SEISMIC EVALUATION OF MASONRY
BUILDING CONGLOMERATIONS OF
ADJACENT STRUCTURES
A Dissertation Submitted in Partial Fulfilment of the Requirements
for the Master Degree in
Earthquake Engineering
By
Adam Rush
Supervisor(s): Dr GUIDO MAGENES
Dr ANDREA PENNA
December, 2007
Istituto Universitario di Studi Superiori di Pavia
Università degli Studi di Pavia
The dissertation entitled “Seismic evaluation of masonry building conglomerations of
adjacent structures”, by Adam Rush, has been approved in partial fulfilment of the
requirements for the Master Degree in Earthquake Engineering.
Guido Magenes 1 …… …
Andrea Penna 2………… …
………
……
Abstract
ABSTRACT
A masonry building conglomeration is a series of masonry buildings in close enough
proximity to one another that they will interact during an seismic event. Recent earthquakes
have demonstrated that single buildings within a masonry conglomeration, like historic city
centres, are susceptible to damage due to the interaction of adjacent buildings. This damage
typically occurs in the form of local failures of individual walls and other structural elements,
sometimes resulting in collapse of the entire building. Understanding of this behaviour and
remediation measures have progressed to the point that with the necessary resources, historic buildings
can be strengthened to prevent these local failures. This study is concerned with buildings that tend not
to exhibit local failure mechanism during an earthquake and are susceptible to global damage due to
building interaction. The goal is to determine which of five major parameters most influence the
behaviour of a building due to inter-building interaction. These parameters are: stiffness of the walls,
height of the building, mass of the building and stiffness of the diaphragm, type of inter-building
connection, and position within a conglomeration. Monotonic pushover analysis is conducted on
various combinations of coupled systems and multiple building conglomerations. The results indicate
that the relative heights of adjacent buildings and the type of inter-building connection are the most
important parameters to consider for future studies.
Keywords: masonry conglomeration; pounding; global response; Tremuri
i
Index
TABLE OF CONTENTS
Page
ABSTRACT ............................................................................................................................................i
TABLE OF CONTENTS .......................................................................................................................ii
LIST OF FIGURES ................................................................................................................................ v
LIST OF TABLES...............................................................................................................................viii
LIST OF SYMBOLS.............................................................................................................................ix
1. INTRODUCTION .............................................................................................................................1
1.1 Background ................................................................................................................................1
1.2 Interaction Connection Types ....................................................................................................4
1.2.1 Pounding Connection.......................................................................................................4
1.2.2 Full Connection................................................................................................................5
1.3 Position within a Row Conglomeration .....................................................................................6
1.3.1 Presence of Heavier Buildings within a Conglomeration ................................................6
2. SEISMIC VULNERABILITY STUDY OF BUILDING CONGLOMERATIONS.........................7
2.1 Parametric Study Program .........................................................................................................7
2.2 Modelling...................................................................................................................................9
2.2.1 Macro-element modelling................................................................................................9
2.2.2 In-plane wall model .......................................................................................................10
2.2.3 3D model........................................................................................................................11
3. SINGLE BUILDINGS ....................................................................................................................12
3.1 System Description ..................................................................................................................12
3.2 Results......................................................................................................................................14
3.2.1 Monotonic Pushover Results .........................................................................................15
3.2.2 Cyclic Pushover Results ................................................................................................16
3.3 Discussion ................................................................................................................................17
ii
Index
4. COUPLED SYSTEM ......................................................................................................................18
4.1 Analysis ...................................................................................................................................18
4.2 Individual Building Results .....................................................................................................18
4.2.1 One Storey, Flexible Wall and Wood Floors Building ..................................................20
4.2.2 One Storey, Flexible Wall and Concrete Floors Building .............................................21
4.2.3 Two Stories, Flexible Wall and Wood Floors Building.................................................22
4.2.4 Two Stories, Flexible Wall and Concrete Floors Building ............................................24
4.2.5 Three Stories, Flexible Wall and Wood Floors Building...............................................25
4.2.6 Three Stories, Flexible Wall and Concrete Floors Building ..........................................26
4.2.7 Four Stories, Flexible Wall and Wood Floors Building ................................................28
4.2.8 Four Stories, Flexible Wall and Concrete Floors Building............................................29
4.2.9 One Storey, Rigid Wall and Wood Floors Building ......................................................30
4.2.10One Storey, Rigid Wall and Concrete Floors Building..................................................32
4.2.11Two Stories, Rigid Wall and Wood Floors Building.....................................................33
4.2.12Two Stories, Rigid Wall and Concrete Floors Building ................................................34
4.2.13Three Stories, Rigid Wall and Wood Floors Building...................................................36
4.2.14Three Stories, Rigid Wall and Concrete Floors Building ..............................................37
4.2.15Four Stories, Rigid Wall and Wood Floors Building.....................................................38
4.2.16Four Stories, Rigid Wall and Concrete Floors Building ................................................39
4.3 Discussion ................................................................................................................................41
4.3.1 Pounding Connection.....................................................................................................41
4.3.2 Full Connection..............................................................................................................42
5. CONGLOMERATIONS .................................................................................................................45
5.1 Analysis ...................................................................................................................................45
5.2 Monotonic Pushover Results ...................................................................................................46
5.2.1 Three building conglomerations ....................................................................................47
5.2.2 Six building conglomerations ........................................................................................51
5.2.3 Nine building conglomerations......................................................................................53
5.2.4 Pounding connections, no concrete floor buildings .......................................................55
5.2.5 Full connections, no concrete floor buildings ................................................................55
5.2.6 Pounding connection, external concrete floor building .................................................57
5.2.7 Full connection, external concrete floor building ..........................................................57
5.2.8 Pounding connection, internal concrete floor building ..................................................58
5.2.9 Full connection, internal concrete floor building...........................................................59
5.3 Discussion ................................................................................................................................59
6. CONLCUSIONS .............................................................................................................................60
iii
Index
6.1 Further Study ...........................................................................................................................60
REFERENCES .....................................................................................................................................61
APPENDIX A – SINGLE BUILDING RESULTS ............................................................................. A1
A.1 Monotonic Pushover Results ..................................................................................................A1
A.1.1 Height............................................................................................................................ A1
A.1.2 Wall and floor stiffness................................................................................................. A7
A.2 Cyclic Pushover Results .......................................................................................................A12
APPENDIX B – COUPLED SYSTEM COMBINATIONS ............................................................... B1
APPENDIX C – ROW CONGLOMERATION COMBINATIONS .................................................. C1
iv
Index
LIST OF FIGURES
Page
Figure 1.1. Arial view of a historic building conglomeration in Italy ........................................2
Figure 1.2. Typical local failure mechanisms [D’Ayala et al., 1996] ........................................3
Figure 1.3. Examples of global masonry building damage due to an earthquake ......................4
Figure 1.4. Examples of pounding and full inter-building connections .....................................5
Figure 2.1. Macro-element panel [Galasco et al., 2004] ..........................................................10
Figure 2.2. Wall construction using macro-elements ...............................................................11
Figure 3.1.
General plan view of prototype building used in analysis – X-axis defined for
the length of building and Y-axis defined for the width of the building ..........................12
Figure 3.2. Elevation view and model of 3 storey tall theoretical building used in analysis ...13
Figure 3.3. Single building models ...........................................................................................14
Figure 3.4. Monotonic pushover curves: rigid walls & concrete floors ...................................15
Figure 3.5. Monotonic pushover curves: 3 storey buildings.....................................................15
Figure 3.6. Effect of wood floors and the lack of a fully rigid diaphragm ...............................16
Figure 3.7. Cyclic pushover curves for 3 storey buildings .......................................................17
Figure 4.1. Example: L12 H2 F1 – L24 H4 F1 – C2 – B2 .......................................................19
Figure 4.2. One storey, flexible wall and wood floors building ...............................................21
Figure 4.3. One storey, flexible wall and concrete floors building...........................................22
Figure 4.4. Two stories, flexible wall and wood floors building..............................................23
Figure 4.5. Two stories, flexible wall and wood floors building..............................................24
Figure 4.6. Two stories, flexible wall and concrete floors building .........................................25
Figure 4.7. Three stories, flexible wall and wood floors building............................................26
Figure 4.8. Three stories, flexible wall and concrete floors building .......................................28
Figure 4.9. Four stories, flexible wall and wood floors building..............................................29
v
Index
Figure 4.10. Four stories, flexible wall and concrete floors building .......................................30
Figure 4.11. One storey, rigid wall and wood floors building..................................................31
Figure 4.12. One storey, rigid wall and concrete floors building .............................................33
Figure 4.13. Two stories, rigid wall and wood floors building ................................................34
Figure 4.14. Two stories, rigid wall and concrete floors building............................................35
Figure 4.15. Three stories, rigid wall and wood floors building...............................................37
Figure 4.16. Three stories, rigid wall and concrete floors building..........................................38
Figure 4.17. Four stories, rigid wall and wood floors building ................................................39
Figure 4.18. Four stories, rigid wall and concrete floors building............................................40
Figure 4.19. Pounding connection ............................................................................................42
Figure 4.20. Full connection .....................................................................................................43
Figure 4.21. Three stories, rigid walls buildings for Row Conglomerations............................44
Figure 5.1. Example: 3 * L24 H3 F1 – C1 – B2 w/ external F2...............................................47
Figure 5.2. 3 building conglomerations results.........................................................................47
Figure 5.3. 3 Building conglomeration models ........................................................................48
Figure 5.4. 3 building conglomeration models .........................................................................49
Figure 5.5. Comparison of wood vs concrete floors.................................................................50
Figure 5.6. 6 building conglomerations results.........................................................................51
Figure 5.7. 6 building conglomeration models .........................................................................52
Figure 5.8. 6 building conglomeration models .........................................................................53
Figure 5.9. 9 building conglomerations results.........................................................................54
Figure 5.10. 9 building conglomeration models .......................................................................54
Figure 5.11. 9 building conglomeration models .......................................................................55
Figure 5.12. Pounding connections, no concrete floor buildings .............................................55
Figure 5.13. Full connections, no concrete floor buildings ......................................................56
Figure 5.14. Model....................................................................................................................56
Figure 5.15. Full connections, no concrete floor buildings without unusual pushover curves.57
Figure 5.16. Pounding connection, external concrete floor building........................................57
Figure 5.17. Full connection, external concrete floor building.................................................58
Figure 5.18. Pounding connection, internal concrete floor building ........................................58
Figure 5.19. Full connection, internal concrete floor building .................................................59
Figure A.1. Monotonic pushover curves: flexible walls & wood floors .................................A3
Figure A.2. Constants: flexible walls & wood floors ..............................................................A3
vi
Index
Figure A.3. Monotonic pushover curves: flexible walls & concrete floors.............................A4
Figure A.4. Constants: flexible walls & concrete floors..........................................................A4
Figure A.5. Monotonic pushover curves: rigid walls & wood floors ......................................A5
Figure A.6. Constants: rigid walls & wood floors ...................................................................A5
Figure A.7. Monotonic pushover curves: rigid walls & concrete floors .................................A6
Figure A.8. Constants: rigid walls & concrete floors ..............................................................A6
Figure A.9. Monotonic pushover curves: 1 storey buildings...................................................A8
Figure A.10. Constant: 1 storey buildings ...............................................................................A8
Figure A.11. Monotonic pushover curves: 2 storey buildings.................................................A9
Figure A.12. Constant: 2 storey buildings ...............................................................................A9
Figure A.13. Monotonic pushover curves: 3 storey buildings...............................................A10
Figure A.14. Constant: 3 storey buildings .............................................................................A10
Figure A.15. Monotonic pushover curves: 4 storey buildings...............................................A11
Figure A.16. Constant: 4 storey buildings .............................................................................A11
Figure A.17. Cyclic pushover curves for 1 storey buildings .................................................A12
Figure A.18. Cyclic pushover curves for 2 storey buildings .................................................A13
Figure A.19. Cyclic pushover curves for 3 storey buildings .................................................A14
Figure A.20. Cyclic pushover curves for 4 storey buildings .................................................A14
vii
Index
LIST OF TABLES
Page
Table 2.1. Wall dimensional .......................................................................................................8
Table 2.2. Interstorey heights......................................................................................................8
Table 2.3. Floor descriptions ......................................................................................................8
Table 3.1. Wall composition.....................................................................................................13
Table 4.1. Notation description for navigating result files .......................................................19
Table 5.1. Notation description for navigating result files .......................................................46
Table A.1. Legend for height comparison ...............................................................................A2
Table A.2. Legend for wall and floor comparison...................................................................A7
Table B.1. Analysis coupled systems ......................................................................................B1
Table C.1. Conglomeration list................................................................................................C1
viii
Index
LIST OF SYMBOLS
Notation
L12
L24
H1
H2
H3
H4
F1
F2
C1
C2
B1
B2
B4
B5
Description
Length of in-plane wall = 12 m
Length of in-plane wall = 24 m
Number of stories = 1 with individual storey heights matching previous table
Number of stories = 2 with individual storey heights matching previous table
Number of stories = 3 with individual storey heights matching previous table
Number of stories = 4 with individual storey heights matching previous table
Floor composition = wood
Floor composition = concrete
Inter-building connection type = pounding
Inter-building connection type = full connection
Building 1 in a coupled or row conglomeration system
Building 2 in a coupled or row conglomeration system
Building 4 in a coupled or row conglomeration system
Building 5 in a coupled or row conglomeration system
9
Chapter 1. Introduction
1. INTRODUCTION
A masonry building conglomeration is a series of masonry buildings in close enough
proximity to one another that they will interact during an seismic event. Recent earthquakes
have demonstrated that single buildings within a masonry conglomeration, like historic city
centres, are susceptible to damage due to the interaction of adjacent buildings. This interaction
causes damage through the transfer of inertial forces either by pounding of adjacent buildings
or through coupling effects in the seismic response. In some instances, damage due to
conglomerations can cause a premature failure of the building. Previous studies of these
conglomerations focus on how pounding between adjacent buildings trigger local failure
mechanisms. Out-of-plane bending of walls is a common local failure mechanism of concern
throughout these studies. These local failures are common among poorly constructed
buildings with weak connections between the walls and floors and poor masonry materials.
Fewer studies focus on the impact that these systems have on the global response of a
building. Those that do address these issues tend to telly on elastic models to draw
conclusions. Since many historic city centres are comprised of masonry buildings, inelastic
models are essential to describe the response of a building to an earthquake. This study
attempts to determine some simple relationships for buildings within a conglomeration in
order to describe the interaction effects within the conglomeration during an earthquake. The
purpose of this study is to determine the role that building interaction should play in
evaluating the seismic vulnerability of historic city centres.
1.1 Background
A typical historic city centre, like many found throughout Europe, consist of mostly masonry
buildings of various shapes, sizes, age, quality and style. The complexity of urban centres is
massive and continues to change today through renovations and continuous construction. As
the 1997 earthquake of Umbria-Marche demonstrated, these historic city centres are
susceptible to lots of damage. Some of the damage occurred due to the interaction between
buildings.
Similarly, the Mexico City earthquake of 1985 caused lots of destruction due to pounding of
adjacent buildings. Since that earthquake, many researchers have focused considerable effort
in studying the effects of pounding within city centres. The focus of pounding research has
been to determine safe distances between structures which adequately prevent pounding from
occurring. Where these safe distances cannot be enforced, various techniques are considered
1
Chapter 1. Introduction
to reduce the effects of pounding. Most of the research in this field, however, has tended to
focus on elastic-homogenous systems, like steel, which do not make up the majority of
buildings in historic city centres.
Figure 1.1. Arial view of a historic building conglomeration in Italy
Previous studies which focus on the vulnerability of historic city centres focus primarily on
the development of local failure mechanisms within buildings. These failures are the most
common type for masonry buildings during an earthquake. They are usually caused by flaws
within a building and can lead to a progressive collapse of the entire structure. Typically,
however, the entire building does not collapse and only part of the building is damaged.
Figure 1.2 shows common types of local failures. Most local failures of primary interest to
researchers are caused by out-of-plane bending of walls or separation of wall components for
multi-leaf masonry wall systems. Local failures tend to be building specific and there are
procedures already in place to address these issues.
2
Chapter 1. Introduction
Figure 1.2. Typical local failure mechanisms [D’Ayala et al., 1996]
Modelling of these failures require specialized models for each building condition and only
require looking at individual building components. The entire building does not need to be
modelled in order to capture local failure mechanisms. The purpose of this study is to
determine what role building interaction plays on assessing the vulnerability of a historic city
centre. If local failure mechanism can be addressed, then the goal of this study is to determine
the levels of increase demands building interaction places on a structure and which factors
influence this demand. The purpose is not to address local failure mechanisms caused by
adjacent buildings, but rather to focus on the global response of a building.
3
Chapter 1. Introduction
Shear Sliding
Rocking
Pounding
Figure 1.3. Examples of global masonry building damage due to an earthquake
This study attempts to model the global behaviour of buildings and capture their interaction
between one another. The goal is to gain a better understanding of how this global building
interaction influences the response of each building. failure mechanisms like shear sliding and
rocking for piers, as seen in Figure 1.3, are of particular interest because they are failure
mechanisms related to the global response of a building. To capture these behaviours and the
changes of behaviour due to building interaction within a conglomeration, a macro-element
modelling program was used which will allow for average inelastic behaviour of masonry
elements. This modelling system is described in greater detail in the following chapter.
1.2 Interaction Connection Types
Much like the historic centres themselves, the interactions between adjacent buildings is a
complex problem with many variables. Distance between buildings, material properties of the
façade systems, and relative stiffness of the two buildings are a few of the factors which
influence the inter-building interaction. A proper representation of the inter-building
connection is needed before being able to capture the global response. To simplify the many
different conditions found within a historic centre, two types of inter-building connections are
considered.
1.2.1 Pounding Connection
The first inter-building connection considered is the pounding connection, which represents
buildings physically separated. Inertial forces between these buildings are transferred when
4
Chapter 1. Introduction
the gap between them closes and the buildings come into contact. This connection models the
response of independent buildings and allows for a transfer of forces when the buildings make
contact under dynamic loading while still enabling the buildings to separate freely when
moving in opposite directions. This connection is achieved by using a zero tension element
that only transfers compressive loads. This zero tension elements share the same compression
strength of masonry and thus included crushing of masonry between the piers when it occurs.
The models shown in Figure 1.4 provide examples of the typical behaviour of the pounding
connection. As can clearly been seen in the figure, the taller and thus more flexible building
pulls away from the shorter and more rigid building in one direction and then transfers its
inertial forces through the zero tension links in the other direction. In many cases, taller and
more flexible buildings tended to develop a soft storey directly above the shorter and more
rigid building when pounding against it.
1.2.2 Full Connection
The second inter-building connection is the full connection. It represents the conditions when
adjacent buildings are in complete contact and even share a load bearing wall between them.
This connection is modelled by a single rigid node shard between two adjacent piers on either
side of the shared bearing wall. Figure 1.4 clearly shows the two smaller piers sharing a rigid
node between the two buildings. The result of this connection is that the buildings tended to
act more like a single structure than individual buildings. In order to maintain similar inertial
properties for comparison purposes between the two systems, the common wall has double
the normal wall thickness of the other walls within the building.
Pounding Connections
Full Connections
Figure 1.4. Examples of pounding and full inter-building connections
5
Chapter 1. Introduction
1.3 Position within a Row Conglomeration
Another important factor to consider is the effect of building position within a conglomeration
on the interaction between the buildings and its own response. In theory, buildings in the
centre of a row conglomeration should be better shielded from increased seismic demands.
