Seismic Risk URM buildings

SEISMIC ASSESSMENT OF UNREINFORCED MASONRY BUILDINGS BY MEANS OF NON-LINEAR STATIC PROCEDURES AND INCREMENTAL DYNAMIC ANALYSIS

Erasmus Mundus Programme ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS i

DECLARATION

Name: JORGE ARTURO AVILA HARO

Email: [email protected]

Title of the

Msc Dissertation:

SEISMIC ASSESSMENT OF UNREINFORCED MASONRY BUILDINGS BY

MEANS OF NON-LINEAR STATIC PROCEDURES AND INCREMENTAL

DYNAMIC ANALYSIS

Supervisor(s): Prof. Ing. Jiří Máca

Year: 2015

I hereby declare that all information in this document has been obtained and presented in accordance

with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I

have fully cited and referenced all material and results that are not original to this work.

I hereby declare that the MSc Consortium responsible for the Advanced Masters in Structural Analysis

of Monuments and Historical Constructions is allowed to store and make available electronically the

present MSc Dissertation.

University: CZECH TECHNICAL UNIVERSITY IN PRAGUE

Date: JULY 29, 2015

Signature: ___________________________


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This page is left blank on purpose.


Erasmus Mundus Programme ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS iii

To my family and friends, I love you all.


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Erasmus Mundus Programme ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS v

ACKNOWLEDGEMENTS

Foremost, I would like to express my sincere gratitude to my advisor Prof. Ing. Jiří Máca for the support of my study and research. Besides my advisor, I would like to thank the rest of the master’s coordinators: Prof. Pere Roca, Prof. Paulo Lourenço, and Prof. Petr Kabele, for their encouragement and concern. I wish to thank the professors, technicians and administrators who took part in the master’s programme for their patience and good willing during this academic year. My sincere thanks also go to the Consortium and Erasmus Mundus programme for the scholarship granted during the academic year 2014/2015. I thank my fellow classmates in both institutions for the sleepless nights we were working together before deadlines, and for all the fun we have had in the last year. Last but not least, I would like to thank my friends and specially my family: my parents Beatriz Haro and Jorge Avila, for their support, their hard work, their advice, and their companionship.


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Erasmus Mundus Programme ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS vii

SEISMIC ASSESSMENT OF UNREINFORCED MASONRY BUILDINGS BY MEANS OF

NON-LINEAR STATIC PROCEDURES AND INCREMENTAL DYNAMIC ANALYSIS

Abstract. In recent years, the use of increasingly accurate and complex analysis methods

for the evaluation of the dynamic response of structures has started to escalate due to the

development of the computational power and methods. Nevertheless, despite being

considered the most accurate methods for the seismic assessment of structures nowadays,

the non-linear dynamic analysis (NDA) still require considerable computational efforts and

time consumption, and therefore the aseismic design of new structures and the assessment

of the existing ones require the use of sufficiently clear and simple procedures, whilst their

accuracy is not compromised. The use of non-linear static procedures (NSPs) has become

and attractive alternative for engineers due to their ease and promptness of implementation,

as well as their recognized accuracy. The performance of two non-linear static procedures

(N2, 10 % fit) is evaluated in this work. The case study used in this work is an existing seven-

storey unreinforced masonry building, fully representative of the typology of the residential

buildings located in the district of L’Eixample in Barcelona, Spain, The structure is

characterized by a load-bearing walls system and unidirectional steel beams-brick vaults

floor system. The accuracy of the NSPs is evaluated by comparison with incremental

dynamic analyses (IDA) whose results are considered as reference values. The comparison

is performed for seven ground motion records and different levels of seismic intensity in

order to take into account the uncertainties of the demand. The selection of the records was

achieved by means of the conditional spectrum (CS) approach. The results obtained from the

studies showed that the N2 method and the 10% fit approach demonstrated a good

performance on the analyzed building.

Keywords: performance-based seismic design, non-linear static procedures, incremental

dynamic analysis, unreinforced masonry, conditional spectrum approach


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Erasmus Mundus Programme ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS ix

SEISMICKÉ POSOUZENÍ NEVYZTUŽENÝCH ZDĚNÝCH BUDOV S POUŽITÍM

NELINEÁRNÍCH STATICKÝCH POSTUPŮ A INKREMENTÁLNÍ DYNAMICKÉ ANALÝZY

Shrnutí. V posledních letech se stále více používají přesné a komplexní analytické metody

pro vyhodnocení dynamické odezvy konstrukcí, které se začaly stupňovat díky vývoji

výpočetního výkonu a metod. I přesto, že i dnes je stále tato považována za nejpřesnější

metodu pro seizmické posuzování staveb, nelineární dynamické analýzy (NDA) i nadále

vyžadují značné úsilí, a to jak z pohledu výpočetních postupů, tak i pohledu časového.

Z toho vyplývá, že navrhování nových struktur a posouzení těch stávajících vyžaduje použití

dostatečně jasných a jednoduchých postupů, zatímco jejich přesnost není ohrožena. Použití

nelineárních statických postupů (NSP) se stalo atraktivní alternativou pro inženýry vzhledem

k jejich snadné a promptní implementaci, jakožto i jejich přesnosti. V této studii je ohodnocen

výkon dvou nelineárních statických postupů (metod N2, 10% fit). Jako případová studie je

v této práci použita existující sedmipodlažní budova z nevyztužené zdivo, která plně

reprezentuje typologii residenčních budov umístěných ve čtvrti L'Eixample Barcelony, ve

Španělsku. Konstrukce se vyznačuje systémem nosných zdí a použitím jednosměrných

ocelových nosníků, které jsou součástí podlahového systému. Přesnost NSP je

vyhodnocena srovnáním inkrementální dynamická analýza metody (IDA), jejíž výsledky jsou

považovány za referenční hodnoty. Pro srovnání se provádí záznamy o pohybu sedmi

pozemních vrstev různých úrovní a seizmické intenzity, kde je brána v úvahu nejistota

poptávky. Výběru záznamů bylo dosaženo pomocí metodologie CS (conditional spectrum).

Výsledky získané z těchto studií ukázaly, že metodologie N2 a 10% fit prokázala dobrý výkon

na analyzované budovy.

Klíčová slova: seismických designových, nelineárních statických postupů, inkrementální

dynamická analýza, nevyztužené zdivo


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Erasmus Mundus Programme ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS xi

EVALUACIÓN SÍSMICA DE EDIFICIOS DE MAMPOSTERÍA NO REFORZADA A TRAVÉS

DE PROCEDIMIENTOS ESTÁTICOS NO-LINEALES Y ANÁLISIS DINÁMICO

INCREMENTAL

Resumen. En años recientes, el uso de métodos de análisis con mayor precisión y

complejidad ha ido en ascenso debido al incremento en el poder computacional y

metodologías. Sin embargo, y a pesar de ser considerados los métodos de mayor precisión

para la evaluación sísmica de estructuras en nuestros días, los análisis dinámicos no-

lineales (NDA) aún requieren esfuerzos considerables de cómputo y tiempo, y por ende el

diseño antisísmico de nuevas estructuras así como la evaluación de las ya existentes

requiere del uso de procedimientos lo suficientemente claros y simples, sin que su precisión

se vea comprometida. El uso de procedimientos estáticos no-lineales (NSPs) se ha

convertido en una alternativa atractiva para los ingenieros debido a su facilidad y rapidez de

implementación, así como por reconocerse su precisión. El desempeño de dos

procedimientos estáticos no-lineales (N2, 10% fit) es evaluado en este trabajo. El caso de

estudio utilizado en este trabajo es un edificio de mampostería no reforzada de siete niveles,

plenamente representativo de la tipología de edificios residenciales que se localizan en el

distrito de L’Eixample en Barcelona, España. La estructura se caracteriza por un sistema de

paredes de carga y forjados de viguetas metálicas y bovedillas de ladrillo. La precisión de

los NSPs es evaluada mediante la comparación con análisis dinámicos incrementales (IDA),

cuyos resultados se consideran como valores de referencia. La comparación se lleva a cabo

para siete registros de aceleraciones y diferentes intensidades sísmica con la finalidad de

tomar en cuenta las incertidumbres presentes en la demanda. La selección de los registros

se logró por medio del método del espectro condicional (CS). Los resultados obtenidos de

los estudios indican que el método N2 y el método 10% fit demuestran tener un buen

desempeño en el edificio analizado.

Palabras clave: diseño sísmico por desempeño, procedimientos estáticos no-lineales,

análisis dinámico incremental, mampostería no reforzada, método del espectro condicional


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Erasmus Mundus Programme ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS 1

TABLE OF CONTENTS 1 INTRODUCTION ................................................................................................................................ 5 1.1 Foreword ................................................................................................................................................... 5 1.2 Aims of the work ..................................................................................................................................... 6 1.3 Outline of the thesis ............................................................................................................................... 7

2 LITERATURE REVIEW ..................................................................................................................... 9 2.1 Performance-‐Based Seismic Design (PBSD) .................................................................................. 9 2.2 Non-‐linear Static Procedures (NSPs) .............................................................................................. 10 2.2.1 The Capacity Spectrum Method (CSM) ................................................................................................... 13

2.3 NSPs used in this work ........................................................................................................................ 18 2.3.1 The N2 method / Eurocode-‐8 ..................................................................................................................... 18 2.3.2 The 10% fit .......................................................................................................................................................... 24

2.4 Incremental Dynamic Analysis ......................................................................................................... 25 3 THE BUILDING ................................................................................................................................ 27 3.1 Historical overview .............................................................................................................................. 27 3.1.1 The Cerdá expansion project ....................................................................................................................... 27 3.1.2 The district of L’Eixample ............................................................................................................................. 28

3.2 General description .............................................................................................................................. 29 3.3 Walls system ........................................................................................................................................... 31 3.4 Floor system ............................................................................................................................................ 34 3.5 Openings .................................................................................................................................................. 35 3.6 Loads and materials ............................................................................................................................. 37 3.6.1 Dead and live loads .......................................................................................................................................... 37 3.6.2 The bricks and the mortars .......................................................................................................................... 37

