Dissertation2007 Rush

8/14/2019 Dissertation2007 Rush

1/91

SEISMIC EVALUATION OF MASONRYBUILDING CONGLOMERATIONS OF

ADJACENT STRUCTURES

A Dissertation Submitted in Partial Fulfilment of the Requirementsfor the Master Degree in

Earthquake Engineering

By

Adam Rush

Supervisor(s): Dr GUIDO MAGENESDr ANDREA PENNA

December, 2007

Istituto Universitario di Studi Superiori di PaviaUniversit degli Studi di Pavia


2/91

The dissertation entitled Seismic evaluation of masonry building conglomerations of adjacent structures, by Adam Rush, has been approved in partial fulfilment of therequirements for the Master Degree in Earthquake Engineering.

Guido Magenes 1

Andrea Penna 2


3/91

Abstract

i

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 earthquakeshave demonstrated that single buildings within a masonry conglomeration, like historic citycentres, are susceptible to damage due to the interaction of adjacent buildings. This damagetypically 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 andremediation measures have progressed to the point that with the necessary resources, historic buildingscan be strengthened to prevent these local failures. This study is concerned with buildings that tend notto 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-buildingconnection, and position within a conglomeration. Monotonic pushover analysis is conducted onvarious combinations of coupled systems and multiple building conglomerations. The results indicatethat the relative heights of adjacent buildings and the type of inter-building connection are the mostimportant parameters to consider for future studies.

Keywords : masonry conglomeration; pounding; global response; Tremuri


4/91

Index

ii

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 ................................................................................................163.3 Discussion................................................................................................................................17


5/91

Index

iii

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 ..................................................204.2.2 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


6/91

Index

iv

6.1 Further Study ...........................................................................................................................60

REFERENCES .....................................................................................................................................61

APPENDIX A SINGLE BUILDING RESULTS............................................................................. A1

A.1 Monotonic Pushover Results ..................................................................................................A1A.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


7/91


8/91

Index

vi

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.........................................................................51Figure 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 ......................................................56Figure 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


9/91

Index

vii

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





10/91

Index

viii

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


11/91

Index

9

LIST OF SYMBOLS

Notation DescriptionL12 Length of in-plane wall = 12 mL24 Length of in-plane wall = 24 mH1 Number of stories = 1 with individual storey heights matching previous tableH2 Number of stories = 2 with individual storey heights matching previous tableH3 Number of stories = 3 with individual storey heights matching previous tableH4 Number of stories = 4 with individual storey heights matching previous tableF1 Floor composition = woodF2 Floor composition = concreteC1 Inter-building connection type = pounding

C2 Inter-building connection type = full connectionB1 Building 1 in a coupled or row conglomeration systemB2 Building 2 in a coupled or row conglomeration systemB4 Building 4 in a coupled or row conglomeration systemB5 Building 5 in a coupled or row conglomeration system


12/91

Chapter 1. Introduction

1

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 earthquakeshave demonstrated that single buildings within a masonry conglomeration, like historic citycentres, are susceptible to damage due to the interaction of adjacent buildings. This interactioncauses damage through the transfer of inertial forces either by pounding of adjacent buildingsor through coupling effects in the seismic response. In some instances, damage due toconglomerations can cause a premature failure of the building. Previous studies of theseconglomerations focus on how pounding between adjacent buildings trigger local failuremechanisms. Out-of-plane bending of walls is a common local failure mechanism of concernthroughout 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 drawconclusions. Since many historic city centres are comprised of masonry buildings, inelasticmodels are essential to describe the response of a building to an earthquake. This studyattempts to determine some simple relationships for buildings within a conglomeration inorder 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 inevaluating 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 ismassive and continues to change today through renovations and continuous construction. Asthe 1997 earthquake of Umbria-Marche demonstrated, these historic city centres aresusceptible 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 effortin 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 fromoccurring. Where these safe distances cannot be enforced, various techniques are considered


13/91


2

to reduce the effects of pounding. Most of the research in this field, however, has tended tofocus 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 onthe development of local failure mechanisms within buildings. These failures are the mostcommon type for masonry buildings during an earthquake. They are usually caused by flawswithin 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 toresearchers 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.


14/91


3

Figure 1.2. Typical local failure mechanisms [DAyala et al ., 1996]

Modelling of these failures require specialized models for each building condition and onlyrequire looking at individual building components. The entire building does not need to bemodelled in order to capture local failure mechanisms. The purpose of this study is todetermine what role building interaction plays on assessing the vulnerability of a historic citycentre. 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 factorsinfluence this demand. The purpose is not to address local failure mechanisms caused byadjacent buildings, but rather to focus on the global response of a building.


15/91


4

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 buildinginteraction influences the response of each building. failure mechanisms like shear sliding androcking for piers, as seen in Figure 1.3, are of particular interest because they are failuremechanisms related to the global response of a building. To capture these behaviours and thechanges of behaviour due to building interaction within a conglomeration, a macro-elementmodelling program was used which will allow for average inelastic behaviour of masonryelements. This modelling system is described in greater detail in the following chapter.