This is because the demands would be distributed between the buildings surrounding it. The
buildings on the end of a conglomeration, however, experience increased demands due to a
build-up of inertial forces throughout the conglomeration and ending with the final building.
Thus some of the inertial forces otherwise resisted by previous buildings are now transferred
to the final one on the end. The purpose of this study is to determine how important the
building’s position is in evaluating the increase of demands it will see and the increase in
seismic vulnerability it should have.
1.3.1 Presence of Heavier Buildings within a Conglomeration
When historic buildings are updated, those updates may consist of replacing the existing
wooden floors with new concrete floors. These floors increase the mass of the building. The
increased mass leads to increased seismic demand on the building part of which is transferred
to adjacent buildings within a conglomeration. This could have an unintentional detrimental
effect on the response of the conglomeration as a whole. The goal is to determine whether
additional study is required for renovation projects because of this effect.
6
Chapter 2. Seismic Vulnerability Study of Building Conglomerations
2. SEISMIC VULNERABILITY STUDY OF BUILDING
CONGLOMERATIONS
The purpose of this study is to determine the role that building interaction should play in
evaluating the seismic vulnerability of historic city centres. To that end, this study evaluates a
set of parameters to determine which create the most detrimental effects due to building
interaction. Monotonic pushover analysis is conducted to characterize the response of the
buildings and provide a basis for comparison.
2.1 Parametric Study Program
A series of theoretical, but realistic, buildings are used in order to draw comparisons between
various parameters. The reasoning behind the theoretical buildings is to study the effects of
building interaction while eliminating typical vulnerability parameters found in masonry
buildings. The goal is to observe global behaviour of buildings. To this end, all of the
theoretical buildings share acceptable parameters to ensure a global building response. The
masonry material uses typical properties found for clay brick masonry and the material is
considered of good quality. Each building uses the same masonry for the models. The walls
are thick enough and sufficiently attached to the floor to ensure out-of-plane stability and
structural redundancy. The roofs are flat, so no additional horizontal thrusts are present. The
plans are very regular, as seen in Figure 3.1. This eliminates torsional effects and stress
concentrations. Diaphragm action was an important parameter to keep in the study and thus
two types of floor systems were used with one being rigid and the other fairly flexible. These
vulnerability parameters are more critical than building interaction effects because if they are
inadequate, then they tend to cause the building to fail regardless of its interaction with
adjacent buildings. For this reason, the theoretical buildings are required to be stable in order
to observe the interaction effects.
The purpose of this study is to determine if otherwise stable buildings are vulnerable to severe
earthquake damage due to the increase seismic demands from building interactions. Several
parameters are considered in evaluating the effects of building interaction on stable buildings.
These parameters are:



Stiffness of the building
Height of the building
Mass of the building and stiffness of the diaphragm
7
Chapter 2. Seismic Vulnerability Study of Building Conglomerations


Type of inter-building connection (Pounding or Full)
Position within a conglomeration
The last two parameters are discussed in greater detail in the previous chapter. These
parameters are directly correlated with the building interaction. The other parameters are
related to the physical properties of the buildings themselves. The total length of the building
is varied in order to create flexible and rigid structures. Buildings were either 12 m or 24 m
long and 12 m wide. The same internal wall configuration was kept but scaled to meet the
overall dimensions of the different buildings. The different length walls are used to create
flexible and rigid building systems. The shorter walls tend to be more flexible and are
governed by a rocking mechanism while the longer walls tend to b more rigid and are
governed by a shear sliding mechanism. The height and number of stories for each building
were also varied. Buildings ranging from 1 to 4 stories tall are considered for this study
because this range encompasses the typical number of stories for load bearing masonry
buildings in historic city centres. Changing the height of the buildings changes the base shear,
the stiffness and the natural period of the building, all of which are important characteristics
in determining building response. The material for the floors is modelled as either wood or
concrete to capture the differences between stiffer diaphragms and buildings masses. These
parameters are listed in Tables 2.1 to 2.3 in greater detail.
Table 2.1. Wall dimensional
Length, L
12 m
24 m
Stiffness
Flexible
Rigid
Table 2.2. Interstorey heights
Storey Number
1 Storey
Building
3m
2 Storey
Building
3m
3m
3 Storey
Building
3m
3m
2.5 m *
4 Storey
Building
1
3m
2
3m
3
3m
4
2.5 m
* Interstorey height increased to 3 m for 3 storey to 4 storey building comparison to make
model creation easier
Table 2.3. Floor descriptions
Flexibility
Rigid
Flexible
Type
Concrete
Wood
8
Chapter 2. Seismic Vulnerability Study of Building Conglomerations
The total number of different individual buildings generated from varying each of the
individual building parameters is 16. The total number of coupled systems generated by
combining all 16 individual buildings to each other including both types of connections is
512. The total number of 3 building row conglomerations generated by combining all 16
individual buildings in every possible combination of 3 buildings including both types of
connections is 16,384. Due to the large number of computations, only monotonic pushover
analysis is conducted. The final number of coupled system and row conglomerations models
is also reduced because of the results from the single building modelling. A list of coupled
systems and row conglomerations are provided within their respective chapters.
2.2 Modelling
Previous studies concerning the interaction of adjacent buildings focused their attention
primarily on the elastic response of the coupled systems. They also refrain from expanding
their findings to a series of buildings as found in conglomerations. There are studies
concerned with predicting damage in a historical city centre. These focused on typical local
failure mechanism observed in damage centres. Though useful information, they neglected to
describe the interaction of building conglomerations to produce such failures. The purpose of
this study is to address the shortfalls of previous studies, namely capturing the nonlinear
changes in building behaviour under the influence of adjacent structures. The focus in this
project is not to capture the local mechanisms of wall behaviour but to focus on the average
behaviour and global response of a building. The construction of macro-elements allows for
the broad and accurate comparisons between building behaviours without highly detailed
analysis.
Nonlinear analysis is crucial to understanding the behaviour of masonry buildings during an
earthquake. For this reason, pushover analysis was conducted in this study. It was used to
determine the overall building characteristics and provide a simple system for comparing the
different buildings and interactions. A modified method of pushover analysis allowed the use
of macroelements. The procedure, modified with an effective algorithm, transformed the
problem of pushing a structure maintaining constant ratios between the applied forces into an
equivalent incremental static analysis with one degree of freedom displacement response
control node [Galasco et al., 2004]. A triangular distribution was used as the distribution of
forces throughout the structure. Figure 3.3 shows the models considered for the single
building case. Failure for monotonic loading is considered when a building reached 80% of
maximum capacity.
2.2.1 Macro-element modelling
Through the use of modelling techniques representing the behaviour of masonry walls in the
form of macro-elements, the nonlinear behaviour of masonry building conglomerations can be
approximated with relatively little computing power. This modeling system permits the
representation of two main in-plane masonry failure modes, with a limited number of degrees
of freedom. These modes, depicted based on mechanical assumptions, are bending-rocking
and shear-sliding mechanism including friction. Using internal variables, the macro-element
takes into account the effect of the limited compressive strength of masonry. The limited
crushing strength of masonry is typically developed in the bending-rocking mechanism
9
Chapter 2. Seismic Vulnerability Study of Building Conglomerations
through a toe crushing effect. This effect is modeled by means of phenomenological nonlinear
constitutive law with stiffness deterioration in compression. The model also considers the
shear-sliding damage evolution, which controls the strength deterioration and the stiffness
degradation of the masonry panel in shear [Galasco et al., 2004].
The macro-element model is a macroscopic representation of a continuous model in which the
parameters are directly correlated to the mechanical properties of the masonry elements. The
macro-element parameters should be considered as representative of an average behaviour of
the masonry panel. The macro-element is defined by six material parameters: the shear
modulus, the axial stiffness, the shear strength of masonry, a non-dimensional coefficient that
controls the inelastic deformation, the global friction coefficient and a factor that controls the
softening phase [Galasco et al., 2004].
The macro-element panel is divided into 3 substructures as shown in Figure 2.#. the bending
and axial effects are concentrated in the two outer substructure, inferior 1 and superior 3. The
shear-deformations are centered within the central substructure. This layer does not contain
any evidence of axial or bending deformations. A complete 2D kinematic model should take
into account the three degrees of freedom for each node “i” and “j” on the extremities: axial
displacement, horizontal displacement and rotation. There are two degrees of freedom for the
central zone: axial displacement δ and rotation φ (Fig 2.#) [Galasco et al., 2004].
Figure 2.5. Macro-element panel [Galasco et al., 2004]
2.2.2 In-plane wall model
A frame representation of the in-plane behaviour of masonry walls is adopted utilizing macroelements for the various frame members as seen in Figure 2.2. Each wall of the building is
subdivided into piers and lintels connected by rigid nodes. The development of the piers is
described above and the lintels are simply 2-node macro-elements. Earthquake damage
observation shows that cracks rarely appear in the rigid nodes of the wall and because of this,
the deformation of these regions is assumed to be negligible relative to the macro-element
10
Chapter 2. Seismic Vulnerability Study of Building Conglomerations
non-linear deformations governing the seismic response. Rigid end offsets are used to transfer
static and kinematic variables between element ends and nodes. Pretension tie rods are also
included in the model as non-compressive elements.
Node
Lintel
Pier
Figure 2.6. Wall construction using macro-elements
2.2.3 3D model
The 3-dimensional masonry buildings are created by joining the in-plane masonry wall
models together. Since the macro-elements only consider in-plane behaviour the floor
elements distribute the horizontal actions to the walls. This distribution of actions depends
upon local flexural behaviour of the floors and the walls. The out-of-plane response of the
walls is not computed because they are considered negligible with respect to the global
building response, which is governed by their in-plane behaviour. This global response is
possible only if vertical and horizontal elements are properly connected. Pretension rods are
used to tie-in the walls to the floors in order to properly connect all of the elements.
The 3D nodes connecting different walls in corners and intersections need to have 5 d.o.f. in
the global coordinate system (uX, uY, uZ, rotX, rotY): the rotational degree of freedom
around vertical Z axis can be neglected because of the membrane behaviour adopted for walls
and floors.
The floor elements are modeled as orthotropic membrane finite elements identified Young
and shear moduli in each principle direction, and Poisson ratio. The principle directions align
with the wall connections to the floors, which are connected by means of stringcourses and
tie-rods. The in-plane floor shear stiffness governs the horizontal action distribution between
the different walls. This solution permits the implementation of static analyses with 3
components of acceleration along the 3 principal directions and 3D dynamic analyses with 3
simultaneous input components, too [Guida Tremuri, 2006]
11
Chapter 3. Single Building
3. SINGLE BUILDINGS
Before a detailed comparison of building interaction can occur, an understanding of the
behaviour of the individual buildings is required. The following section provides the results of
monotonic and cyclic pushover analyzes for single masonry buildings. These results provide
the foundation for comparisons made in subsequent chapters.
3.1 System Description
The theoretical building used consists of eight equally sized rooms in a 2 by 4 unit
configuration, each with one window, except for the corner rooms which have two windows.
Figure 3.1 below shows a building plan. Buildings were coupled along the longitudinal axis
and the width of the building was kept constant at 12 m for simplicity.
Figure 3.7. General plan view of prototype building used in analysis – X-axis defined for the length of
building and Y-axis defined for the width of the building
Tie rods were used in the theoretical building because the focus of this study is on in-plane
behaviour of buildings. The tie rods reduce the importance of analyzing out-of-plane
behaviour of masonry buildings. Only in-plane behaviour was considered because it controls
12
Chapter 3. Single Building
the global response of a building. Interaction with surrounding buildings effects the global
characteristics of a building. Local failures are also caused by building interaction, especially
pounding. These issues though are not considered in this study because they are highly
dependent on the individual building and are difficult to generalize in a large model.
Elevation of 3 storey building with dimensions
Model of 3 story building
Figure 3.8. Elevation view and model of 3 storey tall theoretical building used in analysis
Table 3.4. Wall composition
Properties
Name
Elastic Modulus
Shear Modulus
Specific Weight
Compressive or
Tensile Strength
Shear Strength
Thickness / Diameter
Pre-Tensioned
Masonry
Brick
1800
300
18
180
6
40
Tie Rods
Fe360
206000
78400
78.5
Units
N/mm2
N/mm2
kN/m3
235
N/cm2
30
2000
N/cm2
cm
daN
13
Chapter 3. Single Building
3.2 Results
As stated earlier, the purpose of this chapter is to determine the pushover characteristics of
each of the theoretical buildings to use for comparison purposes later. Below are pictures of
walls from the individual buildings used in the study. These walls resist the lateral forces
produced from the pushover analyzes. The following comparisons are brief to provide a
general overview of the influences on the different building parameters on the response of the
buildings themselves. A more in depth discussion of individual building characteristics can be
found in Appendix A.
1 story, 12 m
1 storey, 24 m
2 story, 12 m
2 storey, 24 m
3 story, 12 m
3 storey, 24 m
4 story, 12 m
4 storey, 24 m
Figure 3.9. Single building models
14
Chapter 3. Single Building
3.2.1 Monotonic Pushover Results
In general, the individual buildings perform as expected. The shortest buildings reach the
highest levels of acceleration and the tallest have the largest displacements. Buildings with
concrete floors tend to have lower levels of acceleration as do buildings with flexible walls. A
few exceptions exist and are discussed in Appendix A in greater detail.
1.5
1.0
1 Storey
3 Stories
Acceleration (g)
0.5
2 Stories
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
-0.5
4 Stories
-1.0
-1.5
Displacement (cm)
Figure 3.10. Monotonic pushover curves: rigid walls & concrete floors
Monotonic Pushover Curves
0.6
Flexible walls,
0.4
Wood floors
Flexible walls,
Rigid walls,
Wood floors
Acceleration (g)
Concrete floors
0.2
0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
-0.2
Rigid walls,
Concrete floors
-0.4
-0.6
Displace ment (cm)
Figure 3.11. Monotonic pushover curves: 3 storey buildings
One important observation to note is that buildings with wood floors tend to have larger
displacements than those with concrete. The reason is because of weak diaphragm action.
This causes most of the load to be concentrated at the interior wall which then fails first and
brings the exterior walls with it. This weak diaphragm action remains in the study because of
the importance of properly representing historical buildings. A concentration of inertial forces
15
Chapter 3. Single Building
or the inability to properly distribute them between the available walls causes the buildings to
be weaker than they would be otherwise. Figure 3.6 shows the three parallel lateral resisting
walls just before failure for buildings with wood floors. As can be clearly seen in this figure,
the interior wall fails first and causes the exterior ones to fail afterwards.
Plan view of final displaced shape from monotonic pushover analysis
Exterior wall
Interior wall
Exterior wall
Figure 3.12. Effect of wood floors and the lack of a fully rigid diaphragm
3.2.2 Cyclic Pushover Results
A general pattern is noticeable in the results for cyclic pushover analysis. For the flexible wall
buildings, the hysteretic loops tend to be narrower than for the rigid wall buildings. This
means that the energy dissipation was also less for these buildings. This makes sense because
the flexible buildings with shorter walls tend to exhibit the rocking mechanism and toe
crushing effect which dissipates less energy than the shear sliding mechanism. The longer,
more rigid wall buildings tend to exhibit the shear sliding mechanism leading to larger
hysteretic loops.
Cyclic pushover analysis is only performed for each of the 16 individual buildings and not for
either the coupled or row conglomeration systems. The reason is because this study is only
concerned with obtaining a general overview of the importance of building interaction in
determining the vulnerability of a city centre. To that end, more parameters are studied and
less analysis is done.
16
-8.00
-6.00
-4.00
-2.00
0.30
0.30
0.20
0.20
0.10
0.10
0.00
0.00
2.00
4.00
6.00
8.00
Acceleration (g)
Acceleration (g)
Chapter 3. Single Building
-2.50
-2.00
-1.50
-1.00
-0.50
-0.10
-0.10
-0.20
-0.20
-0.30
0.40
0.40
0.20
0.20
2.00
3.00
4.00
5.00
Acceleration (g)
Acceleration (g)
0.60
1.00
2.00
2.50
Flexible walls & Concrete floors
0.60
0.00
0.00
1.50
L12_H3_F2
Flexible walls & Wood floors
-1.00
1.00
Displacement (cm)
L12_H3_F1
-2.00
0.50
-0.30
Displacement (cm)
-3.00
0.00
0.00
-2.00
-1.50
-1.00
-0.50
0.00
0.00
-0.20
-0.20
-0.40
-0.40
-0.60
0.50
1.00
1.50
2.00
-0.60
Displacement (cm)
L24_H3_F1
Rigid walls & Wood floors
Displacement (cm)
L24_H3_F2
Rigid walls & Concrete floors
Figure 3.13. Cyclic pushover curves for 3 storey buildings
3.3 Discussion
These theoretical buildings will provide a good background for the future coupled systems
and conglomeration studies. None exhibit local failure mechanisms and all exhibit good inplane wall behaviour. The range of building parameters covers a realistic range of values
typically found within a historic city centre for strictly load bearing masonry buildings.
Monotonic pushover curves for the single buildings provide a basis of comparison to study
the effects of building interaction on a building’s response.
17
Chapter 4. Coupled System
4. COUPLED SYSTEM
The purpose of beginning with the coupled systems is to determine how best to model the
interaction between buildings. This goal was achieved by running monotonic pushover
analysis on various building pairs and comparing the results with the individual buildings.
Two methods for connecting the buildings were developed: a pounding connection where
flexible buildings where able to separate from more rigid buildings and a full connection
between buildings in which the buildings shared a common load bearing wall. Important
interaction groups were determined from the monotonic pushover results and used to focus
the remaining analyzes.
4.1 Analysis
To set a standard analysis procedure for each coupled system, the most flexible building was
used for the control node in both directions. The influence by the choice of the node on the
results has not been studied. One drawback to this approach readily visible is that the
pushover curve for the rigid buildings in the coupled system may not typically include failure
of the building. Thus the maximum displacements of the rigid building are never reached.
Running the models in this manner makes sense because once the more flexible building fails,
not all of its inertial forces are transferred directly into the more rigid building.
The results from the monotonic pushover analysis are arranged in a manner to compare the
different parameters discussed in the previous chapter. A discussion of how changing the
building parameters affect the behaviour of that building can be found in the previous chapter.
This chapter is concerned with how changing the parameters of an adjacent building affect the
interaction between the buildings. Therefore all comparisons are made with the single
building monotonic pushover results.
4.2 Individual Building Results
The results are presented on a building by building basis, highlighting the effects of the
coupling on the building’s response in each case. The individual building pushover curve is
used as a reference point to discuss the effects of other buildings on the curve. Percentage
difference curves are created by taking the difference in acceleration over the average
acceleration at various displacements along each curve as a comparison. The original
pushover curves are provided next to the percentage difference curves for each building. The
percentage difference curves demonstrate the effect of coupling on the response of a building.
18
Chapter 4. Coupled System
Each set is arranged to compare 4 different elements. The first two graphs show the effects of
the pounding connection. The next two show the effects of the full connection. The third set
show the effects of buildings with the same wall length on it. So if the building in question
has a 12 m long wall, then the third set of graphs will show the influences from other
buildings with the same wall length. The final set shows the influences of buildings with a
different wall length. So if the building in question has a 12 m long wall, then the fourth set of
graphs will all have 24 m length walled buildings acting on it.