3.7 Computational model .......................................................................................................................... 38 4 THE DEMAND .................................................................................................................................. 43 4.1 The city of Barcelona ........................................................................................................................... 43 4.1.1 Seismic scenarios .............................................................................................................................................. 43 4.1.2 Site-‐specific response spectra ..................................................................................................................... 44

4.2 Record selection .................................................................................................................................... 46 5 ANALYSES RESULTS ...................................................................................................................... 49 5.1 Modal analysis ........................................................................................................................................ 49 5.2 Non-‐linear static analysis (Pushover) ............................................................................................ 51 5.3 Dynamic analysis ................................................................................................................................... 55

6 COMPARISON OF THE RESULTS ................................................................................................ 57 7 FINAL REMARKS AND CONCLUSIONS ...................................................................................... 59


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LIST OF FIGURES Figure 1 Capacity (pushover) curve of the MDOF ........................................................................ 10 Figure 2 Lateral load patterns ....................................................................................................... 11 Figure 3 Design response spectra for different soil types ............................................................. 11 Figure 4 Transformation of the MDOF system into an equivalent SDOF system ......................... 12 Figure 5 Bilinear representation of the capacity curve of the SDOF system ................................ 12 Figure 6 Calculation of the SDOF target displacement (performance point) ................................ 13 Figure 7 Invariant lateral load pattern according to the fundamental vibration mode of the

structure ................................................................................................................................. 14 Figure 8 CSM - a) MDOF model of the structure; b) elastic response spectra ............................. 14 Figure 9 CSM - Pushover analysis of the MDOF model with a first mode invariant load pattern . 15 Figure 10 CSM - Capacity (pushover) curve ................................................................................ 15 Figure 11 CSM - Transformation of the MDOF capacity curve into the SDOF capacity spectrum 16 Figure 12 CSM - Conversion of the elastic response spectrum from the traditional format into the

acceleration-displacement format .......................................................................................... 17 Figure 13 CSM - Intersection of the capacity and the demand within the established tolerance

limit ........................................................................................................................................ 18 Figure 14 N2 method - Transformation of the MDOF capacity curve into the SDOF capacity

spectrum ................................................................................................................................ 19 Figure 15 N2 method - Fitting procedure according to EC8 (N2 method) .................................... 20 Figure 16 N2 method - Conversion of the elastic response spectrum from the traditional format

into the acceleration-displacement format ............................................................................. 21 Figure 17 N2 method - Demand spectra for constant ductility in acceleration-displacement units

............................................................................................................................................... 22 Figure 18 N2 method – Determination of the target displacement for the equivalent SDOF system

(medium and long period range) ........................................................................................... 23 Figure 19 N2 method – Determination of the target displacement for the equivalent SDOF system

(short period range) ............................................................................................................... 24 Figure 20 10% fit approach – Bilinear fit of the capacity curve of the SDOF system ................... 25 Figure 21 Typical urban layout of blocks of the district of L’Eixample .......................................... 28 Figure 22 Elevation of the front façade and plan views of the base floor and upper levels of the

case study building (dimensions in [cm]) ............................................................................... 30 Figure 23 Isometric and plan views of B01 building: a) typical storey (2nd-7th); b) full height; and c)

base floor (1st) ........................................................................................................................ 31 Figure 24 Metallic columns and girders used in the first level of the buildings ............................. 33 Figure 25 Distribution of metallic columns and girders of the first level ........................................ 33 Figure 26 Connection between slabs and walls. a) Metallic beams; b) wooden beams ............... 34 Figure 27 Iron beams and brick vaults unidirectional slabs. a) Components of the floor system: 1.-

double layer of thin brick, 2.- lime mortar, 3.- I type iron beam, 4.- rubble and plaster infill, 5.- pavement; b) separation of the iron beams between 70 to 80 cm; c), d), e) and f) details of the components and connection of the floor system ............................................................. 35

Figure 28 Discharging elements above openings: a) location of lintels in the 3D model; b) and c) discharging arches above doors; d) iron lintel above a window; e) iron lintel above façade openings ................................................................................................................................ 36

Figure 29 Lintels above façade openings ..................................................................................... 37 Figure 30 TreMuri layouts: a) Base floor (1st) plan; b) Typical storey (2nd – 7th) plan; c) 3D view of

the building; and d) 3D view of the different levels ................................................................ 40



Figure 31 Main constitutive elements of the 3Muri computational model. Base floor (1st): a) Foundation layout; b) Columns (cast iron and masonry); c) Lintels (iron and wood); d) Walls and openings (windows and doors); and e) Slabs ................................................................. 41

Figure 32 Main constitutive elements of the 3Muri computational model. Typical storey (2nd-7th): a) Columns (cast iron and masonry); b) Lintels (iron and wood); and c) Walls and openings (windows and doors) d) Slabs ................................................................................................ 42

Figure 33 5% damped response spectra for the deterministic seismic scenario of Barcelona .... 45 Figure 34 5% damped response spectra for the probabilistic seismic scenario of Barcelona ...... 45 Figure 35 Districts of Barcelona with their corresponding soil type and 5% damped elastic

response spectrum ................................................................................................................. 46 Figure 36 Record selection according to the CS approach ........................................................... 47 Figure 37 First and second mode translations of +X direction ...................................................... 50 Figure 38 First and second mode translations of +Y direction ...................................................... 50 Figure 39 Capacity curve of the +X direction ................................................................................ 51 Figure 40 Capacity curve of the +Y direction ................................................................................ 51 Figure 41 Example of the bilinear representation for the two analyzed methodologies for +X

direction .................................................................................................................................. 52 Figure 42 Example of the calculation of the target displacement of the EC8 approach for +X

direction and a pga=0.06 g ..................................................................................................... 52 Figure 43 EC8 approach results for the +X direction .................................................................... 53 Figure 44 10% fit approach results for the +X direction ................................................................ 53 Figure 45 EC8 approach results for the +Y direction .................................................................... 54 Figure 46 10% fit approach results for the +Y direction ................................................................ 54 Figure 47 IDA results for the different records and their average value for +X direction ............... 55 Figure 48 IDA results for the different records and their average value for +Y direction ............... 56 Figure 49 Comparison between mean results of the analyzed NSPs and the IDA for +X direction

............................................................................................................................................... 58 Figure 50 Comparison between mean results of the analyzed NSPs and the IDA for +Y direction

............................................................................................................................................... 58



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LIST OF TABLES Table 1 Geometric properties of the case study analyzed ............................................................ 32 Table 2 Mechanical properties of masonry ................................................................................... 38 Table 3 Parameters for the deterministic and probabilistic scenarios proposed by the ICC for the

city of Barcelona .................................................................................................................... 44 Table 4 Modal analysis results ..................................................................................................... 49



1 INTRODUCTION

1.1 Foreword

In order to evaluate existing constructions, as well as to adequately design new earthquake resistant structures, the use of transparent and sufficiently simple and accurate procedures is compulsory. In recent years, different design philosophies and methodologies have been developed to make this possible. Early procedures were mainly based on the expert opinion and observations derived from the damages experienced by buildings hit by earthquakes, which resulted in a classification of the structural response taking into account different structural and non-structural parameters (Barbat et al., 1996, Barbat et al., 2010). The main disadvantages of these procedures are their subjectivity and its dependency on the density of the affected built areas that can be analyzed. Some other previous methodologies applied in the existing guidelines were mainly based in a linear elastic structural behavior, being unable to characterize the demand in structural terms (e.g. stiffness, strength, ductility, etc.). In recent years, the use of more sophisticated analysis for the evaluation of the dynamic behavior of structures has started to increase due to the development of the computational power and methods. These procedures permit the use of different ground motion records as well as a range of intensities of the seismic action in order to take into account the possible uncertainties of the demand (Avila-Haro et al., 2013). Among these sophisticated procedures we can mention the incremental dynamic analysis (IDA), developed by Vamvatsikos and Cornell (2002), which aims to obtain a measurement of the structural damage related to the dynamic response of the structure when subjected to successive increments of the intensity of the seismic action. The



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main drawbacks of this type of procedures are the additional information, computational power and time consuming they require, leading to not necessarily more reliable results due to the existing uncertainties of the input data. In other to overcome the aforementioned drawbacks, a series of simplified methodologies have been developed. The assessment of the performance of the structure is achieved by facing its capacity, which is obtained from a non-linear static analysis, with the possible demand that the structure could experience. These procedures are widely used nowadays due to their ease, promptness and adequate accuracy when compared to more complex and time-consuming methodologies (Pujades et al., 2012, González-Drigo et al., 2013). These type of methodologies are commonly known as non-linear static procedures (NSPs) and a large number of them can be found in the literature. The work carried out in this thesis assesses the vulnerability of an unreinforced masonry (URM) building through the IDA approach and two selected NSPs: the N2 method (Fajfar and Gašperšič, 1996) adopted by the Eurocode 8 (2004); and the 10% fit approach (De Luca et al., 2013a). In order to compare the results and therefore determine the accuracy of the simplified NSPs, the results obtained from the IDA will be used as reference values.

1.2 Aims of the work

The current work aims to compare the results obtained from both, non-linear static and non-linear dynamic procedures, in the evaluation of an unreinforced masonry (URM) structure. Despite being considered the most accurate method for the seismic assessment of structures nowadays, the non-linear dynamic analysis (NDA) is commonly applied only in a few particular cases due to the considerable computational efforts and time consumption that it requires. Therefore, the employment of non-linear static procedures (NSPs) in the design or evaluation of structures has became an attractive alternative for engineers due to their ease and swiftness of implementation, and their relatively good accuracy. The results obtained for the different NSPs used in this work are compared with the results obtained from the NDA, which will be considered as reference values. Both, non-linear static and non-linear dynamic analyses are performed and compared for a set of ground motion records and seismic intensities, in order to evaluate the performance and accuracy of the NSPs. Different structural response parameters can be selected in order to assess this comparison, such as: base shear, inter-storey drifts, and top displacement, among others. The case study used in this work is a fully representative residential building located in the district of L’Eixample in Barcelona, Spain. The structure is a typical seven-storey unreinforced masonry building that belongs to the construction period between 1890 and 1940, with load-bearing walls and a unidirectional metallic beams-brick vaults floor system. Seven horizontal acceleration records were selected from the PEER earthquake database (PEER, 2011) using the Conditional Spectrum Approach procedure (Abrahamson and Al Atik, 2010, Jayaram et al., 2011, NIST, 2011) and the site-specific target response spectrum



corresponding to the soil Zone II of the city of Barcelona (Irizarry et al., 2003, Irizarry, 2004, Irizarry et al., 2011).

