hoop spacing was controlled by the requirement that the spacing not exceed one-third of the
least dimension of the boundary element. For both types of boundary elements in this study, the least
dimension was 7.625 in. Therefore, the maximum hoop spacing was 2.54 in., and a 2.5-in. spacing was
specified for the transverse reinforcement in the boundary elements of the wall specimens.
Grade 60, No. 3 transverse hoops spaced at 2.5-in. on center provide an area of reinforcement
that exceeds that required by Equation 2.4. These hoops were provided in the boundary elements of
Specimens BE-1, BE-2 and BE-3.
In order to simultaneously match the maximum hoop spacing
28
requirement and the required area of transverse reinforcement, a smaller bar size was evaluated. ¼-in.
diameter hot rolled round (HRR) A36 wire at a spacing of 2.5-in. on center was determined to satisfy
both requirements. These hoops were used in the boundary elements of Specimen BE-4. Specimens BE1 and BE-2 incorporated No. 3 rectangular hoops in the rectangular boundary elements in these
specimens. Specimen BE-3, with flanged boundary elements, had No. 3 rectangular hoops aligned in the
plane of the wall confining the four No. 6 bars, and No. 3 rectangular hoops aligned transverse to the
wall confining the four No. 3 bars. Specimen BE-4, also with flanged boundary elements, had ¼-in.
diameter HRR wire rectangular hoops in plane confining the four No. 6 bars, and ¼-in. diameter HRR
rectangular hoops aligned transverse to the wall confining the four No. 3 bars (Figure 3.2). For all
specimens, the vertical spacing of the hoops in the boundary elements was 2.5 in. on center. The
boundary element constructed using the smaller diameter HRR wire resulted in reduced rebar
congestion, thereby augmenting the flow of concrete into the boundary elements. The HRR hoops also
reduced material costs and were easier to fabricate. All confining hoops were continued into the
footing 12 in. per ACI-318 Section 21.9.6.4(d) (2011).
Details of the four test specimens evaluated in this study are summarized in Table 3.1. A typical
specimen incorporating the footing, the masonry wall with integral confined concrete boundary
elements, and the loading beam is illustrated in Figure 3.3.
Table 3.1 – Specimen Details
Wall
LW,
Specimen (in.)*
BE-1
56
BE-2
56
BE-3
56
BE-4
56
HLA,
(in.)
112
112
112
112
Aspect
Flexural
P/(f'mAg)
Shear Reinf.
Hoop Reinf.
Ratio
Reinf.
2.0
0
8 #6
2 #3 @ 8 in.
#3 @ 2.5 in.
2.0
0.0625
8 #6
2 #3 @ 8 in.
#3 @ 2.5 in.
2.0
0
8 #6
2 #3 @ 8 in.
#3 @ 2.5 in.
2.0
0
8 #6
2 #3 @ 8 in. ¼-in. HRR @ 2.5 in.
* Nominal value
29
Load Beam
HLA
Footing
Figure 3.3 – Typical Wall Specimen
3.4
Loading Beams
A reinforced loading beam was constructed at the top of each specimen. The dimensions of the
four beams were 60 in. long by 12 in. wide with a depth of 16 in. The beams were cast in place using
concrete with a specified compressive strength of 4000 psi. Reinforcement in the loading beam
consisted of six No. 5 bars enclosed by No. 4 closed hoops and cross ties. The vertical reinforcement
within each wall specimen extended into the loading beam to provide a positive load-transfer
mechanism from the beam to the specimen.
30
3.5
Material Properties
The masonry blocks used for construction were 8x8x16-in. (nominal) standard CMUs and 8x8x8-
in (nominal) half-block CMUs. All blocks were cut into bond beams by professional masons. The end
walls of the blocks were specially notched to accommodate the two horizontal bars that extended
beyond the masonry portion of the wall (see Figure 3.4).
Figure 3.4 – Grout Dam Detail
Three standard blocks were set aside during construction, capped with gypsum cement, and
tested per ASTM C140-11. Mortar conforming to ASTM C270 Type S was used for wall construction and
was mixed on location by the masons. Three 2-in. diamter by 4-in. high mortar test cylinders were
prepared, cured in a lime-saturated water bath, and later tested according to ASTM C780-11. The grout
was an eight-sack mix with only fine aggregate and complied with ASTM C476-10. Three grout prisms
were made during construction, cured in the water bath, capped with gypsum cement, and tested
according to ASTM C1019-11. Three two-block masonry prisms were constructed by the masons, stored
in a water-tight bag, capped with gypsum cement, and tested per ASTM C1314. Three concrete test
cylinders were made the day of the boundary element pour, cured in the water bath, and tested per
ASTM C39. The average compressive strength for each material is presented in Table 3.2.
31
Table 3.2 – Average Material Compressive Strengths, psi
Masonry Units Mortara Grouta Masonry Prismsa Concreteb
3,460
2,880
5,970
2,300
5,030
a
Approximate age of 150 days
Approximate age of 75 days
Note: Samples were tested during wall testing
b
All reinforcement was specified as Grade 60 with the exception of the ¼-in. diameter HRR wire
which was only available in A36. Yield values for the Grade 60 bars, as given in Table 3.3, were obtained
from mill reports provided by the manufacturer. The listed yield value for the HRR wire was
determined through tension tests.
Table 3.3 – Reinforcement Yield Strengths, ksi
Bar Size
1/4 –in. HRR
No. 3
No. 4
Yield Strength
52.0
64.0
69.5
3.6
No. 6
67.5
Wall Specimen Construction
The wall specimens were constructed at the Composite Material and Engineering Center at
Washington State University in Pullman, Washington. Footing cages were tied and placed into wooden
forms. The full-height vertical bars were placed into the footing cage along with the lifting hooks and
PVC tubes. The vertical reinforcement in walls was protected with masking tape to minimize concrete
splatter during the pour. Concrete ordered from a local ready-mix supplier was poured into the footing
forms and consolidated with a vibrator. The top surface of the footings was finished with a trowel, and
the wall-footprint areas were intentionally roughened to increase shear friction at the wall-footing
interface. Strain gages and their wires were protected during the pour to ensure functionality during
testing. The wood forms were removed within 24 hours of the pour. The stages of footing construction
are shown in Figure 3.5.
32
33
Figure 3.5 – Footing Construction – Clockwise from top left: Cage Tying, Cage and Formwork Prior to
Pour, Poured Footing, Finished Footing
Professional masons from Anderson Masonry Inc. of Spokane Valley, WA constructed the
masonry sections of the four specimens on November 30, 2011. The masonry sections were grouted in
one lift on December 1, 2011. CMU clean-outs were utilized per MSJC Section 3.2 F (2011). Boundary
element confining hoops were placed during the masonry construction according to a particular
sequence. First, the appropriate number of boundary element hoops were lowered over the extreme
vertical reinforcement and tied at a later date. Next, a masonry course was laid on full mortar bedding.
Lastly, horizontal reinforcement was correctly oriented, lowered over the vertical reinforcement, and
placed into the CMU slots. This process was repeated until the target wall height was reached as
depicted in Figure 3.6.
(a)
(b)
(c)
(d)
(e)
Figure 3.6 – CMU Construction Sequence: (a) Footing and Existing Reinf., (b) Add boundary element
steel and CMU Couse, (c) Add Horizontal Reinf., (d) Add boundary element steel and CMU course, (e)
Add Horizontal Reinf.
Once the CMUs were placed, plywood forms were carefully positioned at each end of the
masonry to ensure grout fluid pressures did not damage the masonry during the lift. The CMUs were
fully grouted using a vibrator to consolidate the grout. Slight shrinkage of the grout provided a 0.5- to
1.0-in. key at the top of the walls to provide improved connection with the loading beam.
After the masonry construction was complete, the boundary element hoops were placed at the
correct spacing and tied to the vertical reinforcement. Walls at this stage are shown in Figure 3.7.
34
35
Figure 3.7 – Construction Prior to Boundary Element Formwork – From left to right: CMU and
Boundary Element Interface, Boundary Element with Returns, Specimens BE-1, BE-2, and BE-3
Forms were designed and constructed for the boundary element concrete pour. 4000 psi
concrete with 3/8-in. maximum size aggregate and superplasticizers was ordered from a local pre-mix
plant. The concrete was conveyed via a boom-pumper truck, placed into the top of the formwork, and
consolidated with a concrete vibrator. The top surface of the concrete was roughly finished to improve
the connection with the loading beam concrete. This phase of specimen construction is depicted in
Figure 3.8.
Once the formwork was stripped from the walls, construction of the loading beams was started.
Formwork was secured on top of the walls, and the load beam rebar cages were secured to the existing
vertical steel. Again, 4000 psi concrete was supplied by a local ready-mix plant, placed into the loading
beam formwork, consolidated with a concrete vibrator, and finished smooth with a trowel. After curing,
the forms were removed and the specimens were painted white to aid in crack detection during testing.
36
37
Figure 3.8 – Boundary Element Construction – Clockwise from top left: Boundary Element Formwork
Erection, Boundary Element Prior to Concrete Pour, Concrete Placement, Competed Pour
3.7
Test Setup
Each wall specimen was designed with a fixed base to represent a cantilever shear wall. The
footings were anchored to a reaction floor with 1.25-in. diameter steel all-thread bars. Bracing plates
were fastened to the reaction floor at each end of the footing to prevent sliding.
Three identical hydraulic jacks provided the axial load for Specimen BE-2. Each jack has a rated
capacity of 10,000 psi, corresponding to 120 kips of applied force per jack. The jacks were connected in
parallel to maintain equal pressure to each jack. The hydraulic pressure was maintained at a constant
level during testing ensuring the specified axial load remained constant as the three actuators extended
and retracted with the vertical wall deflection. The upward force from these actuators was resisted by a
spreader beam attached to a low-friction trolley system. The trolley was free to move along the main
reaction frame as the specimen was displaced laterally. As a result of this setup, the axial load jacks
were able to move with the specimen while maintaining a constant axial load. This created a free
boundary condition at the top of the wall that created cantilever action in the specimen.
In-plane loading was applied to the specimens using a 220-kip capacity hydraulic actuator
operated under displacement control. The actuator was connected to the main reaction frame and to a
steel end-plate on the north end of each specimen’s loading beam. Lateral load was transferred to each
specimen through two steel end-plates that were affixed to the ends of the loading beam. These steel
plates were coupled together via high-strength steel rods which transferred the load to the south plate
during the pull strokes. The test setup is illustrated in Figure 3.9.
38
Figure 3.9 – Testing Apparatus
3.8
Specimen Instrumentation
Strain gages, displacement potentiometers, a load cell, and a dial gage were utilized during
testing to monitor and acquire data. Two strain gages were placed on the extreme vertical reinforcing
bars 8 in. below the footing surface. Three strain gages were placed at the top of the footing on the
extreme vertical reinforcing bars. Three additional strain gages were placed on these bars at heights of
8, 16, and 24 in. Three other vertical reinforcing bars had strain gages located at the footing/wall
interface. Strain gages were also placed on the horizontal bars located at the first and fifth masonry
course levels. Strain gage locations are depicted in Figure 3.10.
