performance evaluation of planer shear wall with …
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Structural Engineering Thesis
2020-03-17
PERFORMANCE EVALUATION OF
PLANER SHEAR WALL WITH AND
WITHOUT BOUNDARY ELEMENT IN
MULTISTORY BUILDINGS UNDER
HIGH SEISMIC LOAD
Teklay, Habtie
http://hdl.handle.net/123456789/10497
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BAHIR DAR UNIVERSITY
BAHIR DAR INSTITUTE OF TECHNOLOGY
SCHOOL OF RESEARCH AND POSTGRADUATE STUDIES
FACULTY OF CIVIL AND WATER RESOURCE ENGINEERING
MASTERS THESIS
BY
HABTIE TEKLAY FITWI
Bahir Dar, Ethiopia
July 7, 2018
PERFORMANCE EVALUATION OF PLANER SHEAR WALL WITH AND
WITHOUT BOUNDARY ELEMENT IN MULTISTORY BUILDINGS UNDER
HIGH SEISMIC LOAD
By
Habtie Teklay Fitwi
A Thesis submitted to the school of Research and Post Graduate Studies of Bahir Dar
Institute of Technology, BDU in partial fulfillment of the requirements for the
Degree of
Master of Science in the Structural Engineering in the Faculty of Civil and Water
Resource Engineering
Advisor
Dr. Temesgen Wondimu
Bahir-Dar, Ethiopia
July 7, 2018
3
ACKNOWLEDGMENT
First I would like to thank almighty God for his unending blessings.
I would like to thank Ethiopian Roads Authority (ERA) for sponsoring my post
graduate study at Bahir Dar University in the capacity building program to improve
Ethiopian Science and Technology capacities.
I wish to express my deep gratitude to my advisor Dr. Temesgen Wondimu for giving
me the opportunity to carryout research work on this title. I am highly indebted to him
for his valuable thoughts, support, guidance, patience, and profound knowledge
towards the development of my thesis.
I owe a debt of gratitude to all my instructors and the institute as a whole for their
help during my stay in Bahir Dar University.
I would like to express my gratitude to my colleagues for their support and sharing
materials and ideas during the preparation of this thesis.
Finally, I would like to thank my parents and my friend whose unconditional love and
encouragement always enlighten the road that I go and provide me the strength to
overcome many difficulties in the life.
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ABSTRACT
In medium and high rise building, reinforced concrete shear walls are a predominant
lateral load resisting members in shear wall system and wall-frame lateral building
systems under lateral loads. Constructions of medium to high rise buildings in seismic
zone of Ethiopia are becoming significant in number. Thus proper detailing and
construction of shear walls should be considered seriously in achieving a good
seismic performance of such structures for seismic loads. Shear wall unlike column
has a significant stress variation along the cross section. Away from the neutral axis
the stress is getting increased and reaches maximum at the free edges. In addition, due
to reversal nature of seismic actions, free edges of shear wall are subjected to high
stress. So that this portions of shear wall need special treatment. Two kinds of shear
wall design/ detail approaches are considered in the thesis, which are shear wall
designed having boundary element at both free edges based on ES EN 2015 code and
shear wall designed with uniformly spaced reinforcement throughout the wall in a
multistory building as usual case of construction of shear walls in Ethiopia.
In this thesis, the seismic performance of those shear wall types on 15 story buildings
was investigated. To do this, first the whole building structural elements were
designed according to ES EN 2015 code but the second type of shear wall which was
detailed with uniform size and space of reinforcement to simulate the actual practice.
Then a three dimensional pushover analysis was carried out using ETABS software
incorporating definition of nonlinear materials. A smeared multi layer shell elements
was used to model both types of shear wall. The parameters employed for
comparisons were base shear force, top story displacement, internal forces in frames
and formation of plastic hinges.
The results show that shear wall having boundary element in a fifteen story building
has significant difference in global displacement and strength for the overall structure
of the buildings as compared to that of shear wall have no boundary element. Even if
the buildings for both shear wall types have shown elastic state, frame elements in
case-1 building have a better formation of hinges and lesser internal forces have been
observed under pushover analysis. Detail results are discussed in the last chapter.
Keywords- Shear wall, Boundary element, Pushover analysis, Multi-layer
shell element.
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TABLE OF CONTENTS
DECLARATION ........................................................................................................... 1
ACKNOWLEDGMENT................................................................................................ 3
ABSTRACT ................................................................................................................... 4
TABLE OF CONTENTS ............................................................................................... 5
LIST OF TABLES ......................................................................................................... 6
LIST OF FIGURES ....................................................................................................... 7
NOTATIONS ................................................................................................................. 8
CHAPTER ONE .......................................................................................................... 10
1. INTRODUCTION ................................................................................................ 10
1.1 Background ................................................................................................... 10
1.2 Research objective......................................................................................... 12
1.2.1 General objective ................................................................................... 12
1.2.2 Specific objectives ................................................................................. 12
1.3 Scope and Significance of the research ......................................................... 12
1.4 Report organization ....................................................................................... 12
CHAPTER TWO ......................................................................................................... 14
2 LITERATURE REVIEW ..................................................................................... 14
2.1 Overview ....................................................................................................... 14
2.1.1 Shear wall design approaches ................................................................ 14
2.1.2 Analytical study on boundary elements of shear wall ........................... 20
2.1.3 Nonlinear shear wall modeling techniques ............................................ 22
2.1.4 Structural analysis methods ................................................................... 24
CHAPTER THREE ..................................................................................................... 28
3 RESEARCH METHODOLOGY ......................................................................... 28
3.1 Overview ....................................................................................................... 28
3.2 Design and detailing of shear walls in 15 story buildings ............................ 30
3.3 Non-linear modeling of structural elements .................................................. 31
3.4 Non-linear analysis method ........................................................................... 32
CHAPTER FOUR ........................................................................................................ 35
4 DESIGN and ANALYSIS .................................................................................... 35
4.1 OVERVIEW.................................................................................................. 35
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4.2 Design of case buildings ............................................................................... 35
4.3 Non Linear Analysis of Designed case Buildings ......................................... 36
4.3.1 Non linear static analysis of case buildings ........................................... 36
CHAPTER FIVE ......................................................................................................... 39
5 RESUTLTS AND DISCUSSION ........................................................................ 39
5.1 Overview ....................................................................................................... 39
5.2 The designed structural element sections for case-1 & case-2 building ....... 39
5.3 Comparison of case buildings under pushover analysis................................ 40
5.3.1 Capacity (Pushover) curve ..................................................................... 40
5.3.2 Plastic hinge formation .......................................................................... 42
5.3.3 Global story force and displacement of Case Buildings ........................ 44
5.3.4 Internal forces in frame elements ........................................................... 45
CHAPTER SIX ............................................................................................................ 47
6 CONCLUSION AND RECOMMENDATION ................................................... 47
6.1 Conclusion ..................................................................................................... 47
6.2 Recommendation ........................................................................................... 47
7 REFERENCE ....................................................................................................... 48
8 APPENDIX .......................................................................................................... 50
8.1 Appendix - A ................................................................................................. 51
8.2 Appendix - B ................................................................................................. 62
LIST OF TABLES
Table 3-1 Material Properties of Buildings ................................................................ 28
Table 4-1 Distribution of lateral loads over the height of case buildings in both ........ 37
Table 5-1 A typical designed case building floor plan layout. (Using ETABS
software) .............................................................................................................. 40
Table 5-2 Summarized plastic hinge formation of both case buildings in percentage at
last ........................................................................................................................ 42
Table 5-3 Moment increment in case-2 building to that of case-1 building in the
direction ............................................................................................................... 45
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Table 5-4 Increment of Internal forces of columns in case-2 building to that of case-1
.............................................................................................................................. 46
LIST OF FIGURES
Figure 2-1 Simplified compression and tension forces in planner shear wall ............. 16
Figure 2-2 Varying planes strain of linear strain [11] ................................................. 18
Figure 2-3 Wall pier stress-strain relationship [11] .................................................... 18
Figure 2-4 The average ratios of strength and its corresponding displacement in ...... 20
Figure 2-5 The ratios of strength and its equivalent displacement in models with 1 . 21
Figure 2-6 Shear wall and its equivalent frame model ................................................ 23
Figure 2-7 Multi-layer shell element and distribution of bar layers ............................ 23
Figure 2-8 A Generalized pushover curve of RC structure. ....................................... 26
Figure 3-1 Mathematical model of 15 story building. A) Typical floor plan and ....... 30
Figure 3-2 Generalized force- deformation curve for RC Buildings .......................... 31
Figure 3-1 Flow chart of Research Methodology. ....................................................... 34
Figure 5-1 Pushover curves of case-2 building a) In X- direction b) In Y-direction
.............................................................................................................................. 41
Figure 5-2 Pushover curves of case-1 building a) In X- direction b) In Y-direction .. 41
Figure 5-3 Plastic hinge distribution of last step for case-2 building in X-direction a)
on .......................................................................................................................... 43
Figure 5-4 Plastic hinge distribution of last step for case-1 building in x-direction a)
on .......................................................................................................................... 43
Figure 5-5 Plastic hinge distribution of last step for case-1 building in x-direction a)
on .......................................................................................................................... 44
Figure 5-6 Displacement at the center of diaphragms in both case buildings ............ 44
Figure 5-7 Global story forces of both case buildings a) story axial force vs. story . 45
Figure 5-9 Typical floor plans as modeled in ETABS software. ................................. 46
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NOTATIONS
ADRS Acceleration-Displacement Response Spectrum
ATC Applied Technology Council
ACI American Concrete Institution
CM Center of Mass
CP Collapse Prevention
CSM Capacity Spectrum Method
DCM Displacement Coefficient Method
DL Dead Load
EBCS Ethiopian Building Code Standard
ETABS Extended Analysis of Building Structures
FEMA Federal Emergency Management Agency
IO Immediate Occupancy
LL Live Load
LS Life Safety
MDOF Multiple Degree of Freedom
MPA Modal Pushover Analysis
mpa Mega Pascal
ND Nonlinear Dynamic Analysis
NEHRP National Earthquake Hazards Reduction Program
NS Nonlinear Static Analysis
SW Shear wall
2D Two Dimensional
3D Three Dimensional
ao Constant bed rock acceleration
As Area of Reinforcement
Cs Compression force in Steel
Ԑc Concrete Strain
Es Steel Modules Elasticity
Ԑs Steel Strain
g Acceleration of gravity
Δ Roof displacement
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P Axial force
M2 Moment in 2 axis
M3 Moment in 3 axis
Lp Plastic hinge length
L Section depth in the direction of load
Teff Effective period
βeff Effective damping
μ Ductility ratio
β0 Initial damping
To Initial period
Ts Tension force in steel
Sa Spectral acceleration
Sd Spectral displacement
σs Steel Stress
ɸ Bar diameter
@ at
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CHAPTER ONE
1. INTRODUCTION
1.1 Background
In medium and high rise building, reinforced concrete shear walls are a predominant
lateral load resisting members in shear wall system and wall-frame lateral building
systems under lateral loads. Construction of medium to high rise buildings in seismic
zone of Ethiopia becomes significant in number. Thus proper detailed and
construction of shear walls should be considered seriously in achieving a good
seismic performance of such structures under seismic loads. Based on the geometry
and the detailed reinforcements applied, Reinforced concrete shear walls can be of
either shear wall with boundary element or shear wall without boundary element.
Composite wall sections consisting of connected or intersecting rectangular segments
(L-, T-, U-, I- or similar sections) should be taken as integral units and in this case
where effective parts of flanges act together with webs then it is considered as
boundary element (EBCS. 1995). Besides, boundary elements can exist when
longitudinal reinforcements are arranged in bundled manner (closely spaced) and
properly confided with transverse reinforcement at the free edges of single planer
shear wall. Whereas, shear wall without boundary element is found in where the wall
detailed with uniformly spaced and have same size of reinforcement throughout the
length of the member.
