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This thesis is dedicated to
My parents
For their endless love, support and encouragement
For my sisters and brothers…aunts and uncles
For my friends and every one that support me so that this thesis
had accomplished
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DEDICATION
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First of all praise be to Allah for completing this thesis and for provide me the
patient and ambition required to complete the requirements of the master degree. Then I
would like to demonstrates that this thesis is completed with prayer of many, and love
of my family and friends.
Many thanks and gratitude are given to my supervisor Dr. Nazzal Armouti who
had supporting and guiding me with stimulating suggestions and encouragement to go
ahead in all the time of the thesis work.
Special thanks to the thesis committee: Dr. Samih Qaqish, Dr. Abdelqader
Najmi, and Dr. Yahya Qawasmi, for their encouragement, valuable comments and
discussion.
I owe my deepest gratitude to my mother for her support and prayers that make
this thesis possible and to my uncle Eng. Yahya Smadi for his encouragement, help and
guidance.
Last but not least my gratitude towards my parents, family, friends and every
one that support and encourage me.
Rasha M. Al-Sulieman
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ACKNOWLEDGEMENT
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Committee Decision ……………………………………………..................................
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Dedication .................…………………………………..................................................
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Acknowledgement ………………………………………...…..…….............................
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List of Contents...………………………………………………….................................
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List of Tables.....……………….……………………………………………………….
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List of Figures................…………………………….………………………………….
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Abstract ………………………………………..………………….…....….. ………….
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Chapter 1: Introduction……………………………………………………………….
1
1.1 Lateral Load Resisting Systems…………………………………………………….
2
1.1.1 Structural Frame System……………………………………………….............
2
1.1.2 Shear Wall System……………………………………………………………...
2
1.1.3 Dual System…………………………………………………………………….
2
1.2 Shear Wall Types…………………………………………………………………...
3
1.2.1 Cantilever Shear Wall…………………………………………………………...
3
1.2.2 Coupled Shear Wall……………………………………………………………..
4
1.2.3 Multiwall System………………………………………………………………..
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1.3 Methods of Analysis………………………………………………………………..
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1.4 Literature Review ………………………………………………………………….
10
1.5 Study Objective…………………………………………………………………….
13
1.6 Scope of work………………………………………………………………………
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List Of Content
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2.1 Methods Description and Characteristics…………………………………………..
2.1.1 Continuous Medium Method “Lamina Method”……………………………...
2.1.2 Equivalent Frame Method “Wide Column Analogy”…………………………
2.1.3 Finite Element Method………………………………………………………..
2.2 Nonlinear static analysis (pushover)………………………………………………..
2.3 Nonlinearity of the materials………………………………………………………..
2.3.1 Concrete Material………………………………………………………………
2.3.2 Reinforcement………………………………………………………………….
2.4 Type of elements………………………………………………………………........
2.4.1 Shell elements/ Layered shell element…………………………………………
2.4.2 Frame element………………………………………………………………….
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2.5 Hinges properties………………………………………………………………........
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Chapter 3: Research Methodology………………………….….….............................
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3.1 Material properties………………………………………………………………….
3.1.1 Concrete………………………………………………………………………
3.1.2 Reinforcement………………………………………………………………….
3.2 Model geometry and sections……………………………………………………….
3.3 Loads………………………………………………………………………………..
3.3.1 Mass sources………………………………………………………………….
3.3.2 Load cases……………………………………………………………………...
3.4 Boundary Condition………………………………………………………………...
3.5 Shell layered section model…………………………………………………………
3.6 Frames section model…………………………………………………………….....
3.7 Plastic Hinges……………………………………………………………………….
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Chapter 2: Model and Analysis……………………………………………………….
3.7.1 Nonlinear hinge assignment………………………………………………….
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3.7.2 Nonlinear hinge property calculation………………………………………….
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3.7.2.1 P-M3 hinge……………………………………………………………..
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3.7.2.2 Shear hinge……………………………………………………………..