1.3 Outline of the thesis

The work is presented in 7 chapters. A brief review of their content is presented as follows. Chapter 1 provides and introduction and the main goals of the work carried out. In chapter 2 the state of art is reviewed. This chapter focuses on the performance based seismic design (PBSD) philosophy, and on the evolution of the existing non-linear static procedures (NSPs). A description of the non-linear dynamic analysis (NDA) and the bases of the incremental dynamic analysis (IDA) procedure are presented. In chapter 3 a brief historical overview of Barcelona and the district of L’Eixample is provided. The case study analyzed in this work is presented. A complete description of the structural system, its main components and materials, and the computer model, are presented in this section. In chapter 4 the soil characteristics of the building site and the procedure to select the ground motion records to be used in the non-linear dynamic analysis procedure are explained. Chapter 5 provides the results obtained from the modal, non-linear static and non-linear dynamic analyses performed to the structure. Chapter 6 compares the previously obtained results in chapter 6, in order to evaluate the accuracy of the Non-linear Static Procedures when faced with the Non-linear Dynamic Analysis results. Finally, in chapter 7 final remarks and conclusions of the work are drawn and future work lines are proposed.



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2 LITERATURE REVIEW

The purpose of this chapter is to briefly describe the evolution of the non-linear static procedures over time, as well as to describe in detail the non-linear static and dynamic procedures used in this work.

2.1 Performance-Based Seismic Design (PBSD)

Earthquake engineering has significantly evolved over the last century, leading to not only concern about the protection of lives, but also to minimize damage and service interruptions. The later has been possible due to the observation of the effects of major earthquakes and the availability of seismic monitoring data (National Research Council, 2006). Contrary to the previous force-based design philosophy, in which the seismic evaluation of the structures was based on the element stresses caused by the computed equivalent seismic forces, the performance-based methodologies base the seismic evaluation on the deformations induced by the earthquake (de Almeida e Fernandes Bhatt, 2011). The purpose of the performance-based seismic design (PBSD) is to assess, in a realistic manner, the performance of a structure when subjected to an earthquake ground motion in order to facilitate and improve the seismic risk decision-making of engineers and stakeholders. Unlike in other performance based engineering fields, in PBSD the use of full-scale prototypes of the structure and its extensive testing in order to obtain the required experience to produce “identical outputs”, is not economically feasible. Nevertheless, in recent years it has become an attractive alternative for engineers due to the increase of computational power and capabilities, the advances in seismic hazard assessment, the improved knowledge about the ground motion and structural characteristics, and the development of several methodologies (Krawinkler, 1999).



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PSBD can be used in the design of new structures as well as in the evaluation of existing ones. Static and dynamic techniques are available for design and evaluation of structures, and prediction of their performance when subjected to a seismic demand. The aforementioned techniques can also be subdivided in linear or non-linear. The performance-based procedures rely in two main elements: the calculation of the capacity of the structure, and the adequate determination of the demand to be applied to the structure. The degree to which the capacity is able to handle the imposed demand will determine if the performance of the structure is compatible with the initial design objectives.

2.2 Non-linear Static Procedures (NSPs)

Within the possible techniques that the PSBD contemplates, the non-linear static procedures are now widely used in engineering practice due to their accurate prediction of seismic demand parameters in structures. As the name implies, non-linear mathematical relationships are used to model the different elements of the structure, and a static analysis is performed through the application of incremental static loads for the purpose of achieving the ultimate state of the structure. Different codes already include these procedures as a tool for the performance assessment of structures due to their ease, versatility and promptness and several non-linear static procedures (NSPs) can be found in the literature, within which some of them are recent, and some others remain valid despite being proposed, adapted and/or modified several years ago. Nevertheless, the different NSPs share common basis and goals, and have been incorporated in design codes and guidelines as a powerful tool for performance evaluation. Their key aspects can be summarized in two parts: one corresponding to the capacity, and another one corresponding to the demand. The capacity part is accomplished by means of a non-linear static analysis from which the so-called capacity curve (pushover curve) is obtained (Figure 1). The latter is achieved applying a monotonically increasing predefined load pattern to the structure with an outcome that characterizes the relation between the roof displacement (Δroof) of a selected control node (usually at the center of masses) and the corresponding base shear (Vb) at each monotonic increment.

Figure 1 Capacity (pushover) curve of the MDOF

Vb

!roof



There are a number of possibilities regarding the load pattern application that can be used, among which we can differentiate three groups: invariant load vectors; invariant multi-mode vectors; and adaptive load vectors (Kalkan and Kunnath, 2008). Concerning the shape of the load patterns, the most common and used ones are: uniform; triangular; and modal (Figure 2). The procedures belonging to the first group apply monotonically increasing preset load patterns. These approaches fail to consider the contribution of higher modes to the response and the inelastic effects in certain structures. In order to come through these disadvantages, and despite the fact that invariant load vectors are still used, the procedures of group two consider and combine different loading vectors, which are derived from mode shapes. The approaches contained in the third group consider the progressive update of the load vectors as the system modal properties change during the inelastic stage

Figure 2 Lateral load patterns

With regard to the demand part, a proper response spectrum must be selected and used in order to properly characterize the possible ground motions expected in the building site (Figure 3). The possible spectra can be obtained from national codes and guidelines, as well as from more specific micro-zonation studies performed in the area of interest. Depending on the NSPs to be applied, the response spectra to be used can be either an over damped elastic response spectrum or an inelastic response spectrum.

f1

f2

f3

f4

f5

f6

f7

MDOF systemFundamental modeof vibration

f1

f2

f3

f4

f5

f6

f7

Triangular

f1

f2

f3

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f7

Uniform



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Figure 3 Design response spectra for different soil types

In order to compare both, capacity and demand, their results must be properly treated and transformed into an equivalent format and units. The procedure accomplishes this through a series of steps, which include: 1) the transformation of capacity curve of the multi-degree of freedom (MDOF) system into a capacity curve of an equivalent single-degree of freedom (SDOF) system (Figure 4); 2) the calculation of the inelastic displacement (target displacement) that corresponds to the seismic action imposed to the structure in acceleration-displacement units (Figure 5 and Figure 6); and 3) the transformation of the target displacement of the equivalent SDOF system back to the MDOF (de Almeida e Fernandes Bhatt, 2011).

Figure 4 Transformation of the MDOF system into an equivalent SDOF system

Se [g]

T [s]0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.5 1.5 2.51 2 3

5% damped response spectra

m1

m2

m3

m4

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k1

k2

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f7=m7a7

f6=m6a6

f5=m5a5

f4=m4a4

f3=m3a3

f2=m2a2

f1=m1a7

Vb=!( fi )

"roof

k4

m*

k*

F*

Vb*=F*

MDOF system Equivalent SDOF system"roof*

F*

"*roof

MDOF

SDOF

Capacity curve

Vb

"roof



Figure 5 Bilinear representation of the capacity curve of the SDOF system

Figure 6 Calculation of the SDOF target displacement (performance point)

The main differences between the different available NSPs with respect to the capacity are related to the piecewise fit (in most of the cases of two branches –bilinear-) representation of the capacity curve and its transformation into an acceleration-displacement format for comparison purposes. On the other hand, the key differences concerning the demand lie mainly on the type of damped response spectra to be used: elastic or inelastic.

2.2.1 The Capacity Spectrum Method (CSM)

Despite the fact that the capacity spectrum method (CSM) was conceived for the evaluation and retrofit of concrete structures and, therefore, its implementation is beyond the scope of the typology analyzed in this work, its pioneering innovativeness and solid bases are shared and used by the subsequent proposed NSPs approaches and thus, its mention and explanation is compulsory for this study. Considered as one of the first approaches to assess the performance of structures, the method was developed in the early 1970’s by Prof. Sigmund Freeman (Freeman et al., 1975), and gained considerable popularity in the evaluation of concrete structures. The CSM is contained in the ATC-40 (1996) guidelines and it allows, through a graphical representation, to visually compare

F*

d*

APUSHeq

Pushover Curve area of theequivalent SDOF system

F*

d*

= ABIL

Bilinear Fit area of theequivalent SDOF system

Sa

Sd

Capacity curveBilinear representation

Capacity spectrumRespomse spectrumBilineal representationYielding pointTarget displacement

Sa

Sd



CONSTRUCTIONS

and evaluate the capacity and behavior of a certain structure when subjected to the demand of an earthquake ground motion. Within the ATC- 40 guidelines, three iterative procedures can be found: A, B, and C. Procedures A and B are the most clear and convenient for programming, whereas procedure C is a non-programmable but purely graphical method. The CSM approach considers that the predominant response of the structure is the fundamental mode of vibration (1st mode) and, therefore, an invariant modal lateral load pattern is monotonically applied to the structure (Figure 7). The seismic demand is represented through a highly damped elastic response spectrum (Figure 3).

Figure 7 Invariant lateral load pattern according to the fundamental vibration mode of the structure

The main steps of the CSM are summarized hereafter. Note that core of these steps is shared and followed by most of the subsequent NSPs proposals, with some specific modifications for each particular approach.

Step 1

A MDOF model of the structure is developed (Figure 8.a). According to the building site, its corresponding elastic response spectrum is selected (Figure 8.b).

