rose school seismic assessment of two rc school

Università degli Studi di Pavia

EUROPEAN SCHOOL FOR ADVANCED STUDIES IN REDUCTION OF SEISMIC RISK

ROSE SCHOOL

SEISMIC ASSESSMENT OF TWO R.C. SCHOOL BUILDINGS AS PER OPCM 3274-2003

An Individual Study Submitted in Partial Fulfilment of the Requirements for the Doctor of Philosophy Degree in

EARTHQUAKE ENGINEERING

by ARUN MENON

Supervisors: Dr Rui PINHO, Dr Lorenza PETRINI November, 2007

The Individual Study entitled “SEISMIC ASSESSMENT OF TWO R.C. SCHOOL BUILDINGS AS PER OPCM 3274-2003”, by Arun Menon, has been approved in partial fulfilment of the requirements for the Doctor of Philosophy Degree in Earthquake Engineering.

Dr. Rui Pinho …… …

Dr. Lorenza Petrini ………… …

………

……

Abstract

ABSTRACT

Subsequent to the approval of the new National Seismic Code by presidential ordinance in March 2003, a large number of public school buildings have been assessed in accordance with the new code provisions to estimate their seismic vulnerability. The current study discusses the methodology adopted and results obtained for the seismic assessment as per the new seismic code, of two of such reinforced concrete school buildings in the Tuscan Region of Central Italy, constructed in the 1960s and 1970s. The first structure that has been evaluated in accordance with the new Italian Seismic code – OPCM 3274: Technical norms for seismic design, assessment and retrofit of buildings (version 25/03/03), is the lower middle school “Puccetti” in Gallicano, a reinforced concrete school building designed in accordance with the regulations provided for seismic zone category II and constructed between 1962 and 1963. The second building to be evaluated is the Elementary school Pascoli in Barga, a reinforced concrete school building designed and constructed in 1978. Inventory of various data available for the assessment and a detailed description of the structures are presented in the report. Structural modelling, both lumped plasticity and distributed plasticity modelling, are explored within the code prescriptions in order to perform References to the sections utilised from the Italian Seismic code have been provided at appropriate parts of this report. Pr-EN 1992-1-1:1993 and Pr-EN 1998-1:2003 have been used as back-up technical references for some assumptions.

Keywords: seismic assessment; school buildings; Italian seismic code; existing buildings

i

Acknowledgements

ACKNOWLEDGEMENTS

I would like to extend my gratitude to Dr. Rui Pinho and Dr. Lorenza Petrini who guided me through current work. I would also like to acknowledge the technical support from Dr. Ana Beatriz Acevedo Jaramillo in the modelling phase of the work and the advice on various technical issues from Dr. Manuel Alfredo Lopez Menjivar. The financial support extended to me by EUCENTRE, Pavia, under the aegis of the project of seismic assessment of school buildings for the Tuscan Region, is acknowledged.

ii

Index

TABLE OF CONTENTS

Page ABSTRACT ............................................................................................................................................i ACKNOWLEDGEMENTS....................................................................................................................ii TABLE OF CONTENTS ......................................................................................................................iii LIST OF FIGURES ...............................................................................................................................vi LIST OF TABLES...............................................................................................................................viii 1. INTRODUCTION .............................................................................................................................1 2. DATA FOR SEISMIC ASSESSMENT ............................................................................................3 2.1 Inventory of Data Available for the Seismic Assessment of Building A...................................3 2.1.1 Architectural Drawings ....................................................................................................3 2.1.2 Structural Drawings .........................................................................................................3 2.1.3 Material Properties...........................................................................................................3 2.1.4 Miscellaneous ..................................................................................................................4 2.2 Inventory of Data Available for the Seismic Assessments of Building B .................................4 2.2.1 Structural Drawings .........................................................................................................4 2.2.2 Architectural drawings.....................................................................................................4 2.2.3 Details from Design Calculations: ...................................................................................4 2.2.4 Material properties: ..........................................................................................................4 2.2.5 Miscellaneous ..................................................................................................................5 2.3 Description of the Structure (Building – A)...............................................................................5 2.3.1 Introduction......................................................................................................................5 2.3.2 Foundation .......................................................................................................................5 2.3.3 Beams of the superstructure.............................................................................................5 2.3.4 Columns ...........................................................................................................................7 2.3.5 Slabs.................................................................................................................................7 iii