The principles applied for compression members may be used for structural walls as
stated in EBCS-2, 1995, and the bending resistance shall be evaluated and verified as
for columns under unfavorable axial force for the seismic load combination (EBCS-8,
1995). But above the critical region, the code recommends boundary element to be
provide for the height one more story use at least half confined reinforcement
calculated for the critical region at base of the wall. Whereas the new Ethiopian
building code, ES EN-2015 which was adapted from Eurocode-2004 incorporates
condition for the need of shear wall boundary element by specifying the compressive
strength of the extreme fiber of shear wall which is under compressive stress is
limited up to twenty percent of characteristic cylindrical compressive strength of
concrete, i.e. fc>0.2fc‟. Particularly, the two codes (old and new) on reinforcement
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detailing of shear wall have significant different as stated above. In the oldest
Ethiopian code, by default stories above the critical region that is at the base and one
more story, all are detailed using uniformly spaced reinforcement as there is no need
any boundary element. It is commonly practiced in engineering community with
regarding to lesser time to design and simple to construct RC shear walls. The new
Ethiopian building code, unlike the oldest one irrespective of height of story it
declares boundary longitudinal reinforcement and confinement at the edges of shear
wall where the maximum compressive stress at the extreme fiber is beyond 20% of
characteristic cylindrical compressive strength of concrete. RC Shear wall with and
without boundary elements can experience different performances under lateral loads
in the inelastic deformation state (hanish, 2016).
Most buildings including under constructions were designed and detailed according to
the previous Ethiopian code. Even nowadays there is no consistence in
implementation of the new Ethiopian building code. There is no a clear understanding
in between those two types of RC shear wall detailing in the engineering community.
In this thesis, a dual structural system having 15 stories building will be considered.
First the building is designed according to Ethiopian new building code, ES EN 2015.
Shear walls designed and detailed to account both boundary elements and non
boundary elements. The seismic performance of those dual structural systems due to
their shear wall reinforcement details will be investigated through definition of
nonlinear material model. Shear wall will be modeled with a fine mesh of smeared
multi-layer shell elements and for boundary elements confided concrete material
model are used. The main criteria used to compare seismic performances by taking
the demand parameters such as base shear, top story displacement, and formation of
plastic hinges and, internal force. Pushover analysis, a nonlinear static analysis in
which permanent gravity load and gradually increased lateral loads are applied, is
selected to carry out the post-elastic effects of the buildings consideration.
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1.2 Research objective
1.2.1 General objective
This study is concerned with the performance of RC shear wall having boundary
elements with that of the same but have no boundary elements in a multistory building
(dual system). A fifteen stories building have been considered through design and
evaluation of performances for the two cases.
1.2.2 Specific objectives
1. Compare the performance criteria of both types RC planer shear walls using
the demand parameters such as base shear, top floor deformation, and
formation of plastic hinge mechanism.
2. To show the internal stress developed in frame structures due to application of
both types of RC planer shear wall.
3. To give insights in selection of RC shear wall reinforcement detail regarding
with boundary elements according to Ethiopian high seismic zones.
1.3 Scope and Significance of the research
In this thesis, a dual structural system having 15 stories building will be considered.
First the building is designed according to Ethiopian new building code, ES EN 2015.
Shear walls are designed and detailed to account both boundary elements and non
boundary elements and set two building cases i.e. case-1 building and case-2 building.
The seismic performance of those case buildings have been investigated by carryout
non linear static analysis. Design and also pushover analysis are done using ETABS
2016 licensed software.
The thesis gives insight for engineering communities while they are doing design and
construction of shear walls. And it initiates to do farther investigation in detailing of
reinforcements in all types of shear wall.
1.4 Report organization
This thesis consists of five chapters and an Appendix. Chapter one is an introduction
to the research. Chapter two of this thesis presents a literature review consisting of
shear wall design approach; analytical study of boundary element of shear wall,
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structural analysis method, Chapter three presents the research design and
methodology in detail. Chapter four presents the design and analysis case buildings.
Chapter five provides a summary, conclusions, and recommendations made for
further research on this area of study.
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CHAPTER TWO
2 LITERATURE REVIEW
2.1 Overview
Even though there are lots of literatures on boundary elements of shear wall, many of
them are focused on modeling techniques and conducting tests.
As discussed in the introduction part the main goal of this thesis is quantifying the
significant effect of shear wall with and without boundary elements on multistory
buildings. This chapter presents are view of literatures on design approaches of shear
wall, analytical study of boundary element of shear wall and structural analysis
methods.
Depending on the height-to-width ratio structural walls can be classified as tall wall
(hw/lw substantially more than two, squat wall (hw/lw less than two) [2]. The
deformations of a tall wall and a squat wall are governed by flexure and shear,
respectively. Being the major lateral load resistant units in multistory building
structures, shear walls have been studied experimentally and theoretically over the last
fifty years.
2.1.1 Shear wall design approaches
Different building codes put their own provisions and detail procedures for the design
and detail of reinforced concrete shear wall. Among them most practicing engineer
community uses are discussed.
The recent AC1-318- 2014 code [15] states, the need for boundary elements of special
structural wall based on two criteria. First, follows from a displacement-based
approach. The approach assumes that special boundary elements are required to
confine the concrete where the strain at the extreme compression fiber of the wall
exceeds a critical value when the wall is displaced to 1.5 times the design
displacement. That is, compression zones shall be reinforced with special boundary
elements where:
)5.1(600Hw
u
LwC
………………………………. Eqn - 1
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Where: = neutral axis depth
u = Design displacement
w = Length of the wall
w = Height of the wall
The multiplier of 1.5 on design displacement was added to Eqn-1 in the recent 2014
version of this Code to produce detailing requirements more consistent with the
building code performance intent of a low probability of collapse in Maximum
Considered Earthquake level shaking.
Second, the compressed boundary at the critical section resists the tributary gravity
load plus the compressive resultant associated with the bending moment. Recognizing
that this loading condition may be repeated many times during the strong motion, the
concrete is to be confined where the calculated compressive stresses exceed a nominal
critical value equal to 0.2fc′. The stress is to be calculated for the factored forces on
the section assuming linear response of the gross concrete section. The compressive
stress of 0.2fc′ is used as an index value. Even it declares also where the spatial
boundary elements discontinued by which the calculated compressive stress is less
than 0.15fc′. The later approach is also adopted by Indian code.
In previous Ethiopian building code EBCS-1995 [2], the principles applied for
compression members may be used for structural walls, and the bending resistance
shall be evaluated and verified as for columns under unfavorable axial force for the
seismic load combination [3]. But it recommends there is a need to provide boundary
element above the critical region, for the height one more story use at least half
confined reinforcement calculated for the critical region at base of the wall. Analysis
and design of Isolated Shear wall was carried out by considering isolated columns
design procedures for uniaxial bending case according to EBCS-2, 1995 code. And
they recommended it as a preliminary section for shear wall design [14].
In draft final ES EN 2015 code [4], which is fully adopted from Eurocode-2004,
provides the formula below as a condition for the need of boundary elements. The
detail reinforcement calculations of boundary elements were provided in terms of
mechanical volumetric ratio of the required confining reinforcement ωwd with the
values of μφ, curvature ductility as specified here;
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αωwd ≥ 30 μφvd . sy,d . (bc/bo) – 0.035 ……………….. Eqn - 2
Where: ωwd = Mechanical volumetric ratio of confining hoops
μφ = Curvature ductility factor
vd = normalized design axial force (νd= NEd/Ac,fcd)
Ꜫsy,d = the design value of tension steel strain at yield
bc = the gross cross-sectional width
bo= the width of confined core (to the centerline of the hoops)
α = the confinement effectiveness factor,
Eurocode-2004 is one of the shear wall design manual applied for design software
packages. In analysis and design software (such as SAP2000 & ETABS), design of
shear wall section is carried out with Simplified compression and tension forces
approach and checking uniformly reinforced design approaches according to different
code provisions. Simplified compression and tension forces approach is a predefined
the boundary elements (pier edges) and all the factored axial and bending moment are
converted to an equivalent compression and tension forces as shown below.
Figure 2-1 Simplified compression and tension forces in planner shear wall
elevation & plan view. Source: Shear Wall Design Manual [11]
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The program will increment the appropriate B1 dimension to left, right or both
depending on which edge member is inadequate.
…………….. Eqn -3
The program will increment the appropriate B1 dimension to left, right or both
depending on which edge member is inadequate.
This implies in all cases the shear wall section has at list a minimum reinforced
boundary element (pier edge).This method is an approximate but convenient algorism.
Wall piers that are declared overstressed using this algorism could be found to be
adequate if wall pier accurately evaluate using interaction diagram as stated in EC-2
2004 shear wall design manual.
Checking uniformly reinforced design approaches, as the name indicates the shear
wall sections are first checked for boundary elements (pier edge) using equation Eqn -
2. The program creates an interaction surface for the section and uses that interaction
surface to determine the critical flexural demand/capacity ratio for the section.
In the program, a three-dimensional interaction surface is defined with reference to
the P, M2, and M3 axes. The surface is developed using a series of interaction curves
that are created by rotating the direction of the pier neutral axis in equally spaced
increments around a 360-degree circle. Each PMM interaction curve that makes up
the interaction surface is numerically described by a series of discrete points
connected by straight lines. The program uses the requirements of force equilibrium
and strain compatibility to determine the nominal axial load and moment strength (Nr,
M2r, M3r) of the wall pier. The coordinates of these points are determined by rotating
a plane of linear strain on the section of the wall pier.
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Figure 2-2 Varying planes strain of linear strain [11]
In these planes, the maximum concrete strain is always taken as -0.0035 and the
maximum steel strain is varied from -0.0035 to plus infinity.
Figure 2-3 Wall pier stress-strain relationship [11]
The program develops a 3D interaction surfaces at equally rotated angle, which is by
default 15 degree, through the following procedures:
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1. The value for maximum strain in the reinforcing steel is assumed. Then the
strain in all other reinforcing steel is determined based on the assumed plane
of linear strain.
2. The stress in the reinforcing steel is calculated
3. Then the force in the reinforcing steel is calculated
σ
4. The Nr, M2r and M3r values are calculated using equilibrium equations then
make up one point on the wall pier interaction diagram.
5. Additional points on the diagram are obtained by making different
assumptions for the maximum steel stress; that is, considering a different plane
of linear strain, and repeating the above the process.
6. When one interaction curve is complete, the next orientation of the neutral
axis is assumed and the points for the associated new interaction curve are
calculated. This process continues until the points for all of the specified
curves have been calculated.
For a given design load combination, the program generates a demand/capacity ratio
associated with each of the interaction surfaces. The program then uses linear
interpolation between the interaction surfaces to determine the reinforcing ratio that
gives a demand/capacity ratio of 1(0.999). The wall pier demand/capacity ratio is a
factor that gives an indication of the stress condition of the wall with respect to the
capacity of the wall.
The later design approach is an efficient in economic aspect as compared to simplified
C & T design approach. Design of shear wall sections are carried out using checking
uniformly reinforced design approaches in most practicing engineering community.
But a clear difference has been seen in detailing of reinforcement shear wall sections.
Once the section is designed, the program can gives percentage of reinforcement for
each wall sections. Using this reinforcements distributed uniformly throughout the
section without checking boundary elements, since the previous Ethiopian building
code, EBCS-1995, does not recommend to check boundary elements at every wall
sections rather gives insight for engineers to use for the height one more story use at
least half confined reinforcement calculated for the critical region at base of the wall.
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In this paper, design of shear wall has been done using check uniformly reinforced
design approach and detailed according to new Ethiopian building code, EBCS EN
2015.
2.1.2 Analytical study on boundary elements of shear wall
Many researches are done on performance of RC Shear walls lonely or with frame
elements in 2D and 3D multistory building structures considering different
parameters. Among the comparative parameters boundary element is used in
performance analysis of shear walls under various situations. Herein some studies are
described.