1.2 Interaction Connection TypesMuch like the historic centres themselves, the interactions between adjacent buildings is acomplex problem with many variables. Distance between buildings, material properties of thefaade systems, and relative stiffness of the two buildings are a few of the factors whichinfluence the inter-building interaction. A proper representation of the inter-buildingconnection is needed before being able to capture the global response. To simplify the manydifferent conditions found within a historic centre, two types of inter-building connections areconsidered.

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

Rocking

Shear Sliding

Pounding


16/91


5

the gap between them closes and the buildings come into contact. This connection models theresponse of independent buildings and allows for a transfer of forces when the buildings makecontact under dynamic loading while still enabling the buildings to separate freely whenmoving in opposite directions. This connection is achieved by using a zero tension elementthat only transfers compressive loads. This zero tension elements share the same compressionstrength 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 poundingconnection. 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 itsinertial forces through the zero tension links in the other direction. In many cases, taller andmore flexible buildings tended to develop a soft storey directly above the shorter and morerigid building when pounding against it.

1.2.2 F ull Connection

The second inter-building connection is the full connection. It represents the conditions whenadjacent 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 rigidnode between the two buildings. The result of this connection is that the buildings tended toact 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 doublethe 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


17/91


6

1.3 Position within a Row Conglomeration

Another important factor to consider is the effect of building position within a conglomerationon the interaction between the buildings and its own response. In theory, buildings in thecentre 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 transferredto the final one on the end. The purpose of this study is to determine how important the buildings position is in evaluating the increase of demands it will see and the increase inseismic vulnerability it should have.

1.3.1 Presence of H eavier Bu il dings within a Conglomeration

When historic buildings are updated, those updates may consist of replacing the existingwooden floors with new concrete floors. These floors increase the mass of the building. Theincreased mass leads to increased seismic demand on the building part of which is transferredto adjacent buildings within a conglomeration. This could have an unintentional detrimentaleffect 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.


18/91


19/91

Chapter 2. Seismic Vulnerability Study of Building Conglomerations

8

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 arerelated to the physical properties of the buildings themselves. The total length of the buildingis varied in order to create flexible and rigid structures. Buildings were either 12 m or 24 mlong and 12 m wide. The same internal wall configuration was kept but scaled to meet theoverall dimensions of the different buildings. The different length walls are used to createflexible and rigid building systems. The shorter walls tend to be more flexible and aregoverned by a rocking mechanism while the longer walls tend to b more rigid and aregoverned by a shear sliding mechanism. The height and number of stories for each buildingwere 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 characteristicsin 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 Stiffness12 m Flexible24 m Rigid

Table 2.2. Interstorey heights

Storey Number 1 StoreyBuilding

2 StoreyBuilding

3 StoreyBuilding

4 StoreyBuilding

1 3 m 3 m 3 m 3 m2 3 m 3 m 3 m

3 2.5 m * 3 m4 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 TypeRigid Concrete

Flexible Wood


20/91


9

The total number of different individual buildings generated from varying each of theindividual building parameters is 16. The total number of coupled systems generated bycombining all 16 individual buildings to each other including both types of connections is512. The total number of 3 building row conglomerations generated by combining all 16individual 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 modelsis also reduced because of the results from the single building modelling. A list of coupledsystems 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 studiesconcerned with predicting damage in a historical city centre. These focused on typical localfailure mechanism observed in damage centres. Though useful information, they neglected todescribe 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 detailedanalysis.

Nonlinear analysis is crucial to understanding the behaviour of masonry buildings during anearthquake. For this reason, pushover analysis was conducted in this study. It was used todetermine the overall building characteristics and provide a simple system for comparing thedifferent buildings and interactions. A modified method of pushover analysis allowed the useof macroelements. The procedure, modified with an effective algorithm, transformed the problem of pushing a structure maintaining constant ratios between the applied forces into anequivalent incremental static analysis with one degree of freedom displacement responsecontrol 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 M acro-element modell ing

Through the use of modelling techniques representing the behaviour of masonry walls in theform of macro-elements, the nonlinear behaviour of masonry building conglomerations can beapproximated with relatively little computing power. This modeling system permits therepresentation of two main in-plane masonry failure modes, with a limited number of degreesof freedom. These modes, depicted based on mechanical assumptions, are bending-rockingand shear-sliding mechanism including friction. Using internal variables, the macro-element

takes into account the effect of the limited compressive strength of masonry. The limitedcrushing strength of masonry is typically developed in the bending-rocking mechanism


21/91


10

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 theshear-sliding damage evolution, which controls the strength deterioration and the stiffnessdegradation 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. Themacro-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 thatcontrols the inelastic deformation, the global friction coefficient and a factor that controls thesoftening 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. Theshear-deformations are centered within the central substructure. This layer does not containany evidence of axial or bending deformations. A complete 2D kinematic model should takeinto account the three degrees of freedom for each node i and j on the extremities: axialdisplacement, horizontal displacement and rotation. There are two degrees of freedom for thecentral zone: axial displacement and rotation (Fig 2.#) [Galasco et al ., 2004].