Index

2.3.6 Construction Materials.....................................................................................................7 2.4 Description of the Structure (Building – B)...............................................................................7 2.4.1 Introduction......................................................................................................................7 2.4.2 Foundation .......................................................................................................................7 2.4.3 Beams of the superstructure.............................................................................................9 2.4.4 Columns ...........................................................................................................................9 2.4.5 Slabs.................................................................................................................................9 2.4.6 Construction Materials.....................................................................................................9 2.5 Reference Limit States Adopted for the Seismic Assessments..................................................9 2.6 Masses and Loads ....................................................................................................................10 2.6.1 Load combinations.........................................................................................................10 2.6.2 Coefficients and masses for building A .........................................................................10 2.6.3 Coefficients and masses for building B .........................................................................11 2.7 Seismic Input for Structural Assessment .................................................................................12 3. STRUCTURAL MODELLING ......................................................................................................15 3.1 Knowledge Levels and Permissible Analyses .........................................................................15 3.2 Structural Modelling of Building A .........................................................................................17 3.2.1 Lumped plasticity modelling .........................................................................................17 3.2.2 Distributed plasticity modelling.....................................................................................22 3.3 Structural modelling of Building B..........................................................................................23 3.3.1 Lumped plasticity modelling .........................................................................................23 3.3.2 Distributed plasticity modelling.....................................................................................27 4. DISCUSSION OF RESULTS .........................................................................................................29 4.1 Capacity Calculations ..............................................................................................................29 4.2 Modal Analysis ........................................................................................................................31 4.3 Methods of Analysis for Building A........................................................................................35 4.3.1 Introduction....................................................................................................................35 4.3.2 Linear Static Analysis ....................................................................................................35 4.3.3 Gravity Load Assessment ..............................................................................................36 4.3.4 Dynamic Modal Analysis...............................................................................................36 4.3.5 Non-Linear Pushover Analysis ......................................................................................37 4.4 Methods of Analysis for Building B ........................................................................................42 4.4.1 Introduction....................................................................................................................42 4.4.2 Linear Static Analysis ....................................................................................................42 4.4.3 Dynamic Modal Analysis...............................................................................................42 4.4.4 Non-Linear Pushover Analysis ......................................................................................43 iv

Index

4.5 Discussion of Results of Static-Non-Linear Analyses – Building A .......................................48 4.5.1 Limit State of Limited Damage (SL-DL) ......................................................................48 4.5.2 Limit State of Severe Damage (SL-DS) ........................................................................51 4.5.3 Limit State of Collapse (SL-CO) ...................................................................................54 4.6 Discussion of Results of Static-Non-Linear Analyses for Building B.....................................58 5. CONCLUDING REMARKS ..........................................................................................................61 5.1 Building A................................................................................................................................61 5.2 Building B................................................................................................................................62 REFERENCES .....................................................................................................................................64 APPENDIX A...................................................................................................................................... A1 APPENDIX B...................................................................................................................................... A6 APPENDIX C...................................................................................................................................... A9 APPENDIX D.................................................................................................................................... A13 APPENDIX E .................................................................................................................................... A28 APPENDIX F .................................................................................................................................... A64 APPENDIX G.................................................................................................................................... A72

v

List of Figures

LIST OF FIGURES

Page

Figure 2.1: View of the main entrance of the lower middle school "Puccetti" building in Gallicano .............................................................................................................................6 Figure 2.2: Rear view of the school building..............................................................................6 Figure 2.3: View of the front façade of the elementary school "Pascoli" in Barga....................8 Figure 2.4: Rear view of the school building..............................................................................8 Figure 2.5: Elastic horizontal acceleration response spectra for the three limit states .............13 Figure 2.6: Elastic horizontal displacement response spectra for the three limit states ...........13 Figure 3.1: 3D view of the SAP2000 model of the lower middle school "Puccetti" ...............17 Figure 3.2: Plan at -3030 mm level...........................................................................................19 Figure 3.3: Plan at ±0 mm level................................................................................................19 Figure 3.4: Plan at + 3170 mm level and frame numbering .....................................................20 Figure 3.5: Plan at + 6430 mm level.........................................................................................20 Figure 3.6: Plan at + 7740 mm level.........................................................................................21 Figure 3.7: Plan at + 8750 mm level.........................................................................................21 Figure 3.8: Section at y = 0 mm (Frame No: 1Y).....................................................................22 Figure 3.9: Section at x = 0 mm (Frame No.: 1X)....................................................................22 Figure 3.10: SeismoStruct model of the lower middle school "Puccetti" ................................23 Figure 3.11: SAP2000 model of the elementary school "Pascoli"...........................................24 Figure 3.12: Plan at 0mm level .................................................................................................25 Figure 3.13: Plan at 3700mm level and frame numbering........................................................25 Figure 3.14: Plan at 7400mm level ...........................................................................................26 Figure 3.15: Section at Y = 6900mm........................................................................................26 Figure 3.16: Section at X = 10200mm......................................................................................26 vi