39
Figure 3.10 – Specimen Instrumentation: Displacement Potentiometers (Left) and Strain Gages (Right)
Displacement potentiometer locations are also shown in Figure 3.10. Potentiometer locations
were the same for the four specimens. The potentiometers measured the vertical, sliding, and shear
displacements at numerous locations on each specimen. Located at the same elevation as the applied
load, Potentiometer 18 measured the global displacement of the specimens in the direction of loading.
Test frame deflections did not influence this potentiometer because it was secured to a rigid frame
independent of the test frame. A load cell attached to the 220-kip hydraulic actuator measured the
applied in-plane lateral load. Another displacement instrument measured the actuator’s displacement
as part of the loading system’s feedback loop. Potentiometers 15 and 16 were placed at the masonry
40
and boundary element interface to measure slip between the two materials. A dial gage was employed
to measure any sliding between the footing and reaction floor.
3.9
System Control & Data Acquisition
Two computers were utilized for each test. One computer was used to control the lateral
loading by sending a specified load or displacement command to the hydraulic controller attached to
the actuator. This computer also received a feedback signal from the controller to maintain the
specified displacement rate. The second computer was used for data acquisition and recorded
instrument readings every second for the duration of each test. Data scanning was accomplished with
Vishay 5100B scanners. The load application system and data acquisition system computers and the
signal path between the various components are shown in Figure 3.11.
Figure 3.11 – Load Application & Data Acquisition Flow Chart (adapted from Sherman, 2011)
3.10
Test Procedures
The specimens were tested under displacement control. The moment-curvature relationship for
each specimen was determined using the cross-sectional analysis software program XTRACT. The
maximum moment obtained from XTRACT was divided by HLA to obtain the expected peak lateral load.
A flexural failure was expected to occur after reaching this load.
41
Each test regimen consisted of two tests – a preliminary test and a primary test. The preliminary
test protocol consisted of two complete actuator cycles (both negative and positive directions) at loads
corresponding to 20%, 50%, and 75% of the expected peak load determined from the XTRACT analysis.
The specimens were displaced at a rate of 0.3 in./min. using a servo controller feedback. The
preliminary cyclic loading protocol is illustrated in Figure 3.12. Displacements recorded at the 75% peak
load were averaged and used to linearly extrapolate a value for delta-Y (ΔY), where ΔY is the predicted
displacement at specimen yield.
The primary test protocol consisted of two complete cycles (both negative and positive
directions) of displacements at increasing multiples of ΔY. The primary test protocol used in this study is
presented in Figure 3.13. Specimen displacements were sequentially increased until the in-plane-lateral
load was reduced to 50% of the previously recorded maximum in-plane load or until loss of structural
integrity of the specimen, whichever occurred first. Each specimen was displaced at a rate of 0.3
in./min. through 3ΔY, and then displaced at 0.5 in./min. beginning at the first 4ΔY cycle. This higher load
rate was maintained through test completion.
100
75
% of Peak Load
50
25
0
-25
-50
-75
-100
0
1
2
3
Cycle #
4
5
6
Figure 3.12 – Preliminary Test Loading Protocol
42
10
8
6
4
ΔY
2
0
-2
-4
-6
-8
-10
0
1
2
3
4
5
6
Cycle #
7
8
9
Figure 3.13 – Primary Test Loading Protocol
43
10
11
12
CHAPTER 4
TEST RESULTS
4.1
Introduction
This chapter presents test results for the four masonry walls with integral confined concrete
boundary elements of this study. Test observations, load-displacement hysteresis plots, decoupled drift
components, wall curvatures, displacement ductility, curvature ductility, height of plasticity, equivalent
plastic hinge length, energy dissipation, and hysteretic damping are provided for each specimen.
4.2
Specimen BE-1
Specimen BE-1 had a wall aspect ratio of 2.0, four confined No. 6 vertical reinforcing bars
located at the ends of the wall and one No. 4 vertical bar located at mid-length, two No. 3 horizontal
bars spaced at 8 in. on center over the height of the wall, and zero axial load. Confinement of the No. 6
vertical bars at the ends of the wall was provided by No. 3 closed hoops. All vertical reinforcement was
developed in the footing and was continuous throughout the wall height. Using the program XTRACT,
the predicted maximum lateral load capacity for Specimen BE-1 was 65.7 kips. The horizontal
reinforcement yielded during testing in both the first and fifth courses. Yielding of the extreme vertical
reinforcement penetrated into the footing of Specimen BE-1.
Test Observations:
A yield displacement (ΔY) of 0.94 in. for Specimen BE-1 was determined from the preliminary
test. Shear and flexure cracks were observed during the first cycle to 50% of the predicted maximum
load during the preliminary test. Once the preliminary test was complete, the specimen was then
displaced to ±1, 2, 3, 4, and 6 times ΔY for the primary test. Existing shear and flexure cracks continued
44
to propagate and increase in size, and additional cracks formed as the displacement levels increased.
Crushing and vertical splitting of the extreme concrete cover appeared at 3ΔY in both the north and
south toes with significant spalling occurring during loading to 6ΔY. Out-of-plane buckling of the toe
regions was observed during the second cycle of 6ΔY. The second 6ΔY push-stroke target displacement
was not attained due to rapid degradation in load capacity and specimen instability. After reversal of
loading direction, the second 6ΔY target displacement was reached during the pull stroke. The test was
terminated prior to reaching zero displacement due to specimen instability. These and additional test
observations and the associated load and displacement values are presented in Table 4.1. Post-test
photographs of the entire specimen, out-of-plane failure, and the south and north toes are shown in
Figures 4.1, 4.2 and 4.3 respectively.
Load (kips)
-33.3
32.7
33.3
-34.3
-38.8
40.0
-56.6
53.6
Disp. (in.)
-0.37
0.32
0.33
-0.40
-0.46
0.45
-1.12
1.12
-66.1
66.0
69.4
-70.7
-56.6b
55.5b
-2.81
2.81
3.75
-5.62
-5.62
5.59
a
b
Table 4.1 - Specimen BE-1: Test Observations
Test Observation
Flexure and shear cracking (push)a
Critical concrete strain (εcu=0.003) in north toe (pull)
Flexure and shear cracking (pull)a
Critical concrete strain (εcu=0.003) in south toe (push)
1st Yield of extreme vertical reinforcement bar in north toe (push)
1st Yield of extreme vertical reinforcement bar in south toe (pull)
1% drift in push to south
1% drift in pull to north
Onset of toe crushing in south toe (push)a
Onset of toe crushing in north toe (pull)a
Maximum load resistance in pull to north
Maximum load resistance in push to south
20% load degradation from the maximum load resistance in push to south
20% load degradation from the maximum load resistance in pull to north
Denotes visual observation
Calculated value
45
Figure 4.1 – Specimen BE-1 Following Testing
Figure 4.2 – Specimen BE-1 Following Testing:
Out-of-Plane Failure
Figure 4.3 – Specimen BE-1 Following Testing: South Toe (Left) and North Toe (Right)
46
Load-Displacement:
The load-displacement hysteresis curves for the combined preliminary and primary tests for
Specimen BE-1 are provided in Figure 4.4. Six major events were identified following testing, including
reaching the critical concrete strain (εcu = 0.003), first yielding of the extreme vertical reinforcement (εy =
0.00233), attainment of 1% wall drift, the maximum load resistance, the onset of toe crushing, and
failure of the specimen which was defined as 20% degradation in the maximum load resistance. The
average concrete strain was calculated by dividing the measured displacements by the 8-in. gage length
of the bottom string potentiometer at each end of the specimen. Strain gages secured directly to the
vertical reinforcement provided strain readings during testing. One percent drift was determined by
dividing the measured global displacement by the height to the point of load application. The maximum
load resistance was obtained from a load cell attached to the load actuator. The onset of toe crushing
was determined visually during the test. Twenty percent load degradation was defined as the point
following attainment of the maximum lateral load when the load resistance degraded to 80% of the
recorded maximum load resistance for a given loading direction. In the case when 20% load
degradation was reached during the second cycle at a given displacement level, the ultimate
displacement was defined as the peak value associated with that target displacement level.
47
100.0
εcu = 0.003
εy = 0.00233
80.0
1% Drift
Max. Load
Toe Crushing
20% Load Deg.
60.0
Load (kips)
40.0
20.0
Push South
0.0
Pull North
-20.0
-40.0
-60.0
-80.0
-100.0
-8
-6
-4
-2
0
2
4
6
8
Displacement (in.)
Figure 4.4 – Specimen BE-1: Load Displacement Hysteresis
Decoupled Drift Components:
Flexure, shear, and sliding deformations all contributed to the measured total wall
displacement, and determination of their individual components is explained in the following section.
Total displacement was measured with a string potentiometer attached to an external reference frame.
Sliding displacement was measured by two string potentiometers located at the wall-footing interface.
The average of these two readings was considered the sliding deformation component of drift. Sliding
displacements were also measured between the loading beam and the wall and at the interface of the
masonry and concrete boundary elements, but these displacements were very small and deemed
insignificant for each specimen.
48
Shear deformations were calculated using the approach presented by Massone and Wallace
(2004). Two vertically- and two diagonally-oriented string potentiometers were positioned on the
specimen to record the vertical and diagonal displacements of an ‘X’ pattern.
Figure 4.5 – Massone and Wallace (2004): Flexure and Shear Deformations
The distorted ‘X’ pattern is illustrated in Figure 4.5 where the dashed lines represent the undeformed
pattern, the light grey parallelogram represents the shear contribution of displacement, and the solid
black lines represent the combination of shear and flexural displacement. Equation 4.1 is derived from
Figure 4.5.
√
√
(
)(
)
Massone and Wallace (2004) defined α as a distance factor from the top of the wall to the center of
rotation. In both their study and this one, α was assumed to be 0.67, locating the center of rotation at
1/3 of the wall height above the footing. The first term of Equation 4.1 represents deformations due to
the combined shear and flexure deformations of the ‘X’ pattern. The second term represents the flexure
deformations of the pattern and allows for the determination of shear displacements after subtraction
from the first term.
49
Once the average shear displacements were determined by Equation 4.1, the global flexure
displacements were found by subtracting the average shear and sliding displacements from the total
displacements. The decoupled drift components are presented in Figure 4.6. Due to cracking in the wall
leading to pullout of the instrumentation anchorage, invalid potentiometer readings in the ‘X’ pattern
occurred during the 6ΔY cycle, and therefore only the shear and flexure displacements through 4ΔY are
shown in Figure 4.6.
Drift was defined as the in-plane displacement measured at the point of load application divided
by the height to the load application, given as a percentage. The averages for flexure, shear, and sliding
drift components as a percentage of the total drift for the three limit states of critical concrete strain,
peak load, and failure are presented in Table 4.2. Shear and flexure drift components reported for the
peak load in the north direction use the last valid potentiometer readings which actually occurred prior
to the peak load in the north direction. Shear and flexure drift components at failure utilize the last
valid reading from the X pattern for both directions.