For ease in recording each of the different combinations, the following short hand notation
was created for naming files and recording results.
Table 4.5. Notation description for navigating result files
Notation
L12
L24
H1
H2
H3
H4
F1
F2
C1
C2
B1
B2
Description
Length of in-plane wall = 12 m
Length of in-plane wall = 24 m
Number of stories = 1 with individual storey heights matching previous table
Number of stories = 2 with individual storey heights matching previous table
Number of stories = 3 with individual storey heights matching previous table
Number of stories = 4 with individual storey heights matching previous table
Floor composition = wood
Floor composition = concrete
Inter-building connection type = pounding
Inter-building connection type = full connection
Building 1 in a coupled or row conglomeration system
Building 2 in a coupled or row conglomeration system
Example:
L12 H1 F2 – Single building with length = 12 m, 1 storey tall, Concrete floors
L12 H2 F1 - L24 H4 F1 - C2 - B2 – Coupled system with first building having a length of 12
m, a height of 2 stories, and wood floors. The second building has a length of 24 m, height
of 4 stories and wood floors. The connection between the buildings is a full connection
and the data presented is for the second building.
Figure 4.14. Example: L12 H2 F1 – L24 H4 F1 – C2 – B2
19
Chapter 4. Coupled System
4.2.1 One Storey, Flexible Wall and Wood Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L12_H1_F1) building. As can be seen clearly, the pounding connection tends to more
adversely affect the 1 storey building. In the positive direction, or when the 1 storey building
acts on the other building, it reaches failure only on 3 occasions, each of which is with a
building of a similar stiffness next to it. The other times it remains in the elastic range while
the more flexible building reaches failure. As for the full connection, the 1 storey building
acts in conjunction with all of the other buildings in the coupled system and thus the strength
actually increases.
Percent Difference
Monotonic Pushover Curves
100%
L12_H1_F1
0.8
L12 H1 F1 - L12 H1 F1 - C1 - B1
0.6
L12 H1 F1 - L12 H2 F1 - C1 - B1
0%
0.00
0.10
0.20
0.30
0.40
0.50
0.60
L12 H1 F1 - L12 H3 F1 - C1 - B1
0.4
L12 H1 F1 - L12 H4 F1 - C1 - B1
0.2
L12 H1 F1 - L24 H1 F1 - C1 - B1
-50%
L12 H1 F1 - L24 H2 F1 - C1 - B1
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
-0.2
-100%
L12 H1 F1 - L24 H3 F1 - C1 - B1
-0.4
L12 H1 F1 - L24 H4 F1 - C1 - B1
-150%
-0.6
-0.8
-200%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
80%
L12_H1_F1
1.0
L12 H1 F1 - L12 H1 F1 - C2 - B1
0.8
60%
L12 H1 F1 - L12 H2 F1 - C2 - B1
0.4
L12 H1 F1 - L12 H4 F1 - C2 - B1
20%
L12 H1 F1 - L24 H1 F1 - C2 - B1
0%
0.00
L12 H1 F1 - L24 H2 F1 - C2 - B1
0.05
0.10
0.15
0.20
0.25
0.30
0.35
L12 H1 F1 - L24 H3 F1 - C2 - B1
-20%
L12 H1 F1 - L24 H4 F1 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
0.6
L12 H1 F1 - L12 H3 F1 - C2 - B1
40%
0.2
0.0
0.00
………………………
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
-0.2
-0.4
-0.6
-40%
-0.8
-1.0
-60%
Displaceme nt (cm)
Displacement (cm)
20
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
100%
L12_H1_F1
1.0
L12 H1 F1 - L12 H1 F1 - C1 - B1
0.8
L12 H1 F1 - L12 H2 F1 - C1 - B1
50%
0.4
0%
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
L12 H1 F1 - L12 H4 F1 - C1 - B1
L12 H1 F1 - L12 H1 F1 - C2 - B1
-50%
L12 H1 F1 - L12 H2 F1 - C2 - B1
-100%
Acceleration (g)
Percent Difference in Acceleration
0.6
L12 H1 F1 - L12 H3 F1 - C1 - B1
L12 H1 F1 - L12 H3 F1 - C2 - B1
0.2
0.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
-0.2
-0.4
L12 H1 F1 - L12 H4 F1 - C2 - B1
-0.6
-150%
-0.8
-200%
-1.0
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
100%
L12_H1_F1
1.0
L12 H1 F1 - L24 H1 F1 - C1 - B1
0.8
L12 H1 F1 - L24 H2 F1 - C1 - B1
50%
0.4
0%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
L12 H1 F1 - L24 H4 F1 - C1 - B1
L12 H1 F1 - L24 H1 F1 - C2 - B1
-50%
L12 H1 F1 - L24 H2 F1 - C2 - B1
-100%
Acceleration (g)
Percent Difference in Acceleration
0.6
L12 H1 F1 - L24 H3 F1 - C1 - B1
L12 H1 F1 - L24 H3 F1 - C2 - B1
0.2
0.0
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-0.2
-0.4
L12 H1 F1 - L24 H4 F1 - C2 - B1
-0.6
-150%
-0.8
-200%
-1.0
Displacement (cm)
Displacement (cm)
Figure 4.15. One storey, flexible wall and wood floors building
4.2.2 One Storey, Flexible Wall and Concrete Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L12_H1_F2) building. The results indicate that coupling for this building does not have
adverse affects. The negative values found in the percent difference curves are present only
because the coupled building failed prior to the 1 storey building failing. Therefore the
acceleration levels indicated on the graph do not reach the maximum they would have had this
building been able to continue its loading after the other on had failed.
Percent Difference
Monotonic Pushover Curves
150%
L12_H1_F2
0.5
L12 H1 F2 - L12 H1 F2 - C1 - B1
0.4
100%
L12 H1 F2 - L12 H2 F2 - C1 - B1
0.2
L12 H1 F2 - L12 H4 F2 - C1 - B1
0%
0.00
0.10
0.20
0.30
0.40
-50%
0.50
0.60
0.70
L12 H1 F2 - L24 H1 F2 - C1 - B1
L12 H1 F2 - L24 H2 F2 - C1 - B1
L12 H1 F2 - L24 H3 F2 - C1 - B1
-100%
L12 H1 F2 - L24 H4 F2 - C1 - B1
Acceleration (g)
Percent Difference in Acceleration
0.3
L12 H1 F2 - L12 H3 F2 - C1 - B1
50%
0.1
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-0.1
-0.2
-0.3
-150%
-0.4
-200%
-0.5
Displacement (cm)
Displacement (cm)
21
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
100%
L12_H1_F2
1.0
L12 H1 F2 - L12 H1 F2 - C2 - B1
90%
0.8
L12 H1 F2 - L12 H2 F2 - C2 - B1
80%
0.4
60%
L12 H1 F2 - L12 H4 F2 - C2 - B1
50%
L12 H1 F2 - L24 H1 F2 - C2 - B1
40%
L12 H1 F2 - L24 H2 F2 - C2 - B1
30%
L12 H1 F2 - L24 H3 F2 - C2 - B1
-0.2
20%
L12 H1 F2 - L24 H4 F2 - C2 - B1
-0.4
Acceleration (g)
Percent Difference in Acceleration
0.6
L12 H1 F2 - L12 H3 F2 - C2 - B1
70%
10%
0%
0.00
0.2
………………………
0.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
-0.6
0.10
0.20
0.30
0.40
0.50
0.60
-0.8
0.70
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
150%
L12_H1_F2
0.8
L12 H1 F2 - L12 H1 F2 - C1 - B1
0.6
L12 H1 F2 - L12 H2 F2 - C1 - B1
L12 H1 F2 - L12 H3 F2 - C1 - B1
0.4
L12 H1 F2 - L12 H4 F2 - C1 - B1
0.2
50%
0%
0.00
L12 H1 F2 - L12 H1 F2 - C2 - B1
0.10
0.20
0.30
0.40
0.50
0.60
0.70
L12 H1 F2 - L12 H2 F2 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
-0.2
-50%
L12 H1 F2 - L12 H3 F2 - C2 - B1
-0.4
L12 H1 F2 - L12 H4 F2 - C2 - B1
-100%
-0.6
-150%
-0.8
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
150%
L12_H1_F2
1.0
L12 H1 F2 - L24 H1 F2 - C1 - B1
0.8
100%
L12 H1 F2 - L24 H2 F2 - C1 - B1
0.4
L12 H1 F2 - L24 H4 F2 - C1 - B1
0%
0.00
0.10
0.20
0.30
0.40
-50%
0.50
0.60
0.70
L12 H1 F2 - L24 H1 F2 - C2 - B1
L12 H1 F2 - L24 H2 F2 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
0.6
L12 H1 F2 - L24 H3 F2 - C1 - B1
50%
0.2
0.0
0.00
L12 H1 F2 - L24 H3 F2 - C2 - B1
-0.2
L12 H1 F2 - L24 H4 F2 - C2 - B1
-0.4
0.20
0.40
0.60
0.80
1.00
1.20
-100%
-150%
-0.6
-200%
-0.8
Displacement (cm)
Displacement (cm)
Figure 4.16. One storey, flexible wall and concrete floors building
4.2.3 Two Stories, Flexible Wall and Wood Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L12_H2_F1) building. The results from coupling are mostly good for this building. One
clear exception jumps off the graphs. When the flexible walled, 2 storey building is coupled
with a rigid walled 1 storey building, the failure mechanism for the 2 storey building actually
changes. This change actually reduces the strength and displacement capacity of the building.
Figure 4.4 below demonstrates clearly illustrates this change.
22
Chapter 4. Coupled System
Figure 4.17. Two stories, flexible wall and wood floors building
Percent Difference
Monotonic Pushover Curves
150%
L12_H2_F1
0.5
L12 H1 F1 - L12 H2 F1 - C1 - B2
0.4
L12 H2 F1 - L12 H2 F1 - C1 - B1
100%
0.2
50%
L12 H2 F1 - L12 H4 F1 - C1 - B1
0%
0.00
L12 H2 F1 - L24 H1 F1 - C1 - B1
0.10
0.20
0.30
0.40
0.50
0.60
L12 H2 F1 - L24 H2 F1 - C1 - B1
-50%
Acceleration (g)
Percent Difference in Acceleration
0.3
L12 H2 F1 - L12 H3 F1 - C1 - B1
L12 H2 F1 - L24 H3 F1 - C1 - B1
0.1
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-0.1
-0.2
L12 H2 F1 - L24 H4 F1 - C1 - B1
-0.3
-100%
-0.4
-150%
-0.5
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
80%
L12_H2_F1
0.6
L12 H1 F1 - L12 H2 F1 - C2 - B2
40%
L12 H2 F1 - L12 H2 F1 - C2 - B1
20%
L12 H2 F1 - L12 H3 F1 - C2 - B1
0%
0.00
0.4
0.2
L12 H2 F1 - L12 H4 F1 - C2 - B1
0.20
0.40
0.60
0.80
1.00
1.20
-20%
L12 H2 F1 - L24 H1 F1 - C2 - B1
-40%
L12 H2 F1 - L24 H2 F1 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
60%
0.0
0.00
………………………
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
3.50
4.00
4.50
5.00
-60%
-0.2
L12 H2 F1 - L24 H3 F1 - C2 - B1
-80%
L12 H2 F1 - L24 H4 F1 - C2 - B1
-100%
-0.4
-120%
-0.6
-140%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
150%
L12_H2_F1
0.5
L12 H1 F1 - L12 H2 F1 - C1 - B2
0.4
100%
L12 H2 F1 - L12 H2 F1 - C1 - B1
0.2
L12 H2 F1 - L12 H4 F1 - C1 - B1
0%
0.00
0.10
0.20
0.30
0.40
-50%
0.50
0.60
0.70
L12 H1 F1 - L12 H2 F1 - C2 - B2
L12 H2 F1 - L12 H2 F1 - C2 - B1
L12 H2 F1 - L12 H3 F1 - C2 - B1
-100%
L12 H2 F1 - L12 H4 F1 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
0.3
L12 H2 F1 - L12 H3 F1 - C1 - B1
50%
0.1
0.0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
-0.1
-0.2
-0.3
-150%
-0.4
-200%
-0.5
Displacement (cm)
Displacement (cm)
23
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
150%
L12_H2_F1
0.6
L12 H2 F1 - L24 H1 F1 - C1 - B1
L12 H2 F1 - L24 H2 F1 - C1 - B1
0.4
L12 H2 F1 - L24 H3 F1 - C1 - B1
50%
0.2
L12 H2 F1 - L24 H4 F1 - C1 - B1
L12 H2 F1 - L24 H1 F1 - C2 - B1
0%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
L12 H2 F1 - L24 H2 F1 - C2 - B1
-50%
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
1.00
2.00
3.00
4.00
5.00
-0.2
L12 H2 F1 - L24 H3 F1 - C2 - B1
L12 H2 F1 - L24 H4 F1 - C2 - B1
-100%
-0.4
-150%
-0.6
Displacement (cm)
Displacement (cm)
Figure 4.18. Two stories, flexible wall and wood floors building
4.2.4 Two Stories, Flexible Wall and Concrete Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L12_H2_F2) building. The results for this building are similar to the ones for the previous 2
storey building. In this instance, the largest change in the building’s characteristics comes
from being coupled with a shorter and more rigid building both for pounding connection and
the full connection. The pounding connection appears to reduce the building’s capacity in
other cases as well, but not to the same magnitude.
Percent Difference
Monotonic Pushover Curves
100%
L12_H2_F2
0.4
L12 H1 F2 - L12 H2 F2 - C1 - B2
0.3
L12 H2 F2 - L12 H2 F2 - C1 - B1
50%
0.1
L12 H2 F2 - L12 H4 F2 - C1 - B1
0%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
L12 H2 F2 - L24 H1 F2 - C1 - B1
L12 H2 F2 - L24 H2 F2 - C1 - B1
-50%
-100%
Acceleration (g)
Percent Difference in Acceleration
0.2
L12 H2 F2 - L12 H3 F2 - C1 - B1
0.0
0.00
0.20
0.40
0.60
………………………
0.80
1.00
1.20
1.40
1.60
-0.1
L12 H2 F2 - L24 H3 F2 - C1 - B1
-0.2
L12 H2 F2 - L24 H4 F2 - C1 - B1
-0.3
-0.4
-150%
-0.5
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
60%
L12_H2_F2
0.6
L12 H1 F2 - L12 H2 F2 - C2 - B2
40%
L12 H2 F2 - L12 H2 F2 - C2 - B1
0.4
L12 H2 F2 - L12 H3 F2 - C2 - B1
0%
0.00
0.2
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
L12 H2 F2 - L12 H4 F2 - C2 - B1
-20%
L12 H2 F2 - L24 H1 F2 - C2 - B1
-40%
L12 H2 F2 - L24 H2 F2 - C2 - B1
-60%
L12 H2 F2 - L24 H3 F2 - C2 - B1
-80%
L12 H2 F2 - L24 H4 F2 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
20%
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-0.2
-0.4
-100%
-0.6
-120%
Displacement (cm)
Displacement (cm)
24
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
150%
L12_H2_F2
0.5
L12 H1 F2 - L12 H2 F2 - C1 - B2
0.4
L12 H2 F2 - L12 H2 F2 - C1 - B1
100%
0.2
50%
L12 H2 F2 - L12 H4 F2 - C1 - B1
0%
0.00
L12 H1 F2 - L12 H2 F2 - C2 - B2
0.10
0.20
0.30
0.40
0.50
0.60
0.70
L12 H2 F2 - L12 H2 F2 - C2 - B1
-50%
Acceleration (g)
Percent Difference in Acceleration
0.3
L12 H2 F2 - L12 H3 F2 - C1 - B1
L12 H2 F2 - L12 H3 F2 - C2 - B1
0.1
0.0
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
-0.1
-0.2
L12 H2 F2 - L12 H4 F2 - C2 - B1
-0.3
-100%
-0.4
-150%
-0.5
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
80%
L12_H2_F2
0.6
L12 H2 F2 - L24 H1 F2 - C1 - B1
40%
L12 H2 F2 - L24 H2 F2 - C1 - B1
20%
L12 H2 F2 - L24 H3 F2 - C1 - B1
0%
0.00
0.4
0.2
L12 H2 F2 - L24 H4 F2 - C1 - B1
0.20
0.40
0.60
0.80
1.00
1.20
-20%
L12 H2 F2 - L24 H1 F2 - C2 - B1
-40%
L12 H2 F2 - L24 H2 F2 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
60%
0.0
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-60%
L12 H2 F2 - L24 H3 F2 - C2 - B1
-0.2
-80%
L12 H2 F2 - L24 H4 F2 - C2 - B1
-100%
-0.4
-120%
-140%
-0.6
Displacement (cm)
Displacement (cm)
Figure 4.19. Two stories, flexible wall and concrete floors building
4.2.5 Three Stories, Flexible Wall and Wood Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L12_H3_F1) building. Neither type of connection appears to make a consistent change to
the building’s response. Wall type and height does seem to make a difference. Like those
before it, the 3 storey building is most adversely affected by shorter and more rigid buildings,
as seen in the final set of graphs. This is consistent with earlier data in that the change in
failure mechanism for the building reduces the capacity for the building.
Percent Difference
Monotonic Pushover Curves
100%
L12_H3_F1
0.4
L12 H1 F1 - L12 H3 F1 - C1 - B2
0.3
L12 H2 F1 - L12 H3 F1 - C1 - B2
50%
0.1
L12 H3 F1 - L12 H4 F1 - C1 - B1
0%
0.00
1.00
2.00
3.00
4.00
5.00
6.00
L12 H3 F1 - L24 H1 F1 - C1 - B1
L12 H3 F1 - L24 H2 F1 - C1 - B1
-50%
-100%
Acceleration (g)
Percent Difference in Acceleration
0.2
L12 H3 F1 - L12 H3 F1 - C1 - B1
0.0
0.00
1.00
2.00
………………………
3.00
4.00
5.00
6.00
7.00
-0.1
L12 H3 F1 - L24 H3 F1 - C1 - B1
-0.2
L12 H3 F1 - L24 H4 F1 - C1 - B1
-0.3
-0.4
-150%
-0.5
Displacement (cm)
Displacement (cm)
25
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
100%
L12_H3_F1
0.4
L12 H1 F1 - L12 H3 F1 - C2 - B2
0.3
L12 H2 F1 - L12 H3 F1 - C2 - B2
0%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
L12 H3 F1 - L12 H3 F1 - C2 - B1
0.2
L12 H3 F1 - L12 H4 F1 - C2 - B1
0.1
L12 H3 F1 - L24 H1 F1 - C2 - B1
-50%
L12 H3 F1 - L24 H2 F1 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
………………………
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
-0.1
-100%
L12 H3 F1 - L24 H3 F1 - C2 - B1
-0.2
L12 H3 F1 - L24 H4 F1 - C2 - B1
-150%
-0.3
-0.4
-200%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
80%
L12_H3_F1
0.4
L12 H1 F1 - L12 H3 F1 - C1 - B2
60%
0.3
L12 H2 F1 - L12 H3 F1 - C1 - B2
L12 H3 F1 - L12 H3 F1 - C1 - B1
0.2
L12 H3 F1 - L12 H4 F1 - C1 - B1
0.1
20%
0%
0.00
0.50
1.00
1.50
2.00
2.50
3.00
L12 H1 F1 - L12 H3 F1 - C2 - B2
-20%
L12 H2 F1 - L12 H3 F1 - C2 - B2
-40%
Acceleration (g)
Percent Difference in Acceleration
40%
0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
-0.1
L12 H3 F1 - L12 H3 F1 - C2 - B1
-60%
-0.2
L12 H3 F1 - L12 H4 F1 - C2 - B1
-80%
-0.3
-100%
-120%
-0.4
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
200%
L12_H3_F1
0.4
L12 H3 F1 - L24 H1 F1 - C1 - B1
0.3
150%
L12 H3 F1 - L24 H2 F1 - C1 - B1
0.2
L12 H3 F1 - L24 H3 F1 - C1 - B1
0.1
L12 H3 F1 - L24 H4 F1 - C1 - B1
50%
0%
0.00
L12 H3 F1 - L24 H1 F1 - C2 - B1
0.20
0.40
0.60
0.80
1.00
1.20
L12 H3 F1 - L24 H2 F1 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
1.00
2.00
3.00
-0.1
-50%
L12 H3 F1 - L24 H3 F1 - C2 - B1
-0.2
L12 H3 F1 - L24 H4 F1 - C2 - B1
-0.3
-100%
-150%
-0.4
-200%
-0.5
Displacement (cm)
Displacement (cm)
Figure 4.20. Three stories, flexible wall and wood floors building
4.2.6 Three Stories, Flexible Wall and Concrete Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L12_H3_F2) building. The pounding connection appears to consistently adversely affect the
response of this building. Similar to above, shorter and more rigid buildings cause the most
change. The heavier floor system of concrete seems to make it more susceptible to
development of soft-stories at upper levels than with the wood floors. Where rigid walls were
needed to develop a soft-storey up above, now only the change in building elevation is
required. From these results, it appears that heavier and taller buildings are at a greater risk to
changes in their response when coupled with a shorter building next to it.