XYZ

X

Z

m1

m2

m3

m4

m5

m6

m7

k1

k2

k3

k5

k6

k7

!7,1

!6,1

!5,1

!4,1

!3,1

!2,1

!1,1 m1

m2

m3

m4

m5

m6

m7

k1

k2

k3

k4

k5

k6

k7

f1

f2

f3

f4

f5

f6

f7

X

Z

Fundamental mode of vibration

MDOF systemLateral load distribution based on the fundamental mode of vibration

k4



Figure 8 CSM - a) MDOF model of the structure; b) elastic response spectra

Step 2

A non-linear static (pushover) analysis is performed with a monotonically increasing invariant load pattern applied to the structure, based on the fundamental mode of vibration (Figure 9).

Figure 9 CSM - Pushover analysis of the MDOF model with a first mode invariant load pattern

A non-linear force-displacement curve, sometimes referred to as a capacity or pushover curve, is obtained. The pushover curve relates the displacement of a control node at the roof (usually at the center of mass) and the base shear at every increase (Figure 10).

Capacity Demand

Se [g]

T [s]

TB TC TD

a) b)

m1

m2

m3

m4

m5

m6

m7

k1

k2

k3

k4

k5

k6

k7

f1

f2

f3

f4

f5

f6

f7

!roof

Vb="( fi )



CONSTRUCTIONS

Figure 10 CSM - Capacity (pushover) curve

Step 3

The base shear forces and roof displacements of the MDOF system are then converted to equivalent spectral accelerations and spectral displacements, respectively. The spectral values of the equivalent SDOF system define the capacity spectrum (Freeman, 1998). The transformation is achieved through the use of different factors and coefficients related with the modal and mass properties of the structure (Figure 11). For more details on how these factors are obtained and calculated, refer to procedure A of chapter 8 in the ATC-40 (1996) guidelines.

Figure 11 CSM - Transformation of the MDOF capacity curve into the SDOF capacity spectrum

Vb

!roof

m1

m2

m3

m4

m5

m6

m7

k1

k2

k3

k5

k6

k7

f7=m7a7

f6=m6a6

f5=m5a5

f4=m4a4

f3=m3a3

f2=m2a2

f1=m1a7

Vb=!( fi )

"roof

k4

MDOF system

Sa

MDOF

SDOFCapacity curve

Sd

Vb

"roof

Capacity spectrum

Sd = "roof / PF1 / #roof,1

Sa = Vb / W / $1



One of the differences between CSM and other NSPs is the lack of an intermediate step in which the MDOF capacity curve is transformed into an equivalent SDOF curve also in terms of roof displacement and base shear, before being converted to the spectral acceleration-displacement format.

Step 4

The elastic response spectrum that defines the seismic demand should be also transformed into the spectral acceleration-displacement format as can be seen in Figure 12.

Figure 12 CSM - Conversion of the elastic response spectrum from the traditional format into the acceleration-displacement format

Step 5

The previously obtained capacity and elastic response spectra, both in acceleration-displacement format, are now intersected in order to calculate the target displacement (performance point). This calculation involves a series of different sub-steps, which result in an iterative process that is outlined next (for further details see Chapter 8 of ATC-40 (1996)). A trial performance point is estimated and a bilinear representation of the capacity curve is obtained and then transformed into the acceleration-displacement format. The corresponding damping and reduction factors for this trial point are calculated and applied to the demand elastic response spectrum. Both, capacity (bilinearized) and demand spectra are intersected in order to obtain a performance point. If the obtained target displacement converges within the preset tolerance range then the process stops (Figure 13). Otherwise, a new trial performance point should be estimated, and the previous sub-steps should be repeated until the tolerance condition is satisfied.

T [s]

Sae

Sde

! = 5%

Ti

Ti Tj

Tj

Tk

Tk

Sd

Sa

T=2"

#$

%&Sa=

T Sd2"

2Sae

! = 5%

Sde

! = 5%

Sae



CONSTRUCTIONS

Figure 13 CSM - Intersection of the capacity and the demand within the established tolerance limit

Step 6

The obtained performance point of the SDOF should be converted into its corresponding MDOF value by means of the inverse use of the initial estimated transformation factors.

2.3 NSPs used in this work

Among the different NSPs available in the literature, two methodologies were chosen for this work. The Eurocode 8 (2004) is a widely employed methodology. The second approach is a proposal that mainly focuses on the improvement of the piecewise linear fitting of the capacity curve. As most of the common methodologies adopted by codes and guidelines do, the two implemented procedures suggest a two branches piecewise linear fit (bilinear); and the seismic demand is characterized through an inelastic response spectrum.

2.3.1 The N2 method / Eurocode-8

The N2 method was proposed by Professors Peter Fajfar and Matej Fishinger in the late 1980s (Fajfar and Fischinger, 1987, Fajfar and Fischinger, 1988), and subsequently matured and updated in the following decades (Gašperšič et al., 1992, Fajfar and Gašperšič, 1996, Fajfar, 1999, Fajfar et al., 2004, Kreslin and Fajfar, 2012). The original N2 method (Fajfar and Gašperšič, 1996) was adopted by the Eurocode 8 (2004), and combines the non-linear static analysis of a MDOF model with the response spectrum analysis of an equivalent SDOF system. The major difference with respect to the CSM approach is the use

Sd

SDOF capacity spectrumElastic response spectrumSDOF bilinear representation

Yielding point Target (performance) point

Sa



of inelastic demand response spectra, which are indirectly determined from the elastic demand response spectra by means of reduction factors (Fajfar, 2000). The basic steps and derivations of the method are described below. It should be noted that, since the N2 method is in fact a variant of the CSM based on inelastic spectra, some of the steps previously defined in 2.2.1 are identical, and some others experience slight or specific changes that characterize the N2 method. Specifically, Step 1 and Step 2 of the CSM approach (section 2.2.1) remain similar for the N2 method and therefore will not be described again.

Step 3

As in the CSM, the base shear forces (Vb) and roof displacements (Δroof) of the MDOF system are transformed into an equivalent SDOF system. However, in contrast with the CSM approach in which the SDOF is transformed directly into the acceleration-displacement format, the N2 method firstly transforms the MDOF into a SDOF system with force-deformation units (Figure 14).

Figure 14 N2 method - Transformation of the MDOF capacity curve into the SDOF capacity spectrum

The latter is achieved using Eqns. (2.1) and (2.2)

F* = VbΓ (2.1)

m1

m2

m3

m4

m5

m6

m7

k1

k2

k3

k5

k6

k7

f7=m7a7

f6=m6a6

f5=m5a5

f4=m4a4

f3=m3a3

f2=m2a2

f1=m1a7

Vb=!( fi )

"roof

k4

m*

k*

F*

Vb*=F*

MDOF system Equivalent SDOF system"roof*

F*

MDOF

SDOFCapacity curve

Vb

"roof

Capacity curve

D#

D# = "roof / $

F*= Vb / $



CONSTRUCTIONS

D* =Δroof

Γ (2.2) where, F* and D* are the force and roof displacement of the equivalent SDOF system, and Γ is the modal participation factor, which is defined as

Γ =miΦi∑miΦi

2∑ = m*

miΦi2∑ (2.3)

where m* is the equivalent mass of the SDOF system

m*= miΦi∑ (2.4)

The procedure implies a non-iterative bilinear fit process that assumes an elastic-perfectly plastic backbone for the equivalent SDOF system, based on the equilibrium of the areas over and under the fit (A1 and A2 in Figure 15, respectively). The fitting is performed up to the point where a plastic mechanism is developed, which can be assumed equal to the maximum force (Dolšek, 2008).

Figure 15 N2 method - Fitting procedure according to EC8 (N2 method)

The displacement parameter (Dy*) is also determined from the equilibrium of areas and the deformation energy, Em*, calculated up to the displacement Dm* (Eqn. (2.5)).

Dy* = 2 Dm

* − Em*

Fy*

⎛

⎝⎜⎞

⎠⎟ (2.5)

The elastic period of the bilinearized system T* is determined as

F*

A1

A2

Em*

A1 = A2

Dy*

Fy*

Dm* D*

Elastic-perfectly plasticbilinear fit

SDOF capacity curve

Plastic mechanism



T * = 2πm* ⋅Dy

*

Fy* (2.6)

Finally, the SDOF system is transformed into acceleration-displacement units

Sa =F*

m* (2.7)

Sd = D*

(2.8)

Step 4

As was done in the Step 4 of the CSM approach (section 2.2.1), the elastic response spectrum is transformed into the acceleration-displacement format (Figure 16) using the following relation

Sde =T4π 2 Sae (2.9)

where Sae and Sde are the elastic acceleration and displacement spectral values, respectively.

Figure 16 N2 method - Conversion of the elastic response spectrum from the traditional format into the acceleration-displacement format

Sde

! = 5%

Sae

T [s]

Sae

! = 5%

TB TC

TB TC

TD

TD



CONSTRUCTIONS

For an inelastic SDOF system the acceleration-displacement spectrum (Sa-Sd) can be computed by means of a reduction factor, Rµ (Eqns. (2.10) to (2.11)).

Sa =SaeRµ

(2.10)

Sd =µRµ

Sde =µRµ

T 2

4π 2 Sae = µ T 2

4π 2 Sa (2.11)

where µ is the constant ductility factor defined as the ratio between the maximum displacement and the displacement of the yielding point. The reduction factor, Rµ , is directly linked with ductility and the elastic period of the bilinearized system, T*. It can be computed as

Rµ = µ −1( )T*

TC+1 for T * < TC (2.12)

Rµ = µ for T * ≥ TC (2.13)

where TC is the transition period between the constant acceleration and the constant velocity segments of the response spectrum, i.e. between the short-period range and the medium-period range.