Table 4.2 Specimen BE-1: Component Percentages of Total Drift
Limit State Total Drift (%) Sliding (% Total) Shear (% Total) Flexure (% Total)
εcu
0.4
1.8
13.6
84.7
a
Peak Load
4.2
8.85
27.5
63.6a
b
Failure
5.0
9.95
23.7
64.8b
a
b
Value utilizes last reliable potentiometer reading for north direction
Value utilizes last reliable potentiometer readings
50
51
Figure 4.6 – Specimen BE-1: Displacement Components
Wall Curvatures:
Curvatures over the height of the wall were determined based on the calculated strain profiles
obtained using four potentiometers placed along the extreme edges of the wall (mirrored on both sides)
for the first cycle at each displacement level of the primary test only. Readings from the potentiometers
were converted to average strain values and assigned at mid-height of the given gage length.
Calculations utilized Equation 4.2 and were based on the assumption that plane sections remain plane
across the specimen cross section.
|
|
|
|
(Eqn. 4.2)
Where:
φ
= wall curvature at a given cross section (in.-1);
ΔT,C
= measured tensile and compressive displacements (in.);
LGAGE = applicable gage length (in.); and
DGAGES = in-plane distance between gages (in.).
A plot of curvature over the wall height of Specimen BE-1 is shown in Figure 4.7. Curvatures
were asymmetrical for the duration of the test. Potentiometers one and two appeared to provide
questionable displacement results; however, checks of these instruments pre- and post-test indicated
no noticeable problems. The ultimate curvature was defined at the first cycle of 3ΔY for both loading
directions instead of 20% load degradation because of invalid potentiometer readings during the 4ΔY
cycle. Thus, the reported ultimate curvature is a lower-bound value of the actual ultimate curvature.
Curvature values decreased at a height of 20 in. but increased at 32 in. Cracking extended the full height
of the wall and allowed for curvatures at higher wall elevations. Therefore, the calculated curvature
results and the cracking observed during the test suggest that curvatures extended higher than the
region of the wall covered by the instrumentation.
52
36
1Δ
2Δ
3Δ
4Δ
20% Load Deg.
32
28
Wall Height (in.)
24
20
16
12
8
4
Push South
0
-0.005
Pull North
-0.003
-0.001
0.001
0.003
0.005
Curvature (in.-1)
Figure 4.7 – Specimen BE-1: Wall Curvature
Displacement and Curvature Ductility:
Displacement ductility was determined based on establishing equal areas under both an
elastoplastic approximation and the measured load-displacement envelope, as shown in Figure 4.8. The
load-displacement envelope was constructed with the peak loads and displacements from the first cycle
at each displacement level of the preliminary and primary tests. The displacement ductility is defined
as:
(Eqn. 4.3)
Where:
53
μΔ
= displacement ductility;
Δu
= ultimate displacement at test termination or 20% load degradation (in.); and
Δy
= yield displacement of elastoplastic approximation (in.).
Figure 4.8 – Elastoplastic Approximation
The ultimate displacement was defined as the displacement at 20% load degradation of the
peak load or, for the case where 20% load degradation occurred during the second cycle of
displacement, as the peak displacement achieved during testing. The yield displacement was defined as
the intersection of the secant stiffness through the origin and initial extreme tensile reinforcement yield
point, and the yield force of the elastoplastic approximation. The elastoplastic yield force was defined
as:
( )
Where:
54
(Eqn. 4.4)
Py
= yield force of the elastoplastic approximation (kips);
P’y
= yield force at the first yield of the extreme tensile reinforcement (kips);
Δ’y
= yield displacement at the first yield of the extreme tensile reinforcement (in.);
and
Δy
= yield displacement of the elastoplastic approximation (in.).
The displacement ductility for Specimen BE-1 is listed in Table 4.3 for both loading directions
along with the average value. Values for the push-south and pull-north directions utilized the maximum
displacement attained because failure occurred during the second cycle in both directions. The total
drift associated with the average Δu was 5.0%.
Table 4.3 – Specimen BE-1: Displacement Ductility
Displacement
Direction of Load
P'y (kips) Δ'y (in.) Δu (in.) Py (kips)
Push South
-38.8
-0.46
-5.62
-65.2
Pull North
40.0
0.46
5.63
65.0
Average
39.4
0.46
5.63
65.1
Δy (in.)
-0.77
0.74
0.75
μΔ
7.32
7.62
7.47
The curvature ductility was determined by a similar process used to find the displacement
ductility. Curvature ductility was defined as:
(Eqn. 4.5)
Where:
μφ
= curvature ductility;
φu
= ultimate curvature at 20% load degradation or last viable potentiometer
reading (in.-1); and
φy
= yield curvature of the elastoplastic approximation (in.-1).
Specimen BE-1 curvature ductilities for both loading directions as well as the average value are
presented in Table 4.4. Invalid readings from potentiometers used to determine curvatures began
55
occurring during the 4ΔY cycle. Therefore, Table 4.4 only includes values up through 3ΔY as these were
the last reliable readings during the test. Because of this, ultimate curvature values in the elastoplastic
approximation are lower-bound estimates of the actual values.
Direction of
Load
Push South
Pull North
Average
Table 4.4 – Specimen BE-1: Curvature Ductility
Curvature
M'y (kip-in.)
-4351
4481
4416
φ'y (in.-1)
-0.00012
0.00008
0.00010
φu (in.-1)
-0.00045
0.00117
0.00081
My (kip-in.)
-7161
6440
6801
φy (in.-1)
-0.00021
0.00012
0.00016
μφ
2.2
10.0
6.12
Height of Plasticity and Equivalent Plastic Hinge Length:
The height of the plasticity zone (Lp) was defined as the height above the base of the wall where
the average curvatures at failure were higher than the average curvature at the initial yield of the
extreme tensile reinforcement. Final curvature values were established at the point of failure, defined
as 20% load degradation of the maximum load, or when valid readings from the displacement
potentiometers were no longer available. The height of plasticity for Specimen BE-1 is presented in
Table 4.5. Also given in Table 4.5 is the ratio of the average height of plasticity zone to the wall length.
Curvatures exceeded the curvature at the initial yield of the extreme tensile reinforcement throughout
the region of the wall covered by the instrumentation. This indicates that the height of plasticity was
greater than 32 in. above the wall base.
Table 4.5 – Specimen BE-1: Height of Plasticity
Height of Plasticity Zone
Direction of Load
(in.)
Push South
32.0*
Pull North
32.0*
Average
32.0
Lp/Lw
57.5%
* Upper limit of instrumentation
56
The equivalent plastic hinge length (lp) was determined using Equation 4.6 (from Paulay and
Priestly, 1992). The second term in the equation represents the plastic displacement for an idealized
curvature profile over the wall height. The equivalent plastic hinge length for Specimen BE-1 for both
directions, along with the average value, is presented in Table 4.6. A value for the south direction was
not calculated due to smaller than expected curvature results at that location (see Figure 4.7).
)( ) (
(
)
(Eqn 4.6)
Table 4.6 – Specimen BE-1: Equivalent Plastic Hinge Length
Direction of Load
Plastic Hinge Length (in.)
Push South
Pull North
Average
lp/Lw
55.2
55.2
99.2%
Energy Dissipation:
The total energy dissipated in the wall during testing was determined at the end of the
displacement level in which failure occurred for both loading directions or for the previous cycle if the
target displacement was not reached. The area (energy) within the hysteresis loops was obtained by
finding the area of the trapezoid shown in Figure 4.9. Equation 4.7 calculates the area of the trapezoid
relative to the x-axis and assumes a straight line between the data points. The area between the top
and bottom of the loops was calculated by first adding the area for the trapezoidal area for the data
points (Δ1,L1) and (Δ2,L2) and then subtracting the trapezoidal area for the data points (Δ3,L3) and (Δ4,L4).
Equation 4.7 applies in each of the four quadrants.
(Eqn. 4.7)
57
Figure 4.9 – Snook (2005): Energy Dissipation Equation Illustration
The total energy dissipated by Specimen BE-1 was 2116 kip-in. calculated through the first full
cycle of the 6ΔY displacement level. The second cycle was not considered because 6ΔY was not attained
in the push direction.
Equivalent Viscous Damping from Hysteretic Behavior:
Equivalent viscous damping values from hysteretic behavior for each wall specimen were
calculated at the first cycle of the displacement level corresponding to 0.6% and 1.5% drift. These drift
values were selected to approximately correspond to the drifts when moderate and significant levels of
damage would occur in the wall specimens, respectively. Equation 4.8 defines the equivalent viscous
damping for the area illustrated in Figure 4.10.
(Eqn. 4.8)
Where:
Ah
= area within first cycle of the target displacement level (kip-in.);
58
Fm
= maximum force at the target displacement level (kip); and
Δm
= maximum displacement at the target displacement level (in.).
Figure 4.10 – Priestley et al. (2007): Hysteretic Area for Damping Calculation
The area within the first cycle of the displacement level was calculated using the trapezoidal method
previously described for calculating the total energy dissipated by each wall specimen.
The equivalent viscous damping values for Specimen BE-1 at approximately 0.6% and 1.5% drift
are 9.7% and 19.4%, respectively.
4.3
Specimen BE-2
Specimen BE-2 had an aspect ratio of 2.0, four confined No. 6 vertical reinforcing bars located at
the ends of the wall and one No. 4 vertical bar located at mid-length, two No. 3 horizontal bars spaced 8
in. on center, and a 66 kip axial load. Confinement of the No. 6 vertical bars at the ends of the wall was
provided by No. 3 closed hoops. All vertical reinforcement was developed in the footing and was
continuous throughout the wall height. The predicted maximum lateral load capacity using XTRACT for
Specimen BE-2 was 75 kips. The horizontal reinforcement yielded in both the first and fifth courses.
Yielding of the extreme vertical reinforcement penetrated into the footing of Specimen BE-2.
59
Test Observations
From the preliminary test, a ΔY of 0.72 in. was extrapolated from the displacement recorded at
75% of the theoretical peak load. Once ΔY was determined, the wall was displaced to ±1, 2, 3, 4, 6 and 8
times ΔY until at least 20% load degradation was observed in the wall. Both flexural and shear cracks
began developing in the preliminary test during the first 50% peak load cycle. Onset of toe crushing for
the north and south toes was observed during the second 1ΔY and first 2ΔY cycles of the primary test,
respectively. Significant spalling of the concrete cover began during the first 3ΔY cycle in both north and
south toes. The primary test was stopped after the first push south to 8ΔY because of severe out-ofplane buckling of the wall base. The test observations are presented in Table 4.7 and end of test
pictures are shown in Figures 4.11 and 4.12.
Load (kips)
-37.8
37.7
-44.0
-48.4
52.1
Disp. (in.)