26
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
100%
L12_H3_F2
0.3
L12 H1 F2 - L12 H3 F2 - C1 - B2
L12 H2 F2 - L12 H3 F2 - C1 - B2
0.2
L12 H3 F2 - L12 H3 F2 - C1 - B1
0%
0.00
0.1
0.20
0.40
0.60
0.80
1.00
1.20
1.40
L12 H3 F2 - L12 H4 F2 - C1 - B1
L12 H3 F2 - L24 H1 F2 - C1 - B1
-50%
L12 H3 F2 - L24 H2 F2 - C1 - B1
-100%
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
-0.1
L12 H3 F2 - L24 H3 F2 - C1 - B1
L12 H3 F2 - L24 H4 F2 - C1 - B1
-150%
-0.2
-200%
-0.3
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
50%
L12_H3_F2
0.4
L12 H1 F2 - L12 H3 F2 - C2 - B2
0.3
L12 H2 F2 - L12 H3 F2 - C2 - B2
0.20
0.40
0.60
0.80
1.00
1.20
1.40
L12 H3 F2 - L12 H3 F2 - C2 - B1
0.2
L12 H3 F2 - L12 H4 F2 - C2 - B1
0.1
-50%
L12 H3 F2 - L24 H1 F2 - C2 - B1
L12 H3 F2 - L24 H2 F2 - C2 - B1
-100%
Acceleration (g)
Percent Difference in Acceleration
0%
0.00
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
-0.1
L12 H3 F2 - L24 H3 F2 - C2 - B1
-0.2
L12 H3 F2 - L24 H4 F2 - C2 - B1
-150%
-0.3
-0.4
-200%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
100%
L12_H3_F2
0.4
L12 H1 F2 - L12 H3 F2 - C1 - B2
80%
L12 H2 F2 - L12 H3 F2 - C1 - B2
40%
L12 H3 F2 - L12 H3 F2 - C1 - B1
0.2
L12 H3 F2 - L12 H4 F2 - C1 - B1
0.1
20%
0%
0.00
0.50
1.00
1.50
2.00
L12 H1 F2 - L12 H3 F2 - C2 - B2
-20%
L12 H2 F2 - L12 H3 F2 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
0.3
60%
0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
2.00
2.50
3.00
-0.1
-40%
L12 H3 F2 - L12 H3 F2 - C2 - B1
-60%
-0.2
L12 H3 F2 - L12 H4 F2 - C2 - B1
-80%
-0.3
-100%
-120%
-0.4
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
150%
L12_H3_F2
0.4
L12 H3 F2 - L24 H1 F2 - C1 - B1
0.3
L12 H3 F2 - L24 H2 F2 - C1 - B1
50%
0%
0.00
0.20
0.40
0.60
-50%
0.80
1.00
1.20
L12 H3 F2 - L24 H3 F2 - C1 - B1
0.2
L12 H3 F2 - L24 H4 F2 - C1 - B1
0.1
L12 H3 F2 - L24 H1 F2 - C2 - B1
L12 H3 F2 - L24 H2 F2 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
0.50
1.00
1.50
-0.1
L12 H3 F2 - L24 H3 F2 - C2 - B1
-100%
-0.2
L12 H3 F2 - L24 H4 F2 - C2 - B1
-150%
-0.3
-200%
-0.4
Displacement (cm)
Displacement (cm)
27
Chapter 4. Coupled System
Figure 4.21. Three stories, flexible wall and concrete floors building
4.2.7 Four Stories, Flexible Wall and Wood Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L12_H4_F1) building. Similar to the 3 storey building before it, the 4 storey building is most
affected by the height of the building next to it. If the adjacent building is shorter, then the 4
storey building develops a soft storey directly above it which reduces the building’s capacity.
For buildings of a similar height and attached via a full connection, the capacity of the 4
storey building increases.
L12_H4_F1
Percent Difference
Monotonic Pushover Curves
L12 H1 F1 - L12 H4 F1 - C1 - B2
100%
0.3
L12 H2 F1 - L12 H4 F1 - C1 - B2
0.2
L12 H3 F1 - L12 H4 F1 - C1 - B2
L12 H4 F1 - L24 H4 F1 - C1 - B2
0%
0.00
0.1
1.00
2.00
3.00
4.00
5.00
6.00
L12 H4 F1 - L24 H1 F1 - C1 - B1
-50%
L12 H4 F1 - L24 H2 F1 - C1 - B1
Acceleration (g)
Percent Difference in Acceleration
50%
L12 H4 F1 - L24 H3 F1 - C1 - B1
-100%
0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-0.1
L12 H4 F1 - L24 H4 F1 - C1 - B1
-150%
-0.2
-0.3
-200%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
100%
L12_H4_F1
0.3
L12 H1 F1 - L12 H4 F1 - C2 - B2
L12 H2 F1 - L12 H4 F1 - C2 - B2
0.2
L12 H3 F1 - L12 H4 F1 - C2 - B2
0%
0.00
0.1
1.00
2.00
3.00
4.00
5.00
L12 H4 F1 - L12 H4 F1 - C2 - B1
L12 H4 F1 - L24 H1 F1 - C2 - B1
-50%
L12 H4 F1 - L24 H2 F1 - C2 - B1
-100%
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
………………………
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
-0.1
L12 H4 F1 - L24 H3 F1 - C2 - B1
L12 H4 F1 - L24 H4 F1 - C2 - B1
-0.2
-150%
-0.3
-200%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
150%
L12_H4_F1
0.3
L12 H1 F1 - L12 H4 F1 - C1 - B2
L12 H2 F1 - L12 H4 F1 - C1 - B2
0.2
L12 H3 F1 - L12 H4 F1 - C1 - B2
50%
0.1
L12 H4 F1 - L12 H4 F1 - C1 - B1
0%
0.00
L12 H1 F1 - L12 H4 F1 - C2 - B2
0.50
1.00
1.50
2.00
2.50
L12 H2 F1 - L12 H4 F1 - C2 - B2
-50%
L12 H3 F1 - L12 H4 F1 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
-0.1
L12 H4 F1 - L12 H4 F1 - C2 - B1
-100%
-0.2
-150%
-0.3
Displacement (cm)
Displacement (cm)
28
Chapter 4. Coupled System
L12_H4_F1
Percent Difference
Monotonic Pushover Curves
L12 H4 F1 - L24 H1 F1 - C1 - B1
100%
0.3
L12 H4 F1 - L24 H2 F1 - C1 - B1
0.2
L12 H4 F1 - L24 H3 F1 - C1 - B1
L12 H4 F1 - L24 H4 F1 - C1 - B1
0%
0.00
0.1
1.00
2.00
3.00
4.00
5.00
6.00
L12 H4 F1 - L24 H1 F1 - C2 - B1
-50%
L12 H4 F1 - L24 H2 F1 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
50%
L12 H4 F1 - L24 H3 F1 - C2 - B1
-100%
0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
-0.1
L12 H4 F1 - L24 H4 F1 - C2 - B1
-150%
-0.2
-0.3
-200%
Displacement (cm)
Displacement (cm)
Figure 4.22. Four stories, flexible wall and wood floors building
4.2.8 Four Stories, Flexible Wall and Concrete Floors Building
The following are the coupling results for one storey, flexible wall and concrete floor
(L12_H4_F2) building. Again the same conclusions are drawn from these results as from the
previous ones.
L12_H4_F2
Percent Difference
Monotonic Pushover Curves
L12 H1 F2 - L12 H4 F2 - C1 - B2
50%
0.3
L12 H2 F2 - L12 H4 F2 - C1 - B2
0.2
L12 H3 F2 - L12 H4 F2 - C1 - B2
0.50
1.00
1.50
2.00
0.2
2.50
-50%
L12 H4 F2 - L12 H4 F2 - C1 - B2
0.1
L12 H4 F2 - L24 H1 F2 - C1 - B1
0.1
L12 H4 F2 - L24 H2 F2 - C1 - B1
-100%
Acceleration (g)
Percent Difference in Acceleration
0%
0.00
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.1
L12 H4 F2 - L24 H3 F2 - C1 - B1
-0.1
L12 H4 F2 - L24 H4 F2 - C1 - B1
-150%
-0.2
-0.2
-0.3
-200%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
100%
L12_H4_F2
0.3
L12 H1 F2 - L12 H4 F2 - C2 - B2
L12 H2 F2 - L12 H4 F2 - C2 - B2
0.2
L12 H3 F2 - L12 H4 F2 - C2 - B2
0.1
L12 H4 F2 - L12 H4 F2 - C2 - B1
0%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
L12 H4 F2 - L24 H1 F2 - C2 - B1
L12 H4 F2 - L24 H2 F2 - C2 - B1
-50%
L12 H4 F2 - L24 H3 F2 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
………………………
0.50
1.00
1.50
2.00
-0.1
L12 H4 F2 - L24 H4 F2 - C2 - B1
-100%
-0.2
-0.3
-150%
Displacement (cm)
Displacement (cm)
29
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
100%
L12_H4_F2
0.3
L12 H1 F2 - L12 H4 F2 - C1 - B2
80%
0.2
60%
L12 H2 F2 - L12 H4 F2 - C1 - B2
40%
L12 H3 F2 - L12 H4 F2 - C1 - B2
20%
L12 H4 F2 - L12 H4 F2 - C1 - B1
0.1
0%
0.00
0.50
1.00
1.50
2.00
L12 H1 F2 - L12 H4 F2 - C2 - B2
-20%
L12 H2 F2 - L12 H4 F2 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
0.2
0.1
0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
-0.1
-40%
L12 H3 F2 - L12 H4 F2 - C2 - B2
-0.1
-60%
L12 H4 F2 - L12 H4 F2 - C2 - B1
-0.2
-80%
-0.2
-100%
-120%
-0.3
Displacement (cm)
Displacement (cm)
L12_H4_F2
Percent Difference
Monotonic Pushover Curves
L12 H4 F2 - L24 H1 F2 - C1 - B1
50%
0.3
L12 H4 F2 - L24 H2 F2 - C1 - B1
0.2
L12 H4 F2 - L24 H3 F2 - C1 - B1
0.50
1.00
1.50
2.00
2.50
L12 H4 F2 - L24 H4 F2 - C1 - B1
0.1
-50%
L12 H4 F2 - L24 H1 F2 - C2 - B1
L12 H4 F2 - L24 H2 F2 - C2 - B1
-100%
L12 H4 F2 - L24 H3 F2 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
0%
0.00
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.1
L12 H4 F2 - L24 H4 F2 - C2 - B1
-150%
-0.2
-0.3
-200%
Displacement (cm)
Displacement (cm)
Figure 4.23. Four stories, flexible wall and concrete floors building
4.2.9 One Storey, Rigid Wall and Wood Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L24_H1_F1) building. Where the 1 storey building can reached failure under the pounding
connection, the capacity of thee building is less than the single building capacity. Most of the
time, however, the building could not reach capacity. There is one data set that greatly stands
out from the rest and that is the interaction with the 1 storey building of flexible walls in a full
connection. According to the data, when the coupled system acts in the direction of the
flexible walled building, the capacity of the rigid wall building drops. This makes sense
because the adjacent building has just a slightly lower capacity than this one and is at the
same storey height, therefore the collapse mechanism of the weaker building cannot change.
The load transferred to the rigid building weakens it as expected.
30
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
150%
L24_H1_F1
1.5
L24 H1 F1 - L24 H1 F1 - C1 - B1
100%
L24 H1 F1 - L24 H2 F1 - C1 - B1
1.0
L24 H1 F1 - L24 H3 F1 - C1 - B1
0.5
0%
0.00
L24 H1 F1 - L24 H4 F1 - C1 - B1
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
L12 H1 F1 - L24 H1 F1 - C1 - B2
-50%
L12 H2 F1 - L24 H1 F1 - C1 - B2
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-100%
-0.5
L12 H3 F1 - L24 H1 F1 - C1 - B2
-150%
L12 H4 F1 - L24 H1 F1 - C1 - B2
-1.0
-200%
-250%
-1.5
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
40%
L24_H1_F1
1.5
L24 H1 F1 - L24 H1 F1 - C2 - B1
20%
L24 H1 F1 - L24 H2 F1 - C2 - B1
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1.0
0.45
L24 H1 F1 - L24 H3 F1 - C2 - B1
-20%
0.5
L24 H1 F1 - L24 H4 F1 - C2 - B1
-40%
L12 H1 F1 - L24 H1 F1 - C2 - B2
-60%
L12 H2 F1 - L24 H1 F1 - C2 - B2
-80%
Acceleration (g)
Percent Difference in Acceleration
0%
0.00
………………………
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.35
0.40
0.45
0.50
0.35
0.40
0.45
0.50
-0.5
L12 H3 F1 - L24 H1 F1 - C2 - B2
-100%
0.0
0.00
L12 H4 F1 - L24 H1 F1 - C2 - B2
-120%
-1.0
-140%
-1.5
-160%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
60%
L24_H1_F1
1.5
L24 H1 F1 - L24 H1 F1 - C1 - B1
40%
L24 H1 F1 - L24 H2 F1 - C1 - B1
0%
0.00
1.0
L24 H1 F1 - L24 H3 F1 - C1 - B1
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.5
-20%
L24 H1 F1 - L24 H4 F1 - C1 - B1
-40%
L24 H1 F1 - L24 H1 F1 - C2 - B1
-60%
L24 H1 F1 - L24 H2 F1 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
20%
0.0
0.00
………………………
0.05
0.10
0.15
0.20
0.25
0.30
-80%
-0.5
L24 H1 F1 - L24 H3 F1 - C2 - B1
-100%
L24 H1 F1 - L24 H4 F1 - C2 - B1
-120%
-1.0
-140%
-160%
-1.5
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
150%
L24_H1_F1
1.5
L12 H1 F1 - L24 H1 F1 - C1 - B2
L12 H2 F1 - L24 H1 F1 - C1 - B2
1.0
L12 H3 F1 - L24 H1 F1 - C1 - B2
50%
0.5
L12 H4 F1 - L24 H1 F1 - C1 - B2
0%
0.00
0.05
0.10
0.15
0.20
-50%
0.25
0.30
L12 H1 F1 - L24 H1 F1 - C2 - B2
L12 H2 F1 - L24 H1 F1 - C2 - B2
L12 H3 F1 - L24 H1 F1 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
-0.5
-100%
L12 H4 F1 - L24 H1 F1 - C2 - B2
-1.0
-150%
-200%
-1.5
Displacement (cm)
Displacement (cm)
Figure 4.24. One storey, rigid wall and wood floors building
31
Chapter 4. Coupled System
4.2.10 One Storey, Rigid Wall and Concrete Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L24_H1_F2) building. The same observations can be made from this 1 storey, rigid wall
building as with the one above. One interesting note is that only 1 data set matches the
capacity of the individual building, whereas with the wood floors, there are more buildings
that match and exceed the capacity of the single building
Percent Difference
Monotonic Pushover Curves
150%
L24_H1_F2
1.5
L24 H1 F2 - L24 H1 F2 - C1 - B1
L24 H1 F2 - L24 H2 F2 - C1 - B1
1.0
L24 H1 F2 - L24 H3 F2 - C1 - B1
50%
0.5
L24 H1 F2 - L24 H4 F2 - C1 - B1
0%
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
-50%
L12 H1 F2 - L24 H1 F2 - C1 - B2
L12 H2 F2 - L24 H1 F2 - C1 - B2
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
………………………
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
-0.5
L12 H3 F2 - L24 H1 F2 - C1 - B2
-100%
L12 H4 F2 - L24 H1 F2 - C1 - B2
-1.0
-150%
-200%
-1.5
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
40%
L24_H1_F2
1.5
L24 H1 F2 - L24 H1 F2 - C2 - B1
20%
L24 H1 F2 - L24 H2 F2 - C2 - B1
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1.0
0.45
L24 H1 F2 - L24 H3 F2 - C2 - B1
-20%
0.5
L24 H1 F2 - L24 H4 F2 - C2 - B1
-40%
L12 H1 F2 - L24 H1 F2 - C2 - B2
-60%
L12 H2 F2 - L24 H1 F2 - C2 - B2
-80%
Acceleration (g)
Percent Difference in Acceleration
0%
0.00
………………………
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
-0.5
L12 H3 F2 - L24 H1 F2 - C2 - B2
-100%
0.0
0.00
L12 H4 F2 - L24 H1 F2 - C2 - B2
-120%
-1.0
-140%
-1.5
-160%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
60%
L24_H1_F2
1.5
L24 H1 F2 - L24 H1 F2 - C1 - B1
40%
L24 H1 F2 - L24 H2 F2 - C1 - B1
0%
0.00
1.0
L24 H1 F2 - L24 H3 F2 - C1 - B1
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.5
-20%
L24 H1 F2 - L24 H4 F2 - C1 - B1
-40%
L24 H1 F2 - L24 H1 F2 - C2 - B1
-60%
L24 H1 F2 - L24 H2 F2 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
20%
0.0
0.00
………………………
0.10
0.20
0.30
0.40
0.50
0.60
0.70
-80%
L24 H1 F2 - L24 H3 F2 - C2 - B1
-0.5
-100%
L24 H1 F2 - L24 H4 F2 - C2 - B1
-120%
-1.0
-140%
-160%
-1.5
Displacement (cm)
Displacement (cm)
32
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
100%
L24_H1_F2
1.5
L12 H1 F2 - L24 H1 F2 - C1 - B2
L12 H2 F2 - L24 H1 F2 - C1 - B2
1.0
L12 H3 F2 - L24 H1 F2 - C1 - B2
0%
0.00
0.5
0.10
0.20
0.30
0.40
0.50
0.60
L12 H4 F2 - L24 H1 F2 - C1 - B2
L12 H1 F2 - L24 H1 F2 - C2 - B2
-50%
L12 H2 F2 - L24 H1 F2 - C2 - B2
-100%
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
-0.5
L12 H3 F2 - L24 H1 F2 - C2 - B2
L12 H4 F2 - L24 H1 F2 - C2 - B2
-150%
-1.0
-200%
-1.5
Displacement (cm)
Displacement (cm)
Figure 4.25. One storey, rigid wall and concrete floors building
4.2.11 Two Stories, Rigid Wall and Wood Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L24_H2_F1) building. All of the adjacent buildings connected by pounding connections
cause a decrease in capacity of the 2 storey, rigid walled building. The full connection does
not cause nearly as many buildings to fail. This is again due to the fact that a fully connection
coupled system will tend to act as a single unit, which can lead to an increase of capacity from
that of an individual building. This is usually occurs when acting with a taller and more
flexible building. A stress concentration occurs at the change in elevation, similar to what
would occur if the two buildings were actually one.