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Chapter 4: RESULTS AND DISCUSSION…….…….................................................
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4.1 Case 1……………………………………………………………………………....
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4.2 Case 2………………………………………………………………………………
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Chapter 5: CONCLUTION……………………………………………………………
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References……………………………………………………........................................
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Abstract (Arabic)………………………….…................................................................
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3.1
Concrete Material Properties
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3.2
Reinforcement Material Properties
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4.1
Modal Analysis Results for Case 1
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4.2
Modal Analysis Results for Case 2
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List of Tables
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1.1
Shapes Shear Wall
3
1.2
Behavior of Coupled Shear Wall Due to Lateral Load
4
1.3
Various Type of Opening Shape Through Shear Walls
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1.4
Coupling Beam Shear failure
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1.5
Coupling Beam Bending failure
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1.6
Coupling Beams Diagonal Reinforcement
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1.7
Building with Multiwall
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2.1
A Model Test for a Shear Wall of C Shape.
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2.2
A Model Test for a Coupled Shear Wall.
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2.3
The Replacement of the Discrete Shear Forces Qs in the
Connecting Beams by a Shear Flow Function q (Shear Force Per
Unit Height).
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2.4
A Coupled Shear Wall Modeled by an Equivalent Frame Method.
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2.5
Coupling Beams Representation in Equivalent Frame Method.
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2.6
A Coupled Shear Wall Modeled by the Finite Element.
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2.7
Simple Concrete Stress Strain Curve
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2.8
Stress-Strain Relation for Monotonic Loading of Confined and
Unconfined Concrete – Mander Et Al. (1988).
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2.9
Chart of Confined Strength Ratio in Terms of Two Lateral
Confining Stresses for Rectangular Section. Mander. Et., (1988)
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2.10
Rebar Stress Strain Curve
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2.11
Layered Shell Element
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2.12
Force-Deformation for Pushover Hinge (CSI Analysis Reference
Manual).
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3.1
A Plan View of Study Case Building
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3.2
Model of Case 1
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3.3
Model of Case 2
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3.4
Concrete Stress Strain Curve
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List of Figures
3.5
Reinforcement Stress Strain Curve
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3.6
Coupled Beams Section
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3.7
Nonlinear Static Dead Load Case
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3.8
Nonlinear Static Pushover Case
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3.9
Layered Shell Element Definition
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3.10
Shell Layered Element Models for Case 1 and Case 2.
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3.11
Nonlinear Hinges Assignment For Case 1
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3.12
Nonlinear Hinges Assignment For Case 2
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3.13
Generated P-M3 Hinge Property for Shear Wall Case 1
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3.14
Axial-Moment (PMM) interaction surface-case 1
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3.15
Moment-Plastic rotation (M- θp) relation-case 1
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3.16
Shear Hinge V2 -case 1
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4.1
Modal Analysis Results for Case 1
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4.2
Capacity Curve for Case 1
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4.3
P-M3 Hinge result- Case 1
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4.4
Concrete S22 Stress For Shell Layered Element- Case 1
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4.5
Concrete S12 (Shear) Stress For Shell Layered Element- Case 1
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4.6
The Formation of the Plastic Hinge Through the Push Steps-Case 1
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4.7
Plastic Hinge Collapse in the Frame Model- Case 1
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4.8
Modal Analysis Results for Case 2
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4.9
Pushover Curve for Case 2
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4.10
Concrete S22 , S12 Stress For Shell Layered Element - Case 2
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4.11
Plastic Hinges in the Frame - Case 2
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By
Rasha Mufleh ALSulieman
Supervisor
Dr. Nazzal S. Armouti
ABSTRACT
Reinforced concrete shear wall systems are part of the most common used
systems in structures to resist lateral loads. Coupled shear walls are among shear walls
that are used in buildings to resist lateral loads due to their ductility. In this research, a
study building is chosen with a lateral load resisting system of shear walls. The existing
cantilever shear walls and coupled shear wall are analyzed by two methods of modeling,
equivalent frame model using frame elements with plastic hinges and finite element
model using layered shell elements. The two models are subjected to nonlinear static
pushover analysis through monotonically applied horizontal force using SAP 2000
program. A comparison is performed between the two models. The results show that
both models exhibit the same behavior. Moreover, the base shear- displacement curve
for both models proved to be identical. In addition, the period of the two models show
close agreement. It has been also shown that the equivalent frame model can be used
efficiently as a replacement to the shell layered finite element models.