Figure 2.5. Macro-element panel [Galasco et al ., 2004]

2.2.2 I n-plane wall model

A frame representation of the in-plane behaviour of masonry walls is adopted utilizing macro-elements for the various frame members as seen in Figure 2.2. Each wall of the building issubdivided into piers and lintels connected by rigid nodes. The development of the piers isdescribed 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


22/91


11

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 alsoincluded in the model as non-compressive elements.

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 wallmodels together. Since the macro-elements only consider in-plane behaviour the floor elements distribute the horizontal actions to the walls. This distribution of actions dependsupon local flexural behaviour of the floors and the walls. The out-of-plane response of thewalls 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 areused 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. inthe global coordinate system (uX, uY, uZ, rotX, rotY): the rotational degree of freedomaround vertical Z axis can be neglected because of the membrane behaviour adopted for wallsand floors.

The floor elements are modeled as orthotropic membrane finite elements identified Youngand shear moduli in each principle direction, and Poisson ratio. The principle directions alignwith the wall connections to the floors, which are connected by means of stringcourses andtie-rods. The in-plane floor shear stiffness governs the horizontal action distribution betweenthe different walls. This solution permits the implementation of static analyses with 3components of acceleration along the 3 principal directions and 3D dynamic analyses with 3simultaneous input components, too [Guida Tremuri, 2006]

Pier

Lintel

Node


23/91

Chapter 3. Single Building

12

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 providethe 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 unitconfiguration, 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 axisand 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


24/91


13

the global response of a building. Interaction with surrounding buildings effects the globalcharacteristics 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 highlydependent 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 Masonry Tie Rods Units Name Brick Fe360

Elastic Modulus 1800 206000 N/mm 2

Shear Modulus 300 78400 N/mm 2

Specific Weight 18 78.5 kN/m 3

Compressive or Tensile Strength 180 235 N/cm

2

Shear Strength 6 N/cm 2

Thickness / Diameter 40 30 cmPre-Tensioned 2000 daN


25/91


14

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 ageneral 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 befound in Appendix A.

1 story, 12 m 1 storey, 24 m




Figure 3.9. Single building models


26/91


15

3.2.1 M onotoni c Pushover Resul ts

In general, the individual buildings perform as expected. The shortest buildings reach thehighest levels of acceleration and the tallest have the largest displacements. Buildings withconcrete floors tend to have lower levels of acceleration as do buildings with flexible walls. Afew exceptions exist and are discussed in Appendix A in greater detail.

1 Storey

2 Stories

3 Stories

4 Stories

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Displacement (cm)

A c c e l e r a t i o n

( g )

Figure 3.10. Monotonic pushover curves: rigid walls & concrete floors

Flexible walls,

Wood floors

Flexible walls,

Concrete floors

Rigid walls,

Wood floors

Rigid walls,

Concrete floors

Monotonic PushoverCurves

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.00 1.00 2.00 3.00 4.00 5.00 6.0

Displacement (cm)


( g )

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


27/91


16

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 resistingwalls 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 Cycli c Pushover Resul ts

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. Thismeans that the energy dissipation was also less for these buildings. This makes sense becausethe flexible buildings with shorter walls tend to exhibit the rocking mechanism and toecrushing 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 onlyconcerned with obtaining a general overview of the importance of building interaction indetermining the vulnerability of a city centre. To that end, more parameters are studied andless analysis is done.


28/91


17

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

-8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00 6.00 8.00

Displacement (cm)


( g )

L12_H3_F1

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

-2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50

Displacement (cm)


( g )

L12_H3_F2

Flexible walls & Wood floors Flexible walls & Concrete floors

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00

Displacement (cm)


( g )

L24_H3_F1

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

-2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00

Displacement (cm)


( g )

L24_H3_F2

Rigid walls & Wood floors 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 systemsand conglomeration studies. None exhibit local failure mechanisms and all exhibit good in-

plane wall behaviour. The range of building parameters covers a realistic range of valuestypically 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 studythe effects of building interaction on a buildings response.


29/91

Chapter 4. Coupled System

18

4. COUPLED SYSTEM

The purpose of beginning with the coupled systems is to determine how best to model theinteraction 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 whereflexible 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. Importantinteraction groups were determined from the monotonic pushover results and used to focusthe remaining analyzes.

4.1 Analysis

To set a standard analysis procedure for each coupled system, the most flexible building wasused 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 failureof 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 thedifferent 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 thecoupling on the buildings response in each case. The individual building pushover curve isused as a reference point to discuss the effects of other buildings on the curve. Percentagedifference curves are created by taking the difference in acceleration over the averageacceleration 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.


30/91


31/91


20

4.2.1 One Storey, F lexible Wall and Wood F loors 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 moreadversely affect the 1 storey building. In the positive direction, or when the 1 storey buildingacts 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 whilethe more flexible building reaches failure. As for the full connection, the 1 storey buildingacts in conjunction with all of the other buildings in the coupled system and thus the strengthactually increases.