Percent Difference
Monotonic Pushover Curves
40%
L24_H2_F1
0.8
L24 H1 F1 - L24 H2 F1 - C1 - B2
20%
0.6
0%
0.00
0.20
0.40
0.60
0.80
-20%
1.00
1.20
1.40
L24 H2 F1 - L24 H3 F1 - C1 - B1
0.4
L24 H2 F1 - L24 H4 F1 - C1 - B1
0.2
L12 H1 F1 - L24 H2 F1 - C1 - B2
-40%
L12 H2 F1 - L24 H2 F1 - C1 - B2
-60%
Acceleration (g)
Percent Difference in Acceleration
L24 H2 F1 - L24 H2 F1 - C1 - B1
0.0
0.00
………………………
0.50
1.00
1.50
2.00
2.50
-0.2
L12 H3 F1 - L24 H2 F1 - C1 - B2
-80%
-0.4
L12 H4 F1 - L24 H2 F1 - C1 - B2
-100%
-0.6
-120%
-0.8
Displacement (cm)
Displacement (cm)
33
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
100%
L24_H2_F1
1.0
L24 H1 F1 - L24 H2 F1 - C2 - B2
0.8
L24 H2 F1 - L24 H2 F1 - C2 - B1
0.6
L24 H2 F1 - L24 H3 F1 - C2 - B1
0.4
L24 H2 F1 - L24 H4 F1 - C2 - B1
0%
0.00
0.10
0.20
0.30
0.40
0.50
L12 H1 F1 - L24 H2 F1 - C2 - B2
L12 H2 F1 - L24 H2 F1 - C2 - B2
-50%
Acceleration (g)
Percent Difference in Acceleration
50%
L12 H3 F1 - L24 H2 F1 - C2 - B2
0.0
0.00
………………………
0.50
1.00
1.50
2.00
2.50
3.00
-0.2
-0.4
L12 H4 F1 - L24 H2 F1 - C2 - B2
-100%
0.2
-0.6
-0.8
-1.0
-150%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
60%
L24_H2_F1
1.0
L24 H1 F1 - L24 H2 F1 - C1 - B2
40%
0.8
L24 H2 F1 - L24 H2 F1 - C1 - B1
20%
L24 H2 F1 - L24 H3 F1 - C1 - B1
0.20
0.40
0.60
0.80
1.00
1.20
0.4
1.40
-20%
L24 H2 F1 - L24 H4 F1 - C1 - B1
-40%
L24 H1 F1 - L24 H2 F1 - C2 - B2
-60%
L24 H2 F1 - L24 H2 F1 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
0.6
0%
0.00
0.2
0.0
0.00
………………………
0.50
1.00
1.50
2.00
2.50
3.00
3.50
-0.2
-80%
L24 H2 F1 - L24 H3 F1 - C2 - B1
-0.4
-100%
L24 H2 F1 - L24 H4 F1 - C2 - B1
-0.6
-120%
-0.8
-140%
-160%
-1.0
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
100%
L24_H2_F1
0.8
L12 H1 F1 - L24 H2 F1 - C1 - B2
0.6
L12 H2 F1 - L24 H2 F1 - C1 - B2
0%
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
L12 H3 F1 - L24 H2 F1 - C1 - B2
0.4
L12 H4 F1 - L24 H2 F1 - C1 - B2
0.2
0.80
L12 H1 F1 - L24 H2 F1 - C2 - B2
L12 H2 F1 - L24 H2 F1 - C2 - B2
-50%
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
-0.2
L12 H3 F1 - L24 H2 F1 - C2 - B2
-0.4
L12 H4 F1 - L24 H2 F1 - C2 - B2
-100%
-0.6
-150%
-0.8
Displacement (cm)
Displacement (cm)
Figure 4.26. Two stories, rigid wall and wood floors building
4.2.12 Two Stories, Rigid Wall and Concrete Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L24_H2_F2) building. Similar observations can be made from the 2 storey, rigid walled
building with concrete floors as for the previous building with wood floors. The only
difference is that less combinations allow the building to meet its original capacity and none
cause an increase in capacity.
34
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
150%
L24_H2_F2
0.8
L24 H1 F2 - L24 H2 F2 - C1 - B2
0.6
L24 H2 F2 - L24 H2 F2 - C1 - B1
50%
0%
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
-50%
L24 H2 F2 - L24 H3 F2 - C1 - B1
0.4
L24 H2 F2 - L24 H4 F2 - C1 - B1
0.2
L12 H1 F2 - L24 H2 F2 - C1 - B2
L12 H2 F2 - L24 H2 F2 - C1 - B2
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
………………………
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
-0.2
L12 H3 F2 - L24 H2 F2 - C1 - B2
-100%
-0.4
L12 H4 F2 - L24 H2 F2 - C1 - B2
-150%
-0.6
-200%
-0.8
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
20%
L24_H2_F2
0.8
L24 H1 F2 - L24 H2 F2 - C2 - B2
0%
0.00
0.10
0.20
0.30
0.40
0.50
0.6
0.60
L24 H2 F2 - L24 H2 F2 - C2 - B1
L24 H2 F2 - L24 H3 F2 - C2 - B1
0.4
L24 H2 F2 - L24 H4 F2 - C2 - B1
0.2
-40%
-60%
L12 H1 F2 - L24 H2 F2 - C2 - B2
-80%
L12 H2 F2 - L24 H2 F2 - C2 - B2
-100%
Acceleration (g)
Percent Difference in Acceleration
-20%
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
-0.2
L12 H3 F2 - L24 H2 F2 - C2 - B2
-120%
-0.4
L12 H4 F2 - L24 H2 F2 - C2 - B2
-140%
-0.6
-160%
-0.8
-180%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
100%
L24_H2_F2
0.8
L24 H1 F2 - L24 H2 F2 - C1 - B2
0.6
L24 H2 F2 - L24 H2 F2 - C1 - B1
0%
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
L24 H2 F2 - L24 H3 F2 - C1 - B1
0.4
L24 H2 F2 - L24 H4 F2 - C1 - B1
0.2
L24 H1 F2 - L24 H2 F2 - C2 - B2
-50%
L24 H2 F2 - L24 H2 F2 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
-0.2
-100%
L24 H2 F2 - L24 H3 F2 - C2 - B1
-0.4
L24 H2 F2 - L24 H4 F2 - C2 - B1
-150%
-0.6
-200%
-0.8
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
50%
L24_H2_F2
0.8
L12 H1 F2 - L24 H2 F2 - C1 - B2
0.6
L12 H2 F2 - L24 H2 F2 - C1 - B2
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
L12 H3 F2 - L24 H2 F2 - C1 - B2
0.4
L12 H4 F2 - L24 H2 F2 - C1 - B2
0.2
-50%
L12 H1 F2 - L24 H2 F2 - C2 - B2
L12 H2 F2 - L24 H2 F2 - C2 - B2
-100%
Acceleration (g)
Percent Difference in Acceleration
0%
0.00
0.0
0.00
0.20
0.40
0.60
0.80
1.00
1.20
-0.2
L12 H3 F2 - L24 H2 F2 - C2 - B2
-0.4
L12 H4 F2 - L24 H2 F2 - C2 - B2
-150%
-0.6
-200%
-0.8
Displacement (cm)
Displacement (cm)
Figure 4.27. Two stories, rigid wall and concrete floors building
35
Chapter 4. Coupled System
4.2.13 Three Stories, Rigid Wall and Wood Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L24_H3_F1) building. Similar observations can be made as previous made above.
Percent Difference
Monotonic Pushover Curves
150%
L24_H3_F1
0.6
L24 H1 F1 - L24 H3 F1 - C1 - B2
L24 H2 F1 - L24 H3 F1 - C1 - B2
0.4
L24 H3 F1 - L24 H3 F1 - C1 - B1
50%
0.2
L24 H3 F1 - L24 H4 F1 - C1 - B1
0%
0.00
L12 H1 F1 - L24 H3 F1 - C1 - B2
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
L12 H2 F1 - L24 H3 F1 - C1 - B2
Acceleration (g)
Percent Difference in Acceleration
100%
-50%
………………………
0.0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
-0.2
L12 H4 F1 - L24 H3 F1 - C1 - B2
-100%
-0.4
-150%
-0.6
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
40%
L24_H3_F1
0.8
L24 H1 F1 - L24 H3 F1 - C2 - B2
20%
0.6
0.50
1.00
1.50
2.00
2.50
3.00
-20%
L24 H3 F1 - L24 H3 F1 - C2 - B1
0.4
L24 H3 F1 - L24 H4 F1 - C2 - B1
0.2
L12 H1 F1 - L24 H3 F1 - C2 - B2
-40%
L12 H2 F1 - L24 H3 F1 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
L24 H2 F1 - L24 H3 F1 - C2 - B2
0%
0.00
-60%
0.0
0.00
………………………
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
3.50
4.00
4.50
5.00
-0.2
L12 H3 F1 - L24 H3 F1 - C2 - B2
-0.4
-80%
L12 H4 F1 - L24 H3 F1 - C2 - B2
-0.6
-100%
-0.8
-120%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
150%
L24_H3_F1
0.8
L24 H1 F1 - L24 H3 F1 - C1 - B2
0.6
L24 H2 F1 - L24 H3 F1 - C1 - B2
L24 H3 F1 - L24 H3 F1 - C1 - B1
0.4
L24 H3 F1 - L24 H4 F1 - C1 - B1
0.2
50%
0%
0.00
L24 H1 F1 - L24 H3 F1 - C2 - B2
0.20
0.40
0.60
0.80
1.00
1.20
1.40
L24 H2 F1 - L24 H3 F1 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
………………………
0.50
1.00
1.50
2.00
2.50
3.00
-0.2
-50%
L24 H3 F1 - L24 H3 F1 - C2 - B1
-0.4
L24 H3 F1 - L24 H4 F1 - C2 - B1
-100%
-0.6
-150%
-0.8
Displacement (cm)
Displacement (cm)
36
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
100%
L24_H3_F1
0.6
L12 H1 F1 - L24 H3 F1 - C1 - B2
L12 H2 F1 - L24 H3 F1 - C1 - B2
0.4
L12 H3 F1 - L24 H3 F1 - C1 - B2
0.2
L12 H4 F1 - L24 H3 F1 - C1 - B2
0%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
L12 H1 F1 - L24 H3 F1 - C2 - B2
L12 H2 F1 - L24 H3 F1 - C2 - B2
-50%
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
-0.2
L12 H3 F1 - L24 H3 F1 - C2 - B2
L12 H4 F1 - L24 H3 F1 - C2 - B2
-100%
-0.4
-150%
-0.6
Displacement (cm)
Displacement (cm)
Figure 4.28. Three stories, rigid wall and wood floors building
4.2.14 Three Stories, Rigid Wall and Concrete Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L24_H3_F2) building. The effects of coupling on this building are similar to the rigid walled
ones above. One difference is that every building with the same length of wall caused a
reduction in the building’s capacity, as can be seen in the third set of graphs.
Percent Difference
Monotonic Pushover Curves
80%
L24_H3_F2
0.6
L24 H1 F2 - L24 H3 F2 - C1 - B2
60%
L24 H2 F2 - L24 H3 F2 - C1 - B2
0.4
L24 H3 F2 - L24 H3 F2 - C1 - B1
20%
0.2
L24 H3 F2 - L24 H4 F2 - C1 - B1
0%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
L12 H1 F2 - L24 H3 F2 - C1 - B2
-20%
L12 H2 F2 - L24 H3 F2 - C1 - B2
-40%
Acceleration (g)
Percent Difference in Acceleration
40%
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.00
1.20
1.40
-0.2
-60%
L12 H4 F2 - L24 H3 F2 - C1 - B2
-80%
-0.4
-100%
-120%
-0.6
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
100%
L24_H3_F2
0.6
L24 H1 F2 - L24 H3 F2 - C2 - B2
L24 H2 F2 - L24 H3 F2 - C2 - B2
0.4
L24 H3 F2 - L24 H3 F2 - C2 - B1
0%
0.00
0.2
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
L24 H3 F2 - L24 H4 F2 - C2 - B1
L12 H1 F2 - L24 H3 F2 - C2 - B2
-50%
L12 H2 F2 - L24 H3 F2 - C2 - B2
-100%
L12 H3 F2 - L24 H3 F2 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
………………………
0.20
0.40
0.60
0.80
-0.2
L12 H4 F2 - L24 H3 F2 - C2 - B2
-0.4
-150%
-0.6
-200%
Displacement (cm)
Displacement (cm)
37
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
150%
L24_H3_F2
0.6
L24 H1 F2 - L24 H3 F2 - C1 - B2
L24 H2 F2 - L24 H3 F2 - C1 - B2
0.4
L24 H3 F2 - L24 H3 F2 - C1 - B1
50%
0.2
L24 H3 F2 - L24 H4 F2 - C1 - B1
0%
0.00
L24 H1 F2 - L24 H3 F2 - C2 - B2
0.10
0.20
0.30
0.40
0.50
0.60
0.70
L24 H2 F2 - L24 H3 F2 - C2 - B2
-50%
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-0.2
L24 H3 F2 - L24 H3 F2 - C2 - B1
L24 H3 F2 - L24 H4 F2 - C2 - B1
-100%
-0.4
-150%
-0.6
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
60%
L24_H3_F2
0.6
L12 H1 F2 - L24 H3 F2 - C1 - B2
40%
L12 H2 F2 - L24 H3 F2 - C1 - B2
0.4
L12 H3 F2 - L24 H3 F2 - C1 - B2
0%
0.00
0.2
0.20
0.40
0.60
0.80
1.00
1.20
1.40
L12 H4 F2 - L24 H3 F2 - C1 - B2
-20%
L12 H1 F2 - L24 H3 F2 - C2 - B2
-40%
L12 H2 F2 - L24 H3 F2 - C2 - B2
-60%
L12 H3 F2 - L24 H3 F2 - C2 - B2
-80%
L12 H4 F2 - L24 H3 F2 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
20%
0.0
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
-0.2
-0.4
-100%
-120%
-0.6
Displacement (cm)
Displacement (cm)
Figure 4.29. Three stories, rigid wall and concrete floors building
4.2.15 Four Stories, Rigid Wall and Wood Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L24_H4_F1) building. This building performs similarly to the 3 storey counterpart with
wood floors.
Percent Difference
Monotonic Pushover Curves
150%
L24_H4_F1
0.5
L24 H1 F1 - L24 H4 F1 - C1 - B2
0.4
L24 H2 F1 - L24 H4 F1 - C1 - B2
100%
0.2
L24 H4 F1 - L24 H4 F1 - C1 - B1
0%
0.00
L12 H1 F1 - L24 H4 F1 - C1 - B2
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
L12 H2 F1 - L24 H4 F1 - C1 - B2
-50%
L12 H3 F1 - L24 H4 F1 - C1 - B2
L12 H4 F1 - L24 H4 F1 - C1 - B2
Acceleration (g)
Percent Difference in Acceleration
0.3
L24 H3 F1 - L24 H4 F1 - C1 - B2
50%
0.1
0.0
0.00
………………………
0.50
1.00
1.50
2.00
2.50
3.00
3.50
-0.1
-0.2
-0.3
-100%
-0.4
-150%
-0.5
Displacement (cm)
Displacement (cm)
38
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
40%
L24_H4_F1
0.5
L24 H1 F1 - L24 H4 F1 - C2 - B2
0.4
20%
L24 H2 F1 - L24 H4 F1 - C2 - B2
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
L24 H3 F1 - L24 H4 F1 - C2 - B2
0.2
L24 H4 F1 - L24 H4 F1 - C2 - B1
-20%
L12 H1 F1 - L24 H4 F1 - C2 - B2
-40%
L12 H2 F1 - L24 H4 F1 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
0.3
0%
0.00
-60%
L12 H3 F1 - L24 H4 F1 - C2 - B2
0.1
………………………
0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
-0.1
-0.2
-80%
L12 H4 F1 - L24 H4 F1 - C2 - B2
-0.3
-100%
-0.4
-0.5
-120%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
60%
L24_H4_F1
0.5
L24 H1 F1 - L24 H4 F1 - C1 - B2
0.4
40%
L24 H2 F1 - L24 H4 F1 - C1 - B2
0.3
L24 H3 F1 - L24 H4 F1 - C1 - B2
0.2
0%
0.00
0.50
1.00
1.50
2.00
2.50
3.00
L24 H4 F1 - L24 H4 F1 - C1 - B1
-20%
L24 H1 F1 - L24 H4 F1 - C2 - B2
-40%
L24 H2 F1 - L24 H4 F1 - C2 - B2
-60%
L24 H3 F1 - L24 H4 F1 - C2 - B2
-80%
L24 H4 F1 - L24 H4 F1 - C2 - B1
Acceleration (g)
Percent Difference in Acceleration
20%
0.1
0.0
0.00
………………………
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
3.00
3.50
4.00
-0.1
-0.2
-0.3
-100%
-0.4
-120%
-0.5
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
100%
L24_H4_F1
0.5
L12 H1 F1 - L24 H4 F1 - C1 - B2
80%
0.4
60%
L12 H2 F1 - L24 H4 F1 - C1 - B2
40%
L12 H3 F1 - L24 H4 F1 - C1 - B2
20%
L12 H4 F1 - L24 H4 F1 - C1 - B2
0.2
0%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
L12 H1 F1 - L24 H4 F1 - C2 - B2
-20%
L12 H2 F1 - L24 H4 F1 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
0.3
0.1
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.1
-40%
L12 H3 F1 - L24 H4 F1 - C2 - B2
-60%
L12 H4 F1 - L24 H4 F1 - C2 - B2
-80%
-0.2
-0.3
-0.4
-100%
-120%
-0.5
Displacement (cm)
Displacement (cm)
Figure 4.30. Four stories, rigid wall and wood floors building
4.2.16 Four Stories, Rigid Wall and Concrete Floors Building
The following are the coupling results for one storey, flexible wall and wood floor
(L24_H4_F2) building. Coupling is good for the tallest building with rigid walls. Only a few
combinations cause a lowering of the building’s capacity, and all of those are within the full
inter-building connection. The smaller and sometimes more rigid buildings help prop this
building up and the 4 storey rigid wall building has the ability to refrain from developing a
soft-storey at the change of elevation with the shorter adjacent one. It is strange that the taller
building would as little of an effect from the coupling as it does, especially when the 3 storey
rigid walled buildings are greatly affected by it.