-0.34
0.23
-0.45
-0.53
0.33
63.5
69.5
-70.6
-74.3
74.5
-83.5
85.4
-66.8
68.3b
0.50
0.74
-1.12
-1.44
1.12
-4.33
4.35
-5.24
4.35
a
b
Table 4.7 - Specimen BE-2: Test Observations
Test Observation
Flexure and shear cracking (push)a
Flexure and shear cracking (pull)a
1st Yield of extreme vertical reinforcement bar in north toe (push)
Critical concrete strain (εcu=0.003) in south toe (push)
1st Yield of extreme vertical reinforcement bar in south toe (pull)
Critical concrete strain (εcu=0.003) in north toe (pull)
Onset of toe crushing in north toe (pull)a
1% drift in push to south
Onset of toe crushing in south toe (push)a
1% drift in pull to north
Maximum load resistance in push to south
Maximum load resistance in pull to north
20% load degradation from the maximum load resistance in push to south
20% load degradation from the maximum load resistance in pull to north
Denotes visual observation
Calculated value
60
Figure 4.11 – Specimen BE-2 Following Testing
Figure 4.12 – Specimen BE-2 Following Testing: South Toe (Left) and North Toe (Right)
61
Load Displacement:
The load-displacement hysteresis curves for the combined preliminary and primary tests for
Specimen BE-2 are presented in Figure 4.13. Initial yielding of the extreme vertical reinforcement
occurred during the first 75% peak load cycle of the preliminary test. The critical concrete strain was
reached in the south and north toes during the first 75% peak load cycle of the preliminary test and the
first 1ΔY cycle of the primary test, respectively. Toe crushing began in the north and south toes during
the second 1ΔY and first 2ΔY cycles, respectively. 1% drift was reached in the first cycle of 2ΔY in both
the north and south directions. Maximum load resistance was reached at the first 6ΔY cycle, and 20%
peak load degradation was observed in the first 8ΔY cycle in the south direction only. The test was
terminated prior to completion of the north 8ΔY loop due to out-of-plane instability in the specimen.
62
100
εcu = 0.003
εy = 0.00233
80
1% Drift
Max. Load
Toe Crushing
20% Load Deg.
60
Load (kips)
40
20
Push South
0
Pull North
-20
-40
-60
-80
-100
-8
-6
-4
-2
0
2
4
6
8
Displacement (in.)
Figure 4.13 – Specimen BE-2: Load Displacement Hysteresis
Displacement and Drift Components:
Load-displacement hysteresis curves showing the total displacement and the shear, sliding, and
flexure displacement components are given in Figure 4.14. The average total drift and average drift
contributions from shear, sliding, and flexure deformations are presented in Table 4.8 at the critical
concrete strain, peak lateral load and failure. Specimen failure was obtained during the first half of the
first 8ΔY cycle, and wall instability prevented completion of the pull-north 8ΔY loop. BE-2 deformations
were dominated by both flexure and shear responses throughout the duration of the test.
63
64
Figure 4.14 – Specimen BE-2: Displacement Components
Table 4.8 – Specimen BE-2: Component Percentages of Total Drift
Limit State Total Drift (%) Sliding (% Total) Shear (% Total) Flexure (% Total)
εcu
0.5
0.8
18.5
80.9
Peak Load
3.9
6.1
27.8
66.1
Failure
4.3
9.7
29.7
60.7
Wall Curvatures:
A plot of curvatures over the height of Specimen BE-2 is given in Figure 4.15. Curvatures over the
wall height were generally symmetric but with slightly larger values in the push direction. Reductions in
curvature values were observed at 20 in. in the pull-north direction while the curvature remained mostly
constant between 12 in. and 32 in. in the push-south direction.
36
1Δ
2Δ
3Δ
4Δ
6Δ
20% Load Deg.
32
28
Wall Height (in.)
24
20
16
12
8
4
Push South
0
-0.005
Pull North
-0.003
-0.001
0.001
Curvature (in.-1)
Figure 4.15 – Specimen BE-2: Wall Curvature
65
0.003
0.005
Displacement and Curvature Ductility:
The displacement ductilities for the north and south loading directions and the average values for
Specimen BE-2 are given in Table 4.9. The ultimate drift was established at 20% load degradation for the
push south direction during the 8ΔY cycle and at the peak 6ΔY displacement for the pull-north direction.
The average ultimate drift for Specimen BE-2 was 4.3%.
Table 4.9 – Specimen BE-2: Displacement Ductility
Displacement
Direction of Load
P'y (kips)
Δ'y (in.) Δu (in.)
Py (kips)
Δy (in.)
Push South
-44.0
-0.46
-5.25
-76.9
-0.79
Pull North
52.1
0.33
4.35
80.7
0.51
Average
48.1
0.39
4.80
78.8
0.65
μΔ
6.60
8.59
7.60
Specimen BE-2 curvature ductilities for both loading directions along with average values are
presented in Table 4.10.
Direction of Load
Push South
Pull North
Average
Table 4.10 – Specimen BE-2: Curvature Ductility
Curvature
-1
M'y (kip-in.) φ'y (in. ) φu (in.-1) My (kip-in.)
-4933
-0.00014 -0.00246
-8570
5838
0.00005 0.00201
9028
5386
0.00009 0.00224
8799
φy (in.-1)
-0.00024
0.00008
0.00016
μφ
10.4
24.4
17.4
Height of Plasticity and Equivalent Plastic Hinge Length:
The height of plasticity and the ratio of the average height of plasticity zone to the wall length
for Specimen BE-2 are presented in Table 4.11. Curvatures exceeded the curvature at the initial yield of
the extreme tensile reinforcement throughout the extent of the instrumentation indicating that the
height of plasticity was greater than 32 in. above the wall base.
66
Table 4.11 – Specimen BE-2: Height of Plasticity
Height of Plasticity
Direction of Load
Zone (in.)
Push South
32.0*
Pull North
32.0*
Average
32.0*
Lp/Lw
57.5%
* Upper limit of instrumentation
The equivalent plastic hinge length for Specimen BE-2 for both directions and the average value
are presented in Table 4.12. The ratio of the average equivalent plastic hinge length to the wall length is
also provided.
Table 4.12 – Specimen BE-2: Equivalent Plastic Hinge Length
Plastic Hinge Length (in.)
Direction of Load
19.6
Push South
19.5
Pull North
19.5
Average
lp/Lw
35.1%
Energy Dissipation:
The total energy dissipated by Specimen BE-2 was 2336 kip-in. calculated through the second
full cycle of the 6ΔY displacement level. The 8ΔY cycle was not considered because of specimen
instability prior to completing the first pull-north cycle.
Equivalent Viscous Damping:
The equivalent viscous damping values for Specimen BE-2 at approximately 0.6% and 1.5% drift
are 8.0% and 15.8%, respectively.
67
4.4
Specimen BE-3
Specimen BE-3, with wall returns at each end, had an aspect ratio of 2.0, four confined No. 6 and
four confined No. 3 vertical reinforcing bars located at the ends of the wall, one No. 4 vertical bar
located at mid-length, two No. 3 horizontal bars spaced 8 in. on center, and zero axial load.
Confinement of the No. 6 and No. 3 vertical bars at the ends of the wall was provided by No. 3 closed
hoops placed in-plane and transverse to the wall. All vertical reinforcement was developed in the
footing and was continuous throughout the wall height. The predicted maximum lateral load capacity
using XTRACT for Specimen BE-3 was 92 kips. The horizontal reinforcement yielded during testing in
both the first and fifth courses. Yielding of the extreme vertical reinforcement penetrated into the
footing of Specimen BE-3.
Test Observations
From the preliminary test, a ΔY of 1.06 in. was extrapolated from the displacement recorded at
75% of the theoretical peak load. The wall was then displaced to ±1, 2, 3, 4, and 6 times ΔY until at least
20% load degradation was observed in the wall. Both flexural and shear cracks began developing during
the preliminary test during the first cycle to 50% of the predicted maximum load. Onset of toe crushing
occurred during the 2ΔY and 3ΔY cycles for the north and south toes, respectively. Spalling of the
concrete cover began during the 3ΔY cycle in the north toe and 4ΔY cycle in the south toe. Starting
during the first 3ΔY cycle, strain penetration into the south end of the footing associated with extensive
plastic deformation of the extreme vertical bars in the wall resulted in pullout of some of the footing
concrete near the base of the wall. Approximately 0.75 in. of uplift was measured which resulted in
skewing the bottom potentiometer reading at 4ΔY and beyond. The primary test was stopped after the
first 6ΔY cycle due to significant load degradation as a result of low-cycle fatigue fracture of the extreme
68
vertical reinforcement. The tabulated test observations are presented in Table 4.13 and end-of-test
pictures are shown in Figures 4.16 and 4.17.
Load (kips)
-46.3
46.2
-55.4
46.2
59.8
-71.8
-71.3
69.5
80.5
-87.2
-88.5
87.6
-61.0
57.5
a
Disp. (in.)
-0.33
0.29
-0.46
0.29
0.53
-0.94
-1.12
1.12
2.13
-3.17
-4.23
4.25
-6.23
5.42
Table 4.13 – Specimen BE-3: Test Observations
Test Observation
Flexure and shear cracking (push)a
Flexure and shear cracking (pull)a
1st Yield of extreme vertical reinforcement bar in north toe (push)
1st Yield of extreme vertical reinforcement bar in south toe (pull)
Critical concrete strain (εcu=0.003) in north toe (pull)
Critical concrete strain (εcu=0.003) in south toe (push)
1% drift in push to south
1% drift in pull to north
Onset of toe crushing in north toe (pull)a
Onset of toe crushing in south toe (push)a
Maximum load resistance in push to south
Maximum load resistance in pull to north
20% load degradation from the maximum load resistance in push to south
20% load degradation from the maximum load resistance in pull to north
Denotes visual observation
69
Figure 4.16 – Specimen BE-3 Following Testing
Figure 4.17 – Specimen BE-3 Following Testing: South Toe (Left) and North Toe (Right)
70
Load Displacement:
The load-displacement hysteresis curves for the combined preliminary and primary tests for
Specimen BE-3 are presented in Figure 4.18. Initial yielding of the extreme vertical reinforcement
occurred during the first 75% peak load cycle of the preliminary test. The critical concrete strain in the
north and south toe regions was reached during the 75% peak load cycle of the preliminary test and the
1ΔY cycle of the primary test, respectively. Toe crushing began in the north and south toes during the
2ΔY and 3ΔY cycles, respectively. One percent drift was reached in the first cycle of 2ΔY in both the
north and south directions. Maximum load resistance was reached during the 4ΔY cycle, and 20% load
degradation occurred during the 6ΔY cycle. The test was terminated at the conclusion of the first 6ΔY
cycle due to significant load degradation resulting from fractured vertical reinforcement in the toe
regions.
100
εcu = 0.003
εy = 0.00233
80
1% Drift
Max. Load
Toe Crushing
20% Load Deg.
60
Load (kips)
40
20
Push South
0
Pull North
-20
-40
-60
-80
-100
-8
-6
-4
-2
0
2
4
Displacement (in.)
Figure 4.18 – Specimen BE-3: Load Displacement Hysteresis
71
6
8
Displacement and Drift Components:
The average total drift and average drift contributions from shear, sliding, and flexure
deformations are presented in Table 4.14 at the critical concrete strain, peak lateral load and failure
limit states. Load-displacement hysteresis curves showing the total displacement and the shear, sliding,
and flexure displacement components are given in Figure 4.19. Specimen failure was obtained during
the 6ΔY cycle. Shear and flexure displacements were not obtained for the peak-load and failure limit
states due to invalid potentiometer readings at the larger displacement levels. Therefore, the last
reliable readings were utilized. Based on the sliding displacements recorded, Specimen BE-3
deformations were dominated by both flexure and shear responses throughout the duration of the test.