F.M. Darani, (2012) investigated the behavior of low-rise shear wall on different
variables which are wall aspect ratio (h/L), existence of boundary elements, amount of
axial force, longitudinal reinforcement of boundary elements, and horizontal
reinforcement of boundary elements (concrete confinement). His results indicate that
the effect of Concrete Confinement of boundary elements parameter on the
displacement at maximum strength increases with the increasing of wall aspect ratios.
Results have shown that 9 percent increasing in the case h/L=0.5, 23 percent in the
case h/L=1.0, and 34 percent in the case h/L=1.5. It was predictable that with
increasing the effect of bending on the behavior of walls, the positive effect of
concrete confinement of boundary elements also increases.
The existence of boundary elements leads to 2 percent increasing of strength. With an
increase in h/L, the effect of this variable will increase. So, in the case h/L=1, 18
percent and in the case h/L=1.5, 16 percent are the average increases in the strength.
Figure 2-4 The average ratios of strength and its corresponding displacement in
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models with 1 percent longitudinal reinforcement boundary elements and
unconfined concrete to models without boundary elements.
Longitudinal Reinforcements of Boundary Element has various effects on the
behavior of models in different wall aspect ratios. It increased strength in all cases.
Average increase is 9 percent for h/l=0.5, 28 percent for h/l=1.0 and 64 percent for
h/l=1.5. The effect of increasing the parameter on the strength increases with the
aspect ratio of walls.
Figure 2-5 The ratios of strength and its equivalent displacement in models with 1
percent to models with 3 percent longitudinal reinforcements of boundary
elements. Source: F.M. Darani, (2012)
C. Hanish, (2016) studied the behaviors of structural wall modeled in 3D frame
structure; a single wall was provided in the center of the structure only in the direction
of investigation. For the shear wall modeled as equivalent column drop in capacity
was observe after roof displacement of 0.25 m. Whereas no drop in capacity was
observed for shear wall modeled as multi-layered shell element.
The structural walls were modeled by using multilayered shell elements and
equivalent columns. In multi-layered shell element concrete and
reinforcement were modeled as separate layers. An equivalent column member is
modeled as a column with the dimensions and reinforcement of structural
wall. Rigid beams are used to connect the equivalent columns to the others members.
The beams and columns were modeled using 1D elastic frame elements with point
plastic hinges. The beam-column joints were treated as rigid. The finite
dimension of a joint was simulated by assigning end offsets to the connected members
22
with a rigid zone factor equal to 1.the analysis was done using non-linear static
analysis.
2.1.3 Nonlinear shear wall modeling techniques
In modeling and analysis of structural buildings under inelastic range a clear
expectations about portions of the structure that are expected to undergo inelastic
deformations. Depending on the structural configuration, the results of nonlinear
analyses can be sensitive to assumed input parameters and the types of models used
(NEHRP, 2010). Many researchers present different modeling techniques in modeling
of RC shear walls with possible simulation of actual behaviors. This range may from
macro-models such as lumped plasticity to micro-models such as finite element
models and fiber models. Among them most commonly used in analytical and design
software are reviewed as follows.
Equivalent Frame model
This also known as wide column analogy, in this technique shear walls are modeled
using a set of frame elements. The most commonly used macro model technique
which uses a composition of mid-pier frame to represent the shear wall stiffness and a
horizontal frame (rigid arm) to allow proper connections with intersecting beams and
slab components. The most critical point for this model is the proper selection of
rigidity and stiffness property for the horizontal frame which are larger values
compared to other frame elements. Infinite rigidity of the upper frame can highly
overestimate the bending moments especially at the connecting beams. This model is
used widely in practice to model planar shear walls in building structures for linear
and nonlinear analyses (J. Kubin, 2008). It is based on representing the overall
behavior of the RC element, such as the wall deformations, strength, and energy
dissipation capacity. This approach is simple and does not require high numerical
efforts, which makes it suitable to simulate the response of large structures. (Tolgael,
2004)
23
Figure 2-6 Shear wall and its equivalent frame model
Source: Tolgael al, 2004
Multi-layered shell element model
Multi-layered shell element model is listed under the of micro model category (K.
Galal, 2008). The multi-layer shell element is based on the principles of composite
material mechanics and it can simulate the coupled in-plane/out-of-plane bending and
the coupled in-plane bending-shear nonlinear behaviors of RC shear walls. Besides
the traditional elasto-plastic-fracture constitutive model for concrete, which is
efficient but does not give satisfying performance for concrete under complicated
stress condition, a novel concrete constitutive model, referred as micro plane model,
which is originally proposed by Bazant et al., is developed to provide a better
simulation for concrete in shear wall under complicated stress conditions and stress
histories. (Miao, 2006). The shell element is made up of many layers with different
thickness. And different material properties are assigned to various layers (Fig.2-7).
Figure 2-7 Multi-layer shell element and distribution of bar layers
24
Source: Linlinxie el al, 2014
During the finite element calculation, the axial strain and curvature of the middle
layer can be obtained in one element. Then according to the assumption that plane
remains plane, the strains and the curvatures of the other layers can be calculated. And
then the corresponding stress will be calculated through the constitutive relations of
the material assigned to the layer. (Y. Fahjan, 2012) From the above principles, it is
seen that the structural performance of the shear wall can be directly connected with
the material constitutive law.
2.1.4 Structural analysis methods
The method of analyzing building structures is no less important than choosing an
appropriate modeling technique. The analysis can be categorized based on treatments
of response, material property, and application of loads into; Linear & nonlinear,
elastic & inelastic and static & dynamic analysis, respectively. By combining any of
these three methods, unique analysis method with varies degree of complexity is
employed to design and/or evaluate different structures. Linear elastic analysis which
can be performed by using static or dynamic approaches is generally used for
multistory structures due to its simplicity (Tolgael, 2004). Now let‟s see possible
analysis techniques under major categories of elastic and inelastic analysis under
earthquake loading.
Elastic method of analysis
Also known as equivalent lateral force method is performed by considering the
building structure as stationary and the loads acting on the structure as constant.
The effects of all kinds of loads are idealized and simplified in this approach. Lateral
loads are assumed to act at the floor levels of the building. The equivalent lateral force
method recommended in most earthquake codes including EBCS code by specifying
limitations for use. It is preferred by design engineers due to simplicities for elastic
analysis of regular multi-story structures subjected to earthquake loads.
25
2.1.4.1 Linear dynamic analysis
It is based on the behavior of the structural system in a time domain and force
demands on various components are determined by an elastic dynamic analysis. The
modal superposition method and the time history method are the dynamic analysis
methods most commonly suggested by earthquake codes.
Modal superposition is a method in which the equations of motions of floor slabs are
transformed from a set of "n" simultaneous differential equations to a set of "n"
independent equations by making use of normal coordinates. The solutions of these
equations for each independent mode of vibration give the corresponding
displacements and forces. The actual elastic response of the structure under
earthquake force is obtained by superposing the evaluated individual solutions.
Time history analysis provides a method for obtaining the “exact” response of a
structure by applying a selected earthquake motion directly to the base of the structure
as a function of time. For the full duration of the earthquake, instantaneous stresses
throughout the structure are evaluated at small intervals. The maximum stress in any
member can be obtained using the output records. The time history method is not
widely used as an analysis method due to its long computer running time and cost.
2.1.4.2 Inelastic method of analysis
Structures suffer significant inelastic deformation under a strong earthquake and
dynamic characteristics of the structure change with time. Inelastic analytical
procedures help to understand the actual behavior of structures by identifying failure
modes and the potential for progressive collapse. Inelastic analytical procedures
accounting for the above properties are required to investigate the performance of the
structure. Inelastic analysis procedures basically include nonlinear static analysis
which is known as pushover analysis and non-linear time history analysis.
2.1.4.3 Non-linear static analysis
Also known as Pushover analysis is a static-nonlinear analysis method where a
structure is subjected to gravity loading and a monotonic displacement-controlled
lateral load pattern which continuously increases through elastic and inelastic
behavior until an ultimate condition is reached. In pushover analysis, the roof
displacement is plotted against with base shear recorded at each step to get the global
26
pushover curve as shown in figure below. a detail pushover analysis procedure is
described in Abdi M. ( 2012) thesis.
Figure 2-8 A Generalized pushover curve of RC structure.
Source: Abdi Mohammed, 2012
The internal forces and deformations computed at the target displacement are used as
estimates of inelastic strength and deformation demands that have to be compared
with available capacities for a performance check. A 3D nonlinear static analysis for
seismic performance evaluation of an existing multi-story reinforced concrete frame-
shear wall building was done using 3D pushover analysis in many researches. (C.
Hanish, 2016) Nonlinear analyses require thinking about inelastic behavior and limit
states that depend on deformations as well as forces. They also require definition of
component models that capture the force-deformation response of components and
systems based on expected strength and stiffness properties and large deformations
(NEHRP, 2010). In nonlinear push-over analysis which is mainly used in structural
design for determining the lateral capacity and evaluating the seismic performance of
a building, moment curvature relationships for the structural elements are strongly
needed. (Y. Fahjan. 2012)
2.1.4.4 Non-linear time history analysis
Inelastic time history is the most accurate method to predict the force and deformation
demands at various components of the structure. However, the use of inelastic time
history analysis is limited because dynamic response is very sensitive to modeling and
ground motion characteristics. Moreover, computation time, time required for input
27
preparation and interpreting voluminous output make the use of inelastic time history
analysis impractical for seismic performance evaluation.
While buildings are usually designed for seismic resistance using elastic analysis,
most will experience significant inelastic deformations under large earthquakes
enabled by advancements in computing technologies and available test data, nonlinear
analyses provide the means for calculating structural response beyond the elastic
range, including strength and stiffness deterioration associated with inelastic material
behavior and large displacements. As such, nonlinear analysis can play an important
role in the design of new and existing buildings. Linear analysis is the first step that is
usually carried out to verify the model for stiffness. For seismic evaluation and retrofit
of buildings, a performance-based non-linear analysis is recommended. (Sukumer,
2016)
Regarding the inelastic behavior of structures at low performance levels and the
complexity associated with the nonlinear time history analysis, in recent nonlinear
static procedure (NSP) as a simple tool has been developed for estimating seismic
demands in the inelastic Structure. About Pushover analysis method, there are many
guideline documents including ATC-40, FEMA 356 and codes enhances to evaluate
the structures under different performance levels which are not typically addressed in
building codes. Because of this non-linear pushover analysis will be used in the
evaluation of building structures under consideration.
28
CHAPTER THREE
3 RESEARCH METHODOLOGY
3.1 Overview
In resisting of lateral loads shear walls are widely used by engineers. Nowadays
engineering analysis and design software provides alternatives in definition material
properties, geometry, and carry out different structural analysis methods. The performance
evaluations of reinforced concrete shear wall under lateral loads are investigated in many
researches. One of the performance method used to evaluate shear walls is carry out
through the definition of non linear material and applying appropriate non-linear analysis
method under the state of inelastic range. This can be done either by considering shear wall
are a main lateral load resisting member in a 3D multistory building structure or
considering isolated shear wall lonely.
The purpose of this study is identifying the difference in performances of RC planer Shear
walls, which are with and without boundary elements within 3D wall-frame structural
system (dual system) using pushover analysis. The case buildings used throughout the
analysis are first designed and detailed. Then these two case buildings are remodeled for a
non-linear analysis. And these are discussed in this chapter.
Description of Structure
A fifteen story building is carried out analysis and design using ETABS V16.2.0 software
according to ES EN 1998-1:2015 & ES EN 1992-1-1:2015 under the maximum possible
seismic load combinations see in the appendix.
Parameters Amount
Concrete strength (f'c) 20 mpa
Rebar design yield strength (fyd) 347.87 mpa
Modules of elasticity of concrete (Ec) 29000 mpa
Modules of elasticity of rebar (Es) 200000 mpa
Poisson's ratio for concrete (U) 0.2
Poisson's ratio for rebar (U) 0.3
Table 3-1 Material Properties of Buildings
29
Loading Assumptions:
Total Dead Load (D) is equal to DL+SDL Dead Load (DL) is equal to the self-weight
of the members and slabs.