39
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
120%
L24_H4_F2
0.3
L24 H1 F2 - L24 H4 F2 - C1 - B2
100%
L24 H2 F2 - L24 H4 F2 - C1 - B2
0.2
L24 H3 F2 - L24 H4 F2 - C1 - B2
60%
0.1
L24 H4 F2 - L24 H4 F2 - C1 - B1
40%
L12 H1 F2 - L24 H4 F2 - C1 - B2
20%
0%
0.00
L12 H2 F2 - L24 H4 F2 - C1 - B2
0.20
0.40
0.60
0.80
1.00
1.20
Acceleration (g)
Percent Difference in Acceleration
80%
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.40
-0.1
L12 H3 F2 - L24 H4 F2 - C1 - B2
-20%
L12 H4 F2 - L24 H4 F2 - C1 - B2
-40%
-0.2
-60%
-80%
-0.3
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
100%
L24_H4_F2
0.5
L24 H1 F2 - L24 H4 F2 - C2 - B2
0.4
L24 H2 F2 - L24 H4 F2 - C2 - B2
0.3
L24 H3 F2 - L24 H4 F2 - C2 - B2
0.2
L24 H4 F2 - L24 H4 F2 - C2 - B1
0%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
L12 H1 F2 - L24 H4 F2 - C2 - B2
L12 H2 F2 - L24 H4 F2 - C2 - B2
-50%
Acceleration (g)
Percent Difference in Acceleration
50%
L12 H3 F2 - L24 H4 F2 - C2 - B2
0.0
0.00
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
-0.1
-0.2
L12 H4 F2 - L24 H4 F2 - C2 - B2
-100%
0.1
-0.3
-0.4
-0.5
-150%
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
150%
L24_H4_F2
0.3
L24 H1 F2 - L24 H4 F2 - C1 - B2
L24 H2 F2 - L24 H4 F2 - C1 - B2
0.2
L24 H3 F2 - L24 H4 F2 - C1 - B2
50%
0.1
L24 H4 F2 - L24 H4 F2 - C1 - B1
0%
0.00
L24 H1 F2 - L24 H4 F2 - C2 - B2
0.20
0.40
0.60
0.80
1.00
1.20
L24 H2 F2 - L24 H4 F2 - C2 - B2
-50%
Acceleration (g)
Percent Difference in Acceleration
100%
0.0
0.00
c
………………………
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-0.1
L24 H3 F2 - L24 H4 F2 - C2 - B2
L24 H4 F2 - L24 H4 F2 - C2 - B1
-100%
-0.2
-150%
-0.3
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
150%
L24_H4_F2
0.5
L12 H1 F2 - L24 H4 F2 - C1 - B2
0.4
L12 H2 F2 - L24 H4 F2 - C1 - B2
100%
0.2
50%
L12 H4 F2 - L24 H4 F2 - C1 - B2
0%
0.00
L12 H1 F2 - L24 H4 F2 - C2 - B2
0.20
0.40
0.60
0.80
1.00
1.20
1.40
L12 H2 F2 - L24 H4 F2 - C2 - B2
-50%
L12 H3 F2 - L24 H4 F2 - C2 - B2
L12 H4 F2 - L24 H4 F2 - C2 - B2
Acceleration (g)
Percent Difference in Acceleration
0.3
L12 H3 F2 - L24 H4 F2 - C1 - B2
0.1
0.0
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-0.1
-0.2
-0.3
-100%
-0.4
-150%
-0.5
Displacement (cm)
Displacement (cm)
Figure 4.31. Four stories, rigid wall and concrete floors building
40
Chapter 4. Coupled System
4.3 Discussion
As the adjacent building becomes taller and all other parameters remain constant, such as the
wall thickness and material properties, the base shear for the adjacent building increases and it
becomes weaker. As these buildings become weaker, they tend to transfer their inertial forces
through the coupled connection to the stronger building next to it. This proves detrimental for
the building of interest. When the building of interest is the weaker one, then the effects of the
force transfer is slightly more complicated. Sometimes the building becomes stronger because
now the inertial forces are distributed over a larger base. Other times it actually weakens
because a soft storey develops in the upper floors as seen in Figure 4.19.
In general, a flexible building acting on a more rigid building reduces the strength of the rigid
building. The results are easily understood – the flexible building still failed prior to the rigid
building. Weakening of the rigid building, however, is important to understand because it will
factor into repair costs for earthquake damage. Pounding connections tended to exhibit this
behaviour more so than their fully connected counterparts. The fully connected buildings
acted more as a single structure. Because of this, the failure mode of the fully connected
systems sometimes included failure of the rigid building. Other times a soft storey would
develop in the flexible building leading to failure of the system through the soft storey, similar
to the pounding connections. In short, coupling a more flexible building to a rigid building did
not cause the rigid building to fail first, but it did change its behaviour and make it
substantially weaker.
4.3.1 Pounding Connection
Coupled buildings by a pounding connection demonstrate a change in behaviour only when
the more flexible building acts upon the more rigid one. When the more flexible building
moves in the opposite direction of the rigid building, neither building sees a change in their
response curve. Figure 4.19 below provides a few examples of this behaviour. Note that in
each case the rigid building is the 2 storey one and the flexible building is the 4 storey one. In
most cases where the more flexible building extended one storey or more above the rigid one,
a soft storey developed at the interaction of the buildings. Figure 4.19 also demonstrates this
phenomenon. In this condition, both buildings experience a reduction in strength on their
response curves. This suggests that pounding between buildings is almost always at least
slightly detrimental.
41
Chapter 4. Coupled System
Figure 4.32. Pounding connection
4.3.2 Full Connection
The main different between the full connection and the pounding connection is that the full
connection causes the coupled system to act as one building. Neither building is independent
in either direction. Similar to the pounding connection, interaction through a full building
connection between a short building and a taller building tends to lead to the development of a
soft storey just above the shorter building. A major difference is that unlike the pounding
connection, the full connection experiences this change in both directions. This means that
when buildings share walls and are of different heights, there is a chance that a stress
concentration could form where the shorter building ends. This concentration of stresses in no
different than if the coupled system were one building. Figure 4.20 below shows the
development of these soft stories and also the increase demands on the shorter building,
which is not always present in the pounding connection system.
42
Chapter 4. Coupled System
Figure 4.33. Full connection
The type of system that typically causes the greatest decrease in single building capacity is a
coupled system with flexible walls acting against a shorter building with more rigid walls. In
almost every instance, the taller building develops a soft-storey failure mechanism just above
the shorter building and fails at a lower acceleration and displacement than it would on its
own. In studying vulnerability parameters on a larger scale, this condition should be noted and
included and capturing the effect of building interaction.
Another important note is that the pounding connection between buildings tended to change
building responses more than the full connection. This means that buildings which share a
load bearing masonry wall are less likely to observe damage than those that are simply spaced
closely together. There are a few instances when a full connection between buildings is
actually worse than a pounding one. Most notably is again when the building heights are
substantially different and the shorter one has more rigid walls than the taller.
43
Chapter 4. Coupled System
Percent Difference
Monotonic Pushover Curves
100%
L24_H3_F1
0.8
L24 H3 F1 - L24 H3 F1 - C1 - B1
0.6
L24 H3 F1 - L24 H3 F1 - C2 - B1
0%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
L24 H3 F2 - L24 H3 F2 - C1 - B1
0.4
L24 H3 F2 - L24 H3 F2 - C2 - B1
0.2
Acceleration (g)
Percent Difference in Acceleration
50%
1.40
-50%
0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
-0.2
-0.4
-100%
-0.6
-150%
-0.8
Displacement (cm)
Displacement (cm)
Percent Difference
Monotonic Pushover Curves
100%
L24_H3_F2
0.8
L24 H3 F1 - L24 H3 F1 - C1 - B1
0.6
L24 H3 F1 - L24 H3 F1 - C2 - B1
0%
0.00
0.20
0.40
0.60
0.80
-50%
1.00
1.20
1.40
L24 H3 F2 - L24 H3 F2 - C1 - B1
0.4
L24 H3 F2 - L24 H3 F2 - C2 - B1
0.2
Acceleration (g)
Percent Difference in Acceleration
50%
0.0
0.00
1.00
2.00
3.00
-0.2
-0.4
-100%
-0.6
-150%
-0.8
Displacement (cm)
Displacement (cm)
Figure 4.34. Three stories, rigid walls buildings for Row Conglomerations
Of all the buildings in this study, building interaction influences the response of the 3 storey,
rigid walled buildings more than any other type of system. An influence of the interaction can
even be seen in the pounding condition between the same buildings. Because of these
differences, the 3 storey rigid walled building with wood floors is the building of choice for
the row conglomeration study described in the following chapter.
44
Chapter 5. Simple Conglomeration
5. CONGLOMERATIONS
One of the remaining relations to observe is the effect on building responses with respect to
its location within a longer building conglomeration. This section on building conglomeration
addresses that relationship. The purpose is to indicate what positions impact the building’s
response the most.
5.1 Analysis
A conglomeration consists of a row of buildings oriented in much the same fashion as the
coupled system. They consist of 3, 6 and 9 buildings with either pounding or full connections
between each building. A building with concrete floors is included either as an external
building or an internal building in each group of conglomerations to model the effects of a
heavier building acting on lighter ones. A full list of conglomerations analyzed is listed in
Table 5.1 below.
From the coupled system analysis in the previous chapter, 3 storey buildings with rigid walls
and wood floors were determined to have the most impact on adjacent building response.
These buildings were thus the only ones considered in the conglomeration study. This was
done in order to limit the number of models required to capture the impact of position in a
row of buildings on a building’s behaviour. A list of the different conglomerations in this
study is located in Appendix C.
To reduce the number of models further, only data was collected for an exterior building and
an interior building for each of the conglomerations. The interior building was the middle
building, or in the case of the 6 building conglomeration, the fourth building from the left. A
mix of different inter-building connections within a conglomeration is not considered in this
study. Other parameters, such as building height and wall thickness, are also excluded from
the conglomeration portion of the study. The focus of the row conglomeration is on building
position. Including other parameters previously studied in the coupled systems chapter would
complicate the study of this parameter to the point that obtaining useful information would
become difficult. For that reason, a changing pattern of building connections is not considered
necessary to understand the influence of building interaction based on a buildings position.
Such a study would complicate the parameter too much to extract useful information.
45
Chapter 5. Simple Conglomeration
5.2 Monotonic Pushover Results
The standard building of study for the row conglomeration is the 3 storey, rigid walled
building with wood floors. The results are presented for each type of row conglomeration for
this building, highlighting the effects of the conglomeration on the building’s response in each
case. The 3 storey building pushover curve is used as a reference point to discuss the effects
of other buildings on the curve. Percentage difference curves are created by taking the
difference in acceleration over the average acceleration at various displacements along each
curve as a comparison. The original pushover curves are provided next to the percentage
difference curves for each case. The percentage difference curves demonstrate the effect of
the conglomeration on the response of the building.
Table 5.6. Notation description for navigating result files
Notation
L12
L24
H1
H2
H3
H4
F1
F2
C1
C2
B1
B2
B4
B5
Description
Length of in-plane wall = 12 m
Length of in-plane wall = 24 m
Number of stories = 1 with individual storey heights matching previous table
Number of stories = 2 with individual storey heights matching previous table
Number of stories = 3 with individual storey heights matching previous table
Number of stories = 4 with individual storey heights matching previous table
Floor composition = wood
Floor composition = concrete
Inter-building connection type = pounding
Inter-building connection type = full connection
Building 1 in a coupled or row conglomeration system
Building 2 in a coupled or row conglomeration system
Building 4 in a row conglomeration system
Building 5 in a row conglomeration system
Example:
L12 H1 F2 – Single building with length = 12 m, 1 storey tall, Concrete floors
3 * L24 H3 F1 – C1 – B2 w/ external F2 – This is a 3 building row conglomeration system
with first building having a length of 24 m, a height of 3 stories, and concrete floors. The
second building has a length of 24 m, height of 3 stories and wood floors. The third
building has a length of 24 m, height of 3 stories and wood floors. The connection
between the buildings is a pounding connection and the data presented is for the second
building, or the interior building of the row conglomeration.
46
Chapter 5. Simple Conglomeration
Figure 5.35. Example: 3 * L24 H3 F1 – C1 – B2 w/ external F2
5.2.1 Three building conglomerations
The following results are for the 3 building conglomeration systems. The most noticeable
trend in the data is a negative effect due to the influence of surrounding buildings within a
conglomeration, with a few exceptions. These exceptions occur only when the
conglomeration is fully connected between each building. With the buildings being fully
connected, the conglomeration actually gains capacity. This trend is illustrated in Figure 5.2
below.
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
3 * L24 H3 F1 - C1 - B1
40%
0.8
3 * L24 H3 F1 - C1 - B2
0.6
20%
3 * L24 H3 F1 - C2 - B1
0.50
1.00
1.50
2.00
2.50
3 * L24 H3 F1 - C2 - B2
0.2
-20%
3 * L24 H3 F1 - C1 - B2 w/ external F2
-40%
3 * L24 H3 F1 - C1 - B3 w/ external F2
Acceleration (g)
Percent Difference in Acceleration
0.4
0%
0.00
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.2
-60%
3 * L24 H3 F1 - C2 - B2 w/ external F2
-80%
3 * L24 H3 F1 - C2 - B3 w/ external F2
-0.4
3 * L24 H3 F1 - C1 - B1 w/ internal F2
-100%
-0.6
-0.8
Displacement (cm)
Displacement (cm)
Figure 5.36. 3 building conglomerations results
A - 3 Buildings - L24 H3 F1 – Pounding Connection
47
Chapter 5. Simple Conglomeration
B - 3 Buildings - L24 H3 F1 – Full Connection
Figure 5.37. 3 Building conglomeration models
The above figure illustrates the failure mechanism of buildings with only wood floors. The
plan view for both the pounding and full connection conglomerations show that the middle
wall fails prior to the exterior walls. The elevation below each of the plan views is of the
interior wall. The failure mechanism appears to be similar for both conglomerations. Walls on
both the first and second storey fail in shear while the top storey wall does not fail. The
biggest difference between the conglomerations is that the smaller walls at the end of each
building do not fail in the pounding connection while they do fail in the full connection. This
is partly the reason why building that are fully connected perform better than those using the
pounding connection.
A - 3 Buildings - L24 H3 F1 – Pounding Connection w/ external F2 on the left
48
Chapter 5. Simple Conglomeration
B - 3 Buildings - L24 H3 F1 – Full Connection w/ external F2 on the left
C - 3 Buildings - L24 H3 F1 – Pounding Connection w/ internal F2 in the centre
D - 3 Buildings - L24 H3 F1 – Full Connection w/ internal F2 in the centre
Figure 5.38. 3 building conglomeration models
49
Chapter 5. Simple Conglomeration
Another interesting point is the transfer of inertial forces between buildings when a concrete
floor building is included in the conglomeration. This transfer is most noticeable when
observing the pounding connection systems. As seen in group A of Figure 5.4 above, the
external concrete floor building is on the left and the wood floor buildings are the 2 on the
right. The internal wall elevation shows that inertial forces are transferred from the concrete
floor building to the wood floor building because the buildings on the right actually separate
from the concrete building. This notion is confirmed by observing the external wall elevations
in that the walls all move the same amount. This is because the concrete floors are stiff
enough to distribute the inertial forces to the exterior walls of the concrete building which
then gets transferred to the exterior walls of the wood floor buildings on the right.
This concept is again illustrated in group C of Figure 5.4. Here, the internal building has
concrete floors while both external buildings have wood floors. The exterior wall elevations
shows the same phenomenon occurring is described above. The wood floor building on the
left does not show any signs of failure in the exterior walls because the wood floors are not
stiff enough to transfer the inertial forces to these walls. On the other hand, the wood floor
building on the right does show signs of failure in the exterior walls because of load
transferred from the concrete floor building. Again the exterior building furthest to the right
separates from the concrete building at failure. This is seen in the interior wall elevation of
group C.
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
L24_H3_F2
20%
0.6
10%
0.50
1.00
1.50
2.00
2.50
0.2
-10%
Acceleration (g)
Percent Difference in Acceleration
0.4
0%
0.00
-20%
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-30%
-0.2
-40%
-0.4
-50%
-0.6
-60%
Displacement (cm)
Displacement (cm)
Figure 5.39. Comparison of wood vs concrete floors
These observations are of particular interest when comparing them to the behaviour between
the individual 3 story buildings. Above in Figure 5.5, a 3 storey building with wood floors
and rigid walls is compared to a 3 storey building with concrete floors and rigid walls. As can
be seen in the graphs, the two buildings observe similar levels of maximum acceleration and
quite different levels of ultimate displacement. The building with concrete floors fails at a
lower displacement level than the one with wood floors. The building with concrete floors
also has a shallower initial ascent than the one with wood floors. This makes sense because
50
Chapter 5. Simple Conglomeration
the one with concrete floors is heavier and thus will have larger forces from the same
acceleration levels as the building with wood floors. In this regard, it is particularly interesting
to note that in group A of Figure 5.5 above, the building with concrete floors on the left does
not have as large of displacements as those with wood floor on the right. This clearly suggests
that some of its inertial forces are transferred to the other buildings resulting in larger
displacements at lower levels of acceleration.
None of the above observations are noticeable in the full connection systems. This is because
the concrete floors distribute the inertial forces to the exterior walls for the entire system.
When comparing the plan view of these building conglomerations with that of the original full
connection system, i.e. the one without any concrete floor diaphragms present, one notices
that the failure mode is different. All three walls appear to displace the same distance at
failure, whereas the interior wall of the original system clearly displaces further. The
difference, however, is that the increase of inertial forces due to the increase of dead load
from the concrete floors still negatively effects the other buildings as seen in Figure 5.4
above. Unlike the original conglomeration system where the strength of the system actually
increase, these decrease.
5.2.2 Six building conglomerations
The following results are for the 6 building conglomeration systems. The results are similar
for the 6 building conglomerations as for the 3 building conglomerations. Each of the
different conglomerations negatively influenced the standard 3 storey building’s response. All
of the conglomerations reduce the ultimate strength of the building and some also reduce the
ultimate displacement obtained. There are a few outliers as seen in Figure 5.6 below. One
system observed a very low acceleration at its ultimate displacement, clearly smaller than
80% of the highest value. This is the result of the convergence being too large for that
particular model. The other two outliers are caused by an very large displacement of the
system after the first iteration. This occurs in one of the 9 building conglomerations as well
and is discussed in more detail later.
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
6 * L24 H3 F1 - C1 - B1
50%
0.6
6 * L24 H3 F1 - C1 - B4
0.4
0.50
1.00
1.50
2.00
2.50
6 * L24 H3 F1 - C2 - B1
6 * L24 H3 F1 - C2 - B4
-50%
6 * L24 H3 F1 - C1 - B4 w/ external F2
-100%
6 * L24 H3 F1 - C1 - B6 w/ external F2
-150%
0.2
Acceleration (g)
Percent Difference in Acceleration
0%
0.00
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.2
6 * L24 H3 F1 - C2 - B4 w/ external F2
-200%
6 * L24 H3 F1 - C2 - B6 w/ external F2
6 * L24 H3 F1 - C1 - B1 w/ internal F2
-250%
-0.4
-0.6
Displacement (cm)
Displacement (cm)
Figure 5.40. 6 building conglomerations results
51
Chapter 5. Simple Conglomeration
A - 6 Buildings - L24 H3 F1 – Pounding Connection
B - 6 Buildings - L24 H3 F1 – Full Connection
Figure 5.41. 6 building conglomeration models
The failure mode is similar between the standard 3 storey building conglomerations when
comparing the pounding and full connections as seen above. Because all of the buildings have
wood floors acting as a weak diaphragm, the interior wall observes the largest displacements
of the system.