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Displacement (cm)

P e r c e n t D i f f e r e n c e i n A c c e l e r a t i o n

L12_H1_F1L12 H1 F1 - L12 H1 F1 - C1 -B1

L12 H1 F1 - L12 H2 F1 - C1 -B1

L12 H1 F1 - L12 H3 F1 - C1 -B1

L12 H1 F1 - L12 H4 F1 - C1 -B1

L12 H1 F1 - L24 H1 F1 - C1 -B1

L12 H1 F1 - L24 H2 F1 - C1 -B1

L12 H1 F1 - L24 H3 F1 - C1 -B1

L12 H1 F1 - L24 H4 F1 - C1 -B1

Monotonic Pushover Curves

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

Displacement (cm)


( g )

Percent Difference

-60%

-40%

-20%

0%

20%

40%

60%

80%

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Displacement (cm)


L12_H1_F1L12 H1 F1 - L12 H1 F1 - C2 -B1

L12 H1 F1 - L12 H2 F1 - C2 -B1

L12 H1 F1 - L12 H3 F1 - C2 -B1

L12 H1 F1 - L12 H4 F1 - C2 -B1

L12 H1 F1 - L24 H1 F1 - C2 -B1

L12 H1 F1 - L24 H2 F1 - C2 -B1

L12 H1 F1 - L24 H3 F1 - C2 -B1

L12 H1 F1 - L24 H4 F1 - C2 -B1


-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Displacement (cm)


( g )


32/91


21

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Displacement (cm)


L12_H1_F1L12 H1 F1 - L12 H1 F1 - C1 -B1

L12 H1 F1 - L12 H2 F1 - C1 -B1

L12 H1 F1 - L12 H3 F1 - C1 -B1

L12 H1 F1 - L12 H4 F1 - C1 -B1

L12 H1 F1 - L12 H1 F1 - C2 -B1

L12 H1 F1 - L12 H2 F1 - C2 -B1

L12 H1 F1 - L12 H3 F1 - C2 -B1

L12 H1 F1 - L12 H4 F1 - C2 -B1


-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

Displacement (cm)


( g )

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Displacement (cm)


L12_H1_F1L12 H1 F1 - L24 H1 F1 - C1 -B1

L12 H1 F1 - L24 H2 F1 - C1 -B1

L12 H1 F1 - L24 H3 F1 - C1 -B1

L12 H1 F1 - L24 H4 F1 - C1 -B1

L12 H1 F1 - L24 H1 F1 - C2 -B1

L12 H1 F1 - L24 H2 F1 - C2 -B1

L12 H1 F1 - L24 H3 F1 - C2 -B1

L12 H1 F1 - L24 H4 F1 - C2 -B1


-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Displacement (cm)


( g )

Figure 4.15. One storey, flexible wall and wood floors building

4.2.2 One Storey, F lexible Wall and Concrete F loors Buil ding

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 haveadverse 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 theacceleration 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

-200%

-150%

-100%

-50%

0%

50%

100%

150%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Displacement (cm)


L12_H1_F2L12 H1 F2 - L12 H1 F2 - C1 -B1

L12 H1 F2 - L12 H2 F2 - C1 -B1

L12 H1 F2 - L12 H3 F2 - C1 -B1

L12 H1 F2 - L12 H4 F2 - C1 -B1

L12 H1 F2 - L24 H1 F2 - C1 -B1

L12 H1 F2 - L24 H2 F2 - C1 -B1

L12 H1 F2 - L24 H3 F2 - C1 -B1

L12 H1 F2 - L24 H4 F2 - C1 -B1


-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Displacement (cm)


( g )


33/91


22

Percent Difference

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Displacement (cm)


L12_H1_F2L12 H1 F2 - L12 H1 F2 - C2 -B1

L12 H1 F2 - L12 H2 F2 - C2 -B1

L12 H1 F2 - L12 H3 F2 - C2 -B1

L12 H1 F2 - L12 H4 F2 - C2 -B1

L12 H1 F2 - L24 H1 F2 - C2 -B1

L12 H1 F2 - L24 H2 F2 - C2 -B1

L12 H1 F2 - L24 H3 F2 - C2 -B1

L12 H1 F2 - L24 H4 F2 - C2 -B1


-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Displacement (cm)


( g )

Percent Difference

-150%

-100%

-50%

0%

50%

100%

150%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Displacement (cm)


L12_H1_F2L12 H1 F2 - L12 H1 F2 - C1 -B1

L12 H1 F2 - L12 H2 F2 - C1 -B1

L12 H1 F2 - L12 H3 F2 - C1 -B1

L12 H1 F2 - L12 H4 F2 - C1 -B1

L12 H1 F2 - L12 H1 F2 - C2 -B1

L12 H1 F2 - L12 H2 F2 - C2 -B1

L12 H1 F2 - L12 H3 F2 - C2 -B1

L12 H1 F2 - L12 H4 F2 - C2 -B1


-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

Displacement (cm)