Super-imposed Dead Load (SDL) is equal to 1.5kN/m². SDL includes partitions & floor
finishes
Live Load (L) is equal to 4.0 kN/m².
Geometry of the Building
Symmetry in both plan and elevation
No of bays in X direction = 3
No of bays in Y direction = 5
Story height = 3.0m except ground floor which is 4.0m
Beam size = 0.30m x 0.50m
Column size = 0.60m x 0.60m (story 1 – story 3),
0.50m x 0.50m (story 4 – story 7),
0.40m x 0.40m (story 8 – story 15)
Shear wall size = SW1, SW2, SW3 & SW4 (0.30m x 2.50m),
SW5& SW8 (0.30m x 2.50m),
SW6 & SW7 (0.30m x 2.50m)
A. Typical floor plan (in ETABS software)
30
B. Analytical 3D model (in ETABS software)
Figure 3-1 Mathematical model of 15 story building. A) Typical floor plan and
B) 3D model
3.2 Design and detailing of shear walls in 15 story buildings
Particularly shear walls are designed and detailed in two ways. That is, one is having edge
boundary element and, the other is without any boundary element. This was done by using
uniformly reinforced design approaches as discussed in literature review. After completed
the design, shear walls reinforcement percentages (longitudinal and shear) are displayed at
each story of the building and two shear wall reinforcement detailing are considered. One,
Distribute this rebar percentage simply using uniform spacing throughout shear wall length
with appropriate bar size & spacing. Shear wall detailed in this way is taken for non linear
modeling of shear wall without boundary element and named Case-2 building. Second, the
program is assigned to check boundary elements at their ends using Euro code 8-2004 (ES
EN 1998-1:2015). The program provided boundary elements for every maximum
normalized extreme fiber compressive stress which is greater than 0.15. If boundary
elements are required, the program calculates the minimum required length of the boundary
zone and reinforcement at each end of the shear wall. Shear wall detailed in this way is
31
taken for non-linear modeling of shear wall with boundary element of shear wall and
named Case-1 building.
3.3 Non-linear modeling of structural elements
Beam and column
For nonlinear procedures, beams and columns are recommended to be modeled using
concentrated plastic hinge models or distributed plastic hinge models so that they are
capable of representing inelastic response. A representation of the monotonic load-
deformation relationships are given in Figure 3.2.
In this study beams and columns are modeled by 3D frame elements. To obtain the bending
moments and forces at the beams and columns faces beam-column joints are modeled by
giving end-offsets to the frame elements to make the joint region as a stiff or rigid zone.
The beam-column joints are as considered to be rigid. The column ends at foundation are
assumed as fixed. Nonlinear hinge properties at the possible yield locations are considered
for all the frame elements. By assigning „Rigid diaphragm‟ action at each floor level the
structural effect of slabs due to their in-plane stiffness is taken into account.
Figure 3-2 Generalized force- deformation curve for RC Buildings
Where: IO, LS, and CP stand for immediate occupancy, life safety, and collapse
Prevention respectively.
Shear wall
Shear walls are modeled using multilayer shell element to simulate the real behavior of the
structure under large deformation. Now days, Researchers are doing on RC shear wall
modeled with multilayer shell element by taking isolate shear wall having different
parameters and compare the results with laboratory test results. Miao, (2006) illustrated that
the multi-layer shell element model were correctly simulate the coupled in-plane/out-plane
32
bending failure for tall walls by considering different shear wall span ratios. Multi layer
shell element is made up of many layers with different thickness. The rebar layer set as
orthotropic with two principal axes as illustrated in figure 2.7. Fajhan, (2012) evaluated on
the consistency of different approaches for nonlinear shear wall modeling that are used in
practice by considering different number of stories using nonlinear two dimensional
nonlinear finite element.
3.4 Non-linear analysis method
The performance of planner shear wall of the case buildings evaluated after conduction non
linear static analysis is (pushover analysis). It is carried out using ETABS latest version
software.
In a nonlinear static analysis of a building, a nonlinear analytical model of the building is
subjected to monotonically increasing lateral forces until a predetermined target
displacement. The target displacement of the building presents the maximum displacement
that will be experienced by the building during a particular earthquake. The result of a
pushover analysis is the calculation of force and deformation demands on the building at
the target displacement. These demands are checked against acceptable force and
deformation capacities. The steps performing a nonlinear static analysis are [17]:
1. Create the basic computer model (without the pushover data) in the usual manner.
2. Define properties and acceptance criteria for the pushover hinges. User defined
properties are recommended.
3. Locate the pushover hinges on the model by selecting one or more frame members
and assigning them one or more hinge properties and hinge locations.
4. Define the pushover load cases. Typically the first pushover load case is used to
apply gravity load and then subsequent lateral pushover load cases are specified to
start from the final conditions of the gravity pushover. Pushover load cases can be
force controlled, that is, pushed to a certain defined force level, or they can be
displacement controlled, that is, pushed to a specified displacement. Typically a
gravity load pushover is force controlled and lateral pushovers are displacement
controlled.
5. Run the basic static analysis. Then run the static nonlinear pushover analysis.
6. Display the pushover curve.
33
7. Display the capacity spectrum curve.
8. Review the pushover displaced shape and sequence of hinge formation on a step-by-
step basis.
9. Review member forces on a step by-step basis.
After pushover analysis and getting results case buildings were evaluated using demand
parameters such as base shear, top story displacement, and formation of plastic hinges and,
internal force developed in the overall structure. Overall flow of design of case buildings
and evaluation of those buildings using pushover analysis is illustrated in figure.
34
Figure 3-1 Flow chart of Research Methodology.
Analyze and Design
(Using ES EN 2015 code)
Shear Walls
SWs without Boundary
Element
Designed Case-1 Building Designed Case-2 Building
Re-model
Model 15 story building (Using ETABS software)
Frame Elements
SWs with Boundary
Element
Beams and Columns
Apply Hinges in frame
element
Apply gravity and lateral
pushover load case
Run analysis
Apply Hinges in frame
element
Apply gravity and lateral
pushover load case
Run analysis
Summarize results Summarize results
Evaluate performance of Case-
1 and Case-2 buildings using
base shear, top displ, and
plastic formation mechanism...
35
CHAPTER FOUR
4 DESIGN AND ANALYSIS
4.1 OVERVIEW
As previously discussed the main objective of this research is to evaluate the performances
of planner shear walls in multistory building structure using pushover analysis. In this
thesis the performance of the overall structure including planner shear wall which were
designed for possible maximum seismic load combinations examined using 3D dimensional
model on ETABS software. The design of a fifteen story case buildings considering both
planer shear wall types, which is designed by considering high seismic zone in Ethiopia,
can give a better comparative approach for non linear analysis of case buildings as a whole
building structures and those shear wall types that are, specially detailed having boundary
elements and normal way of uniformly distributed reinforcement shear walls.
4.2 Design of case buildings
In order to evaluate the performance of shear walls against lateral loads under pushover
analysis the buildings are designed using a possible maximum seismic load combinations
see in the appendix. A two similar fifteen story buildings have been designed. But they are
differ only in shear wall reinforcement detailing and named as case-1 building and case-2
building. Case-2 building has a uniformly distributed reinforcement throughout along its
shear wall length. And the other, case-1 building has a well detailed reinforcement at free
edges of its shear wall by checking for the need of boundary element. If it needs,
reinforcement is detailed accordingly. All designed element sections and reinforcement for
building structural elements are illustrated in the appendix part.
Seismic parameters used in analysis and design of case buildings are:
Ground accelerations ag = 0.2g
Soil category = B
Behavior structure factor = 3.6
Spectrum type = 1
Behavior factor, by ES EN 1998-1:2015, is computed with the following
relationship.
q = Kw x qo > 1.5
36
qo = 3au/a1 for DCM (ductile class medium)
qo is basic value of behavior factor. This depends the types of structural choice
au/a1 is taken 1.2 for dual system
Kw is the factor reflecting the prevailing failure mode in structural system. Take 1.
=> q = 1 x 3 x 1.2 = 3.6
The aforementioned data are implementing for the design of the case buildings using the
latest version of ETABS software. And the results are presented in the next chapter.
4.3 Non Linear Analysis of Designed case Buildings
As part of any seismic building design or evaluation procedure, the structural engineer must
perform an analysis of the building, incorporating the seismic hazard at the building site, to
obtain building response quantities. The building response quantities are from a
mathematical calculated model of the building subjected to gravity force (Dead and Live
load) and lateral earthquake forces. Building performance is deemed acceptable if these
quantities are within the limits of acceptable building response. Building analysis methods
can be differentiated based on whether the mathematical building model is linear or
nonlinear, and whether the earthquake forces are applied in a static or dynamic manner as
described in literature review part.
Pushover analysis delivers all these benefits for an additional computational effort
(modeling nonlinearity and change in analysis algorithm) over the linear static analysis.
4.3.1 Non linear static analysis of case buildings
In a NS analysis of a building, a nonlinear analytical model of the building is subjected to
monotonically increasing lateral forces until a predetermined target displacement. The
target displacement of the building presents the maximum displacement that will be
experienced by the building during a particular earthquake. The result of a pushover
analysis is the calculation of force and deformation demands on the building at the target
displacement. These demands are checked against acceptable force and deformation
capacities.
The steps are three major parts that are creating analytical model, run analysis and review
the pushover analysis results as described in literature review part.
In this study, analytical model for carryout pushover analysis is used for the case building
structures which is intended for evaluation of overall structures including planar shear wall.
37
Frame sections that are beams and columns are defended using section designer wizards in
ETABS software and assigned it to far end of beams and columns half of section depth
away from the beam-column connections. Three push over load case are defined. The first
applies gravity load (dead load plus 30% of live load) to the structure, the second applies
push x distribution of lateral load over the height of the structure, and the third applies push
y distribution of lateral load over the height of the structure using displacement control. For
both push x and push y load cases distribution of loads over the height of the structure is
defined in static load pattern which is increased vertically as shown below in the table
Table 4-1 Distribution of lateral loads over the height of case buildings in both
X and Y directions.
The same is applied for the push y directions. The case building is then analyzed for both
linear static for gravity load and continue for non linear static push x and push y. Finally the
analysis result is reviewing.
Fb (Kn) =Cs*Geq. 1769.48091
Ft (Kn)
=0.07*T*Fb. 164.086767
Ftot (Kn) =Fb - Ft 1605.39414
story hi, m Geq. Gi*hi Fy or Fx (Kn)
15 46 1743.75 80212.5 811.51792
14 43 1743.75 74981.25 758.59283
13 40 1743.75 69750 705.66775
12 37 1743.75 64518.75 652.74267
11 34 1743.75 59287.5 599.81759
10 31 1743.75 54056.25 546.89251
9 28 1743.75 48825 493.96743
8 25 1743.75 43593.75 441.04235
7 22 1743.75 38362.5 388.11726
6 19 1743.75 33131.25 335.19218
5 16 1743.75 27900 282.2671
4 13 1743.75 22668.75 229.34202
3 10 1743.75 17437.5 176.41694
2 7 1743.75 12206.25 123.49186
1 4 1743.75 6975 70.566775
SUM(Gi*hi) 158681.3
38
A nonlinear pushover analysis of the selected building is carried out as per FEMA 440 for
evaluating the structural seismic response. In this analysis gravity loads and a representative
lateral load pattern are applied to frame structure. The lateral loads were applied
monotonically in a step-by-step manner. The applied lateral loads were acceleration in the
X- direction representing the forces that would be experienced by the structures when
subjected to ground shaking. The applied lateral forces were applied according to EBCS 8
(see in table). P–Delta effects were also considered in account. At each stage, structural
elements experience a stiffness change as shown in Figure, where IO, LS, and CP stand for
immediate occupancy, life safety and collapse prevention respectively.