A – 6 Buildings - L24 H3 F1 – Pounding Connection w/ external F2 on the left
B - 6 Buildings - L24 H3 F1 – Full Connection w/ external F2 on the left
52
Chapter 5. Simple Conglomeration
C - 6 Buildings - L24 H3 F1 – Pounding Connection w/ internal F2 in the centre
D - 6 Buildings - L24 H3 F1 – Full Connection w/ internal F2 in the centre
Figure 5.42. 6 building conglomeration models
The effects of the concrete building on the behaviour of the conglomeration are similar for the
6 building systems as for the 3 building systems. The concrete floors distribute the inertial
forces from the interior walls to the exterior walls as seen most clearly in the plan views for
the full building connections. These show that all three walls have approximately the same
displacement at failure. The concrete floor building is not as effective at distributing the loads
between walls through a pounding connection as through a full connection. This observation
is similar to that made for the 3 building conglomerations. The pounding connection systems
also depict a separation of buildings.
5.2.3 Nine building conglomerations
The following results are for the 9 building conglomeration systems. The results for the 9
building conglomerations are very similar to those for the other conglomerations. Clearly the
size of the conglomeration is not a major factor in determining the influence on a building.
The important factors appear to be whether the system has pounding or full building
connections. Pounding connections are more detrimental to the standard building’s response.
For larger conglomerations, the full connection also appears to have a negative effect on the
building’s response.
53
Chapter 5. Simple Conglomeration
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
9 * L24 H3 F1 - C1 - B1
50%
0.6
9 * L24 H3 F1 - C1 - B5
0.4
0.50
1.00
1.50
2.00
2.50
9 * L24 H3 F1 - C2 - B1
9 * L24 H3 F1 - C2 - B5
-50%
9 * L24 H3 F1 - C1 - B5 w/ external F2
-100%
9 * L24 H3 F1 - C1 - B9 w/ external F2
-150%
0.2
Acceleration (g)
Percent Difference in Acceleration
0%
0.00
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.2
9 * L24 H3 F1 - C2 - B5 w/ external F2
-200%
9 * L24 H3 F1 - C2 - B9 w/ external F2
9 * L24 H3 F1 - C1 - B1 w/ internal F2
-250%
-0.4
-0.6
Displacement (cm)
Displacement (cm)
Figure 5.43. 9 building conglomerations results
Similar to the 6 building conglomerations earlier, the 9 building conglomeration results
contain a few uncharacteristic responses. The full connection between all wood buildings also
experiences an initial large displacement under the first step of the analysis as does the 6
building conglomerations with the same setup. Likewise, the conglomeration with an external
concrete floor building experiences a very large final displacement at a level of acceleration
lower than 80% of the highest acceleration, similar to the same system type for the 6 building
conglomerations. The wall elevations for the 9 building conglomerations are not presented in
the following figures because they are very small due to their long length. The plan views
illustrate similar trends as seen for in the 6 building systems.
A - 9 Buildings - L24 H3 F1 – Pounding Connection
B - 9 Buildings - L24 H3 F1 – Full Connection
Figure 5.44. 9 building conglomeration models
A - 9 Buildings - L24 H3 F1 – Pounding Connection w/ external F2 on the left
B - 9 Buildings - L24 H3 F1 – Full Connection w/ external F2 on the left
C - 9 Buildings - L24 H3 F1 – Pounding Connection w/ internal F2 in the centre
54
Chapter 5. Simple Conglomeration
D - 9 Buildings - L24 H3 F1 – Full Connection w/ internal F2 in the centre
Figure 5.45. 9 building conglomeration models
The most important note to make about the 9 building conglomerations is that the wood floor
buildings begin to develop the global behaviour as the individual buildings due to the long
length of the system. As seen in the plan view for group B, the building on the end of the
conglomeration has larger displacements at the centre wall than the outer walls. The concrete
floor building on the far left, however, has very similar displacements for each of the walls.
This means that when the conglomeration becomes longer, the benefit of having a rigid floor
diaphragm is lost for the overall system. This leaves only negative effects from the additional
weight from the concrete floors being transferred throughout the system.
5.2.4 Pounding connections, no concrete floor buildings
The following results are for the pounding connection conglomeration systems without any
concrete floor buildings in the conglomeration. All of the conglomerations caused a decrease
in the highest acceleration obtained by the standard building in its response. There is no clear
difference between the size of the conglomeration or position within a conglomeration in
affecting standard building’s response.
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
3 * L24 H3 F1 - C1 - B1
40%
0.6
6 * L24 H3 F1 - C1 - B1
20%
0.4
3 * L24 H3 F1 - C1 - B2
0.50
1.00
1.50
2.00
2.50
0.2
6 * L24 H3 F1 - C1 - B4
-20%
9 * L24 H3 F1 - C1 - B5
-40%
Acceleration (g)
Percent Difference in Acceleration
9 * L24 H3 F1 - C1 - B1
0%
0.00
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.2
-60%
-0.4
-80%
-0.6
-100%
Displacement (cm)
Displacement (cm)
Figure 5.46. Pounding connections, no concrete floor buildings
5.2.5 Full connections, no concrete floor buildings
The following results are for the full connection conglomeration systems without any concrete
floor buildings in the conglomeration. For the 3 building conglomeration, the capacity of the
standard building increases due to the interaction with the other buildings. Both the ultimate
displacement and maximum acceleration increase for this system. In this case, the full
connection essentially joins the buildings together which increases the capacity of the
55
Chapter 5. Simple Conglomeration
standard building. This is similar to the effect observed in a few of the coupled systems from
the previous chapter. Longer conglomerations observe a more detrimental effect from the
influence of adjacent buildings. For both the 6 and 9 building conglomerations, the standard
building decreases in strength. This is due to the fact that the full connection between
buildings is not strong enough to link the buildings together over longer conglomerations.
As can be seen in Figure 5.13 below, a few of the full connection row conglomerations have
an unusual pushover curve. This curve is caused by a discrepancy within these files. The first
step in the pushover analysis causes a jump to a large displacement. Figure 5.14 shows the
models at the beginning of the analysis and after one step. Clearly the building exhibits large
displacements after the first step of the analysis. Throwing out this data, we obtain Figure
5.15 below. This only occurred in systems without concrete floors.
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
3 * L24 H3 F1 - C2 - B1
50%
0.8
6 * L24 H3 F1 - C2 - B1
0.6
0%
0.00
0.50
1.00
1.50
2.00
2.50
9 * L24 H3 F1 - C2 - B1
0.2
6 * L24 H3 F1 - C2 - B4
-100%
9 * L24 H3 F1 - C2 - B5
Acceleration (g)
Percent Difference in Acceleration
0.4
3 * L24 H3 F1 - C2 - B2
-50%
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.2
-150%
-0.4
-200%
-0.6
-0.8
-250%
Displacement (cm)
Displacement (cm)
Figure 5.47. Full connections, no concrete floor buildings
At rest
After first step
Figure 5.48. Model
56
Chapter 5. Simple Conglomeration
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
3 * L24 H3 F1 - C2 - B1
40%
0.8
20%
0.6
3 * L24 H3 F1 - C2 - B2
0.50
1.00
1.50
2.00
2.50
0.2
-20%
9 * L24 H3 F1 - C2 - B5
-40%
Acceleration (g)
Percent Difference in Acceleration
0.4
0%
0.00
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.2
-60%
-0.4
-80%
-0.6
-0.8
-100%
Displacement (cm)
Displacement (cm)
Figure 5.49. Full connections, no concrete floor buildings without unusual pushover curves
5.2.6 Pounding connection, external concrete floor building
The following results are for the pounding connection conglomeration systems with a
building with concrete floors on the far left side of the conglomeration. All of the
conglomerations caused a decrease in the highest acceleration obtained by the standard
building in its response. The effect of a heavier floor system appears to be detrimental to the
other buildings within a conglomeration where the buildings are connected by pounding
connections.
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
3 * L24 H3 F1 - C1 - B3 w/ external F2
50%
0.6
6 * L24 H3 F1 - C1 - B6 w/ external F2
0.4
9 * L24 H3 F1 - C1 - B9 w/ external F2
0.50
1.00
1.50
2.00
2.50
3 * L24 H3 F1 - C1 - B2 w/ external F2
-50%
6 * L24 H3 F1 - C1 - B4 w/ external F2
9 * L24 H3 F1 - C1 - B5 w/ external F2
-100%
0.2
Acceleration (g)
Percent Difference in Acceleration
0%
0.00
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.2
-150%
-0.4
-0.6
-200%
Displacement (cm)
Displacement (cm)
Figure 5.50. Pounding connection, external concrete floor building
5.2.7 Full connection, external concrete floor building
The following results are for the full connection conglomeration systems with a building with
concrete floors on the far left side of the conglomeration. All of the conglomerations caused a
decrease in the highest acceleration and ultimate displacement obtained by the standard
building in its response. The effect of a heavier floor system appears to be detrimental to the
other buildings even though, as seen before, the presence of a stiffer diaphragm helps
distribute loads to the exterior walls and relieve the interior one. The overall effect is that the
57
Chapter 5. Simple Conglomeration
weight of the concrete floors transferred through the conglomeration decreases the capacity of
the buildings adjacent to it.
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
3 * L24 H3 F1 - C2 - B3 w/ external F2
0%
0.00
0.6
0.50
1.00
1.50
2.00
2.50
6 * L24 H3 F1 - C2 - B6 w/ external F2
-10%
0.4
9 * L24 H3 F1 - C2 - B9 w/ external F2
-30%
3 * L24 H3 F1 - C2 - B2 w/ external F2
-40%
6 * L24 H3 F1 - C2 - B4 w/ external F2
-50%
9 * L24 H3 F1 - C2 - B5 w/ external F2
-60%
0.2
Acceleration (g)
Percent Difference in Acceleration
-20%
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.2
-70%
-80%
-0.4
-90%
-0.6
-100%
Displacement (cm)
Displacement (cm)
Figure 5.51. Full connection, external concrete floor building
5.2.8 Pounding connection, internal concrete floor building
The following results are for the pounding connection conglomeration systems with a
building with concrete floors at the centre of the conglomeration. Note that only external
building positions are considered for the standard 3 storey building because the building with
concrete floors occupies the centre most position of each conglomeration. The effects of the
conglomeration and the presence of the concrete floors are similar to the previous systems.
The standard building decreases in capacity, especially when acted upon by the heavier
building and the rest of the conglomeration.
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
3 * L24 H3 F1 - C1 - B1 w/ internal F2
50%
0.6
6 * L24 H3 F1 - C1 - B1 w/ internal F2
0.50
1.00
1.50
2.00
2.50
0.4
9 * L24 H3 F1 - C1 - B1 w/ internal F2
-50%
0.2
Acceleration (g)
Percent Difference in Acceleration
0%
0.00
-100%
0.0
0.00
-150%
-0.2
-200%
-0.4
0.50
1.00
1.50
2.00
2.50
-0.6
-250%
Displacement (cm)
Displacement (cm)
Figure 5.52. Pounding connection, internal concrete floor building
58
Chapter 5. Simple Conglomeration
5.2.9 Full connection, internal concrete floor building
The following results are for the full connection conglomeration systems with a building with
concrete floors at the centre of the conglomeration. Note that only external building positions
are considered for the standard 3 storey building because the building with concrete floors
occupies the centre most position of each conglomeration. The effects of the conglomeration
and the presence of the concrete floors are similar to the pounding system with the same
orientation above. The standard building decreases in capacity both in acceleration and
displacement.
L24_H3_F1
Percent Difference
Monotonic Pushover Curves
3 * L24 H3 F1 - C2 - B1 w/ internal F2
0%
0.00
0.6
0.50
1.00
1.50
2.00
2.50
6 * L24 H3 F1 - C2 - B1 w/ internal F2
-10%
0.4
9 * L24 H3 F1 - C2 - B5 w/ internal F2
-30%
0.2
Acceleration (g)
Percent Difference in Acceleration
-20%
-40%
-50%
-60%
0.0
0.00
0.50
1.00
1.50
2.00
2.50
-0.2
-70%
-0.4
-80%
-0.6
-90%
Displacement (cm)
Displacement (cm)
Figure 5.53. Full connection, internal concrete floor building
5.3 Discussion
Except for the fully connected buildings in the 3 building row conglomeration, the influence
of adjacent buildings appears to be negative. In only one instance did the strength of the
building remain the same, and that was the fully connected buildings in the row
conglomeration with all of them having wood floors. Position does not appear to play much of
a role. The decrease in capacity of the buildings appears to be roughly the same percentage
regardless of position within the row conglomeration. Adding a heavier building to the row
conglomeration also does not appear to make a more significant impact on the building’s
overall response, however, in certain cases it does cause for the inertial forces to distribute
between the three walls more effectively.
59
Chapter 6. Conclusions
6. CONLCUSIONS
These results are to be used to gain a general understanding of building interaction between
masonry systems. Five factors have been considered on a preliminary level: building height,
wall length, floor type, inter-building connections, and position within a conglomeration. A
more in depth study of variable would have to be pursued before levels of design are possible
to be obtained. This study does suggest that the most important parameters in understanding
building interaction are the building’s height and the inter-building connection. Only the latter
parameter is included in the conglomeration study of the previous chapter while the former is
included in the coupled system analysis.
6.1 Further Study
Future study is needed in order to better quantify the effects of inter-building interaction
within a conglomeration. This study indicates that the most important parameters to consider
in future studies are the buildings’ heights and the inter-building connections. These
conclusions are simply drawn from the parameters studied. Other parameters need to be
studied in order to fully understand the inter-building relationship. Torsion, differential
ground motions, and different building materials are all very important topics that this study
does not cover. When these other parameters are considered, the importance of floor systems
and building position may increase. Eventually studies of different building materials may
provide useful coefficients to capture the effect of inter-building reaction on a city-wide scale.
This would ultimately allow for better hazard estimates for future earthquakes.
60
References
REFERENCES
Abrams, D. P. [2001] “Performance-based engineering concepts for unreinforced masonry building
structures,” Progress in Structural Engineering and Materials; Vol. 3, pp. 38-56.
Augusti, G., Ciampoli, M. [2000] “Heritage buildings and seismic reliability,” Progress in Structural
Engineering and Materials; Vol. 2, pp. 225-237.
Benedetti, D., Benzoni, G.M. [1991] “Identification of equivalent structural schemes for coupled
systems,” Earthquake Engineering and Structural Dynamics; Vol. 20, No. 4, pp. 317-333.
Binda, L., Anzani, A. [1998] “Rehabilitation and reuse of historic masonry buildings in Europe,”
Progress in Structural Engineering and Materials; Vol. 1, No. 3, pp. 217-278.
Binda, L., Saisi, A. [2005] “Research on historic structures in seismic areas in Italy,” Progress in
Structural Engineering and Materials; Vol. 7, pp. 71-85.
Borri, A., Cangi, G. [2004] “Vulnerabilità ed interventi di prevenzione sismica nei centri storici umbri
dell’alta val tiberina,” Proceedings of 9th Congresso Nazionale “L’ingegneria Sismic in Italia,”
Genoa, Italy.
Borri, A., De Maria, D., Piccarreta, M. [2004] “Osservazione dei danni negli edifici di aggregazioni
storiche dell’Umbria,” Proceedings of 9th Congresso Nazionale “L’ingegneria Sismic in Italia,”
Genoa, Italy.
Cattari, S., Curti, E., Giovinazzi, S., Lagomarsino, S., Parodi, S., Penna, A. [2004] “Un modello
meccanico per l’analisi di vulnerabilità del costruito in muratura a scala urbana,” Proceedings of
9th Congresso Nazionale “L’ingegneria Sismic in Italia,” Genoa, Italy.
Dialer, C. P. [2002] “Typical masonry failures and repairs: a German Engineer’s view,” Progress in
Structural Engineering and Materials; Vol. 4, pp. 332-339.
D’Ayala D., Spence R., Oliveira C., Silva P. [1996] ”Vulnerability of buildings in historic town
centres: a limit-state approach,” Proceedings of XI World Conference on Earthquake Engineering,
Mexico.
Galasco, A., Lagomarsino, S., Penna, A., Resemini, S. [2004] “Non-linear seismic analysis of masonry
structures,” Proceedings of 13th World Conference on Earthquake Engineering, Vancouver,
Canada.
Jankowski, R. [2006] “Analytical expression between the impact damping ratio and the coefficient of
restitution in the non-linear viscelastic model of structural pounding,” Earthquake Engineering and
Structural Dynamics; Vol. 35, pp. 517-524.
61
References
Lourenço P.B., [2002] “Computations on historic masonry structures,” Progress in Structural
Engineering and Materials; Vol. 4, pp. 301-319.
Magenes, G., [2006] “Masonry building design in seismic areas: recent experiences and prospects
from a European standpoint,” First European Conference on Earthquake Engineering and
Seismology; keynote address K9.
Muthukumar, S., DesRoches, R. [2006] “A Hertz contact model with non-linear damping for pounding
simulation,” Earthquake Engineering and Structural Dynamics; Vol. 35, pp. 811-828.
Penelis, G. G. [2002] “Strucutural restoration of historical buildings in seismic areas,” Progress in
Structural Engineering and Materials; Vol. 4, pp. 64-73.
Rush, A., Leafer, D. [2004] “Physical and chemical properties of pre-regulated American cements,”
Proceedings of 4th International Seminar on Structural Analysis of Historical Constructions,
Padua, Italy.
Stavroulakis, G., Abdalla, K. [1991] “Contact between adjacent structures,” Journal of Structural
Engineering; Vol. 117, No. 10, pp. 2838-2850.
Tobriner, S., Comerio, M., Green, M. [1997] “Reconnaissance report on the Umbria-Marche, Italy
earthquakes of 1997,” EERI Special Earthquake Report; pp 1-12.
Westermo, B.D. [1989] “The dynamics of interstructural connection to prevent pounding,” Journal
Earthquake Engineering and Structural Dynamics; Vol. 18, pp. 687-699.
Zhang, W. S., Xu, Y. L. [1999] “Dynamic characteristics and seismic reponse of adjacent buildings
linked by discrete dampers,” Earthquake Engineering and Structural Dynamics; Vol. 28, pp. 11631185.
62
Appendix A – Single Building Results
APPENDIX A – SINGLE BUILDING RESULTS
This section contains results from pushover analysis for single buildings in greater detail than
presented in the previous chapters.
A.1 Monotonic Pushover Results
In general, the individual buildings perform as expected. The shortest buildings reach the
highest levels of acceleration and the tallest have the largest displacements, with a few
exceptions. Buildings with concrete floors tend to have lower levels of acceleration as do
buildings with flexible walls.
One important observation to note is that buildings with wood floors tend to have larger
displacements than those with concrete. The reason is because of weak diaphragm action.
This cause most of the load to be concentrated at the interior wall which then fails first and
brings the exterior walls with it. This weak diaphragm action remains in the study because of
the importance of properly representing historical buildings. A concentration of inertial forces
or the inability to properly distribute them between the available walls causes the buildings to
be weaker than they would be otherwise. Figure 3.6 shows the three parallel lateral resisting
walls just before failure for buildings with wood floors. As can be clearly seen in this figure,
the interior wall fails first and causes the exterior ones to fail afterwards.
The results from monotonic pushover analysis are provided below. Note that the displacement
axis for the negative monotonic pushover curves has been changed to the positive
displacement axis for better comparison purposes.