List of Figures

Figure 3.17: Plan view of SeismoStruct model of elementary school "Pascoli"......................27 Figure 3.18: 3D view of the SeismoStruct model of elementary school "Pascoli" ..................28 Figure 4.1: Fundamental mode shapes (1-4) of Building A from SAP2000 ............................32 Figure 4.2: First mode shape of Building B from SAP2000.....................................................33 Figure 4.3: Fundamental mode shapes (2, 3 and 6) of Building B from SAP2000 ..................34 Figure 4.4: Comparison of capacity curves for load distributions 1 and 2 applied in the Xdirection for the Ultimate Limit State...............................................................................39 Figure 4.5: Comparison of the MDOF and SDOF capacity curves for the structure ...............40 Figure 4.6: Equivalent SDOF and bilinear systems..................................................................41 Figure 4.7: Comparison of capacity curves for load distributions 1 and 2 applied in the xdirection ............................................................................................................................45 Figure 4.8: Comparison of the MDOF and SDOF capacity curves for the structure ...............46 Figure 4.9: Equivalent SDOF and bilinear systems..................................................................47

vii

List of Tables

LIST OF TABLES

Page

Table 3.1: Knowledge levels as a function of the information available and the consequent methods of the analyses permitted and partial material safety factors (Table 11.1translated from OPCM 3274: 2003) ..........................................................................16 Table 3.2: Definition of the survey and material test levels for buildings in reinforced concrete (Table 11.3a translated from OPCM 3274: 2003) ............................................................16 Table 4.1: Mode periods and mode mass participation factors of Building A .........................31 Table 4.2: Mode periods and mode mass participation factors of Building B .........................33 Table 4.3: ρmax/ρmin ratios for the three limit states..............................................................37 Table 4.4: Load distribution 1 - Mass proportional ..................................................................38 Table 4.5: Load distribution 2 - Proportional to product of mass and mode shape (X direction) ...........................................................................................................................................38 Table 4.6: Load distribution 2 - Proportional to product of mass and mode shape (Y direction) ...........................................................................................................................................38 Table 4.7: Parameters required to compute Γ factor.................................................................39 Table 4.8: ρmax/ρmin ratios for the three limit states..............................................................43 Table 4.9: Load distribution 1 - Mass proportional ..................................................................44 Table 4.10: Load distribution 2 - Proportional to product of mass and mode shape (X direction) ...........................................................................................................................44 Table 4.11: Load distribution 2 - Proportional to product of mass and mode shape (Y direction) ...........................................................................................................................44 Table 4.12: Summary of pushover analyses performed............................................................44 Table 4.13: Parameters required to compute Γ factor...............................................................45

viii

List of Tables

Table 4.14: Summary of maximum demand to capacity ratios for all elements and all limit states in flexure, shear and rotation (Building B) .............................................................59

ix

Chapter 1. Introduction

1. INTRODUCTION In the aftermath of the subsequent approval of the new National Seismic Code by presidential ordinance in March 2003, a large number of public school buildings within the Italian territory have been assessed in accordance with the new code provisions to estimate their seismic vulnerability. A large proportion of these school buildings have not been designed to satisfactory levels of seismic resistance. The intention of the Italian government is to execute a creditable but cumbersome programme of seismic assessment and subsequently, retrofit or demolition for those school buildings that represent the highest risk, of the 60,000-odd school buildings in Italy, based on a retroactive application of the modern seismic design requirements [Grant et al., 2007]. The current study discusses the methodology adopted and results obtained for the seismic assessment as per the new seismic code, of two of such reinforced concrete school buildings in the Tuscan Region of Central Italy, constructed in the 1960s and 1970s. The first structure that has been evaluated in accordance with the new Italian Seismic code – OPCM 3274: Technical norms for seismic design, assessment and retrofit of buildings (version 25/03/03), is the lower middle school “Puccetti” in Gallicano, a reinforced concrete school building designed in accordance with the regulations provided for seismic zone category II and constructed between 1962 and 1963. Major repair to the roof and addition of a new room with an isolated foundation were carried out in 1980 in this school building. The second building to be evaluated is the elementary school “Pascoli” in Barga, a reinforced concrete school building designed and constructed in 1978 by – design studio Eng. A. Bagiotti of Viareggio and construction company Lorenzini Pietro of Barga, respectively. The present report is organised into five chapters. The first chapter introduces the premise under which the assessment of the school buildings were carried out and the scope and aim of the research. The second chapter details the inventory of various data (architectural and structural drawings, in-situ experimental results on construction material properties, etc.) available for the assessment and provides a detailed description of the structures evaluated in the current investigation. Chapter three deals with the structural modelling of the school buildings, both lumped plasticity and distributed plasticity-based numerical codes, executed within the seismic code 1