Using analysis software, several types of output can be obtained from the nonlinear static
pushover analysis:
1. Base shear versus displacement at a specified control joint can be plotted.
2. Base shear versus displacement at a specified control joint can be plotted in the
ADRS format where the vertical axis is spectral acceleration and the horizontal axis
is spectral displacement. The demand spectra can be superimposed on that plot.
3. The sequence of hinge formation and the color-coded state of each hinge can be
viewed graphically, on a step-by-step basis, for each step of the pushover.
4. The member forces can be viewed graphically, on a step-by-step basis, for each step
of the analysis.
5. Tabulated values of base shear versus displacement at each point along the pushover
curve, along with tabulations of the number of hinges beyond certain control points
on their hinge property force-displacement curve can be viewed
6. Tabulated values of the capacity spectrum (ADRS capacity and demand curves), the
effective period, and the effective damping can be viewed.
In this thesis, analysis outputs are described using in graphical and in tabular forms this will
be discussed in the next chapter.
39
CHAPTER FIVE
5 RESUTLTS AND DISCUSSION
5.1 Overview
The case buildings, frames, and shear walls are designed and detailed according to ES EN
2015. For both cases all frame elements are designed with similar concrete section and
reinforcement amount except for shear walls which have same design output but have
different reinforcement details. These case buildings are used through performance
evaluation of planner shear walls into two independent fifteen story case buildings. A
fifteen stories frame with planner shear walls having boundary element is named as case-1
building & the other fifteen stories, frame with same planner shear wall but have no
boundary element, is named as case-2 building.
Using analysis software, several types of output can be obtained from the nonlinear static
pushover analysis. These two case buildings were analyzed using static pushover analysis.
Among them most commonly used outputs are, Base shear versus displacement, formation
of plastic hinge, internal forces developed in frame elements and others are discussed for
the two building cases in this chapter.
5.2 The designed structural element sections for case-1 & case-2 building
For the design of two case buildings ES EN 1991 &1998: 2015 are used. Because of
buildings have symmetric geometry in both plan and sections, SW1, SW2, and SW3 &
SW4 have the same internal force and denoted as SW3; similarly SW5 & SW8 and; SW6 &
SW7 have the same internal forces and they are denoted by SW2 & SW3 respectively, as
shown in figure 5.1. All design output for Shear walls which are designed with and without
considering boundary element for case-1 and case-2 buildings respectively and Frame
elements are shown in detail in the appendix.
Shear wall reinforcements have been decreased dramatically to the minimum rebar
requirement at first story and kept the same above stories for both case buildings. In case-1
building, almost all shear walls have boundary elements at their free edge which is from
ground up to 13th
story. It implies that there is significant difference between the previous
and new version of Ethiopian building codes in detailing of shear wall reinforcement.
40
Table 5-1 A typical designed case building floor plan layout. (Using ETABS software)
5.3 Comparison of case buildings under pushover analysis
5.3.1 Capacity (Pushover) curve
In pushover analysis, the behavior of the structure is depends upon the capacity curve that
represents the relationship between the base shear force and the roof displacement and the
capacity curve represent the global response of the structure. Due to this it is convenient
and simple to understand.
Pushover /Capacity curves in X- and Y- direction
The capacity curves for Push X and Push Y directions are plotted in the figure 5-2 and
figure 5-3 for case-1 and case-2 buildings respectively. The curves are tending to linear and
do not go large displacement. Most of the hinges formed in both case buildings are in the linear
range at performance level B which shows that the buildings are safe for the designed earthquake
forces.
41
a) b)
Figure 5-1 Pushover curves of case-2 building a) In X- direction b) In Y-direction
Figure 5-2 Pushover curves of case-1 building a) In X- direction b) In Y-direction
Number of plastic hinges at different performance level
The number of plastic hinges and their formation at different performance level for the case-2
building in X and Y direction is shown in the appendix. All hinges are formed under intermediate
occupancy (IO) and among them 24.7% & 15% of it is beyond yielding point (level B) for push in
X and Y direction respectively at the last step. The remaining are still in the zone of elastic state.
Similarly case-1 building, plastic hinge formations at different performance levels are shown
in the appendix. 18.6% & 8.2% hinge are beyond yielding point for push x and push y
respectively and the remaining are still in their elastic state. As compared to that of case- 2
building, lesser plastic hinges formation and are recorded in case-1 buildings as
summarized in table 5.2. It gives insights to see how shear wall having boundary elements
performed a higher capacity than with that of the shear wall without boundary element in a
multistory building.
42
Case Building Push direction Plastic hinge beyond
yielding Point (%)
case-2 X 24.7
Y 15
case-1 X 16.6
Y 8.2
Table 5-2 Summarized plastic hinge formation of both case buildings in percentage at last
step.
5.3.2 Plastic hinge formation
Pushover analysis is carried out only in the direction of larger displacement. Generally, it
has been found that the investigated structures in both X and Y directions subjected the
appropriate load combination have remained within the immediate occupancy (IO)
performance level. The formation of hinges at the last step of pushover analysis for the
case-1 and case-2 buildings subjected to design earthquake at are still in the Intermediate
occupancy performance level see figures in the appendix. The Intermediate occupancy
performance levels implicit the buildings are designed properly take into account between
favorable condition and the life safety of the people. Most of the hinges formed in the case-
2 buildings are in the linear range at performance level IO which shows that the buildings
are safe for expected earthquake forces. On the lower part of the case-2 building pushed in
X-direction most of the hinges are formed in both columns and beams near to shear walls.
And in the Y- direction hinges are formed pin both beams and columns parallel up to
middle stories on near to shear walls but other axis other than shear wall are appeared
development of hinges only in beams which implies the short beam connecting shear wall
and the adjoining columns itself are affected by the stiffness of shear wall. Hinges are
formed at last steps are show in the appendix for both case buildings and both push
directions. Columns near to at the bottom of shear walls and beams in most stories are
reached in their yielding stage for both case buildings. Comparatively, all hinge formations
are similar for both case building, except column hinges which are formed in a single
column only at first story on axis x1 in case-1 building but in case-2 building, hinges are
formed in four consecutive stories starting from the ground. This implies, shear wall having
43
boundary element in case-1 building has capable of resisting lateral loads in a better way
than shear walls without boundary elements.
Figure 5-3 Plastic hinge distribution of last step for case-2 building in X-direction a) on
axis x1 and b) axis x3.
Figure 5-4 Plastic hinge distribution of last step for case-1 building in x-direction a) on
axis x1 b) on axis x3.
44
Figure 5-5 Plastic hinge distribution of last step for case-1 building in x-direction a) on
axis x1 b) on axis x3.
5.3.3 Global story force and displacement of Case Buildings
Both case buildings have significant difference at each story level as shown in the figure
5.6 (the tabular form is put in the appendix part). At the 15th story of case-1 building, it is
displaced to 88.81mm and 113.38mm under push x and push y respectively. Similarly
Case-2 building is displaced to 109.14mm and 149.66mm under push x and push y
respectively. Case-1 building reduces 24% and 18% of top displacement for under push in
the x and y directions respectively.
Figure 5-6 Displacement at the center of diaphragms in both case buildings
Both Story axial force and moment have significant difference at each story level as shown
in the figure 5.7 (the tabular form is put in the appendix part). At the 1st story of case-1
building, the story axial force is 55,267.82 KN and 44,842.19 KN under push x and push y
respectively. And also the story moment is 86,4450.68 KNm and 56,0518.71 KNm under
push x and push y respectively. Similarly in Case-2 building the story axial force under
push x and push y are 45,284.31KN and 35,144.66 KN respectively. And also the story
moment is 75,6724.66 KNm and 43,9319.63 KNm under push x and push y respectively.
Case-1 building under push x and push y are 18% and 21.6% in story axial force and 12.4%
and 20% in story moment higher than Case-2 building respectively
0
20
40
60
80
100
120
140
160
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Dis
pla
cem
ent,
mm
Story level
pushX Case-1 bldg
pushY Case-1 bldg
pushX Case-2 bldg
pushY Case-2 bldg
45
Figure 5-7 Global story forces of both case buildings a) story axial force vs. story
level. b) story moment force vs. story level.
5.3.4 Internal forces in frame elements
Frame elements have critical locations along their length where stress is expected to be
concentrated we call it plastic hinge. During applying step by step lateral loads on the
building, it forms plastic hinges accordingly as described above. Besides, building frames
experience different forces at each step. Beams and columns are compared at different
location on floors and stories for the two case buildings. As shown in the figure 5.4, beams,
B2 and B15 are compare for case-1 building and case-2 building under the push in x
direction and in the y direction respectively. B2, B15, and B37 are selected by considering
their location from the shear walls in order to see the effect of shear wall on beams. In
addition, variation in stories is also considered and which are story -1, -7 and -15. Beams in
case-2 building have been shown a higher force in all cases as shown in the figure 5-8 (the
bar charts are shown in the appendix part).
Beam
name
Increment of moment in case-2 building relative to case-1 building at
story levels (%)
Story 1 Story 7 Story 15 Average of three stories
B2 17.24 15.01 8.20 13.48
B15 26.28 13.43 31.41 27.15
B37 40.78 18.96 41.22 33.65
Table 5-3 Moment increment in case-2 building to that of case-1 building in the direction
of longitudinal axis of the beam.
0
10000
20000
30000
40000
50000
60000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sto
ry a
xia
l fo
rce,
KN
Story level
push x case-1 bldg
push y case-1 bldg
push x case-2 bldg
push y case-2 bldg
0
100000
200000
300000
400000
500000
600000
700000
800000
900000
1000000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sto
ry M
om
ent
forc
e, K
Nm
Story level
push y case-1 bldg
push x case-1 bldg
push x case-2 bldg
push y case-2 bldg
46
Figure 5-8 Typical floor plans as modeled in ETABS software.
Similar to beams, Case-2 building columns have been shown a higher moments in the direction
of push for all selected locations on floor and variation stories. But the axial forces are less as
compared to case-1 building see in the figure 5-10 (the bar charts are shown in the appendix
part). This implies there will be failure mode variations in the two buildings. In case-1 building,
boundary element has a role in resisting moments and the columns intern to carry axial loads
with minimal moments which leads the column fails under compression failure mode.
Column
name
Increment of internal forces in case-2 building relative to case-1 building at story
levels (in %)
Story 1 Story 7 Story 15 Average of three stories
Axial
force
Moment
(m3)
Axial
force
Moment
(m3)
Axial
force
Moment
(m3)
Axial
force
Moment
(m3)
C17 -29.8 37.2 -33.1 18.1 -43.8 12.6 -35.57 -22.63
C20 -23.2 37.5 -29.6 17.6 -38.7 2.9 -30.50 19.33
Table 5-4 Increment of Internal forces of columns in case-2 building to that of case-1
building.
47
CHAPTER SIX
6 CONCLUSION AND RECOMMENDATION
6.1 Conclusion
The performances of planner shear walls with and without boundary elements in 15 stories
building is analyzed using a non linear static procedure and from the results shown, the
following are concluded:
1. In both case buildings, shear walls have significance for multistory buildings in
resisting the assumed seismic load if they are uniformly arranged in the floor.
2. Both case buildings have similar behavior in plastic hinge formation mechanisms in
frame elements. But hinge in columns near to shear wall for case-1 is less than case-
2 building when we consider push y load case in y direction of buildings.
3. Forces developed in beams under pushover analysis have story average of 13.48%,
27.15%, and 33.65% increment of moment force for beams B2, B15, and B37
respectively for Case-2 building as compared to Case-1 building.
4. Case-1 building as global structural system reduces 24% and 18% of top
displacement for under pushes in the x and y directions respectively. Besides it is
higher than Case-2 building under push x and push y are 18% and 21.6% in story
axial force and 12.4% and 20% in story moment higher respectively.
5. A force developed in columns under pushover analysis has 22% lesser axial force
and 19.33% higher in flexural moment for case-2 building as compared to case-1
building. This may lead columns to be failed in compression mode.
6. Planer shear walls with boundary element at their ends have an effect in minimizing
internal force developed in beams and columns of building in dual system in better
way than same wall but without boundary element.