A.1.1 Height
The effect of height on the global response of a building is as expected. For a given level of
displacement, the acceleration required to reach that displacement is greater for the shorter
buildings and lower for the taller buildings with largest difference between the 1 storey
building and the 4 storey building.
The results are divided by wall type and floor type. A general pushover curve summarizes the
results for the difference combinations by comparing the different building heights under that
combination to one another. The following 4 graphs after the large monotonic pushover curve
provide the percent difference between the different buildings for better comparison purposes.
A1
Appendix A – Single Building Results
Table A.7. Legend for height comparison
1 Storey
2 Stories
3 Stories
4 Stories
A2
Appendix A – Single Building Results
0.8
0.6
0.4
Acceleration (g)
0.2
0.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
-0.2
-0.4
-0.6
-0.8
Displacement (cm)
Figure A.54. Monotonic pushover curves: flexible walls & wood floors
150%
0%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-20%
100%
Percent Difference in Acceleration
Percent Difference in Acceleration
-40%
-60%
-80%
-100%
-120%
-140%
50%
0%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.6
0.7
0.8
0.9
-50%
-160%
-100%
-180%
-200%
-150%
Displacement (cm)
Displacement (cm)
1 story base building
2 storey base building
200%
200%
180%
160%
100%
50%
0%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
-50%
0.7
0.8
0.9
Percent Difference in Acceleration
Percent Difference in Acceleration
150%
140%
120%
100%
80%
60%
40%
-100%
20%
0%
-150%
0.0
Displacement (cm)
3 story base building
0.1
0.2
0.3
0.4
0.5
Displacement (cm)
4 story base building
Figure A.55. Constants: flexible walls & wood floors
A3
Appendix A – Single Building Results
0.4
0.3
0.2
Acceleration (g)
0.1
0.0
0.0
0.5
1.0
1.5
2.0
2.5
-0.1
-0.2
-0.3
-0.4
-0.5
Displacement (cm)
Figure A.56. Monotonic pushover curves: flexible walls & concrete floors
50%
150%
100%
0%
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Percent Difference in Acceleration
Percent Difference in Acceleration
0.0
-50%
-100%
-150%
50%
0%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.5
0.6
0.7
-50%
-100%
-150%
-200%
-200%
-250%
-250%
Displacement (cm)
Displacement (cm)
1 story base building
2 storey base building
250%
200%
150%
Percent Difference in Acceleration
50%
0%
0.0
0.1
0.2
0.3
0.4
-50%
-100%
0.5
0.6
0.7
Percent Difference in Acceleration
200%
100%
150%
100%
50%
-150%
-200%
0%
0.0
-250%
Displacement (cm)
3 story base building
0.1
0.2
0.3
0.4
Displacement (cm)
4 story base building
Figure A.57. Constants: flexible walls & concrete floors
A4
Appendix A – Single Building Results
1.5
1.0
Acceleration (g)
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
-0.5
-1.0
-1.5
Displacement (cm)
Figure A.58. Monotonic pushover curves: rigid walls & wood floors
150%
20%
0%
0.0
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.4
100%
0.5
Percent Difference in Acceleration
Percent Difference in Acceleration
-20%
-40%
-60%
-80%
-100%
-120%
-140%
50%
0%
0.0
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
-50%
-100%
-160%
-150%
-180%
Displacement (cm)
Displacement (cm)
1 story base building
2 storey base building
200%
180%
160%
150%
50%
0%
0.0
0.1
0.1
0.2
0.2
0.3
-50%
0.3
0.4
0.4
0.5
Percent Difference in Acceleration
Percent Difference in Acceleration
140%
100%
120%
100%
80%
60%
40%
20%
-100%
0%
0.0
-150%
Displacement (cm)
3 story base building
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
Displacement (cm)
4 story base building
Figure A.59. Constants: rigid walls & wood floors
A5
Appendix A – Single Building Results
1.5
1.0
Acceleration (g)
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
-0.5
-1.0
-1.5
Displacement (cm)
Figure A.60. Monotonic pushover curves: rigid walls & concrete floors
0%
150%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-20%
100%
Percent Difference in Acceleration
Percent Difference in Acceleration
-40%
-60%
-80%
-100%
-120%
-140%
50%
0%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-50%
-100%
-160%
-150%
-180%
-200%
-200%
Displacement (cm)
Displacement (cm)
1 story base building
2 storey base building
200%
200%
180%
150%
50%
0%
0.0
0.1
0.2
0.3
0.4
0.5
-50%
0.6
0.7
0.8
0.9
Percent Difference in Acceleration
Percent Difference in Acceleration
160%
100%
140%
120%
100%
80%
60%
40%
-100%
20%
0%
0.0
-150%
Displacement (cm)
3 story base building
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Displacement (cm)
4 story base building
Figure A.61. Constants: rigid walls & concrete floors
A6
Appendix A – Single Building Results
A.1.2 Wall and floor stiffness
Below are a serious of graphs depicting the results for monotonic pushover analysis
comparing the effects of wall and floor stiffness on the response of a building. As can be
expected, wall stiffness was more important to the difference of a building response than floor
stiffness. Another important note to consider is the level of change of wall stiffness versus the
level of change of floor stiffness.
The results are divided by building height. A general pushover curve summarizes the results
for the difference combinations by comparing the different building wall types and floor types
under that combination to one another. The following 4 graphs after the large monotonic
pushover curve provide the percent difference between the different buildings for better
comparison purposes.
Table A.8. Legend for wall and floor comparison
Flexible walls,
Wood floors
Flexible walls,
Concrete floors
Rigid walls,
Wood floors
Rigid walls,
Concrete floors
A7
Appendix A – Single Building Results
1.5
1.0
Acceleration (g)
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
-0.5
-1.0
-1.5
Displacement (cm)
Figure A.62. Monotonic pushover curves: 1 storey buildings
140%
140%
120%
120%
80%
60%
40%
20%
0%
0.0
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
-20%
Percent Difference in Acceleration
Percent Difference in Acceleration
100%
100%
80%
60%
40%
20%
-40%
0%
0.0
-60%
0.1
0.1
0.2
0.3
0.3
0.4
0.4
0.5
Displacement (cm)
Displacement (cm)
Flexible walls & Wood floors base building
Flexible walls & Concrete floors base building
60%
80%
40%
60%
20%
40%
0%
0.0
0.1
0.1
0.2
0.2
0.3
0.3
0.4
-20%
-40%
-60%
-80%
0.4
0.5
Percent Difference in Acceleration
Percent Difference in Acceleration
0.2
-20%
-80%
20%
0%
0.0
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
-20%
-40%
-60%
-100%
-80%
-120%
-100%
-120%
-140%
Displacement (cm)
Displacement (cm)
Rigid walls & Wood floors base building
Rigid walls & Concrete floors base building
Figure A.63. Constant: 1 storey buildings
A8
Appendix A – Single Building Results
0.8
0.6
0.4
Acceleration (g)
0.2
0.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
-0.2
-0.4
-0.6
-0.8
Displacement (cm)
Figure A.64. Monotonic pushover curves: 2 storey buildings
120%
100%
100%
80%
80%
Percent Difference in Acceleration
Percent Difference in Acceleration
120%
60%
40%
20%
0%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
60%
40%
20%
0%
0.9
0.0
-20%
0.1
0.2
0.3
-40%
0.5
0.6
0.7
0.8
0.9
-40%
Displacement (cm)
Displacement (cm)
Flexible walls & Wood floors base building
Flexible walls & Concrete floors base building
40%
40%
20%
20%
0%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-20%
-40%
-60%
-80%
-100%
0.8
0.9
Percent Difference in Acceleration
Percent Difference in Acceleration
0.4
-20%
0%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-20%
-40%
-60%
-80%
-100%
-120%
-120%
Displacement (cm)
Rigid walls & Wood floors base building
Displacement (cm)
Rigid walls & Concrete floors base building
Figure A.65. Constant: 2 storey buildings
A9
Appendix A – Single Building Results
Monotonic Pushover Curves
0.6
0.4
Acceleration (g)
0.2
0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
-0.2
-0.4
-0.6
Displacement (cm)
Figure A.66. Monotonic pushover curves: 3 storey buildings
120%
120%
100%
Percent Difference in Acceleration
Percent Difference in Acceleration
100%
80%
60%
40%
20%
80%
60%
40%
20%
0%
0.0
0%
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-20%
1.4
-20%
-40%
Displacement (cm)
Displacement (cm)
Flexible walls & Wood floors base building
Flexible walls & Concrete floors base building
40%
20%
20%
0%
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Percent Difference in Acceleration
Percent Difference in Acceleration
0.0
-20%
-40%
-60%
-80%
-100%
0%
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-20%
-40%
-60%
-80%
-100%
-120%
-120%
Displacement (cm)
Displacement (cm)
Rigid walls & Wood floors base building
Rigid walls & Concrete floors base building
Figure A.67. Constant: 3 storey buildings
A10
Appendix A – Single Building Results
0.5
0.4
0.3
Acceleration (g)
0.2
0.1
0.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
-0.1
-0.2
-0.3
-0.4
-0.5
Displacement (cm)
Figure A.68. Monotonic pushover curves: 4 storey buildings
150%
120%
100%
100%
60%
40%
20%
0%
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-20%
Percent Difference in Acceleration
Percent Difference in Acceleration
80%
50%
0%
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-50%
-40%
-60%
-80%
-100%
Displacement (cm)
Displacement (cm)
Flexible walls & Wood floors base building
Flexible walls & Concrete floors base building
20%
150%
0%
0.2
0.4
0.6
0.8
1.0
1.2
1.4
100%
Percent Difference in Acceleration
Percent Difference in Acceleration
0.0
-20%
-40%
-60%
-80%
-100%
50%
0%
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-50%
-100%
-120%
-140%
-150%
Displacement (cm)
Rigid walls & Wood floors base building
Displacement (cm)
Rigid walls & Concrete floors base building
Figure A.69. Constant: 4 storey buildings
A11
Appendix A – Single Building Results
A.2 Cyclic Pushover Results
A general pattern is noticeable in the results for cyclic pushover analysis. For the flexible wall
buildings, the hysteretic loops tend to be narrower than for the rigid wall buildings. This
means that the energy dissipation was also less for these buildings. This makes sense because
the flexible buildings with shorter walls tend to exhibit the rocking mechanism and toe
crushing effect which dissipates less energy than the shear sliding mechanism. The longer,
more rigid wall buildings tend to exhibit the shear sliding mechanism leading to larger
hysteretic loops.
0.40
1.00
0.80
0.30
0.60
0.20
0.40
-2.00
-1.50
-1.00
-0.50
0.00
0.00
0.50
1.00
1.50
2.00
-0.20
Acceleration (g)
Acceleration (g)
0.10
0.20
-0.80
-0.60
-0.40
-0.20
0.00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.60
0.80
1.00
-0.10
-0.40
-0.20
-0.60
-0.30
-0.80
-1.00
-0.40
Displacement (cm)
Displacement (cm)
-0.60
-0.40
L12_H1_F2
Flexible walls & Wood floors
Flexible walls & Concrete floors
1.50
1.50
1.00
1.00
0.50
0.50
-0.20
0.00
0.00
0.20
0.40
0.60
Acceleration (g)
Acceleration (g)
L12_H1_F1
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.00
-0.50
-0.50
-1.00
-1.00
-1.50
Displacement (cm)
L24_H1_F1
Rigid walls & Wood floors
0.20
0.40
-1.50
Displacement (cm)
L24_H1_F2
Rigid walls & Concrete floors
Figure A.70. Cyclic pushover curves for 1 storey buildings
A12
Appendix A – Single Building Results
0.50
0.40
0.40
0.30
0.30
0.20
0.20
-8.00
-6.00
-4.00
0.00
0.00
-2.00
2.00
4.00
6.00
-0.10
Acceleration (g)
Acceleration (g)
0.10
0.10
-1.50
-1.00
-0.50
0.00
0.00
0.50
1.00
1.50
2.00
-0.10
-0.20
-0.20
-0.30
-0.30
-0.40
-0.40
-0.50
-0.50
Displacement (cm)
Displacement (cm)
-8.00
-6.00
L12_H2_F2
Flexible walls & Wood floors
Flexible walls & Concrete floors
0.80
0.80
0.60
0.60
0.40
0.40
0.20
0.20
-4.00
-2.00
0.00
0.00
2.00
4.00
6.00
8.00
Acceleration (g)
Acceleration (g)
L12_H2_F1
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.00
-0.20
-0.20
-0.40
-0.40
-0.60
-0.60
-0.80
0.20
0.40
0.60
0.80
1.00
1.50
2.00
2.50
-0.80
Displacement (cm)
Displacement (cm)
L24_H2_F1
L24_H2_F2
Rigid walls & Wood floors
Rigid walls & Concrete floors
-8.00
-6.00
-4.00
-2.00
0.30
0.30
0.20
0.20
0.10
0.10
0.00
0.00
2.00
4.00
6.00
8.00
Acceleration (g)
Acceleration (g)
Figure A.71. Cyclic pushover curves for 2 storey buildings
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.00
-0.10
-0.10
-0.20
-0.20
-0.30
Displacement (cm)
L12_H3_F1
Flexible walls & Wood floors
0.50
1.00
-0.30
Displacement (cm)
L12_H3_F2
Flexible walls & Concrete floors
A13
-3.00
-2.00
-1.00
0.60
0.60
0.40
0.40
0.20
0.20
0.00
0.00
1.00
2.00
3.00
4.00
5.00
Acceleration (g)
Acceleration (g)
Appendix A – Single Building Results
-2.00
-1.50
-1.00
-0.50
0.00
0.00
-0.20
-0.20
-0.40
-0.40
-0.60
0.50
1.00
1.50
2.00
-0.60
Displacement (cm)
Displacement (cm)
L24_H3_F1
L24_H3_F2
Rigid walls & Wood floors
Rigid walls & Concrete floors
-8.00
-6.00
-4.00
-2.00
0.25
0.25
0.20
0.20
0.15
0.15
0.10
0.10
0.05
0.05
0.00
0.00
2.00
4.00
6.00
8.00
-0.05
Acceleration (g)
Acceleration (g)
Figure A.72. Cyclic pushover curves for 3 storey buildings
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.00
0.50
1.00
1.50
2.00
-0.05
-0.10
-0.10
-0.15
-0.15
-0.20
-0.20
-0.25
-0.25
Displacement (cm)
Displacement (cm)
L12_H4_F1
L12_H4_F2
Flexible walls & Wood floors
Flexible walls & Concrete floors
0.20
0.50
0.40
0.15
0.30
0.10
0.20
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
0.00
1.00
-0.10
2.00
3.00
4.00
Acceleration (g)
Acceleration (g)
0.05
0.10
-1.50
-1.00
-0.50
0.00
0.00
0.50
1.00
1.50
-0.05
-0.20
-0.10
-0.30
-0.40
-0.50
Displacement (cm)
L24_H4_F1
Rigid walls & Wood floors
-0.15
-0.20
Displacement (cm)
L24_H4_F2
Rigid walls & Concrete floors
Figure A.73. Cyclic pushover curves for 4 storey buildings
A14
Appendix B – Coupled System Combinations
APPENDIX B – COUPLED SYSTEM COMBINATIONS
Below is the table of different coupled system combinations used in this study.
Table B.9. Analysis coupled systems
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H2 F1
L12 H2 F2
L12 H2 F1
L12 H2 F2
L12 H2 F1
L12 H2 F2
L12 H3 F1
L12 H3 F2
L12 H3 F1
L12 H3 F2
L12 H4 F1
L12 H4 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H2 F1
L12 H2 F2
L12 H2 F1
L12 H2 F2
-
L12 H1 F1
L12 H1 F2
L12 H2 F1
L12 H2 F2
L12 H3 F1
L12 H3 F2
L12 H4 F1
L12 H4 F2
L12 H2 F1
L12 H2 F2
L12 H3 F1
L12 H3 F2
L12 H4 F1
L12 H4 F2
L12 H3 F1
L12 H3 F2
L12 H4 F1
L12 H4 F2
L12 H4 F1
L12 H4 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
-
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
L12 H2 F2
L12 H2 F1
L12 H2 F2
L12 H2 F1
L12 H2 F2
L12 H3 F1
L12 H3 F2
L12 H3 F1
L12 H3 F2
L12 H4 F1
L12 H4 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H2 F1
L12 H2 F2
L12 H2 F1
L12 H2 F2
L12 H2 F1
L12 H2 F2
L12 H2 F1
L12 H2 F2
L12 H3 F1
L12 H3 F2
L12 H3 F1
L12 H3 F2
L12 H3 F1
-
L12 H2 F2
L12 H3 F1
L12 H3 F2
L12 H4 F1
L12 H4 F2
L12 H3 F1
L12 H3 F2
L12 H4 F1
L12 H4 F2
L12 H4 F1
L12 H4 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
-
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
B1
Appendix B – Coupled System Combinations
L12 H2 F1
L12 H2 F2
L12 H2 F1
L12 H2 F2
L12 H3 F1
L12 H3 F2
L12 H3 F1
L12 H3 F2
L12 H3 F1
L12 H3 F2
L12 H3 F1
L12 H3 F2
L12 H4 F1
L12 H4 F2
L12 H4 F1
L12 H4 F2
L12 H4 F1
L12 H4 F2
L12 H4 F1
L12 H4 F2
L24 H1 F1
L24 H1 F2
L24 H1 F1
L24 H1 F2
L24 H1 F1
L24 H1 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H2 F1
L24 H2 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H1 F1
L12 H1 F2
L12 H2 F1
-
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H4 F1
L24 H4 F2
L12 H1 F1
L12 H1 F2
L12 H2 F1
L12 H2 F2
L12 H3 F1
L12 H3 F2
L12 H4 F1
L12 H4 F2
L12 H2 F1
-
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C2
C1
C1
C1
C1
C1
C1
C1
C1
C1
L12 H3 F2
L12 H3 F1
L12 H3 F2
L12 H4 F1
L12 H4 F2
L12 H4 F1
L12 H4 F2
L12 H4 F1
L12 H4 F2
L12 H4 F1
L12 H4 F2
L24 H1 F1
L24 H1 F2
L24 H1 F1
L24 H1 F2
L24 H1 F1
L24 H1 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H2 F1
L24 H2 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
-
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H1 F1
L24 H1 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H2 F1
L24 H2 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H3 F1
L24 H3 F2
L24 H4 F1
L24 H4 F2
L24 H4 F1
L24 H4 F2
-
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
B2
Appendix C – Row Conglomeration Combinations
APPENDIX C – ROW CONGLOMERATION COMBINATIONS
Below is the table of different row conglomeration system combinations used in this study.
Table C.10. Conglomeration list
Number of
Total Wall
Number
Floor
Inter-Building
Position of Building with
Buildings
Length (m)
of Stories
Type
Connection Type
Concrete Floors
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
6
6
6
6
6
6
9
9
9
9
9
9
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Wood
Pounding
Full
Pounding
Full
Pounding
Full
Pounding
Full
Pounding
Full
Pounding
Full
Pounding
Full
Pounding
Full
Pounding
Full
Exterior building
Exterior building
Interior building
Interior building
Exterior building
Exterior building
Interior building
Interior building
Exterior building
Exterior building
Interior building
Interior building
C1
MSc Dissertation 2007
Seismic evaluation of masonry building conglomerations of adjacent structures
Adam Rush