Chapter 1. Introduction

prescriptions in order to perform different seismic analysis methods. The chapter also delves into the choice of knowledge level based on the available information for the seismic assessment, which has a bearing on the type of analysis permissible for the seismic assessment. The procedure for the capacity calculations of the structural elements and the results of the modal analyses and subsequent seismic analyses are discussed in depth in Chapter four. The performance of the two structures to the various limit states, as inferred from static non-linear analyses (or pushover) is described in this chapter. Chapter five contains concluding remarks on the seismic assessment of the two school buildings. References to the sections utilised from the Italian Seismic code have been provided at appropriate parts of this report. Eurocode-2 [Pr-EN 1992-1-1:1993] and Eurocode-8 [Pr-EN 1998-1:2003, Pr-EN 1998-3:2003] have been used as supporting technical references for some assumptions. The current study treats the seismic verification of the two reinforced concrete moment resisting frames only with respect to the beams and columns (flexural, shear and rotation capacity versus demands) of the reinforced concrete frames. The seismic verification of reinforced concrete beam-column joints and the foundation are beyond the scope of the current work.

2

Chapter 2. Data for Seismic Assessment

2. DATA FOR SEISMIC ASSESSMENT 2.1 Inventory of Data Available for the Seismic Assessment of Building A The lower middle school “Puccetti” in Gallicano will be referred to as “Building A” in successive sections of the technical report. Information in the form of architectural and structural drawings, descriptive details, photographs, results of in-situ non-destructive and destructive testing, etc. that were available as supporting documents in the assessment procedure is enumerated here. 2.1.1 Architectural Drawings Three architectural drawings pertaining to the foundation and basement, ground floor and first floor prepared by Eng. Mario Agretti and approved in 1960 were available. 2.1.2 Structural Drawings Sixteen structural drawings pertaining to the foundation and basement layouts, details of the entrance portal and other frames, prepared by the firm Fulgenti Gino, Gallicano (Eng. Michele Giannini) in 1961 were available. Details of the foundation beams, floor beams, ceiling beams, ridge beams, storm water drain beams and roof beams, and the columns were available for most of the frames from these drawings. Four drawings pertaining to the repair and addition works in 1980 (construction of a new lecture hall and repair of the roof) were available, providing details of the foundation of the new room, beam and column sections and plans, sections and reinforcement details of the portion of the roof that was repaired. Drawings were prepared by Eng. Italo Mocci of Pisa. From the repair and addition works carried out in 1980, structural details of the prefabricated floor slab (floor slab constructed out of small, partially prestressed, beams in reinforced concrete interspaced with masonry blocks) were obtained from the product brochure of RDB S.p.A. (® Celersap P. R38 Monotrave and Bitrave). 2.1.3 Material Properties Mean value of the compressive strength of concrete adopted for the structural assessment has been based on the results of the in-situ, destructive and non-destructive investigations to test the quality of concrete carried out by the Tuscan Region in 2002 in a separate experimental campaign (programme of investigation on reinforced concrete public buildings in seismic zones). Laboratory tests were not performed to determine the quality of reinforcement steel in