Figure 17 N2 method - Demand spectra for constant ductility in acceleration-displacement units

µ=1

µ>1

TB TC

Ti

Tj

Sa

Sd



Step 5

The seismic demand for the equivalent SDOF system is obtained by calculating the reduction factor Rµ as

Rµ =Sae T

*( )Say

(2.14)

where Sae(T*) represents the intersection between the elastic period of the bilinearized system, T*, and the elastic demand spectrum. The displacement demand is then obtained

µ = Rµ

Sd = Sde T*( )

⎫⎬⎪

⎭⎪T * ≥ TC (2.15)

Figure 18 N2 method – Determination of the target displacement for the equivalent SDOF system (medium and long period range)

µ = 1 (elastic)

µ>1

TCSa

Sd

T*

Sae

Say

Dy*=Sdy Sd=Sde



CONSTRUCTIONS

µ = Rµ −1( )TCT * +1

Sd = µDy* = Sde

Rµ

1+ Rµ −1( )TCT *⎛⎝⎜

⎞⎠⎟

⎫

⎬⎪⎪

⎭⎪⎪

T * < TC (2.16)

Figure 19 N2 method – Determination of the target displacement for the equivalent SDOF system (short period range)

Step 6

The target displacement value corresponding to the control node of the MDOF system is given by

Δroof = Γ ⋅D* (2.17)

2.3.2 The 10% fit

Proposed by De Luca, Vamvatsikos and Iervolino (De Luca et al., 2013a), this bilinear fit improvement aims to decrease the error introduced in the conventional static pushover analysis by the piecewise linear fitting of the capacity curve (Figure 20). The approach stands up for the intersection between the capacity curve and the fitted elastic segment at 10 % of the maximum base shear in order to better capture the initial stiffness. Another main difference of this approach is the setting of a subsequent plastic segment at the maximum strength value (peak base shear value), ignoring the equilibrium of energies, as happens in other procedures (De Luca et al., 2013b).

µ = 1 (elastic)

TCSa

Sd

T*

Sae

Say

Sdy Sde Sd



As in the abovementioned methodologies, the seismic demand is represented by means of an inelastic response spectrum, which results from the scaling of the elastic response spectra and the use of the proper R-µ-T relations.

Figure 20 10% fit approach – Bilinear fit of the capacity curve of the SDOF system

2.4 Incremental Dynamic Analysis

In recent years, the use of increasingly accurate and sophisticated analysis methods for the evaluation of the dynamic behavior of structures has started to escalate due to the development of the computational power and methods. Proposed by Vamvatsikos and Cornell (2002), the incremental dynamic analysis (IDA) has become a valuable tool of seismic engineering, allowing to estimate the performance of a structure subjected to seismic loads by means of non-linear dynamic analyses, which are performed for a single or several different ground motion records in order to take into account the uncertainties of the demand. This ground motion records are scaled to different intensity values, thus producing specific results of the dynamic response of the structure for each case that can be evaluated in function of predefined parameter, e.g. maximum displacement of a control node located in the roof of the structure. For the purposes of this work and in order to compare the results and therefore determine the accuracy of the selected simplified NSPs, the results obtained from the IDA approach will be used as reference values.

F*

Dy*

Fy*

0.10Fmax*D*

F max

*



CONSTRUCTIONS



3 THE BUILDING

3.1 Historical overview

3.1.1 The Cerdá expansion project

By the half of the 19th century, the existing population density within the walls that surrounded the city of Barcelona reached an extreme situation. In contrast, the adjacent territory was completely deserted due to the military ordinances of the time that prohibited any construction that could be reached by the cannons of the nearby fortifications. Therefore, the need to bring down the walls in order to expand the city was compulsory. The latter was possible due to a political change occurred in 1854, which resulted in a call for an expansion project issued by the city hall of the city in 1858. Several engineers and architects presented their proposals for the new configuration of the expanded city, and finally the project was awarded to the civil engineer Ildefons Cerdá. By that time, Cerdá was already working in a topographic survey of the region, which facilitated his understanding and therefore his conception of the expansion project. Since the project was directly awarded by the central government based in Madrid, some local political and social actors opposed to its implementation, and finally the original proposed project



CONSTRUCTIONS

suffered important modifications in order to accomplish the requirements imposed by the government of the city and the displeased stakeholders. Details about the conception, specifications and main features of the Cerdá project can be found in different references, such as: Grau and Nadal (1997), Ribas (2004), Sobrequés i Callicó (2008). Some of the most relevant architectonical particularities of the Cerdá project are mentioned in the next sections.

3.1.2 The district of L’Eixample

To date, the district of L’Eixample has approximately a quarter of a million of inhabitants, 8,658 buildings and a population density of 33,148 inhabitants per km2. A large number of these buildings are more than 100 years old, the majority of which were built before 1960 and being 1931 the average year of construction. Nowadays, nearly the 73% of the buildings of the district of L’Eixample correspond to unreinforced brick masonry buildings (Lantada, 2007). Due to the construction practices of the time, the buildings were erected with common lateral load bearing walls, which were shared with the contiguous buildings although they were built independently. This resulted in an urban layout with large aggregates consisting of 113-meter side squared blocks (also known as islands), separated by 20-meter wide streets. Therefore, the design of the buildings is limited by the orthogonal shape of the blocks, leading to the use of repetitive patterns (Figure 21).

Figure 21 Typical urban layout of blocks of the district of L’Eixample

According to their location within the block, two different types of buildings can be observed: 1) those located in the different corners of the block, known as chamfer buildings; and 2) those located in the central part of one of the sides of the block. On the other hand, depending on the



surrounding buildings, three options can also be distinguished: 1) adjacent buildings on both sides; 2) adjacent building on one side (partially isolated structure); and 3) non-adjacent buildings on either side (isolated structure). The perimeter in plan of the central buildings is rectangular, with a normal ratio between the longitudinal and transverse dimensions of approximately two to one or higher. The perimeter of the chamfer buildings is typically pentagonal. Further details can be found in Ajuntament de Barcelona; Corporació Metropolitana de Barcelona (1985), Permanyer (1990), Garcia Espuche (1990), Busquets (2004), Permanyer (2011)

3.2 General description

For the purposes of this work, a real existing 7-storey unreinforced masonry (URM) building, representative of the district of L’Eixample in Barcelona, Spain, is analyzed The structure is part of a block of aggregates located in a main street of the city, with a load-bearing walls system and shallow foundations running through surface pads under the walls. It was, however, modeled and analyzed as an independent (isolated) structure. The structure presents a rectangular base with a diaphanous base level mainly used for commercial purposes, characterized by high ceilings and the absence of walls as much as possible due to the use of metallic columns and girders. The upper levels are commonly used as dwellings, having lower ceilings and the presence of symmetrical bearing and partition walls.



CONSTRUCTIONS

Figure 22 Elevation of the front façade and plan views of the base floor and upper levels of the case study building (dimensions in [cm])

The floor system is composed of unidirectional slabs oriented in parallel with the shorter direction of the area to be covered, mainly built with metallic girders and brick vaults, and a compression layer on top. The architectural and structural features of the building have been obtained from different structural plans and drawings, contemporary documents, technical reports, the judgment of experts, and different field visits (Pujades et al., 2012, González-Drigo et al., 2013, Avila-Haro et al., 2013).

300

300

300

300

300

280

500

20

20

20

20

20

20

30

45

201270

1775

Ground floor Upper levelsFront façade



Figure 23 Isometric and plan views of B01 building: a) typical storey (2nd-7th); b) full height; and c) base floor (1st)

3.3 Walls system

Load-bearing walls and masonry or cast iron columns compose the main resisting system of the lower levels, i.e. ground floor and mezzanine (if any). In the upper levels, load-bearing walls mainly support the load.

a)

b)

c)



CONSTRUCTIONS

Depending on the type and location of the wall, different wall thickness can be found in the structure. Some of the most common dimensions for each element are: 1) intermediate lateral walls, with 30 cm thickness at the ground floor and 15 cm thickness at upper levels; 2) façades, with a 45 to 60 cm thickness at ground level and 30 cm thickness at upper levels; 3) stairwell and central core, with 30 cm thickness at ground level and 15 to 30 cm thickness at upper levels; 4) internal load-bearing walls, with 10 to 15 cm thickness; and 5) internal partition walls, with less than 10 cm thickness. Further details about the architectonic characteristics of the distinctive masonry buildings of the district of L’Eixample can be found in Paricio (2001). Table 1 provides and overview of the different dimensions of the case study building analyzed in this work.

Table 1 Geometric properties of the case study analyzed

Storey Properties 1 2 3 4 5 6 7 Height** 520 320 320 320 320 320 300 Intermediate lateral walls 30 15 15 15 15 15 15 Front façade 45 30 30 30 30 30 30 Back façade 45 30 30 30 30 30 30 Stairwell and central core walls 30 15 15 15 15 15 15 Internal load-bearing walls - 15 15 15 15 15 15 Internal partition walls - 5 5 5 5 5 5 Dimensions in [cm] ** Including a 20 cm thickness slab

According to the thickness of the wall, different brickworks can be found in the structure. The quality of the bricks and the mortar also varies depending the location of the element and the load to be supported, passing through ordinary bricks and lime mortar for low range loads up to high resistance bricks with Portland cement for main loads and slender pillars. The constructive solution adopted for the lower levels in which metallic columns and girders (Figure 24 and Figure 25) substitute the load-bearing walls, ensures larger diaphanous spaces for commercial and catering activities in the first floor, and for administrative activities in the mezzanines (if any).



Figure 24 Metallic columns and girders used in the first level of the buildings

Figure 25 Distribution of metallic columns and girders of the first level

In addition to the façades, inner courtyards and intermediate lateral walls, other load-bearing walls can be found parallel to the façade, above the previously mentioned girders. The contribution of the wall system conformed by the partition walls is generally considered as not significant to the strength of the structure. The system is composed by walls with thickness lower than 10 cm and therefore, for modeling and analysis purposes, is not considered.



CONSTRUCTIONS

The lack of proper connection (sometimes null) between the inner walls and the façades or intermediate inner walls, precludes their participation as bracing walls. In addition, weak areas can be located over the lintels and parapets placed above openings (i.e. windows or doors). Several walls present different openings (doors and windows), whose dimensions tend to decrease as the level increases. The latter leads to the existence of large openings in the lower levels, which, despite having greater thickness, can produce weak areas.

3.4 Floor system

From 1890 to 1940, unidirectional slabs, with iron beams and brick vaults, composed most of the floors systems. According the time of construction, wooden beams can be observed in older buildings, meanwhile steel or precast reinforced concrete beams can be found in subsequent periods. The slabs are simply supported on bearing walls or main beams, depending on the level of the building, presenting barely sufficient connection to these elements (Figure 26). The support length directly depends on the thickness of the receiving element. Common support lengths are: 15 cm for intermediate lateral walls; 30 cm for façades in lower levels; and 10-15 cm for façades in upper levels.