Limit State
εcu
Peak Load
Failure
a
Table 4.14 – Specimen BE-3: Component Percentages of Total Drift
Total Drift (%)
Sliding (% Total)
Shear (% Total)
Flexure (% Total)
0.7
3.8
5.7
2.6
9.5
12.5
26.8
70.6
a
59.0a
59.0a
33.6
33.6a
Results are from last reliable potentiometer readings
72
73
Figure 4.19 – Specimen BE-3: Displacement Components
Wall Curvatures:
A plot of curvatures over the height of Specimen BE-3 is given in Figure 4.20. Curvatures over the
wall height were generally symmetric, but with slightly larger values at the base of the wall in the pull
direction. The ultimate curvature was defined at the first cycle of 4ΔY, instead of at 20% load
degradation of the maximum load attained, because of invalid potentiometer readings at the 6ΔY
displacement level. Curvatures were mostly constant for both directions from 12 in. to 32 in. of wall
height and appeared to extend beyond 32 in.
36
1Δ
2Δ
32
3Δ
28
4Δ
20% Load Deg.
Wall Height (in.)
24
20
16
12
8
4
Push South
0
-0.007
-0.005
Pull North
-0.003
-0.001
0.001
0.003
Curvature (in.-1)
Figure 4.20 – Specimen BE-3: Wall Curvature
74
0.005
0.007
Displacement and Curvature Ductility:
The displacement ductilities for the north and south loading directions along with average values
for Specimen BE-3 are shown in Table 4.15. The ultimate drift was recorded at 20% load degradation for
both loading directions. The average ultimate drift for Specimen BE-3 was 5.2%.
Table 4.15 – Specimen BE-3: Displacement Ductility
Displacement
Direction of Load
P'y (kips) Δ'y (in.) Δu (in.) Py (kips) Δy (in.)
Push South
-55.4
-0.46
-6.23
-84.3
-0.70
Pull North
46.2
0.29
5.42
80.0
0.51
Average
50.8
0.38
5.82
82.1
0.61
μΔ
8.8
10.7
9.8
Curvature ductilities for both loading directions along with averages are presented in Table 4.16.
Direction of Load
Push South
Pull North
Average
Table 4.16 – Specimen BE-3: Curvature Ductility
Curvature
-1
M'y (kip-in.) φ'y (in. ) φu (in.-1) My (kip-in.)
-6209
-0.00011 -0.00393
-9414
5179
0.00012 0.00438
8888
5694
0.00011 0.00415
9151
φy (in.-1)
-0.00016
0.00020
0.00018
μφ
24.16
22.15
23.16
Height of Plasticity and Equivalent Plastic Hinge Length:
The height of plasticity and the ratio of the average height of plasticity zone to the wall length
for Specimen BE-3 are presented in Table 4.17. Curvatures exceeded the curvature at the initial yield of
the extreme tensile reinforcement throughout the extent of the instrumentation, indicating that the
height of plasticity was greater than 32 in. above the wall base.
Table 4.17 – Specimen BE-3: Height of Plasticity
Height of Plasticity
Direction of Load
Zone (in.)
Push South
32.0*
Pull North
32.0*
Average
32.0*
Lp/Lw
57.5%
* Upper limit of instrumentation
75
The equivalent plastic hinge length for Specimen BE-3 for both directions along with the average
value is presented in Table 4.18. The ratio of the average equivalent plastic hinge length to the wall
length is also provided.
Table 4.18 – Specimen BE-3: Equivalent Plastic Hinge Length
Plastic Hinge Length (in.)
Direction of Load
14.0
Push South
Pull North
11.0
Average
lp/Lw
12.5
23.0%
Energy Dissipation:
The total energy dissipated by Specimen BE-3 was 2923 kip-in. calculated through the 6ΔY
displacement level.
Equivalent Viscous Damping:
The equivalent viscous damping values for Specimen BE-3 at approximately 0.6% and 1.5% drift
are 11.5% and 20.1%, respectively.
4.5
Specimen BE-4
Specimen BE-4, with wall returns at each end, had an aspect ratio of 2.0, four confined No. 6 and
four confined No. 3 vertical reinforcing bars located at the ends of the wall, one No. 4 vertical bar
located at mid-length, two No. 3 horizontal bars spaced 8-in. on center, and zero axial load.
Confinement of the No. 6 and No. 3 vertical bars at the ends of the wall was provided by ¼-in. diameter
HRR wire closed hoops placed in-plane and transverse to the wall. All vertical reinforcement was
developed in the footing and was continuous throughout the wall height. The predicted maximum
lateral load capacity using XTRACT for Specimen BE-4 was 92 kips. The horizontal reinforcement yielded
76
during testing in both the first and fifth courses. Yielding of the extreme vertical reinforcement
penetrated into the footing of Specimen BE-4.
Test Observations
From the preliminary test, a ΔY of 1.04 inches was extrapolated from the displacement recorded
at 75% of the theoretical peak load. The wall was then displaced to ±1, 2, 3, 4, and 6 times ΔY until at
least 20% load degradation was observed in the wall. Both flexural and shear cracks began developing
during the preliminary test while cycling to 50% of the predicted maximum load. Onset of toe crushing
occurred during the 2ΔY cycle for both directions. Spalling of the concrete cover began during the 3ΔY
cycle in the north toe and 4ΔY cycle in the south toe. The primary test was stopped after the first 6ΔY
cycle due to low-cycle fatigue fracture in the extreme vertical bars. The test observations are presented
in Table 4.19, and end-of-test pictures are shown in Figures 4.21 and 4.22.
Load (kips)
-46.3
46.3
-54.0
-67.9
49.8
63.4
-70.2
-84.2
69.3
80.9
-87.7
87.2
-59.5
59.9
Table 4.19 – Specimen BE-4: Test Observations
Disp. (in.) Test Observation
-0.34
Flexure and shear cracking (push)*
0.27
Flexure and shear cracking (pull)*
-0.46
1st Yield of extreme vertical reinforcement bar in north toe (push)
-0.74
Critical concrete strain (εcu=0.003) in south toe (push)
0.32
1st Yield of extreme vertical reinforcement bar in south toe (pull)
0.58
Critical concrete strain (εcu=0.003) in north toe (pull)
-1.11
1% drift in push to south
-2.09
Onset of toe crushing in south toe (push)*
1.11
1% drift in pull to north
2.09
Onset of toe crushing in north toe (pull)*
-4.17
Maximum load resistance in push to south
4.17
Maximum load resistance in pull to north
-4.64
20% load degradation from the maximum load resistance in push to south
6.29
20% load degradation from the maximum load resistance in pull to north
* Denotes visual observation
77
Figure 4.21 – Specimen BE-4 Following Testing
Figure 4.22 – Specimen BE-4 Following Testing: South Toe (Left) and North Toe (Right)
78
Load Displacement:
The load-displacement hysteresis curves for the combined preliminary and primary tests for
Specimen BE-4 are presented in Figure 4.23. Initial yielding of the extreme vertical reinforcement and
the critical concrete strain were attained during the first 75% peak load cycle of the preliminary test.
Toe crushing began in both directions during the first 2ΔY cycle. One percent drift was reached in the
first cycle of 2ΔY in both directions. Maximum load resistance was reached at the first 4ΔY cycle, and
20% post-peak load degradation was observed during the 6ΔY cycle. The test was terminated at the
conclusion of the first 6ΔY cycle due to fracturing of the extreme vertical reinforcement.
100
εcu = 0.003
εy = 0.00233
80
1% Drift
Max. Load
Toe Crushing
20% Load Deg.
60
Load (kips)
40
20
0
Push South
Pull North
-20
-40
-60
-80
-100
-8
-6
-4
-2
0
2
4
Displacement (in.)
Figure 4.23 – Specimen BE-4: Load Displacement Hysteresis
79
6
8
Displacement and Drift Components:
The average total drift and average drift contributions from shear, sliding, and flexure
deformations are presented in Table 4.20 at the critical concrete strain, peak lateral load and failure
limit states. Load-displacement hysteresis curves showing the total displacement and the shear, sliding,
and flexure displacement components are given in Figure 4.24. Specimen failure occurred during the
6ΔY cycle. Shear and flexure displacements were not obtained for the peak load and failure limit states
for the north direction due to invalid potentiometer readings at the larger displacements. Based on the
measured displacements, Specimen BE-4 deformations were dominated by both flexure and shear
responses throughout the duration of the test.
Limit State
εcu
Peak Load
Failure
a
b
Table 4.20 – Specimen BE-4: Component Percentages of Total Drift
Total Drift (%)
Sliding (% Total)
Shear (% Total)
Flexure (% Total)
0.6
2.4
25.5
72.2
a
3.7
10.3
33.6
55.9a
4.9
12.9
40.4b
47.6b
Value utilizes last reliable potentiometer reading for north direction
Value utilizes last reliable potentiometer readings
80
81
Figure 4.24 – Specimen BE-4: Displacement Components
Wall Curvatures:
A plot of curvatures over the height of Specimen BE-4 is given in Figure 4.25. Curvatures over the
wall height were generally symmetric but with slightly larger values at the base of the wall in the push
direction. The ultimate curvature was established after the first cycle of 4ΔY instead of at 20% load
degradation of the maximum load attained because of invalid potentiometer readings at the 6ΔY
displacement level. Curvatures decreased up to 20 in. of wall height and increased slightly at 32 in.
36
1Δ
2Δ
3Δ
4Δ
20% Load Deg.
32
28
Wall Height (in.)
24
20
16
12
8
4
Push South
0
-0.005
Pull North
-0.003
-0.001
0.001
Curvature (in.-1)
Figure 4.25 – Specimen BE-4: Wall Curvature
82
0.003
0.005
Displacement and Curvature Ductility:
The displacement ductilities for Specimen BE-4 for the north and south loading directions along
with average values are shown in Table 4.21. The ultimate drift was recorded at 20% load degradation
for both loading directions. The average ultimate drift for Specimen BE-4 was 4.9%.
Table 4.21 – Specimen BE-4: Displacement Ductility
Displacement
Direction of Load
P'y (kips) Δ'y (in.) Δu (in.) Py (kips) Δy (in.)
Push South
Pull North
Average
-54.0
49.8
51.9
-0.46
0.33
0.39
-4.64
6.29
5.46
-82.5
80.8
81.7
-0.71
0.53
0.62
μΔ
6.57
11.9
9.3
Lower-bound estimates of Specimen BE-4 curvature ductilities and averages for both directions
are given in Table 4.22.
Direction of Load
Push South
Pull North
Average
Table 4.22 – Specimen BE-4: Curvature Ductility
Curvature
M'y (kip-in.)
-6047
5582
5815
φ'y (in.-1)
-0.00009
0.00009
0.00009
φu (in.-1)
-0.00115
0.00125
0.00120
My (kip-in.)