( g )

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

150%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Displacement (cm)


L12_H1_F2L12 H1 F2 - L24 H1 F2 - C1 -B1

L12 H1 F2 - L24 H2 F2 - C1 -B1

L12 H1 F2 - L24 H3 F2 - C1 -B1

L12 H1 F2 - L24 H4 F2 - C1 -B1

L12 H1 F2 - L24 H1 F2 - C2 -B1

L12 H1 F2 - L24 H2 F2 - C2 -B1

L12 H1 F2 - L24 H3 F2 - C2 -B1

L12 H1 F2 - L24 H4 F2 - C2 -B1


-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Displacement (cm)


( g )

Figure 4.16. One storey, flexible wall and concrete floors building

4.2.3 Two Stories, F lexible Wall and Wood F loors Bui lding

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. Oneclear exception jumps off the graphs. When the flexible walled, 2 storey building is coupledwith a rigid walled 1 storey building, the failure mechanism for the 2 storey building actuallychanges. This change actually reduces the strength and displacement capacity of the building.Figure 4.4 below demonstrates clearly illustrates this change.


34/91


23

Figure 4.17. Two stories, flexible wall and wood floors building

Percent Difference

-150%

-100%

-50%

0%

50%

100%

150%

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Displacement (cm)


L12_H2_F1L12 H1 F1 - L12 H2 F1 - C1 -B2

L12 H2 F1 - L12 H2 F1 - C1 -B1

L12 H2 F1 - L12 H3 F1 - C1 -B1

L12 H2 F1 - L12 H4 F1 - C1 -B1

L12 H2 F1 - L24 H1 F1 - C1 -B1

L12 H2 F1 - L24 H2 F1 - C1 -B1

L12 H2 F1 - L24 H3 F1 - C1 -B1

L12 H2 F1 - L24 H4 F1 - C1 -B1


-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Displacement (cm)


( g )

Percent Difference

-140%

-120%

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Displacement (cm)

P e r c e n t D i f f e r e n c e

i n A c c e l e r a t i o n

L12_H2_F1L12 H1 F1 - L12 H2 F1 - C2 -B2

L12 H2 F1 - L12 H2 F1 - C2 -B1

L12 H2 F1 - L12 H3 F1 - C2 -B1

L12 H2 F1 - L12 H4 F1 - C2 -B1

L12 H2 F1 - L24 H1 F1 - C2 -B1

L12 H2 F1 - L24 H2 F1 - C2 -B1

L12 H2 F1 - L24 H3 F1 - C2 -B1

L12 H2 F1 - L24 H4 F1 - C2 -B1


-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00

Displacement (cm)


( g )

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

150%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Displacement (cm)


L12_H2_F1L12 H1 F1 - L12 H2 F1 - C1 -B2

L12 H2 F1 - L12 H2 F1 - C1 -B1

L12 H2 F1 - L12 H3 F1 - C1 -B1

L12 H2 F1 - L12 H4 F1 - C1 -B1

L12 H1 F1 - L12 H2 F1 - C2 -B2

L12 H2 F1 - L12 H2 F1 - C2 -B1

L12 H2 F1 - L12 H3 F1 - C2 -B1

L12 H2 F1 - L12 H4 F1 - C2 -B1


-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00

Displacement (cm)

A c c e l e r a t i o n ( g

)


35/91


36/91


25

Percent Difference

-150%

-100%

-50%

0%

50%

100%

150%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Displacement (cm)


L12_H2_F2L12 H1 F2 - L12 H2 F2 - C1 -B2

L12 H2 F2 - L12 H2 F2 - C1 -B1

L12 H2 F2 - L12 H3 F2 - C1 -B1

L12 H2 F2 - L12 H4 F2 - C1 -B1

L12 H1 F2 - L12 H2 F2 - C2 -B2

L12 H2 F2 - L12 H2 F2 - C2 -B1

L12 H2 F2 - L12 H3 F2 - C2 -B1

L12 H2 F2 - L12 H4 F2 - C2 -B1


-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Displacement (cm)


( g )

Percent Difference

-140%

-120%

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Displacement (cm)


L12_H2_F2L12 H2 F2 - L24 H1 F2 - C1 -B1

L12 H2 F2 - L24 H2 F2 - C1 -B1

L12 H2 F2 - L24 H3 F2 - C1 -B1

L12 H2 F2 - L24 H4 F2 - C1 -B1

L12 H2 F2 - L24 H1 F2 - C2 -B1

L12 H2 F2 - L24 H2 F2 - C2 -B1

L12 H2 F2 - L24 H3 F2 - C2 -B1

L12 H2 F2 - L24 H4 F2 - C2 -B1


-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Displacement (cm)


( g )

Figure 4.19. Two stories, flexible wall and concrete floors building

4.2.5 Three Stori es, Flexible Wall and Wood F loors Buil ding

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 tothe buildings 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 infailure mechanism for the building reduces the capacity for the building.