6.2 Recommendation
Different shear wall types under both with and without boundary element have to be
assessed to have concrete ideals on the need for boundary elements at the free edges
of shear wall.
Buildings having various numbers of stories need to be analyzed for both cases to
have a refined conclusion.
48
7 REFERENCE
[1] Fahjan, Doran, Akbas and Kubin. (2012). Pushover Analysis for Performance Based-
Seismic Design of RC Frames with Shear Walls.15 WCEE, Lisboa
[2] EBCS-2. (1995). Design of Reinforced Structure for Earthquake Resistance . Ministry
of Works and Urban Development, Addis Ababa, Ethiopia.
[3] EBCS-8. (1995). Design of Reinforced Structure for Earthquake Resistance . Ministry
of Works and Urban Development Addis Ababa, Ethiopia.
[4] ES EN 1998-1. (2015). Design of Structure for Earthquake Resistance: Part-1 General
Rules,Seismic Actions, Rules for Buildings. Minstry of Urban Development,
Housing and Construction.Addis Ababa, Ethiopia.
[5] Miao, Lu, Jiang & Ye. (2006). Design Nonlinear FE Model for RC Shear Walls Based
on Multi-layer Shell Element and Micro plane Constitutive Model. Department of
Civil Engineering, Tsinghua University Beijing, China.
[6] Galal and H. El-Sokkary. (2008). Advancement in modeling of shear wall. Presented
for Department of Civil Engineering, the 14th
World Conference on Earthquake
Engineering, Beijing, China.
[7] Tolga A. (2004). Load Analysis of Shear Wall-Frame Structures. Thesis presented
for Middle East Technical University, In Partial Fulfillment Of The requirements
for the Degree Of Doctor Of Philosophy.
[8] Applied Technology Council, ATC-40. (1996). Seismic Evaluation and Retrofit of
Concrete Buildings Vol 1-2, Redwood City, California.
[9] Abdi Mohammed. (2012). Comparison of Conventional and Modal Pushover
Analysis of Buildings, thesis presented to Addis Ababa Engineering Faculty, Addis
Ababa, Ethiopia.
[10] J. Kubin, Y. M. Fahjan and M. T. Tan. (2008). Comparison of Practical Approaches
For Modeling Shear walls In Structure analyses Of Buildings. Department of
Earthquake and Structural Science, Gebze Institute of Technology, Gebze,
Kocaeli, Turkey.
[11] CSI. (2015). Shear wall Design manual Ec2 with EC8 for ETABS 2016. Computers
and Structures, Inc. Berkeley, USA.
49
[12] NEHRP. (2010). Nonlinear Structural Analysis for Seismic Design A Guide for
Practicing Engineers, NEHRP Seismic Design Technical Brief No. 4, Prepared
For U.S. Department of Commerce Building and Fire Research Laboratory
National Institute of Standards and Technology Gaithersburg.
[13] Sukumer, hemamathi, kokila & hanish. (2016). A Comparative Study on Non-Linear
Analysis of Frame with and without Structural Wall System. SSRG
International Journal of Civil Engineering, vol. 3 Issues 3.
[14] Suresh, RajKiran &Naga Raju. (2015). Design Method of Reinforced Concrete Shear
Wall Using EBCS 1995. American Journal of Engineering Research (AJER),
Volume-4, Issue-3, pp-31 -43.
[15] ACI 318. (2014). Building Code Requirements for Structural Concrete and
Commentary. Reported by ACI Committee 318, Farmington Hills, U.S.A
[16] Tarek M. Alguhane, Ayman H. Seismic Assessment of an Existing Dual System RC
Buildings in Madinah City. World Academy of Science, Engineering and
Technology International Journal of Computer and Systems EngineeringVol: 9,
No: 10, 2015.
[17] Ashraf H. & Stephen P. (1998). Practical Three Dimensional Nonlinear Static
Pushover Analysis. Published in Structure Magazine, Computers and Structures,
Inc., Berkeley, CA.
50
8 APPENDIX
51
8.1 Appendix - A
Design out puts of case-1 and case-2 buildings
Typical designed floor plan layout, column, and shear wall layout
A. Columns and Beams Cross Sectional Dimensions and Reinforcements for
both Case Buildings
Dimensions and reinforcements used in both case buildings model for columns, C1
Section Name Column Dimensions Column Longitudinal
Reinforcement bw (cm) h (cm)
C1 @ story 1 60 60 12 ɸ 20
C1 @ story 2 60 60 12 ɸ 20
C1 @ story 3 60 60 12 ɸ 20
C1 @ story 4 50 50 8 ɸ 20
C1 @ story 5 50 50 8 ɸ 20
C1 @ story 6 50 50 8 ɸ 20
C1 @ story 7 40 40 8 ɸ 16
C1 @ story 8 40 40 8 ɸ 16
C1 @ story 9 40 40 8 ɸ 16
C1 @ story 10 40 40 8 ɸ 16
C1 @ story 11 40 40 8 ɸ 16
C1 @ story 12 40 40 8 ɸ 16
C1 @ story 13 40 40 8 ɸ 16
C1 @ story 14 40 40 8 ɸ 16
C1 @ story 15 40 40 8 ɸ 16
52
Dimensions and reinforcements used in both case buildings model for columns, C2
Section Name
Column Dimensions Column
Longitudinal
Reinforcement bw (cm) h (cm)
C1 @ story 1 60 60 12 ɸ 24
C1 @ story 2 60 60 12 ɸ 24
C1 @ story 3 60 60 12 ɸ 24
C1 @ story 4 50 50 12 ɸ 20
C1 @ story 5 50 50 12 ɸ 20
C1 @ story 6 50 50 12 ɸ 20
C1 @ story 7 40 40 8 ɸ 20
C1 @ story 8 40 40 8 ɸ 20
C1 @ story 9 40 40 8 ɸ 20
C1 @ story 10 40 40 8 ɸ 20
C1 @ story 11 40 40 8 ɸ 16
C1 @ story 12 40 40 8 ɸ 16
C1 @ story 13 40 40 8 ɸ 16
C1 @ story 14 40 40 8 ɸ 16
C1 @ story 15 40 40 8 ɸ 16
Dimensions and reinforcements used in both case buildings model for columns, C3
Section Name
Column
Dimensions Column Longitudinal
Reinforcement bw (cm) h (cm)
C1 @ story 1 60 60 12 ɸ 24
C1 @ story 2 60 60 12 ɸ 24
C1 @ story 3 60 60 12 ɸ 24
C1 @ story 4 50 50 10 ɸ 24
C1 @ story 5 50 50 10 ɸ 24
C1 @ story 6 50 50 10 ɸ 24
C1 @ story 7 40 40 10 ɸ 20
C1 @ story 8 40 40 10 ɸ 20
53
Dimensions and reinforcements used in both case buildings model for columns, C4
Section Name Column Dimensions Column Longitudinal
Reinforcement bw (cm) h (cm)
C1 @ story 1 60 60 14 ɸ 24
C1 @ story 2 60 60 14 ɸ 24
C1 @ story 3 60 60 12 ɸ 24
C1 @ story 4 50 50 10 ɸ 24
C1 @ story 5 50 50 10 ɸ 24
C1 @ story 6 50 50 10 ɸ 24
C1 @ story 7 40 40 10 ɸ 24
C1 @ story 8 40 40 10 ɸ 20
C1 @ story 9 40 40 10 ɸ 20
C1 @ story 10 40 40 10 ɸ 20
C1 @ story 11 40 40 10 ɸ 20
C1 @ story 12 40 40 8 ɸ 20
C1 @ story 13 40 40 8 ɸ 20
C1 @ story 14 40 40 8 ɸ 20
C1 @ story 15 40 40 8 ɸ 20
Dimensions and reinforcements used in both case buildings model for beams, on axis
Y1, Y3,Y4 & Y6.
C1 @ story 9 40 40 10 ɸ 20
C1 @ story 10 40 40 10 ɸ 20
C1 @ story 11 40 40 10 ɸ 16
C1 @ story 12 40 40 10 ɸ 16
C1 @ story 13 40 40 10 ɸ 16
C1 @ story 14 40 40 10 ɸ 16
C1 @ story 15 40 40 10 ɸ 16
54
Note that at both sides of shear walls beams are symmetry and have same rebar detail.
Section Name
Beam
Dimensions Beam reinforcement
Transverse
reinforcement bw
(cm)
h
(cm) top Bottom
On axis Y1,Y3,Y4 & Y6 @ story 1 30 50 3 ɸ 20 2 ɸ 20 ɸ 8 c/c 180
" @ story 2 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 180
" @ story 3 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 4 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150
" @ story 5 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150
" @ story 6 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150
" @ story 7 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150
" @ story 8 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150
" @ story 9 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150
" @ story 10 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 11 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 12 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 13 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 14 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 180
" @ story 15 30 50 3 ɸ 16 3 ɸ 16 ɸ 8 c/c 180
Dimensions and reinforcements used in both case buildings model for beams, on axis
Y2 & Y5
Note that at both sides of shear walls beams are symmetry and have same rebar detail.
Section Name
Beam
Dimensions
Beam
reinforcement Transverse
reinforceme
nt
Beam
reinforcement Transverse
reinforcement bw
(cm)
h
(cm) top Bottom top
Botto
m
On axis Y2 & Y5 @ story 1 30 50 3 ɸ 20 2 ɸ 20 ɸ 8 c/c 150 3 ɸ 16 3 ɸ 16 ɸ 8 c/c 180
" @ story 2 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
55
" @ story 3 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
" @ story 4 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
" @ story 5 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
" @ story 6 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
" @ story 7 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
" @ story 8 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
" @ story 9 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
" @ story 10 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 3 ɸ 16 3 ɸ 16 ɸ 8 c/c 180
" @ story 11 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 3 ɸ 16 3 ɸ 16 ɸ 8 c/c 180
" @ story 12 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 3 ɸ 16 3 ɸ 16 ɸ 8 c/c 180
" @ story 13 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 3 ɸ 16 3 ɸ 16 ɸ 8 c/c 180
" @ story 14 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 3 ɸ 16 3 ɸ 16 ɸ 8 c/c 180
" @ story 15 30 50 3 ɸ 16 3 ɸ 16 ɸ 8 c/c 150 3 ɸ 16 3 ɸ 16 ɸ 8 c/c 180
Table 7.7 Dimensions and reinforcements used in both case buildings model for beams,
On axis X1 & X4
Note that at both sides of shear walls beams are symmetry and have same rebar detail.
Section Name
Beam
Dimensions
Beam
reinforcement Transverse
reinforcement
Beam
reinforcement Transverse
reinforcement bw
(cm)
h
(cm) top Bottom top Bottom
On axis X1 & X4 @ story 1 30 50 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 3 ɸ 20 3 ɸ 20 ɸ 8 c/c 180
" @ story 2 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150
" @ story 3 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 5 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
" @ story 4 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 6 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
" @ story 5 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 6 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
" @ story 6 30 50 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 6 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
" @ story 7 30 50 4 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 6 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
" @ story 8 30 50 4 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 6 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
" @ story 9 30 50 4 ɸ 20 4 ɸ 20 ɸ 8 c/c 150 6 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
" @ story 10 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 6 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
56
" @ story 11 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150 6 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
" @ story 12 30 50 4 ɸ 20 2 ɸ 20 ɸ 8 c/c 150 6 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
" @ story 13 30 50 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 5 ɸ 20 5 ɸ 20 ɸ 8 c/c 150
" @ story 14 30 50 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 5 ɸ 20 4 ɸ 20 ɸ 8 c/c 150
" @ story 15 30 50 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 4 ɸ 20 4 ɸ 20 ɸ 8 c/c 150
Dimensions and reinforcements used in both case buildings model for beams,
On axis X2 & X3
Note that at both sides of shear walls beams are symmetry and have same rebar detail.