-8888
8719
8803
φy (in.-1)
-0.00014
0.00013
0.00014
μφ
8.366
9.411
8.9
Height of Plasticity and Equivalent Plastic Hinge Length:
The height of plasticity and the ratio of the average height of plasticity zone to the wall length
for Specimen BE-4 are presented in Table 4.23. Curvatures exceeded the curvature at the initial yield of
the extreme tensile reinforcement throughout the extent of the instrumentation indicating that the
height of plasticity was greater than 32 in. above the wall base.
83
Table 4.23 – Specimen BE-4: Height of Plasticity
Height of Plasticity
Direction of Load
Zone (in.)
Push South
32.0*
Pull North
32.0*
Average
32.0*
Lp/Lw
57.5%
* Upper limit of instrumentation
The equivalent plastic hinge length for Specimen BE-4 for both directions and the average value
are presented in Table 4.24. The ratio of the average equivalent plastic hinge length to the wall length is
also provided.
Table 4.24 – Specimen BE-4: Equivalent Plastic Hinge Length
Plastic Hinge Length (in.)
Direction of Load
42.7
Push South
Pull North
64.4
Average
53.6
lp/Lw
96.3%
Energy Dissipation:
The total energy dissipated by Specimen BE-3 was 2641 kip-in. calculated through the 6ΔY
displacement level.
Equivalent Viscous Damping:
The equivalent viscous damping values for Specimen BE-3 at approximately 0.6% and 1.5% drift
are 11.4% and 19.8%, respectively.
4.6
Summary
This chapter presented test results for the four masonry walls with integral confined concrete
boundary elements evaluated in this study. Brief descriptions were given of the response of each
84
specimen during testing. End-of-test photographs and plots of load-displacement hystereses as well as
curvatures versus wall height were provided for each specimen. Test observations, decoupled drift
components, displacement ductility, curvature ductility, height of plasticity, and the equivalent plastic
hinge length were presented. Energy dissipation and hysteretic damping values were determined for
each specimen.
85
CHAPTER 5
ANALYSES AND COMPARISONS OF WALL PERFORMANCE
5.1
Introduction
In this chapter, wall performance is evaluated with respect to predicted load capacity, drift,
displacement ductility, height of plasticity, equivalent plastic hinge length, energy dissipation and
hysteretic damping. Results from the wall tests of this study are also compared with results obtained by
Kapoi (2012) to evaluate the performance of masonry walls with integral confined concrete boundary
elements in comparison to similar masonry walls without boundary elements.
5.2
Theoretical Predictions
The average experimental and predicted lateral load capacities for each specimen and the ratios
of the experimental-to-predicted capacities are presented in Table 5.1. The predicted capacities were
obtained using the software program XTRACT and underestimated the experimental capacities of
Specimens BE-1 and BE-2 by 6% and 12%, respectively. The experimental-to-predicted ratios for
Specimens BE-1 and BE-2 also correlate well with those for Specimens C7 and C8 in the study by Kapoi
(2012). In contrast, predicted capacities for Specimens BE-3 and BE-4 overestimated the experimental
capacities by 4% and 5%, respectively. These specimens achieved higher lateral load capacities leading
to greater shear deformations, which are not accounted for in XTRACT. Banting and El Dakhakhni
(2012) also found shear behavior influenced their predicted capacities and recommended that shear
deformations be included in analyses for walls in which a significant shear response is expected.
86
Table 5.1 Predicted and Experimental Capacities
Predicted
Average
Aspect
Vexp/
Specimen
P/(f'mAg) Capacity (kips) Experimental
Ratio
VXTRACT
Capacity (kips)
XTRACT
BE-1
2.0
0
65.7
70.1
1.07
BE-2
2.0
0.0625
74.8
84.5
1.13
BE-3
2.0
0
92.0
88.1
0.96
BE-4
2.0
0
91.8
87.5
0.95
a
C7
2.0
0
55.5
59.2
1.07
a
C8
2.0
0.0625
64.4
70.4
1.09
a
5.3
Kapoi (2012)
Drift
Table 5.2 lists the average total drift for the four specimens at three limit-states: critical
concrete strain (εcu = 0.003), peak load and failure defined as 20% load degradation from the maximum
load attained during testing. Values at peak load and at failure were 1.5 to 2 times larger than those
reported by Kapoi (2012) when comparing Specimens BE-1 and BE-2 to the similar masonry wall
specimens without boundary elements, Specimens C7 and C8, respectively. However, when comparing
the total drifts obtained at εcu and εmu for these same specimens, Kapoi’s results were greater than those
found in this study, particularly for Specimen C7.
Table 5.2 - Total Wall Drift at Three Limit States
Total Drift (%)
Aspect
Specimen
P/(f'mAg) Vertical Reinf.
Peak
Ratio
εcu
Failure
Load
BE-1
2.0
0
8 #6, 1#4
0.3
4.2
5.0
BE-2
2.0
0.0625
8 #6, 1#4
0.5
3.9
4.3
BE-3
2.0
0
8 #6, 8 #3, 1#4 0.7
3.8
5.7
BE-4
a
b
C7
a
C8
a
2.0
2.0
2.0
0
0
0.0625
8 #6, 8 #3, 1#4
8 #6, 1 #4
8 #6, 1 #4
Peak/
εcu
Failure/
εcu
14.0
7.8
5.4
17.0
8.6
8.14
0.6
3.7
4.9
6.2
8.2
1.1
b
2.1
2.8
1.9
2.5
0.6
b
2
2.7
3.3
4.5
Kapoi (2012)
εmu
87
Similar to the results reported by Sherman (2011) and Kapoi (2012), the total drifts at wall
failure significantly exceeded the total drifts recorded at εcu. The smallest total drift at the recorded
peak load was more than 5 times greater than the total drift at εcu.
The average values of total drift and the average drift contributions from sliding, shear, and
flexural deformations are given in Table 5.3. The average sliding contribution for Specimen BE-2 was
expected to be lower than for Specimen BE-1 due to the addition of axial load. However, the results
contradict this expectation. Shear and flexure average drift contributions at failure were not available
for Specimens BE-1, BE-3 and BE-4, and therefore the last reliable readings are presented. Specimen BE2 shows larger drift contributions from sliding and shear than those for Specimen C8 of Kapoi (2012).
This is most likely attributable to the higher lateral load capacity in Specimen BE-2 leading to greater
shear deformations when compared to Specimen C8. Confinement of the toe steel in Specimen BE-2
restrained lateral bucking of the vertical reinforcement and helped reduced spalling of the toe regions.
As a result of this confinement, the hinge zone extended to a higher wall elevation, and greater drifts
were achieved.
Table 5.3 Components of Wall Drifts at Failure
Aspect
Total Drift Sliding
Shear
Flexure
Specimen
P/(f'mAg) Vertical Reinf.
Ratio
(%)
(% Total) (% Total) (% Total)
BE-1
2.0
0
8 #6, 1#4
5.0
9.9
23.7a
64.8a
BE-2
2.0
0.0625
8 #6, 1#4
4.3
9.7
29.7
60.7
a
BE-3
2.0
0
8 #6, 8 #3, 1#4
5.2
12.5
33.6
59.0a
a
BE-4
2.0
0
8 #6, 8 #3, 1#4
4.9
12.9
40.4
47.6a
C7b
2.0
0
8 #6, 1 #4
2.8
9.8
b
C8
2.0
0.0625
8 #6, 1 #4
2.3
0.4
7
92.6
a
b
5.4
Value utilizes last reliable potentiometer readings
Kapoi (2012)
Displacement Ductility
The average yield displacements, ultimate displacements and displacement ductility factors for
the specimens of this study as well as for Specimens C7 and C8 of Kapoi (2012) are given in Table 5.4.
88
Displacement ductility values for BE-1 and BE-2 are approximately 1.5 times larger than for the similar
masonry walls without boundary elements tested by Kapoi (2012).
Table 5.4 - Average Yield, Ultimate Displacement, and Displacement Ductility
Specimen
BE-1
BE-2
BE-3
BE-4
C7a
C8a
a
Aspect
Ratio
2.0
2.0
2.0
2.0
2.0
2.0
P/(f'mAg)
0
0.0625
0
0
0
0.0625
Yield Disp., ΔY Ultimate
Disp.
(in.)
Disp., Δu (in.) Ductility, μΔ
8 #6, 1#4
0.75
5.63
7.5
8 #6, 1#4
0.65
4.80
7.6
8 #6, 8 #3, 1#4
0.61
5.82
9.8
8 #6, 8 #3, 1#4
0.62
5.46
9.3
8 #6, 1 #4
0.69
3.13
4.8
8 #6, 1 #4
0.56
3.03
5.4
Vertical Reinf.
Kapoi (2012)
The yield displacements are larger for the specimens with boundary elements and without
returns at the ends of the walls, reflecting the greater stiffness of the walls with returns. Specimen BE-4
had an earlier failure point than Specimen BE-3 due to low-cycle fatigue bar fracture during the final
push-south cycle at 6ΔY, causing a smaller ultimate displacement for the south direction. The larger
displacement ductility factors of these specimens can be attributed to the restraint provided by the wall
returns against out-of-plane instability.
5.5
Height of Plasticity and Equivalent Plastic Hinge Length
The average height of plasticity, the average plastic hinge length, and the ratios of these values
with respect to the wall length are given in Table 5.5. The listed height of plasticity values are lowerbound estimates of the actual values because all curvatures at specimen failure, or the last valid
potentiometer reading, exceeded the average yield curvature at every level of measurement. This
indicates that significant curvatures extended above the region of the wall covered by the
instrumentation, and as a result the height of plasticity was greater than the height of the top tier of
instruments. For two of the specimens, the calculated plastic hinge lengths were less than the heights
of plasticity. The plastic hinge lengths in Specimen BE-2 and the similar masonry wall without boundary
89
elements tested by Kapoi (2012), Specimen C8, were both approximately 20 in. Walls without axial load
had larger plastic hinge lengths then the walls with axial load. These findings indicate that the plastic
hinge length is influenced by both the presence of axial loading and the use of boundary elements.
Table 5.5 - Height of Plasticity and Plastic Hinge Length
Height of
Aspect
Plastic Hinge
Specimen
P/(f'mAg) Vertical Reinf. Plasticity,
L /L (%) lp/Lw (%)
Ratio
Length, lp (in.) p w
Lp (in.)
BE-1
2.0
0
8 #6, 1#4
32.0a
55.2
57.5
99.2
a
BE-2
2.0
0.0625
8 #6, 1#4
32.0
19.5
57.5
35.1
BE-3
2.0
0
8 #6, 8 #3, 1#4
32.0a
12.5
57.5
22.5
a
BE-4
2.0
0
8 #6, 8 #3, 1#4
32.0
53.6
57.5
96.3
b
C7
2.0
0
8 #6, 1 #4
29.3
29.7
53.0
53.0
C8b
2.0
0.0625
8 #6, 1 #4
29.4
23.3
53.0
42.0
a
b
5.6
Upper limit of instrumentation
Kapoi (2012), lower-bound estimates for Lp and lp
Energy Dissipation
The total energy dissipated by each wall specimen is presented in Table 5.6. Results for
Specimens BE-1 and BE-2 were 2.8 and 2.4 times larger than Specimens C7 and C8, respectively. By
comparing the load-displacement hysteresis curves presented in Figures 5.1 and 5.2, it can be seen that
masonry walls with integral confined concrete boundary elements dissipated significantly more energy
than similar masonry walls without boundary elements tested by Kapoi (2012).