Percent Difference

-150%

-100%

-50%

0%

50%

100%

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Displacement (cm)


L12_H3_F1L12 H1 F1 - L12 H3 F1 - C1 -B2

L12 H2 F1 - L12 H3 F1 - C1 -B2

L12 H3 F1 - L12 H3 F1 - C1 -B1

L12 H3 F1 - L12 H4 F1 - C1 -B1

L12 H3 F1 - L24 H1 F1 - C1 -B1

L12 H3 F1 - L24 H2 F1 - C1 -B1

L12 H3 F1 - L24 H3 F1 - C1 -B1

L12 H3 F1 - L24 H4 F1 - C1 -B1


-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Displacement (cm)


( g )


37/91


38/91


27

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Displacement (cm)


L12_H3_F2L12 H1 F2 - L12 H3 F2 - C1 -B2

L12 H2 F2 - L12 H3 F2 - C1 -B2

L12 H3 F2 - L12 H3 F2 - C1 -B1

L12 H3 F2 - L12 H4 F2 - C1 -B1

L12 H3 F2 - L24 H1 F2 - C1 -B1

L12 H3 F2 - L24 H2 F2 - C1 -B1

L12 H3 F2 - L24 H3 F2 - C1 -B1

L12 H3 F2 - L24 H4 F2 - C1 -B1


-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

Displacement (cm)


( g )

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Displacement (cm)


L12_H3_F2L12 H1 F2 - L12 H3 F2 - C2 -B2

L12 H2 F2 - L12 H3 F2 - C2 -B2

L12 H3 F2 - L12 H3 F2 - C2 -B1

L12 H3 F2 - L12 H4 F2 - C2 -B1

L12 H3 F2 - L24 H1 F2 - C2 -B1

L12 H3 F2 - L24 H2 F2 - C2 -B1

L12 H3 F2 - L24 H3 F2 - C2 -B1

L12 H3 F2 - L24 H4 F2 - C2 -B1


-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

Displacement (cm)


( g )

Percent Difference

-120%

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

0.00 0.50 1.00 1.50 2.00

Displacement (cm)


L12_H3_F2L12 H1 F2 - L12 H3 F2 - C1 -B2

L12 H2 F2 - L12 H3 F2 - C1 -B2

L12 H3 F2 - L12 H3 F2 - C1 -B1

L12 H3 F2 - L12 H4 F2 - C1 -B1

L12 H1 F2 - L12 H3 F2 - C2 -B2

L12 H2 F2 - L12 H3 F2 - C2 -B2

L12 H3 F2 - L12 H3 F2 - C2 -B1

L12 H3 F2 - L12 H4 F2 - C2 -B1


-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Displacement (cm)


( g )

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

150%

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Displacement (cm)


L12_H3_F2L12 H3 F2 - L24 H1 F2 - C1 -B1

L12 H3 F2 - L24 H2 F2 - C1 -B1

L12 H3 F2 - L24 H3 F2 - C1 -B1

L12 H3 F2 - L24 H4 F2 - C1 -B1

L12 H3 F2 - L24 H1 F2 - C2 -B1

L12 H3 F2 - L24 H2 F2 - C2 -B1

L12 H3 F2 - L24 H3 F2 - C2 -B1

L12 H3 F2 - L24 H4 F2 - C2 -B1


-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Displacement (cm)


( g )


39/91


28

Figure 4.21. Three stories, flexible wall and concrete floors building

4.2.7 F our Stori es, Flexible Wall and Wood F loors Buil ding 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 mostaffected by the height of the building next to it. If the adjacent building is shorter, then the 4storey building develops a soft storey directly above it which reduces the buildings capacity.For buildings of a similar height and attached via a full connection, the capacity of the 4storey building increases.

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Displacement (cm)


L12_H4_F1

L12 H1 F1 - L12 H4 F1 - C1 -B2

L12 H2 F1 - L12 H4 F1 - C1 -B2

L12 H3 F1 - L12 H4 F1 - C1 -B2

L12 H4 F1 - L24 H4 F1 - C1 -B2

L12 H4 F1 - L24 H1 F1 - C1 -B1

L12 H4 F1 - L24 H2 F1 - C1 -B1

L12 H4 F1 - L24 H3 F1 - C1 -B1

L12 H4 F1 - L24 H4 F1 - C1 -B1


-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Displacement (cm)


( g )

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

0.00 1.00 2.00 3.00 4.00 5.00

Displacement (cm)


L12_H4_F1L12 H1 F1 - L12 H4 F1 - C2 -B2

L12 H2 F1 - L12 H4 F1 - C2 -B2

L12 H3 F1 - L12 H4 F1 - C2 -B2

L12 H4 F1 - L12 H4 F1 - C2 -B1

L12 H4 F1 - L24 H1 F1 - C2 -B1

L12 H4 F1 - L24 H2 F1 - C2 -B1

L12 H4 F1 - L24 H3 F1 - C2 -B1

L12 H4 F1 - L24 H4 F1 - C2 -B1


-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00

Displacement (cm)


( g )