Section Name
Beam
Dimensions Beam reinforcement
Transverse
reinforcement bw (cm)
h
(cm) top Bottom
On axis X2 & X3 @ story 1 30 50 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
" @ story 2 30 50 4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
" @ story 3 30 50 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 180
" @ story 4 30 50 5 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 5 30 50 5 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 6 30 50 5 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 7 30 50 5 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 8 30 50 5 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 9 30 50 5 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 10 30 50 5 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
" @ story 11 30 50 5 ɸ 20 2 ɸ 20 ɸ 8 c/c 180
" @ story 12 30 50 5 ɸ 20 2 ɸ 20 ɸ 8 c/c 180
" @ story 13 30 50 5 ɸ 20 2 ɸ 20 ɸ 8 c/c 180
" @ story 14 30 50 5 ɸ 20 2 ɸ 20 ɸ 8 c/c 180
" @ story 15 30 50 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
Beam reinforcement Transverse
reinforcement
Beam reinforcement Transverse
reinforcement top Bottom top Bottom
3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
57
B. Shear wall concrete section dimension and reinforcement for Case-2 Building
Dimensions and reinforcements used in case-2 buildings model for SW1
Section name Longitudinal rebar
per layer
shear rebar per
layer
SW1 @ S1 ɸ 20 c/c 125 ɸ 12 c/c 70
SW1 @ S2 ɸ 12 c/c 250 ɸ 12 c/c 75
SW1 @ S3 ɸ 12 c/c 250 ɸ 12 c/c 90
SW1 @ S4 ɸ 12 c/c 250 ɸ 12 c/c 95
SW1 @ S5 ɸ 12 c/c 250 ɸ 12 c/c 100
SW1 @ S6 ɸ 12 c/c 250 ɸ 12 c/c 115
SW1 @ S7 ɸ 12 c/c 250 ɸ 12 c/c 130
SW1 @ S8 ɸ 12 c/c 250 ɸ 12 c/c 140
SW1 @ S9 ɸ 12 c/c 250 ɸ 12 c/c 160
SW1 @ S10 ɸ 12 c/c 250 ɸ 12 c/c 190
SW1 @ S11 ɸ 12 c/c 250 ɸ 12 c/c 230
SW1 @ S12 ɸ 12 c/c 250 ɸ 12 c/c 300
SW1 @ S13 ɸ 12 c/c 250 ɸ 12 c/c 450
SW1 @ S14 ɸ 12 c/c 250 ɸ 12 c/c 450
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 4 ɸ 20 3 ɸ 16 ɸ 8 c/c 150
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 4 ɸ 20 2 ɸ 20 ɸ 8 c/c 150
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 180
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 4 ɸ 20 3 ɸ 20 ɸ 8 c/c 150
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 4 ɸ 20 3 ɸ 16 ɸ 8 c/c 150
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 4 ɸ 20 3 ɸ 16 ɸ 8 c/c 150
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 4 ɸ 20 3 ɸ 16 ɸ 8 c/c 150
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 4 ɸ 20 3 ɸ 16 ɸ 8 c/c 150
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 150
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 150
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
4 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180 3 ɸ 20 3 ɸ 16 ɸ 8 c/c 180
58
SW1 @ S15 ɸ 12 c/c 250 ɸ 12 c/c 230
Dimensions and reinforcements used in case-2 buildings model for SW2,
Section name Longitudinal rebar
per layer
shear rebar per
layer
SW2 @ S1 ɸ 20 c/c 90 ɸ 12 c/c 50
SW2 @ S2 ɸ 12 c/c 250 ɸ 12 c/c 85
SW2 @ S3 ɸ 12 c/c 250 ɸ 12 c/c 85
SW2 @ S4 ɸ 12 c/c 250 ɸ 12 c/c 95
SW2 @ S5 ɸ 12 c/c 250 ɸ 12 c/c 100
SW2 @ S6 ɸ 12 c/c 250 ɸ 12 c/c 110
SW2 @ S7 ɸ 12 c/c 250 ɸ 12 c/c 120
SW2 @ S8 ɸ 12 c/c 250 ɸ 12 c/c 140
SW2 @ S9 ɸ 12 c/c 250 ɸ 12 c/c 160
SW2 @ S10 ɸ 12 c/c 250 ɸ 12 c/c 180
SW2 @ S11 ɸ 12 c/c 250 ɸ 12 c/c 220
SW2 @ S12 ɸ 12 c/c 250 ɸ 12 c/c 280
SW2 @ S13 ɸ 12 c/c 250 ɸ 12 c/c 430
SW2 @ S14 ɸ 12 c/c 250 ɸ 12 c/c 430
SW2 @ S15 ɸ 12 c/c 250 ɸ 12 c/c 220
Dimensions and reinforcements used in case-2 buildings model for SW3
Section
name
Longitudinal
rebar per layer
shear rebar per
layer
SW3 @ S1 ɸ 20 c/c 110 ɸ 12 c/c 60
SW3 @ S2 ɸ 12 c/c 250 ɸ 12 c/c 80
SW3 @ S3 ɸ 12 c/c 250 ɸ 12 c/c 90
SW3 @ S4 ɸ 12 c/c 250 ɸ 12 c/c 100
SW3 @ S5 ɸ 12 c/c 250 ɸ 12 c/c 110
SW3 @ S6 ɸ 12 c/c 250 ɸ 12 c/c 120
SW3 @ S7 ɸ 12 c/c 250 ɸ 12 c/c 130
SW3 @ S8 ɸ 12 c/c 250 ɸ 12 c/c 140
59
SW3 @ S9 ɸ 12 c/c 250 ɸ 12 c/c 160
SW3 @ S10 ɸ 12 c/c 250 ɸ 12 c/c 190
SW3 @ S11 ɸ 12 c/c 250 ɸ 12 c/c 220
SW3 @ S12 ɸ 12 c/c 250 ɸ 12 c/c 280
SW3 @ S13 ɸ 12 c/c 250 ɸ 12 c/c 430
SW3 @ S14 ɸ 12 c/c 250 ɸ 12 c/c 430
SW3 @ S15 ɸ 12 c/c 250 ɸ 12 c/c 220
1. Shear wall concrete section dimension and reinforcement for Case-1 Building
Dimensions and reinforcements used in case-1 buildings model for SW1
Section
name
Boundary element web element
boundary
element
length
longitudinal
rebar per
layer
shear rebar
longitudinal
rebar per
layer
shear rebar per
layer
SW1 @ S1 944 7ɸ 22 ɸ 12 c/c 100 3ɸ 25 ɸ 12 c/c 75
SW1 @ S2 743 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 100
SW1 @ S3 629 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 100
SW1 @ S4 565 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 125
SW1 @ S5 500 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 125
SW1 @ S6 450 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 150
SW1 @ S7 450 4ɸ 14 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 175
SW1 @ S8 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 200
SW1 @ S9 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 250
SW1 @ S10 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 250
SW1 @ S11 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 325
SW1 @ S12 No need - ɸ 12 c/c 100 7ɸ 14 ɸ 12 c/c 450
SW1 @ S13 No need - ɸ 12 c/c 100 7ɸ 14 ɸ 12 c/c 450
SW1 @ S14 No need - ɸ 12 c/c 100 7ɸ 14 ɸ 12 c/c 450
SW1 @ S15 No need - ɸ 12 c/c 100 7ɸ 14 ɸ 12 c/c 450
60
Dimensions and reinforcements used in case-1 buildings model for SW2
Section
name
Boundary element web element
boundary
element
length
longitudinal
rebar per
layer
shear rebar
longitudinal
rebar per
layer
shear rebar
per layer
SW2 @ S1 1050 8ɸ 25 ɸ 12 c/c 100 6ɸ 28 ɸ 12 c/c 75
SW2 @ S2 789 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 100
SW2 @ S3 726 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 100
SW2 @ S4 659 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 125
SW2 @ S5 589 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 125
SW2 @ S6 520 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 150
SW2 @ S7 450 4ɸ 14 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 175
SW2 @ S8 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 200
SW2 @ S9 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 250
SW2 @ S10 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 250
SW2 @ S11 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 325
SW2 @ S12 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 450
SW2 @ S13 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 450
SW2 @ S14 No need - ɸ 12 c/c 100 7ɸ 14 ɸ 12 c/c 450
SW2 @ S15 No need - ɸ 12 c/c 100 7ɸ 14 ɸ 12 c/c 450
Dimensions and reinforcements used in case-1 buildings model for SW3
Section name
Boundary element web element
boundary
element length
longitudinal
rebar per layer shear rebar
longitudinal
rebar per layer
shear rebar per
layer
SW3 @ S1 975 8ɸ 22 ɸ 12 c/c 100 3ɸ 25 ɸ 12 c/c 75
SW3 @ S2 750 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 100
SW3 @ S3 697 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 100
SW3 @ S4 636 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 125
SW3 @ S5 50 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 125
SW3 @ S6 500 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 150
SW3 @ S7 450 6ɸ 12 ɸ 12 c/c 100 5ɸ 12 ɸ 12 c/c 150
61
SW3 @ S8 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 175
SW3 @ S9 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 250
SW3 @ S10 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 250
SW3 @ S11 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 325
SW3 @ S12 450 4ɸ 14 ɸ 12 c/c 100 4ɸ 14 ɸ 12 c/c 450
SW3 @ S13 No need - ɸ 12 c/c 100 7ɸ 14 ɸ 12 c/c 450
SW3 @ S14 No need - ɸ 12 c/c 100 7ɸ 14 ɸ 12 c/c 450
SW2 @ S15 No need - ɸ 12 c/c 100 7ɸ 14 ɸ 12 c/c 450
Design load combinations used in design of case buildings, according to EBCS EN 2015
are:
Comb = 1.35(DL + SDL) Comb = 1(DL +SDL) + 0.3LL - 1EQx
Comb = 1.35(DL +SDL) + 1.5LL Comb = 1(DL +SDL) + 0.3LL + 1EQx-
Comb = 1(DL +SDL) + 0.3LL + 1EQx Comb = 1(DL +SDL) + 0.3LL - 1EQx-
Comb = 1(DL +SDL) + 0.3LL + 1EQx+ Comb = 1(DL +SDL) + 1EQx-
Comb = 1(DL +SDL) + 0.3LL - 1EQx+ Comb = 1(DL +SDL) - 1EQx-
Comb = 1(DL +SDL) + 0.3LL + 1EQy Comb = 1(DL +SDL) + 1EQx+
Comb = 1(DL +SDL) + 0.3LL - 1EQy Comb = 1(DL +SDL) - 1EQx+
Comb = 1(DL +SDL) + 0.3LL + 1EQy- Comb = 1(DL +SDL) + 1EQy-
Comb = 1(DL +SDL) + 0.3LL - 1EQy- Comb = 1(DL +SDL) - 1EQy-
Comb = 1(DL +SDL) + 0.3LL + 1EQy+ Comb = 1(DL +SDL) + 1EQy+
Comb = 1(DL +SDL) + 0.3LL - 1EQy+ Comb = 1(DL +SDL) - 1EQy+
Comb = 1(DL +SDL) + 1EQx Comb = 1(DL +SDL) - 1EQx
62
8.2 APPENDIX-B
Pushover analysis results of both case buildings
Step Monitored Displ Base Force A-B B-IO IO-LS LS-CP CP-C Total mm kN
0 0 0 2100 0 0 0 0 2100 1 23.333 9520.2821 2091 9 0 0 0 2100 2 111.406 37709.907 1776 324 0 0 0 2100 3 112.094 37831.0801 1774 326 0 0 0 2100 4 154.999 47340.1317 1582 518 0 0 0 2100 5 155.086 47350.2134 1582 518 0 0 0 2100 6 156.299 47574.0205 1576 524 0 0 0 2100
plastic hinge formation at different performance level for case-2 building for Push-x.
Number of plastic hinge formation at different performance level for case-2 building for
Push-y.
Step
Monitored
Displ Base Force
A-B B-IO IO-LS LS-CP CP-C Total
mm kN
0 0 0 2100 0 0 0 0 2100
1 26.022 15071.9027 2097 3 0 0 0 2100
2 102.168 51198.606 1823 277 0 0 0 2100
3 102.187 51183.9248 1823 277 0 0 0 2100
4 118.609 57245.9234 1709 391 0 0 0 2100
Number of plastic hinge formation at different performance level for case-1 building
for Push-x.