Figure 26 Connection between slabs and walls. a) Metallic beams; b) wooden beams

In our study case, iron beams and brick vaults, define the floor system of the structure. The beams are 70 to 80 cm apart, and small thin vaults are placed in-between with an average thickness ranging between 15 and 20 cm. The vaults are composed of two to three layers of thin bricks, which are then infilled by a compression layer made of rubble and plaster. This layer is then leveled and covered with tile pavement. Further details of the various elements that compose the floor system can be observed in Figure 27.



Figure 27 Iron beams and brick vaults unidirectional slabs. a) Components of the floor system: 1.- double layer of thin brick, 2.- lime mortar, 3.- I type iron

beam, 4.- rubble and plaster infill, 5.- pavement; b) separation of the iron beams between 70 to 80 cm; c), d), e) and f) details of the components and

connection of the floor system

3.5 Openings



CONSTRUCTIONS

Discharging arches or wooden and iron lintels are common solutions that can be observed in the URM buildings of the district of L’Eixample (Figure 29 and Figure 28). These can be found above doorways and windows of the different walls of the structure, according to the wall thickness. In the case of thin partition walls and small spans, wooden lintels are mainly used. Lintels composed by two or more I section beams can be found for large openings on walls with considerable thickness. The support length varies according to the dimension of the element to be supported. As it was mentioned in section 3.3, dimensions of the openings tend to decrease as the level increases, and they can be found mainly in the façades and inner nuclei of the building.

Figure 28 Discharging elements above openings: a) location of lintels in the 3D model; b) and c) discharging arches above doors; d) iron lintel above a

window; e) iron lintel above façade openings



Figure 29 Lintels above façade openings

3.6 Loads and materials

3.6.1 Dead and live loads

The load values used in this work are in accordance with the contemporary city council regulation documents, prior to the first codes and guidelines that started to appear in the 1960’s (Ministerio de la Vivienda, 1963, Ministerio de la Vivienda, 1988). A permanent load of 350 kg/m2 is assigned to all levels, consisting of 200 kg/m2 corresponding to the floor weight; 100 kg/m2 corresponding to the load from the partition walls; and 50 kg/m2 corresponding to weight of tiled floor pavement. On the other hand, a variable load of 200 kg/m2 is assigned to the intermediate floors, and a 100 kg/m2 load for the last floor (terrace) (González-Drigo et al., 2013).

3.6.2 The bricks and the mortars

As it was mentioned before, the studied building corresponds to the construction period between 1890 and 1940. Therefore, the bricks and their manufacture were prior to the mechanized era, leading to the existence of different qualities of bricks, which tend to increase as the firing grade augmented (Schindler and Bassegoda, 1955). The color of the pieces serves as an indicator of their strength and quality, varying from reddish tones for the lower strength bricks (around 7 MPa) up to pale ochre tones for the higher strength one (around 15 MPa). The mortars used in the brickwork of these structures was also conditioned to the element to be constructed, having lime and bastard mortars, natural (roman) mortars, and Portland cement.



CONSTRUCTIONS

The constructive purpose of the bricks was also directly linked with their dimensions, having ordinary bricks of 29x14x5.5 cm for the construction of load-bearing walls; bricks of 29x14x4.5 cm used in partition walls; medium and thin bricks of 29x14x3 cm and 29x14x2 cm, respectively, for the construction of vaults. The building studied in this work is made of solid clay ceramic bricks, with good adherence and texture. Despite the lack of additional technical reports and specific mechanical tests that could shed light on the properties of the studied building, the mechanical properties used in this work (Table 2) were obtained and extrapolated from contemporary documents and existing tests results, taking into account the expertise and sound opinion of architects and civil engineers.

Table 2 Mechanical properties of masonry

Mechanical parameter Inferior limit Average value Superior limit Units Specific weight, γ -- 18 -- kN/m3 Compressive strength, f’m 215 300 385 N/cm2 Elastic modulus, E 107500 150000 192500 N/cm2 Shear modulus, G 35833 50000 64167 N/cm2 Shear strength, τ 6.45 9.00 11.55 N/cm2

3.7 Computational model

The 3D non-linear model of the building under study in this work was developed and analyzed using the computer program TreMuri (Galasco et al., 2002), which is widely used and recognized in the analysis and simulation of the non-linear behavior of masonry structures The analysis is performed by means of constitutive laws derived from experimental tests and a macroelement approach (Lagomarsino et al., 2002), which reduces the computational load. The program adopts the a macro-element approach (Gambarotta and Lagomarsino, 1997), which permits to represent the two main in-plane masonry failure mechanisms, i.e. bending-rocking and shear-sliding, by means of a macroscopic representation of a continuous model through a limited number of degrees of freedom (eight). The analyzed building was modeled on the basis of original floor plans, architectural drawings, and diverse technical documents that provided relevant data. The latter was seconded with the use of guidelines and manuals contemporary to the construction time of the structure, as well as the expert judgment of architects and civil engineers, and several field visits. The modeling process consists in a series of ordered steps, which start with the definition of the geometry of the different levels and elements as a line layout (Figure 30a and Figure 30b). Then, the type of element and properties that correspond to each line of the layout should be defined. The program enables the definition of different types of elements such as columns, beams, and walls, among others. In a simultaneous step, the knowledge level and material properties can be defined (this can be modified or updated later) in order to properly assign them to the different elements of the structure. In the event of the existence of doors or windows, this should be defined according to their geometric properties. Similarly, in the case of the presence of lintels above the openings, their



longitude and position should be defined. Auxiliary nodes can be drawn in order to facilitate the definition of these elements. The next step involves the definition of the different slabs. The geometric and material properties of the adopted floor system must be defined, as well as their directionality. Live and dead loads are also defined at this point. The previous steps are followed for each level until the full structure is properly defined (Figure 30c and Figure 30d). Security checks can be run during the process in order to avoid any error or oblivion. For the study case building of this work, the main constitutive elements for each type of level are shown in Figure 31 and Figure 32. It can be observed that in the ground floor there is a higher concentration of columns (Figure 31b) and beams (Figure 31c). As pointed out before, this is in order to assure a more diaphanous space in which the different commercial and catering activities can take place. On the contrary, for upper levels, the presence of load-bearing walls at these locations can be observed. The existence of different lintels above the location of windows and doors can also be noticed. Once the definition of the model has been accomplished, the different modal, static and dynamic analyses can be performed either in the commercial version of the software or in the research one. In order to automatize, and therefore perform several incremental analyses, the research version of the program was used for this work and the results are shown in chapter 5.



CONSTRUCTIONS

Figure 30 TreMuri layouts: a) Base floor (1st) plan; b) Typical storey (2nd – 7th) plan; c) 3D view of the building; and d) 3D view of the different levels

a)

d)

c)

b)



Figure 31 Main constitutive elements of the 3Muri computational model. Base floor (1st): a) Foundation layout; b) Columns (cast iron and masonry); c) Lintels (iron and wood); d) Walls and openings (windows and doors); and

e) Slabs

a) b)

c) d)

e)



CONSTRUCTIONS

Figure 32 Main constitutive elements of the 3Muri computational model. Typical storey (2nd-7th): a) Columns (cast iron and masonry); b) Lintels (iron

and wood); and c) Walls and openings (windows and doors) d) Slabs

b)

c) d)

a)



4 THE DEMAND

4.1 The city of Barcelona

The Mediterranean basin concentrates a vast number of cities in which the socioeconomic activities and population density is substantial. At the same time, the vulnerability of a large number of buildings of more than 100 hundred years old without any consideration of the seismic actions in their construction, increases the seismic risk of these urban areas. The city of Barcelona is located in a low-to-moderate seismic hazard region in the northeast of the Iberian Peninsula, with a VI to VII macroseismic intensity in accordance with the European macroseismic scale, EMS’98, and is divided in 10 districts (Figure 35).

4.1.1 Seismic scenarios

In the framework of the Risk UE project (Milutinovic and Trendafiloski, 2003), several studies were performed in order to better characterize the different types zones and soils of the city (Irizarry, 2004). Two specific seismic scenarios resulted as an outcome of this work. Similarly, different microzoning studies (Cid, 1998, Secanell et al., 2004) were carried out in order to obtain specific site response spectra for these two scenarios (Pujades et al., 2012). The first scenario, which is called deterministic scenario, assumes that the historical seismicity contains sufficient information to assess the seismic hazard of a certain region. This scenario was therefore defined by the historical event occurred in 1448 in Cardedeu, with a 7km depth, and an



CONSTRUCTIONS

epicentral distance and intensity of 25 km and VIII (EMS’98), respectively (Susagna and Goula, 1999, Secanell et al., 2004). The second scenario, which is called probabilistic scenario, was obtained based on the attenuation law of Ambrasseys et al. (1996) and on the regional parameters obtained by Secanell et al. (2004), matching the ground motion with a 10% probability of occurrence in 50 years, i.e. 475 return period ground motions.

4.1.2 Site-specific response spectra

Both scenarios were defined in terms of 5% damped elastic response spectra, and four soil types (seismic zones) were identified in the city (Figure 35). The elastic response spectra parameters for the deterministic and probabilistic scenarios of the four soil zones of Barcelona are presented in Table 3.

Table 3 Parameters for the deterministic and probabilistic scenarios proposed by the ICC for the city of Barcelona

Parameters Soil

Zone pga (g) TB TC BC d TD BD

I 0.188 0.10 0.39 1.91 1.70 2.30 0.09 0.136 0.10 0.40 2.00 1.34 2.85 0.14

II 0.194 0.10 0.22 2.45 1.43 2.20 0.09 0.141 0.10 0.23 2.50 1.28 2.21 0.14

III 0.169 0.10 0.22 2.29 1.40 2.00 0.10 0.122 0.10 0.19 2.57 1.12 1.77 0.20

R 0.100 0.10 0.23 2.26 1.12 1.75 0.23 0.072 0.10 0.25 2.29 0.98 1.75 0.34

Deterministic scenario Probabilistic scenario

The expressions (Eqn. (2.18)) needed to obtain 5% damped elastic response spectra for both scenarios (Figure 33 and Figure 34) are described as follows.