Specimen
BE-1
BE-2
BE-3
BE-4
C7c
C8c
Table 5.6 - Total Energy Dissipation
Aspect
Total Energy
P/(f'mAg) Vertical Reinf.
Ratio
Dissipation (kip-in.)
2.0
0
8 #6, 1#4
2116a
2.0
0.0625
8 #6, 1#4
2336b
2.0
0
8 #6, 8 #3, 1#4
2923a
2.0
0
8 #6, 8 #3, 1#4
2641a
2.0
0
8 #6, 1#4
764
2.0
0.0625
8 #6, 1#4
981
a
Calculated through 1st Full Cycle of 6ΔY
Calculated through 2nd Full Cycle of 6ΔY
c
Kapoi (2012)
b
90
100
BE-1
C7
80
60
Load (kips)
40
20
Push South
0
Pull North
-20
-40
-60
-80
-100
-8
-6
-4
-2
0
2
Displacement (in.)
4
6
8
Figure 5.1 – Load-Displacement Hystereses for Specimens BE-1 and C7
100
BE-2
C8
80
60
Load (kips)
40
20
Push South
0
Pull North
-20
-40
-60
-80
-100
-8
-6
-4
-2
0
2
4
6
Displacement (in.)
Figure 5.2 – Load-Displacement Hystereses for Specimens BE-2 and C8
91
8
5.7
Equivalent Viscous Damping
The equivalent viscous damping values from hysteretic behavior for each wall specimen are
given in Table 5.7. Displacement levels were chosen to be as close to 0.6% and 1.5% drift as possible.
These values of drift were selected to approximately correspond to the drifts producing moderate and
significant levels of damage in the wall specimens, respectively. The average equivalent viscous
damping values for the wall specimens with boundary elements at approximately 0.6% and 1.5% drift
are 10 % and 19%, respectively. These averages are approximately 4% greater in the damping value
than those for the similar masonry walls without boundary elements tested by Kapoi (2012).
Table 5.7 - Equivalent Viscous Damping
a
5.8
Specimen
Aspect
Ratio
P/(f'mAg)
Vertical Reinf.
BE-1
2.0
0
8 #6, 1#4
BE-2
2.0
0.0625
8 #6, 1#4
BE-3
2.0
0
8 #6, 8 #3, 1#4
BE-4
2.0
0
8 #6, 8 #3, 1#4
C7a
2.0
0
8 #6, 1 #4
C8a
2.0
0.0625
8 #6, 1 #4
Drift (%) Damping (%)
0.6
1.7
0.7
1.3
0.7
1.9
0.7
1.9
0.7
1.4
0.5
1.5
9.7
19.4
8.0
15.8
11.5
20.1
11.4
19.8
6.2
15.9
6.1
14.8
Kapoi (2012)
Effects of Wall Parameters on Behavior
In this section, the effects of different parameters on the behavior of the masonry walls with
integral confined concrete boundary elements are evaluated. Where applicable, results from Specimens
BE-1 and BE-2 are also compared to test results for the two similar masonry wall specimens without
boundary elements tested by Kapoi (2012), Specimens C7 and C8. Parameters evaluated are the effects
of axial-compressive stress, boundary element geometry, and confining reinforcement type.
92
5.8.1
Axial Compressive Stress
The effects of axial compressive stress on wall performance are evaluated in this section.
Details for the test specimens considered are presented in Table 5.8. Specimens BE-1 and BE-2
consisted of masonry walls with rectangular confined concrete boundary elements, and Specimens C7
and C8 consisted of masonry walls without boundary elements.
Table 5.8 - Axial Compressive Stress Evaluation
Axial Compressive
Specimen Aspect Ratio P/(f'mAg)
Stress (psi)
BE-1
2.0
0
0
BE-2
2.0
0.0625
156
C7a
2.0
0
0
a
C8
2.0
0.0625
158
a
Kapoi (2012)
The load-displacement envelopes for the considered specimens are given in Figure 5.3. Kapoi
(2012) found that the initial wall stiffness increased as the axial compressive stress increased. The
results for Specimens BE-1 and BE-2 are consistent with this conclusion. It can also be seen that peak
load capacity increased with the increased axial compressive stress. The walls with rectangular
boundary elements had approximately 80% greater values of drift at failure than for the comparable
masonry walls without boundary elements (4.7% compared to 2.6%).
Table 5.3 lists various components of wall drifts at failure for the considered specimens. For the
walls with boundary elements, Specimens BE-1 and BE-2, the presence of axial loading resulted in
increased shear contributions and decreased flexural contributions, likely because of the higher load
capacity in the wall with axial loading. There was essentially no difference in the sliding component of
drift. For the walls without boundary elements, Specimens C7 and C8, Kapoi (2012) observed a decrease
in the sliding drift contributions when compressive axial load was applied. Average drift contributions
from shear and flexure were not obtained for Specimen C7 due to invalid instrument readings resulting
from wall damage.
93
100
BE-1
BE-2
C7
C8
80
60
Load (kips)
40
20
Push South
0
Pull North
-20
-40
-60
-80
-100
-6
-4
-2
0
2
4
6
Displacement (in.)
Figure 5.3 – Load-Displacement Envelopes for Axial Compressive Stress Comparison
From Table 5.4, it can be seen that yield displacements were larger in the rectangular walls
without axial loading in both studies. The walls with rectangular boundary elements had larger yield
displacements than the masonry walls tested by Kapoi (2012). Displacement ductility values for the
walls with rectangular boundary elements, Specimens BE-1 and BE-2, were essentially the same.
However, in the masonry walls without boundary elements, Specimens C7 and C8, the presence of axial
loading resulted in an increase in the displacement ductility value. From Table 5.5, it can be seen that
the ratio of plastic hinge length to wall length decreased from 99% for Specimen BE-1 to 35% for
Specimen BE-2 as a result of the presence of axial loading. Kapoi (2012) found a similar trend for
Specimens C7 and C8, though with not as substantial a decrease, suggesting that the presence of axial
stress decreases the plastic hinge length.
94
Axial loading resulted in a 10% increase in energy dissipation in Specimens BE-1 and BE-2, while
for Specimens C7 and C8 the increase was approximately 28% (Table 5.6). Axial loading resulted in a
20% decrease in equivalent viscous damping value for Specimens BE-1 and BE-2, while the decrease for
Specimens C7 and C8 was around 8% (Table 5.7). These findings indicate that axial loading increases
energy dissipation but it decreases the equivalent viscous damping value.
5.8.2
Boundary Element Geometry
In this section, the performances of two wall specimens with different boundary element
geometries are compared. Specimen BE-1 had a rectangular confined boundary element, and Specimen
BE-3 had a boundary element with returns running transverse to the length of the wall. Neither
specimen had axial loading. Figure 5.4 presents the load-displacement envelopes for these two
specimens. The initial wall stiffness and the average peak load were greater for Specimen BE-3 than for
Specimen BE-1. Loads at failure for Specimen BE-3 were 4.6 kips and 26.1 kips larger than Specimen BE1 for the push-south and pull-north directions, respectively.
From Table 5.2, average total drifts at failure for Specimens BE-1 and BE-3 were 5.0% and 5.7%,
respectively. From Table 5.3, the three components of drift at failure varied. Specimen BE-3 showed
more drift from sliding and from shear than did Specimen BE-1. However, flexure components of
average drift at failure were 6% greater for Specimen BE-1 than for Specimen BE-3.
95
100
BE-1
80
BE-3
60
Load (kips)
40
20
Push South
0
Pull North
-20
-40
-60
-80
-100
-8.0
-6.0
-4.0
-2.0
0.0
2.0
Displacement (in.)
4.0
6.0
8.0
Figure 5.4 – Load-Displacement Envelopes for Boundary Element Geometry Comparison
The average yield displacement for Specimen BE-1 was greater than that for Specimen BE-3
(see Table 5.4). However, Specimen BE-3 experienced a larger ultimate displacement than did Specimen
BE-1, resulting in a larger displacement ductility value. From Table 5.6, it can be seen that the total
energy dissipation values for Specimen BE-1 and Specimen BE-3 are 2116 kip-in. and 2923 kip-in.,
respectively. For the comparable masonry wall without boundary elements tested by Kapoi, Specimen
C7, the total energy dissipation value is 764 kip-in. The load-displacement hystereses for Specimens BE1 and Specimen BE-3 are shown in Figure 5.5 and illustrate the significant differences between the
comparable loading cycles in the two specimens. The equivalent viscous damping increased slightly with
the addition of boundary element returns (Table 5.7). These findings indicate that boundary elements
with returns result in substantially increased energy dissipation by providing greater resistance to wall
instability.
96
100
BE-1
BE-3
80
60
Load (kips)
40
20
Push South
0
Pull North
-20
-40
-60
-80
-100
-8
-6
-4
-2
0
Displacement (in.)
2
4
6
8
Figure 5.5 – Load-Displacement Hystereses for Specimens BE-1 and BE-3
5.8.3
Confining Reinforcement
Specimens BE-3 and BE-4 both incorporated confined boundary elements with returns at the
ends of the walls. Specimen BE-3 used No. 3, Grade 60 bars for the transverse reinforcement, while
Specimen BE-4 used ¼-in. diameter, A36 wire for the transverse reinforcement. Figure 5.6 shows the
load-displacement envelopes for these specimens. Both specimens performed almost identically up to
wall failure.
97
100
BE-3
80
BE-4
60
Load (kips)
40
20
0
-20
-40
-60
-80
-100
-8.0
-6.0
-4.0
-2.0
0.0
2.0
Displacement (in.)
4.0
6.0
8.0
Figure 5.6 – Load-Displacement Envelopes for Confining Reinforcement Comparison
From Table 5.5, it can be seen that the plastic hinge lengths for these two specimens were
significantly different. However, the calculated plastic hinge lengths for both specimens were affected
by the extent of plasticity exceeding the range of instrumentation on the walls.
Specimen BE-3 dissipated 11% more energy than Specimen BE-4 as indicated in Table 5.6. The
load-displacement hysteresis plots for both specimens are given in Figure 5.7 and illustrate the nearly
identical responses of the two walls. From Table 5.7, the equivalent viscous damping values were
approximately the same for both specimens.
98
100
BE-3
BE-4
80
60
Load (kips)
40
20
0
-20
-40
-60
-80
-100
-8
-6
-4
-2
0
2
Displacement (in.)
4
6
8
Figure 5.7 – Load-Displacement Hystereses for Specimens BE-3 and BE-4
5.9
Summary and Conclusions
In this chapter, the performance of masonry walls with integral confined concrete boundary
elements was evaluated and results were compared similar masonry walls tested by Kapoi (2012).