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EFFICIENCY OF EQUIVALENT FRAME METHOD IN COUPLED
SHEAR WALLS IN SEISMIC ANALYSIS
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CHAPTER ONE
In Jordan, reinforced concrete shear walls systems, which are efficient for
multistory buildings up to 35 story range, are the most common systems that used in
structures to resist the lateral earthquake loads.
Shear wall is one of lateral load resisting systems, that can resist a high fraction
of lateral load. To be effective and sufficient, it must be located in suitable place within
the building where the designer must satisfy the basic criteria of stiffness, strength, and
ductility. Lateral load resisting systems are many types but buildings having shear walls
as lateral load resisting system are relatively stiffer, and hence reduce the second order
effects, the needed strength can be achieved through appropriate longitudinal and
transverse reinforcement details where ductility can be obtained with special detailing
measures. In addition, buildings behavior with shear walls subjected to earthquake
excitation is more reliable since shear walls are able to hold most of their vertical load,
even after cracks occur. In shear wall systems, there is no need to separate the
nonstructural elements from the lateral load resisting system.
When Shear walls having openings, for mechanical or architectural purposes,
their behavior would change depending on, the size and location of the opening, turning
it into one of shear wall types.
One type of shear walls with openings is Coupled shear wall which is a
continuous wall with vertical rows of opening created for windows and doors, coupled
by beams that interconnecting the blade walls across the openings.
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INTRODUCTION
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1.1
Lateral Load Resisting Systems
Reinforced concrete (RC) frames consist of horizontal elements (beams) and
vertical elements (columns) connected by rigid joints. RC frames provide resistance to
both gravity and lateral loads through bending in beams and columns.
1.1.2 Shear Wall System
Shear walls are those vertical walls which can serve architecturally as partitions
or cores of elevator and stairs and structurally by holding the gravity load and resisting
the horizontal earthquake forces. Shear walls can be economical up to about 35 stories.
1.1.3 Dual System
When concrete rigid frames connected with shear walls and share together the
resistant of the lateral load this system is called dual system or wall frame system. This
system is appropriate for buildings with 40-60 stories.
“Selection of structural system for building is influenced primarily by the
intended function, architectural consideration, internal traffic flow, height and aspect
ratio, and to a lesser extent, the intensity of loading”. (Pauly and Preistly, 1992, p.g 15)
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1.1.1 Structural Frame System
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1.2
Shear Wall Types
When a shear wall is not connected to any other walls and continuous to the base
without any openings it can be classified as short, squat or vertical cantilever according
to their height/width ratio as shown in Figure 1.1.
Figure 1.1 Shapes of Shear Wall
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1.2.1 Cantilever Shear Wall
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For future work its recommended to use the nonlinear link spring in order to
improve the plasticity behaviour at the plastic regions.
More models are needed in order to improve the behaviour of different types of
shear walls using the equivalent frame model.
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Future work
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ACI318 M (2005), Building Code Requirements for Structural Concrete and Geometry,
American Concrete Institute.
Agarwal, P. and Shrikhande, M. (2006), Earthquake Resistant Design of Structures,
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rehabilitation of buildings.
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References
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Ho S.Y. and Wang, C. Y. (2006), Determination of the Plastic Hinge Properties of RC
structure containing Brick Walls, Structural Engineering of Taiwan, China.
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Naeim, F. (2001), The Seismic Design Handbook, 2nd Edition, Springer.
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Hughes T. J. R. (2000), The Finite Element Method: Linear Static and Dynamic Finite
Element Analysis, Dover.