Percent Difference

-150%

-100%

-50%

0%

50%

100%

150%

0.00 0.50 1.00 1.50 2.00 2.50

Displacement (cm)


L12_H4_F1L12 H1 F1 - L12 H4 F1 - C1 -B2

L12 H2 F1 - L12 H4 F1 - C1 -B2

L12 H3 F1 - L12 H4 F1 - C1 -B2

L12 H4 F1 - L12 H4 F1 - C1 -B1

L12 H1 F1 - L12 H4 F1 - C2 -B2

L12 H2 F1 - L12 H4 F1 - C2 -B2

L12 H3 F1 - L12 H4 F1 - C2 -B2

L12 H4 F1 - L12 H4 F1 - C2 -B1


-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Displacement (cm)


( g )


40/91


29

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Displacement (cm)


L12_H4_F1

L12 H4 F1 - L24 H1 F1 - C1 -B1

L12 H4 F1 - L24 H2 F1 - C1 -B1

L12 H4 F1 - L24 H3 F1 - C1 -B1

L12 H4 F1 - L24 H4 F1 - C1 -B1

L12 H4 F1 - L24 H1 F1 - C2 -B1

L12 H4 F1 - L24 H2 F1 - C2 -B1

L12 H4 F1 - L24 H3 F1 - C2 -B1

L12 H4 F1 - L24 H4 F1 - C2 -B1


-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Displacement (cm)


( g )

Figure 4.22. Four stories, flexible wall and wood floors building

4.2.8 F our Stori es, Fl exible Wall and Concrete Fl oors Buil ding

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.

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

0.00 0.50 1.00 1.50 2.00 2.50

Displacement (cm)


L12_H4_F2

L12 H1 F2 - L12 H4 F2 - C1 -B2

L12 H2 F2 - L12 H4 F2 - C1 -B2

L12 H3 F2 - L12 H4 F2 - C1 -B2

L12 H4 F2 - L12 H4 F2 - C1 -B2

L12 H4 F2 - L24 H1 F2 - C1 -B1

L12 H4 F2 - L24 H2 F2 - C1 -B1

L12 H4 F2 - L24 H3 F2 - C1 -B1

L12 H4 F2 - L24 H4 F2 - C1 -B1


-0.3

-0.2

-0.2

-0.1

-0.1

0.0

0.1

0.1

0.2

0.2

0.3

0.00 0.50 1.00 1.50 2.00 2.50

Displacement (cm)


( g )

Percent Difference

-150%

-100%

-50%

0%

50%

100%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Displacement (cm)


L12_H4_F2L12 H1 F2 - L12 H4 F2 - C2 -B2

L12 H2 F2 - L12 H4 F2 - C2 -B2

L12 H3 F2 - L12 H4 F2 - C2 -B2

L12 H4 F2 - L12 H4 F2 - C2 -B1

L12 H4 F2 - L24 H1 F2 - C2 -B1

L12 H4 F2 - L24 H2 F2 - C2 -B1

L12 H4 F2 - L24 H3 F2 - C2 -B1

L12 H4 F2 - L24 H4 F2 - C2 -B1


-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.00 0.50 1.00 1.50 2.00

Displacement (cm)


( g )


41/91


30

Percent Difference

-120%

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

0.00 0.50 1.00 1.50 2.00

Displacement (cm)


L12_H4_F2L12 H1 F2 - L12 H4 F2 - C1 -B2

L12 H2 F2 - L12 H4 F2 - C1 -B2

L12 H3 F2 - L12 H4 F2 - C1 -B2

L12 H4 F2 - L12 H4 F2 - C1 -B1

L12 H1 F2 - L12 H4 F2 - C2 -B2

L12 H2 F2 - L12 H4 F2 - C2 -B2

L12 H3 F2 - L12 H4 F2 - C2 -B2

L12 H4 F2 - L12 H4 F2 - C2 -B1


-0.3

-0.2

-0.2

-0.1

-0.1

0.0

0.1

0.1

0.2

0.2

0.3

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Displacement (cm)


( g )

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

0.00 0.50 1.00 1.50 2.00 2.50

Displacement (cm)


L12_H4_F2

L12 H4 F2 - L24 H1 F2 - C1 -B1

L12 H4 F2 - L24 H2 F2 - C1 -B1

L12 H4 F2 - L24 H3 F2 - C1 -B1

L12 H4 F2 - L24 H4 F2 - C1 -B1

L12 H4 F2 - L24 H1 F2 - C2 -B1

L12 H4 F2 - L24 H2 F2 - C2 -B1

L12 H4 F2 - L24 H3 F2 - C2 -B1

L12 H4 F2 - L24 H4 F2 - C2 -B1


-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.00 0.50 1.00 1.50 2.00 2.50

Displacement (cm)


( g )

Figure 4.23. Four stories, flexible wall and concrete floors building

4.2.9 One Storey, Rigid Wall and Wood F loors Bui lding

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 poundingconnection, the capacity of thee building is less than the single building capacity. Most of thetime, however, the building could not reach capacity. There is one data set that greatly standsout from the rest and that is the interaction with the 1 storey building of flexible walls in a fullconnection. According to the data, when the coupled system acts in the direction of theflexible 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 thesame storey height, therefore the collapse mechanism of the weaker building cannot change.The load transferred to the rigid building weakens it as expected.