Sa T( )pga

1+ TBTC

BC −1( ) 0 ≤ T ≤ TB

BC TB ≤ T ≤ TCTCT

⎡⎣⎢

⎤⎦⎥

d

BC TC ≤ T ≤ TD

TDT

⎡⎣⎢

⎤⎦⎥

2

BD TD ≤ T

⎧

⎨

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

(2.18)



where Sa(T) is the ordinate of the elastic response spectrum; T is the vibration period of a linear single-degree-of-freedom system; pga is the peak ground acceleration; BC is the factor defined as Samax/pga; TB and TC are the limits of the constant spectral acceleration range; d is a variable exponent; TC is a corner period at the beginning of constant velocity region; TD is the beginning of the constant displacement response range; and BD is the factor defined as Sa(TD)/pga.

Figure 33 5% damped response spectra for the deterministic seismic scenario of Barcelona

Figure 34 5% damped response spectra for the probabilistic seismic scenario of Barcelona



CONSTRUCTIONS

Figure 35 Districts of Barcelona with their corresponding soil type and 5% damped elastic response spectrum

4.2 Record selection

The conditional spectrum approach (CS) procedure (Abrahamson and Al Atik, 2010, Jayaram et al., 2011, NIST, 2011) was applied in order to select seven compatible horizontal acceleration components from the PEER earthquake database (PEER, 2011), that matched the deterministic scenario target response spectrum corresponding to the soil Zone II of the city of Barcelona in which the district of L’Eixample is located. By means of a Monte-Carlo simulation from a target distribution, the method generates a probabilistic response spectrum, from which a set of ground motions with matching response spectra (in log scale) is selected (Jayaram et al., 2011, NIST, 2011). The target values are closely matched, as the number of simulated spectra is higher. The similarity of the target with the selected ground motion spectra is measured using the sum of the squared errors. In contrast with other methodologies, the CS not only matches the target mean, but also the target variance (Figure 36).



Figure 36 Record selection according to the CS approach

The seven selected records were properly scaled to different intensity values, i.e. pga, in order to evaluate the dynamic response of the structure for different possible states. The considered pga values for the scaling process yield between 0.2 and 0.22 g, at every 0.01 g. The upper limit was selected taking into account that the expected pga in Barcelona for the deterministic scenario of soil Zone II is 0.141 g (see section 4.1.2).

10 !2 10 !1 10 010!2

10!1

100

T [s]

S a [g]

Median response spectrum

+2! response spectra

Response spectra of simulatedground motions

-2! response spectra

Matching records

T



CONSTRUCTIONS



5 ANALYSES RESULTS

The results of the different analysis performed for this work are shown in this chapter. The analyses were performed with the research version of the software TreMuri for the case study building in the transversal (+X) and longitudinal (+Y) directions. In order to determine the procedures followed to obtain these results, refer to Chapters 2 and 4.

5.1 Modal analysis

The results from the performed modal analysis are summarized in Table 4 and Figure 37 and Figure 38.

Table 4 Modal analysis results

Mode T [s] Mx [%] My [%] Direction 1 0.80 87.64 0.30 X 2 0.27 9.77 0.01 1 0.61 0.60 72.39 Y 2 0.58 0.14 5.79

It can be observed that the first and second modes of vibration are translational for both directions of the structure, and the third one is rotational.



CONSTRUCTIONS

Figure 37 First and second mode translations of +X direction

Figure 38 First and second mode translations of +Y direction

1st Mode 2nd Mode+X direction+X

+Y

1st Mode 2nd Mode+X

+Y

+Y direction



5.2 Non-linear static analysis (Pushover)

The results of the non-linear static analyses are presented as a table with the values of the target displacement for the MDOF system, as well as in xxx

Figure 39 Capacity curve of the +X direction

Figure 40 Capacity curve of the +Y direction

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 30

100

200

300

400

500

600

700

800

droof, [cm]

V base

, [kN

]

Pushover Curvedroof=2.8104 [cm]Vbasemax=748.4186 [kN]droof80=2.9427 [cm]Vbase80=598.7349 [kN]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 50

200

400

600

800

1000

1200

1400

droof, [cm]

V base

, [kN

]

Pushover Curvedroof=4.7897 [cm]Vbasemax=1224.1624 [kN]droof70=4.8274 [cm]Vbase70=979.3299 [kN]



CONSTRUCTIONS

Figure 41 Example of the bilinear representation for the two analyzed methodologies for +X direction

Figure 42 Example of the calculation of the target displacement of the EC8 approach for +X direction and a pga=0.06 g

0 0.5 1 1.5 2 2.5 30

0.05

0.1

0.15

Sd, [cm]

Sa,

[g]

EC810% fit

0 0.5 1 1.5 2 2.50

0.05

0.1

0.15

0.2

Sd, [cm]

Sa, [

g]



Figure 43 EC8 approach results for the +X direction

Figure 44 10% fit approach results for the +X direction

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. 1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0. 2 0.21 0.220

2

4

6

8

10

12

pga, [g ]

d roof, [

cm]

PGA vs Droof IB1 Dir X. EC8

IDA

Mean Values

Rec 02Rec 03Rec 04Rec 05Rec 06Rec 07

Rec 01

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. 1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0. 2 0.21 0.220

1

2

3

4

5

6

7

8

9

pga, [g ]

d roof, [

cm]

PGA vs Droof IB1 Dir X. 10fit

IDA


Rec 01

Mean Values



CONSTRUCTIONS

Figure 45 EC8 approach results for the +Y direction

Figure 46 10% fit approach results for the +Y direction

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. 1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0. 2 0.21 0.220

1

2

3

4

5

6

7

8

9

10

pga, [g ]

d roof, [

cm]

PGA vs Droof IB1 Dir Y. EC8

IDA

Mean Values


Rec 01

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. 1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0. 2 0.21 0.220

1

2

3

4

5

6

7

8

pga, [g ]

d roof, [

cm]

PGA vs Droof IB1 Dir Y. 10fit

IDA

Mean Values


Rec 01



5.3 Dynamic analysis

The incremental results of the non-linear dynamic analysis are presented hereafter. The mean values are also calculated and included in the graphics in order to ease the comparison of an average response.

Figure 47 IDA results for the different records and their average value for +X direction

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. 1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0. 2 0.21 0.220

2

4

6

8

10

12

14

pga, [g ]

d roof, [

cm]

Rec 02Rec 03Rec 04Rec 05Rec 06Rec 07Mean Values

Rec 01



CONSTRUCTIONS

Figure 48 IDA results for the different records and their average value for +Y direction

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.220

2

4

6

8

10

12

14

16

pga, [g ]

d roof, [

cm]


Rec 01

Mean Values



6 COMPARISON OF THE RESULTS

Finally, the comparison between the different NSPs analyzed in this work and the IDA results are compared for the different pgas and ground motion records used. The roof displacement was selected as the parameter to evaluate the performance and accuracy of the simplified methods. It can be observed that the NSPs approaches tend to provide higher values than those obtained through the IDA for almost all the intensity measures considered in the analysis. The latter is in accordance with what is reported in the literature and with what would be expected from more conservative methodologies that incorporate simplifying assumptions that lead to the use of higher safety factors in order to surpass the different uncertainties. The 10% fit shows closer results to those reported by the IDA since it captures in a better way the elastic branch of the capacity, which results to be a very sensitive parameter in the performance of these methodologies.



CONSTRUCTIONS

Figure 49 Comparison between mean results of the analyzed NSPs and the IDA for +X direction

Figure 50 Comparison between mean results of the analyzed NSPs and the IDA for +Y direction

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. 1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0. 2 0.21 0.220

1

2

3

4

5

6

7

8

pga, [g ]

d roof, [

cm]

IDAEC810fit

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. 1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0. 2 0.21 0.220

1

2

3

4

5

6

7

8

pga, [g ]

d roof, [

cm]

IDAEC810fit



7 FINAL REMARKS AND CONCLUSIONS

The validity and applicability of the static pushover analysis have been extensively studied in literature, becoming an attractive alternative and useful tool for the seismic assessment of structures. Regarding the NSPs, it is clear that most of them share the same basics and principles, differing mainly in the idealization of the capacity as a bilinear representation, and in the response spectra to be used in order to represent the demand. Special attention is required for the selection and subsequent processing of the ground motion records that will represent the demand to be imposed to the structure, since the response of the structure and therefore the obtained results are highly sensitive. The conditional spectrum (CS) approach can be considered an appropriate and useful approach in order to select different ground motion records since it takes into account several of the structure itself. . The correct definition and modeling of the structure and its elements is fundamental in order to reduce the possible uncertainties in the input data of the model. The sufficient knowledge of the mechanical parameters and particularities of the materials would lead to a better understanding and therefore results. The results obtained in this work show that the applied NSPs can successfully characterize the response of the analyzed building with sufficient accuracy, leading to enormous time saving and computational efforts, without compromising the results.



CONSTRUCTIONS

Different research lines can be continued with regard to this topic, e.g. the proposal of modified factors in order to use other NSPs, which were originally conceived for different typologies, and therefore their factors and parameters are not adequate.,



REFERENCES

ABRAHAMSON, N. A. & AL ATIK, L. 2010. Scenario Spectra for Design Ground Motions and Risk Calculation. 9th US National and 10th Canadian Conference on Earthquake Engineering. Toronto, Canada.

AJUNTAMENT DE BARCELONA; CORPORACIÓ METROPOLITANA DE BARCELONA 1985. Inicis de la Urbanística Municipal de Barcelona. Mostra dels Fons Municipals de Plans i Projectes d'Urbanisme 1750-1930, Barcelona, Spain.

AMBRASSEYS, N., SIMPSON, K. & BOMMER, J. 1996. Prediction of horizontal response spectra in Europe. Earthquake Engineering and Structural Dynamics, 25, 371-400.

ATC-40 1996. Seismic Evaluation and Retrofit of Concrete Buildings. California, U.S.A.: California Seismic Safety Commission.