Step
Monitored
Displ Base Force A-B B-IO IO-LS LS-CP CP-C Total
mm kN
0 0 0 2100 0 0 0 0 2100
1 -1.756 14142.9324 2098 2 0 0 0 2100
2 -6.76 46446.0406 1924 176 0 0 0 2100
Step Monitored Displ Base Force A-B B-IO IO-LS LS-CP CP-C Total
mm kN 0 0 0 2100 0 0 0 0 2100 1 19.007 8732.5391 2096 4 0 0 0 2100 2 81.032 32546.3751 1880 220 0 0 0 2100 3 81.057 32549.9194 1878 222 0 0 0 2100 4 95.219 36921.7102 1784 316 0 0 0 2100
63
Number of plastic hinge formation at different performance level for case-1 building for
Push-y.
Beam forces for both case buildings
Beam force (B2) at 1, 7 & 15 stories under push x for the two case buildings.
0
50
100
150
200
1 2 3 4
M3
, K
N-m
Steps
B2 at Story 1 due to push x case-2 building
case-1 building
0
50
100
150
200
250
300
1 2 3 4
M3
, K
N-m
Steps
B2 at Story 7 due to push x case-2 building
case-1 building
0
20
40
60
80
100
120
140
1 2 3 4
M3
, K
N-m
Steps
B2 at Story 15 due to push x
case-2building
0
20
40
60
80
100
120
1 2
M3
, K
Nm
Steps
B15 at story 1 for push y
case-2 building
case-1 building
0
50
100
150
200
1 2
M3
, K
Nm
Steps
B15 at story 7 for push y
case-2 building
case-1 building
0
10
20
30
40
50
1 2
M3
, K
Nm
Steps
B15 at story 15 for push y
case-2 building
case-1 building
64
Beam force (B15) at 1, 7, & 15 stories under push y for the two case buildings.
Beam force (B37) at 1, 7, & 15 stories under push y for the two case buildings.
Column forces for the both case building
0
20
40
60
80
100
120
1 2
M3
, K
Nm
Steps
B37 at story 1 for push y
case-2 building
case-1 building
0
20
40
60
80
100
120
1 2
M3
, K
Nm
Steps
B37 at story 7 for push y case-2buildingcase-1building
0
2
4
6
8
10
1 2
M3
, K
Nm
Steps
B37 at story 15 for push y
case-2 building
case-1 building
0
500
1000
1500
2000
2500
1 2 3 4
P, K
N
Steps
C17 at story 1 for push x
case-2 building
case-1 building
0
200
400
600
800
1 2 3 4
M3
, K
Nm
Steps
C17 at story 1 for push x
cae-2 building
case-1 building
0
500
1000
1500
1 2 3 4
P, K
N
Steps
C17 at story 7 for push x
case-2 building
case-1 building
0
50
100
150
200
250
1 2 3 4
M3
, K
Nm
Steps
C17 at story 7 for push x
case-2 building
case-1 building
65
Column force (C17) at 1, 7 & 15 stories under push x for the two case buildings.
Column force (C20) at 1, 7 & 15 stories under push y for the two case buildings.
0
50
100
150
200
1 2 3 4
P, K
N
Steps
C17 at story 15 for push x
case-2 building
case-1 building
0
50
100
150
200
250
1 2 3 4
M3
, K
Nm
Steps
C17 at story 15 for push x
case-2 building
case-1 building
0
1000
2000
3000
4000
1 2
P, K
N
Steps
C20 at story 1 for push y
case-2 building
case-1 building
0
100
200
300
400
500
1 2
M3
, K
Nm
Steps
C20 at story 1 for push y
case-2 buiding
case-1 building
0
200
400
600
800
1000
1200
1 2
P, K
N
Steps
C20 at story 7 for push y
case-2 building
case-1 building
0
50
100
150
200
250
1 2
M3
, K
Nm
Steps
C20 at story 7 for push y
case-2 buiding
case-1 building
0
10
20
30
40
1 2
P, K
N
Steps
C20 at story 1 for push y
case-2 building
case-1 building
0
5
10
15
20
1 2
M3
, K
Nm
Steps
C20 at story 1 for push y
case-2 buiding
case-1 building
66
TABLE: Diaphragm Center of Mass Displacements of case-1 building under push x.
Story Diaphragm
Load Case/Combo
UX UY RZ Point
X Y Z (mm) (mm) (rad) (m) (m) (m)
Story15 D1 PUSH Y1 Max 0.003 88.807 0.000898 17 12.5 7.5 46 Story14 D1 PUSH Y1 Max 0.003 84.96 0.000864 18 12.5 7.5 43 Story13 D1 PUSH Y1 Max 0.003 80.449 0.000823 19 12.5 7.5 40 Story12 D1 PUSH Y1 Max 0.002 75.253 0.000775 20 12.5 7.5 37 Story11 D1 PUSH Y1 Max 0.002 69.6 0.00072 21 12.5 7.5 34 Story10 D1 PUSH Y1 Max 0.001 63.449 0.000658 22 12.5 7.5 31 Story9 D1 PUSH Y1 Max 0.001 56.816 0.000591 23 12.5 7.5 28 Story8 D1 PUSH Y1 Max 0.0003324 49.796 0.00052 24 12.5 7.5 25
Story7 D1 PUSH Y1 Max 0 42.479 0.000446 25 12.5 7.5 22 Story6 D1 PUSH Y1 Max 0 35.107 0.000371 26 12.5 7.5 19 Story5 D1 PUSH Y1 Max 0 27.961 0.000297 27 12.5 7.5 16 Story4 D1 PUSH Y1 Max 0 21.017 0.000225 28 12.5 7.5 13 Story3 D1 PUSH Y1 Max 0 14.35 0.000154 29 12.5 7.5 10 Story2 D1 PUSH Y1 Max 0 8.323 0.00009 30 12.5 7.5 7 Story1 D1 PUSH Y1 Max 0 3.214 0.000035 31 12.5 7.5 4
TABLE: Diaphragm Center of Mass Displacements of Case -2 Building under push y.
Story Diaphragm
Load Case/Combo
UX UY RZ Point
X Y Z
(mm) (mm) (rad) (m) (m) (m) Story15 D1 push x1 Max 149.662 0.066 0 18 12.5 7.5 46 Story14 D1 push x1 Max 144.956 0.065 0 19 12.5 7.5 43 Story13 D1 push x1 Max 139.051 0.064 0 20 12.5 7.5 40 Story12 D1 push x1 Max 132.003 0.063 0 1792 12.5 7.5 37 Story11 D1 push x1 Max 124.083 0.064 0 1793 12.5 7.5 34 Story10 D1 push x1 Max 114.912 0.066 0 1794 12.5 7.5 31 Story9 D1 push x1 Max 104.486 0.068 0 1795 12.5 7.5 28 Story8 D1 push x1 Max 92.98 0.069 0 1796 12.5 7.5 25 Story7 D1 push x1 Max 80.7 0.066 0 1797 12.5 7.5 22 Story6 D1 push x1 Max 67.976 0.061 0 1798 12.5 7.5 19 Story5 D1 push x1 Max 55.193 0.052 0 1799 12.5 7.5 16
Story4 D1 push x1 Max 42.297 0.043 0 1800 12.5 7.5 13 Story3 D1 push x1 Max 29.547 0.034 0 1801 12.5 7.5 10 Story2 D1 push x1 Max 17.575 0.027 0 1802 12.5 7.5 7 Story1 D1 push x1 Max 7.169 0.018 0 1803 12.5 7.5 4
67
TABLE: Story Forces of case1 building under push x
Story Load Case/Combo Location P MY kN kN-m
Story15 PUSH X1 Max Top 3562.2754 44527.9688 Story14 PUSH X1 Max Top 7080.8314 90779.7534 Story13 PUSH X1 Max Top 10599.3872 139158.633 Story12 PUSH X1 Max Top 14118.4046 189533.4484 Story11 PUSH X1 Max Top 17737.6841 243010.1066 PUSH X1 Max Top 21357.6741 298203.6926 Story9 PUSH X1 Max Top 24977.6639 354966.1017 Story8 PUSH X1 Max Top 28597.6537 413154.1845 Story7 PUSH X1 Max Top 32217.6434 472624.0319 Story6 PUSH X1 Max Top 35837.6331 533227.3629
Story5 PUSH X1 Max Top 39638.4162 597066.0481 Story4 PUSH X1 Max Top 43438.4028 661725.5925 Story3 PUSH X1 Max Top 47238.626 727066.0048 Story2 PUSH X1 Max Top 51252.8728 795587.1595 Story1 PUSH X1 Max Top 55267.8183 864450.6864
TABLE: Story Forces of case1 building under push y
Story Load Case/Combo Location P MY kN kN-m
Story15 PUSH Y1 Max Top 2890.208 36129.394 Story14 PUSH Y1 Max Top 5744.953 71814.8261
Story13 PUSH Y1 Max Top 8599.693 107502.392 Story12 PUSH Y1 Max Top 11454.81 143195.3769 Story11 PUSH Y1 Max Top 14391.27 179905.3215 Story10 PUSH Y1 Max Top 17328.3 216622.1333 Story9 PUSH Y1 Max Top 20265.35 253338.9109 Story8 PUSH Y1 Max Top 23202.39 290054.3831 Story7 PUSH Y1 Max Top 26139.43 326768.8442 Story6 PUSH Y1 Max Top 29076.49 363482.2964 Story5 PUSH Y1 Max Top 32160.22 402026.9999 Story4 PUSH Y1 Max Top 35243.29 440561.9904 Story3 PUSH Y1 Max Top 38326.37 479098.3463 Story2 PUSH Y1 Max Top 41583.54 519803.897 Story1 PUSH Y1 Max Top 44842.19 560518.7151
TABLE: Story Forces of case-2 building under push x
Story Load Case/Combo Location P MY kN kN-m
Story15 push x1 Max Top 2094.3347 26178.8105 Story14 push x1 Max Top 4989.2944 64848.4192 Story13 push x1 Max Top 7884.1986 105852.5487
68
Story12 push x1 Max Top 10779.1027 149039.6914
Story11 push x1 Max Top 13782.7305 195613.5985 Story10 push x1 Max Top 16786.2474 244065.4137 Story9 push x1 Max Top 19789.7638 294244.0971 Story8 push x1 Max Top 22793.2798 345992.5167 Story7 push x1 Max Top 25796.7954 399149.4243 Story6 push x1 Max Top 28800.3107 453552.2105 Story5 push x1 Max Top 32002.7752 511520.1633 Story4 push x1 Max Top 35205.3271 570410.0668 Story3 push x1 Max Top 38407.9666 630052.2648 Story2 push x1 Max Top 41846.3442 693207.3402 Story1 push x1 Max Top 45284.3145 756724.6637
TABLE: Story Forces of case-2 building under push y
Story Load Case/Combo Location P MY kN kN-m
Story15 push y1 Max Top 1625.392 20319.4487 Story14 push y1 Max Top 3872.141 48405.9273 Story13 push y1 Max Top 6118.847 76493.802 Story12 push y1 Max Top 8365.554 104583.6229 Story11 push y1 Max Top 10696.64 133727.9527 Story10 push y1 Max Top 13027.64 162871.4445 Story9 push y1 Max Top 15358.64 192014.2764 Story8 push y1 Max Top 17689.64 221155.9499
Story7 push y1 Max Top 20020.63 250295.8307 Story6 push y1 Max Top 22351.63 279434.6628 Story5 push y1 Max Top 24837.01 310500.0143 Story4 push y1 Max Top 27322.44 341563.9329 Story3 push y1 Max Top 29807.94 372626.4688 Story2 push y1 Max Top 32476.44 405974.6786 Story1 push y1 Max Top 35144.66 439319.6263