42/91


31

Percent Difference

-250%

-200%

-150%

-100%

-50%

0%

50%

100%

150%

0. 00 0.0 5 0.10 0.15 0. 20 0 .25 0.30 0.35 0.40

Displacement (cm)


L24_H1_F1L24 H1 F1 - L24 H1 F1 - C1 -B1

L24 H1 F1 - L24 H2 F1 - C1 -B1

L24 H1 F1 - L24 H3 F1 - C1 -B1

L24 H1 F1 - L24 H4 F1 - C1 -B1

L12 H1 F1 - L24 H1 F1 - C1 -B2

L12 H2 F1 - L24 H1 F1 - C1 -B2

L12 H3 F1 - L24 H1 F1 - C1 -B2

L12 H4 F1 - L24 H1 F1 - C1 -B2


-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Displacement (cm)


( g )

Percent Difference

-160%

-140%

-120%

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

0. 00 0 .0 5 0 .1 0 0 .1 5 0 .2 0 0 .2 5 0. 30 0 .35 0 .4 0 0 .45

Displacement (cm)


L24_H1_F1L24 H1 F1 - L24 H1 F1 - C2 -B1

L24 H1 F1 - L24 H2 F1 - C2 -B1

L24 H1 F1 - L24 H3 F1 - C2 -B1

L24 H1 F1 - L24 H4 F1 - C2 -B1

L12 H1 F1 - L24 H1 F1 - C2 -B2

L12 H2 F1 - L24 H1 F1 - C2 -B2

L12 H3 F1 - L24 H1 F1 - C2 -B2

L12 H4 F1 - L24 H1 F1 - C2 -B2


-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Displacement (cm)


( g )

Percent Difference

-160%

-140%

-120%

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

0. 00 0 .0 5 0 .1 0 0 .1 5 0 .2 0 0 .2 5 0. 30 0 .35 0 .4 0 0 .45

Displacement (cm)


L24_H1_F1L24 H1 F1 - L24 H1 F1 - C1 -B1

L24 H1 F1 - L24 H2 F1 - C1 -B1

L24 H1 F1 - L24 H3 F1 - C1 -B1

L24 H1 F1 - L24 H4 F1 - C1 -B1

L24 H1 F1 - L24 H1 F1 - C2 -B1

L24 H1 F1 - L24 H2 F1 - C2 -B1

L24 H1 F1 - L24 H3 F1 - C2 -B1

L24 H1 F1 - L24 H4 F1 - C2 -B1


-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Displacement (cm)


( g )

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

150%

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Displacement (cm)


L24_H1_F1L12 H1 F1 - L24 H1 F1 - C1 -B2

L12 H2 F1 - L24 H1 F1 - C1 -B2

L12 H3 F1 - L24 H1 F1 - C1 -B2

L12 H4 F1 - L24 H1 F1 - C1 -B2

L12 H1 F1 - L24 H1 F1 - C2 -B2

L12 H2 F1 - L24 H1 F1 - C2 -B2

L12 H3 F1 - L24 H1 F1 - C2 -B2

L12 H4 F1 - L24 H1 F1 - C2 -B2


-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Displacement (cm)


( g )

Figure 4.24. One storey, rigid wall and wood floors building


43/91


32

4.2.10 One Storey, Rigid Wall and Concrete F loors 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 thecapacity of the individual building, whereas with the wood floors, there are more buildingsthat match and exceed the capacity of the single building

Percent Difference

-200%

-150%

-100%

-50%

0%

50%

100%

150%

0.00 0.0 5 0. 10 0.15 0.20 0 .2 5 0. 30 0 .35 0.40

Displacement (cm)


L24_H1_F2L24 H1 F2 - L24 H1 F2 - C1 -B1

L24 H1 F2 - L24 H2 F2 - C1 -B1

L24 H1 F2 - L24 H3 F2 - C1 -B1

L24 H1 F2 - L24 H4 F2 - C1 -B1

L12 H1 F2 - L24 H1 F2 - C1 -B2

L12 H2 F2 - L24 H1 F2 - C1 -B2

L12 H3 F2 - L24 H1 F2 - C1 -B2

L12 H4 F2 - L24 H1 F2 - C1 -B2


-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Displacement (cm)

A c c e l e r a

t i o n

( g )

Percent Difference

-160%

-140%

-120%

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

0 .0 0 0. 05 0 .1 0 0 .1 5 0 .2 0 0 .2 5 0 .30 0 .3 5 0. 40 0 .4 5

Displacement (cm)

P e r c e n t D i f f e r e n c e i n A

c c e l e r a t i o n

L24_H1_F2L24 H1 F2 - L24 H1 F

Dissertation2007 Rush

Documents