AVILA-HARO, J., GONZÁLEZ-DRIGO, R., VARGAS, Y., PUJADES, L. G. & BARBAT, A. 2013. Deterministic and Probabilistic Earthquake Scenarios for the Seismic Risk Analysis of URM buildings. Key Engineering Materials, 525-526, 537-540.

BARBAT, A., CARREÑO, M. L., PUJADES, L., LANTADA, N., CARDONA, O. D. & MARULANDA, M. C. 2010. Seismic vulnerability and risk evaluartion methods for urban areas. A review with application to a pilot area. Structure and Infrastructure Engineering, 6, 17-38.

BARBAT, A., YÉPEZ, F. & CANAS, J. A. 1996. Damage scenarios simulation for risk assessment in urban zones. Earthquake Spectra, 2, 371-394.

BUSQUETS, J. R. 2004. Barcelona. La construcción urbanística de una ciudad compacta, Barcelona.

CID, J. 1998. Zonación sísmica de la ciudad de Barcelona basada en métodos de simulación numérica de efectos locales. PhD., Universitat Politècnica de Catalunya, UPC.

DE ALMEIDA E FERNANDES BHATT, C. A. 2011. Seismic Assessment of Existing Buildings Using Nonlinear Static Procedures (NSPs) - A New 3d Pushover Procedure. PhD in Civil Engineering, Universidade Técnica de Lisboa. Instituto Superior Técnico.

DE LUCA, F., VAMVATSIKOS, D. & IERVOLINO, I. 2013a. Improving Static Pushover Analysis by Optimal Bilinear Fitting of Capacity Curves. In: M. PAPADRAKIS ET AL. (ed.) Computational Methods in Earthquake Engineering. Springer Netherlands.

DE LUCA, F., VAMVATSIKOS, D. & IERVOLINO, I. 2013b. Near-optimal piecewise linear fits of static pushover capacity curves for equivalent SDOF analysis. Earthquake Engineering and Structural Dynamics, 42, 523-543.

DOLŠEK, M. 2008. PBEE Toolbox - Examples of application. Ljubljana, Slovenia.: University of Ljubljana, Faculty of Civil and Geodetic Engineering.

EUROCODE-8-1 2004. Design of Structures for Earthquake Resistance. Part 1: General Rules, Seismic Actions and Rules for Buildings. Comité Européen de Normalisation.

FAJFAR, P. 1999. Capacity Spectrum Method Based on Inelastic Demand Spectra. Earthquake Engineering and Structural Dynamics, 979-993.

FAJFAR, P. 2000. A Nonlinear Analysis Method for Performance Based Seismic Design. Earthquake Spectra, 16, 573-592.

FAJFAR, P., DOLŠEK, M., MARUŠIĆ, D. & PERUŠ, I. Extension of the N2 method - Asymetric buildings, infilled frames and incremental N2. In: FAJFAR, P. & KRAWINKLER, H., eds.



CONSTRUCTIONS

Performance-based seismic design concepts and implementation, 2004 Bled, Slovenia. Pacific Earthquake Engineering Research Center, PEER.

FAJFAR, P. & FISCHINGER, M. 1987. Non-linear seismic analysis of RC buildings: implications of a case study. European Earthquake Engineering, 1, 31-43.

FAJFAR, P. & FISCHINGER, M. N2 - A method for non-linear seismic analysis of regular buildings. Ninth World Conference on Earthquake Engineering, August 2-9, 1988 1988 Tokyo-Kyoto, Japan.

FAJFAR, P. & GAŠPERŠIČ, P. 1996. The N2 method for the seismic damage analysis of RC buildings. Earthquake Engineering and Structural Dynamics, 25, 31-46.

FREEMAN, S. A. The Capacity Spectrum Method as a Tool for Seismic Design. Eleventh European Conference on Earthquake Engineering, 1998 Paris, France.

FREEMAN, S. A., NICOLETTI, J. P. & TYRELL, J. V. Evaluation of Existing Buildings for Seismic Risk - A Case Study of Puget Sound Naval Shipyard. U.S. National Conference on Earthquake Engineering, 1975 Bremerton, Wasington. EERI, 113-122.

GALASCO, A., LAGOMARSINO, S. & PENNA, A. 2002. TREMURI Program: Seismic Analyser of 3D Masonry Building. University of Genoa.

GAMBAROTTA, L. & LAGOMARSINO, S. 1997. Damage models for the seismic response of brick masonry shear walls, Part II: the continuum model and its applications. Earthquake Engineering and Structural Dynamics, 26.

GARCIA ESPUCHE, A. 1990. El Quadrat d'Or. Centre de la Barcelona modernista. La formació d'un espai urbà privilegiat, Barcelona, Spain.

GAŠPERŠIČ, P., FAJFAR, P. & FISCHINGER, M. 1992. An approximate method for seismic damage analysis of buildings. Tenth World Conference on Earthquake Engineering. Rotterdam, Netherlands.

GONZÁLEZ-DRIGO, R., AVILA-HARO, J., BARBAT, A., PUJADES, L., VARGAS, Y., LAGOMARSINO, S. & CATTARI, S. 2013. Modernist URM buildings of Barcelona. Seismic Vulnerability and Risk Assessment. International Journal of Architectural Heritage.

GRAU, R. & NADAL, M. 1997. La Unificación Municipal del Pla de Barcelona 1874-1897, Barcelona, Spain

IRIZARRY, J. 2004. An Advanced Approach to Seismic Risk Assessment. Application to the Cultural Heritage and the Urban System of Barcelona. PhD., Universitat Politècnica de Catalunya, UPC.

IRIZARRY, J., GOULA, X. & SUSAGNA, T. 2003. Analytical Formulation for the Elastic Acceleration-Displacement Response Spectra Adapted to Barcelona Soil Conditions. Barcelona, Spain: Institut Cartogràfic de Catalunya.

IRIZARRY, J., LANTADA, N., PUJADES, L., BARBAT, A., GOULA, X., SUSAGNA, T. & ROCA, A. 2011. Ground-shaking scenarios and urban risk evaluation of Barcelona using the Risk-UE capacity spectrum method. Bulletin of Earthquake Engineering, 9, 441-446.

JAYARAM, N., LIN, T. & BAKER, J. W. 2011. A Computationally Efficient Ground Motion Selection Algorithm for Matching a Target Response Spectrum Mean and Variance. Earthquake Spectra, 27, 797-815.

KALKAN, E. & KUNNATH, S. K. 2008. Assessment of current nonlinear static procedures for seismic evaluation of buildings. Engineering Structures, 29, 305-316.

KRAWINKLER, H. 1999. Challenges and progress in Performance-Based Earthquake Engineering. International Seminar on Seismic Engineering for Tomorrow - In Honor of Professor Hiroshi Akiyama. Tokyo, Japan.



KRESLIN, M. & FAJFAR, P. 2012. The extended N2 method considering higher mode effects in both plan and elevation. Bulletin of Earthquake Engineering, 10, 695-715.

LAGOMARSINO, S., GALASCO, A. & PENNA, A. 2002. Pushover and dynamic analysis of URM buildings by means of a non-linear macro-element model. International Conference on Earthquake Loss Estimation and Risk Reduction. Bucharest: RISK-UE project.

LANTADA, N. 2007. Aplicación de Técnicas GIS a Estimación de Riesgos Naturales. PhD, Universitat Politècnica de Catalunya.

MILUTINOVIC, Z. V. & TRENDAFILOSKI, G. S. 2003. WP4: Vulnerability of Current Buildings. RISK-UE Project Handbook.

MINISTERIO DE LA VIVIENDA 1963. Norma MV 101-1962. Acciones en la Edificación. Spanish Official Bulletin. Madrid, Spain: Ministerio de la Vivienda.

MINISTERIO DE LA VIVIENDA 1988. NBE-AE/88 Norma Básica de la Edificación. Acciones en la Edificación. Spanish Official Bulletin. Madrid, Spain: Ministerio de la Vivienda.

NATIONAL RESEARCH COUNCIL 2006. Improved Seismic Monitoring - Improved Decision-Making: Assessing the Value of Reduced Uncertainty, Washington, DC, The National Academies Press.

NIST 2011. Selecting and Scaling Earthquake Ground Motions for Performing Response-History Analyses, NIST GCR 11-917-15. Gaithersburg, Maryland: by NEHRP Consultants Join Venture for the National Institute of Standards and Technology.

PARICIO, A. 2001. Secrets d'un Sistema Constructiu, Barcelona, España, Edicions UPC. PEER 2011. New Ground Motion Selection Procedures and Selected Motions for the PEER

Transportation Research Program. California, USA: Pacific Earthquake Engineering Research Center.

PERMANYER, L. 1990. Historia de L'Eixample., Barcelona. PERMANYER, L. 2011. L'Eixample. 150 Anys d'Historia, Barcelona, Spain. PUJADES, L., BARBAT, A., GONZÁLEZ-DRIGO, R. & AVILA-HARO, J. 2012. Seismic

Performance of a Block of Buildings Representative of the Typical Construction in the Eixample District in Barcelona (Spain). Bulletin of Earthquake Engineering, 331-349.

RIBAS, M. 2004. Barcelona i la Catalunya-ciutat. SCHINDLER, R. & BASSEGODA, B. 1955. Tratado moderno de construcción de edificios.,

Barcelona, Spain. SECANELL, R., GOULA, X., SUSAGNA, T., FLETA, J. & ROCA, A. 2004. Seismic hazard

zonation of Catalonia, Spain, integrating uncertainties. Journal of Seismology, 8, 24–40. SOBREQUÉS I CALLICÓ, J. 2008. Historia de Barcelona., Barcelona. SUSAGNA, T. & GOULA, X. 1999. Cataleg de Sismicitat. Atlas Sismic de Catalunya. . In:

CATALUNYA, I. C. F. D. (ed.). Barcelona. VAMVATSIKOS, D. & CORNELL, C. A. 2002. Incremental Dynamic Analysis. Earthquake

Engineering and Structural Dynamics, 31, 491-514.

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