Predicted load capacity, drift, displacement ductility, height of plasticity, equivalent plastic hinge length,
total energy dissipation, and hysteretic damping were presented and discussed. The effects of various
parameters on wall performance were evaluated, including the effects from axial loading, boundary
element geometry, and type of transverse confining reinforcement.
XTRACT conservatively predicted the capacities of the walls with rectangular boundary elements
by 7% and 13% for walls with and without axial loading, respectively. These results are similar to those
obtained by Kapoi (2012) for comparable masonry walls. Load predictions for both flanged walls in this
study were overestimated by 4% and 5%, likely due to greater shear deformations associated with larger
lateral load capacities in these specimens. This finding indicates that shear deformations should be
99
included in analyses for walls in which a significant shear response is expected. Drift values at peak
load and at failure ranged from 5.4 to 14 times the drifts at the point of reaching the critical concrete
strain. Walls with confined concrete boundary elements had achieved ultimate drifts that were nearly
twice those for the similar masonry walls without boundary elements tested by Kapoi (2012). The walls
with rectangular boundary elements had less drift contributions from sliding and shear at failure than
the walls with flanged boundary elements. Displacement ductilities were approximately 30% larger for
the walls with flanged boundary elements than for walls with rectangular boundary elements. The
displacement ductilities were about 50% larger for the masonry walls with integral confined concrete
boundary elements when compared to the similar masonry walls without boundary elements tested by
Kapoi (2012).
Total energy dissipation values were approximately 2 to 3 times larger in the walls with confined
concrete boundary elements than for the similar masonry walls without boundary elements tested by
Kapoi (2012). Equivalent viscous damping values in the walls with confined boundary elements were
approximately 4% greater in the damping value than those for the similar masonry walls without
boundary elements tested by Kapoi (2012).
Axial compressive stress was found to increase the
initial stiffness and load capacities in the walls. Specimens had larger displacement capacities without
the presence of axial loading. The initial yield displacement and ultimate displacement were larger for
Specimen BE-1 than for Specimen BE-2. However, the displacement ductilities were nearly identical at
7.5. The total energy dissipated increased with the presence of axial loading, while the equivalent
viscous damping decreased.
Wall returns improved the stability of the walls between peak load and failure. Greater initial
stiffness and larger peak loads were attained in Specimen BE-3 with wall returns compared to Specimen
BE-1 without wall returns. A larger average total drift at failure and greater contributions from sliding
and shear occurred in the wall with the flanged boundary elements, both likely a result of larger lateral
100
load capacities. The displacement ductility value was greater for the flanged specimen, and improved
energy dissipation occurred along with an increase in hysteretic damping with the addition of wall
returns. Walls with rectangular boundary elements failed when the entire boundary element at the wall
base buckled out of plane. In the flanged walls, failure was caused by low-cycle fatigue fracture of the
tensile steel.
Walls with No. 3 bars and ¼-in. diameter wire for the transverse hoop reinforcement in the
boundary elements performed almost identically through peak load for both types of confinement.
Overall, very significant improvements in performance were achieved in the masonry walls with
integral confined concrete boundary elements when compared to similar masonry walls without
confinement. Boundary elements with returns provided added stability at large displacements, allowing
for significant increases in energy dissipation and ductility.
101
CHAPTER 6
SUMMARY, CONCLUSIONS, RECOMMENDATIONS AND FUTURE RESEARCH
6.1
Summary
This project was funded by the National Institute of Standards and Technology (NIST) as part of a
joint study between researchers at the University of California at San Diego, the University of Texas at
Austin and Washington State University to develop improved performance-based design provisions and
methodologies for reinforced concrete masonry shear walls. The objective of research reported in this
thesis is to investigate the behavior of masonry walls incorporating integral confined concrete boundary
elements at each end under lateral loading. Results from this study provide a basis for establishing
prescriptive detailing requirements for designing masonry walls with integral confined concrete
boundary elements.
Four, fully grouted, concrete masonry shear walls with integral confined concrete boundary
elements were designed according to the provisions of the 2011 MSJC and the 2011 ACI-318 codes. The
walls had an aspect ratio of 2.0 and two different axial compressive stress magnitudes of 0 and
0.0625f’m. Two walls had rectangular concrete boundary elements and the remaining two walls had
confined concrete boundary elements with flanges. The walls were constructed and tested at the WSU
Composite Materials and Engineering Center (CMEC). The reinforced concrete masonry portions of the
walls were constructed by professional masons and the WSU researchers constructed the confined
concrete boundary elements.
The wall specimens were subjected to a prescribed cyclic, in-plane lateral displacement
sequence. Specimen response was monitored by displacement potentiometers, strain gages, a load cell,
and a dial gage. Data recording and actuator control employed two integrated computer systems.
Recorded measurements from the instruments were used to plot load displacement hysteresis curves
102
from which energy dissipation and equivalent viscous damping values were calculated for each
specimen. Sliding, shear, and flexure displacement components were measured and/or calculated from
multiple displacement potentiometers. Sliding shear was monitored between the loading beam and the
top of the specimen and at the masonry-to-boundary element interface. Curvatures over the wall
height were established and utilized in determining the height of plasticity and the curvature ductility
for each wall. Displacement ductility was calculated from an elastoplastic approximation for each
specimen and the equivalent plastic hinge lengths were determined. Visual observations were recorded
during testing and used to describe wall behavior.
The effects of axial compressive stress, boundary element geometry and type of transverse
reinforcement in the boundary elements were evaluated to determine their influence on wall
performance. Wall performance was evaluated based on the peak load capacity, drift, displacement
ductility, equivalent plastic hinge length, energy dissipation, and equivalent viscous damping value. Test
results in this research were compared to results from tests on two similar masonry walls without
boundary elements performed by Kapoi (2012). Recommendations were provided for the design of
integral confined concrete boundary elements for application in masonry walls.
6.2
Conclusions
The four walls in this study displayed a flexural failure mode. Displacement ductilities ranged
between 7.5 and 9.8, with the larger values being achieved in the wall specimens with wall returns as a
result of additional stability from the returns.
The software program XTRACT was used to estimate the
peak load capacity of each specimen. The walls with rectangular boundary elements had experimental
peak load capacities that were 7% and 13% greater than predicted capacities obtained from XTRACT.
The walls with flanged boundary elements had experimental peak load capacities 4% and 5% less than
the predicted capacities. This unconservative trend for the walls with flanged boundary elements
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results from larger lateral load capacities leading to the larger shear deformations in these walls.
XTRACT does not consider shear response when calculating the moment-curvature of a cross section.
Effects of Confining Concrete Boundary Elements: The initial stiffness of reinforced masonry
walls with confined concrete boundary elements correlated well with the similar masonry walls without
boundary elements. Yield displacements from an elastoplastic approximation were larger in the walls
with boundary elements. The presence of boundary elements also increased the ultimate
displacements, with drifts at failure reaching 5.2%. Greater shear response was observed in the walls
with boundary elements because of larger lateral capacity and reduced the flexure contributions at
failure. Displacement ductility values increased with the inclusion of boundary elements. Total energy
dissipation was approximately 2.6 times greater in walls with boundary elements than in the similar
masonry walls without boundary elements.
Effects of Axial Compressive Stress: The presence of axial compressive stress caused an
increase in the initial wall stiffness and the peak load capacity. The yield displacement from the
elastoplastic approximation and the ultimate displacement were lower for the wall with axial
compressive stress. However, the resulting displacement ductilities were almost identical, indicating
that axial compressive stress did not seem to have much effect on the calculated displacement ductility.
Wall drifts and drift contributions were similar in both specimens. The total energy dissipation
increased 10% with the addition of axial loading.
Effects of Boundary Element Geometry: The initial stiffness was greater in the two specimens
with flanged boundary elements. The recorded peak loads were also significantly larger in the flanged
specimens. Drifts at failure were comparable at approximately 5% for both specimens. Displacement
ductility was 31% greater for the walls with flanged boundary elements compared to walls with
rectangular geometry. The total energy dissipated by the flanged specimens was 38% more than the
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wall with rectangular boundary elements. All of these benefits were a result of the increased out-ofplane stability provided by the flanged boundary elements.
Effects of Boundary Element Confining Hoops: Two flanged walls incorporated different bar
sizes for the transverse hoops. One type used No. 3 hoops, while the other employed ¼-in. round wire.
Both types of hoops were spaced at 2.5-in. on center over the height of the boundary elements. Wall
responses with the two types of transverse hoops were nearly identical.
6.3
Recommended Guidelines for Designing Integral Confined Concrete Boundary Elements
Integral confined concrete boundary elements should be designed according to the following
guidelines. The required geometric size of the boundary element should be determined by either
Section 3.3.6.5.3 or Section 3.3.6.5.4 of the 2011 MSJC.
First, to ensure adequate confinement of the concrete core in the boundary elements,
determine the required spacing of the transverse reinforcement from the smallest of the following:
1.)
One-third the minimum boundary element dimension;
2.)
Six times the diameter of the smallest longitudinal bar in the boundary element;
(
3.)
)
Where:
so
= the center-to-center spacing of transverse reinforcement with length lo (in.),
shall not exceed 6 in. and need not be less than 4 in.;
and
hx
= maximum center-to-center horizontal spacing of crossties or hoop legs on all
faces of the column or boundary element (in.).
Second, to prevent buckling of the longitudinal steel of the boundary element, calculate the
required area of transverse reinforcement for the spacing determined above as follows:
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Where:
Ash
= the total cross-sectional area of transverse reinforcement (including crossties)
within spacing s and perpendicular to dimension bc;
s
= the center-to-center spacing of transverse reinforcement (in.);
bc
= the cross-sectional dimension of the boundary element core measured to the
outside edges of the transverse reinforcement composing area Ash (in.);
f’c
= the specified concrete compressive strength (psi); and
fyt
= the specified yield strength of transverse reinforcement (psi).
Finally, check shear friction at the interface between the masonry wall and the concrete
boundary element to ensure the specified horizontal reinforcement has the required capacity. To do so,
calculate the shear stress at the interface assuming elastic behavior and using mechanics principles.
Then, determine the average shear capacity on the interface using the following equation:
where:
b
= the width of the wall (in.); and
sh
= the spacing of the horizontal reinforcement (in.)
From ACI 318-11,
(
)
but not greater than 80bd for normal weight
concrete and where contact surfaces are clean, free of laitance, and not intentionally roughened. Av is
the cross-sectional area of the shear reinforcement (in2), fyv is the tensile yield stress of the horizontal
reinforcement (psi), and d is the distance from the extreme compression fiber to the centroid of the
vertical tension reinforcement (in.). The horizontal reinforcement spacing shall not be larger than four
times the minimum boundary element dimension nor exceed 24 in.
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6.4
Future Research
Only four specimens were tested and therefore limit the conclusions of this study. Additional
wall tests should be conducted that compare the effect of axial compressive stress, boundary element
geometry, and boundary element confinement reinforcement to provide additional results and
corroborate the findings of this research. Future research should investigate how confining boundary
elements utilizing grout behave compared to the concrete boundary elements investigated herein.
107
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