3


the structure. The value of yield strength of steel has been adopted from the structural drawings of the repair and addition works on the building in 1980. 2.1.4 Miscellaneous Twelve photographs showing mainly the exterior of the structure formed a part of the information available to assess the structure. A site visit to the school building on 18.02.2004 also helped in gathering crucial information pertaining to the geometry of the frames required to model the structure. 2.2 Inventory of Data Available for the Seismic Assessments of Building B The elementary school Pascoli in Barga will hereafter be referred to as “Building B” in successive sections of the technical report. Information in the form of architectural and structural drawings, descriptive details, photographs, results of in-situ non-destructive and destructive testing, etc. that were available to aid the assessment procedure is enumerated here. 2.2.1 Structural Drawings The following structural drawings (issued by the construction firm on 14th June, 1978) were available for the assessment: 1. Floor plans – Foundation plan, first floor plan, second floor plan and roof plan; 2. Reinforcement details of the basement boiler room; 3. Structural and reinforcement details of the foundation beams; 4. Reinforcement details of the beams of the second floor 5. Reinforcement details of the beams of the roof slab 2.2.2 Architectural drawings Architectural drawings of the ground and first stories of the school building provided information on the location and layout of masonry partition walls. 2.2.3 Details from Design Calculations: The design calculations illustrated in the design report were performed as per law no. 1086 of 5/11/1971, law no. 64 of 2/2/1974 and D.M. (ministerial decree) of 3/3/1975. Details of the material properties of steel have been obtained from this report. Few details of the floor slabs, in terms of their geometry, rib reinforcement, loading data and construction materials were acquired from the design report. Design loads and structural details of the staircases and loads of the masonry infill panels were other details acquired from the design report. 2.2.4 Material properties: Information on material properties were acquired from two main sources, namely, the design report and in-situ material quality tests. Mean value of the compressive strength of concrete has been based on the results of the in-situ, destructive and non-destructive investigations to 4


test the quality of concrete carried out by the Tuscan Region in 2002 and 2003 in a separate experimental campaign (programme of investigation on reinforced concrete public buildings in seismic zones). Laboratory tests have not been performed to determine the quality of reinforcement steel in the structure. 2.2.5 Miscellaneous A number of photographs showing the exterior and the interior of the structure formed part of the information available to assess the structure. Structural drawings pertaining to the beams of the top floor and details of the slab sections and intermediate ribs were not available for the assessment. 2.3

Description of the Structure (Building – A)

2.3.1 Introduction The lower middle school “Puccetti” is a two-storied reinforced concrete framed structure with masonry infill, prefabricated floor slabs, a small basement floor and sloping roofs of varying height (see Figure 2.1 and Figure 2.2). The structure is roofed by inclined reinforced concrete slabs supported by short columns rising above the second storey. The building has a C-shaped plan form with re-entrant corners and one arm of the ‘C’ is longer than the other. The original structure was constructed between 16.02.62 and 28.09.63, as per the regulation R.D. no. 2229/39. The main entrance to the structure originally led to a double-height space supported by a massive portal frame on one end. In the year 1980, this space was altered to accommodate a new classroom on the first floor thereby transforming the double-height space into two vertically partitioned spaces. The reinforced concrete frame of the new classroom was constructed within the original structure of the school but isolated right from the foundation level. A considerably large portion of the roof was also repaired in 1980. Both the addition and the repair works were carried out in accordance with the building norms: law no.64 of 2/2/1974. 2.3.2 Foundation The foundation of the original structure is composed of continuous inverted mono-directional beams 980mm deep. The alignment of these primary foundation beams varies with their location and they are connected by smaller square beams of depth 380mm in the perpendicular direction. 2.3.3 Beams of the superstructure The structure is composed of unidirectional frames with few of these interconnected by beams. Most of the beams in the structure are 360mm wide and 460mm deep and few are 360mm wide and 540mm deep. The beam of the entrance portal is 1150mm deep. Drawings pertaining to the repair works carried out on the roof (in 1980) indicate that the beams supporting one section of the roof are 380mm wide and 350mm deep. In one other section of the building, the beams supporting the roof are apparently 400mm wide and 610mm deep with the end section of the beam widening to a depth of 780mm. Longitudinal reinforcement bars of diameters 14mm, 16mm and 20mm have been used in the beams of the superstructure and 8mm bars have been used along with 16mm bars in the foundation beams. Transverse 5


reinforcement is of 6mm diameter stirrups at a spacing of either 200mm or 250mm. Stirrups in the foundation beams are of 8mm diameter with a spacing of 275mm.

Figure 2.1: View of the main entrance of the lower middle school "Puccetti" building in Gallicano

Figure 2.2: Rear view of the school building

6


2.3.4 Columns The reinforced concrete columns throughout the building are square with side dimension 380 mm. Perimeter columns have eight longitudinal reinforcement bars of 16mm diameter whereas interior columns have six bars of 16mm diameter. Transverse reinforcement bars are of 8mm diameter at a spacing of 160mm. Columns of the entrance portal are of dimension 400mm by 600mm and increase to 400mm by 900mm at the beam column joint with four numbers of 20mm diameter longitudinal reinforcement bars and 6mm diameter transverse reinforcement bars at a spacing of 200 mm. The stirrup hooks are bent at 90°, and not 135° as required for anti-seismic applications. 2.3.5 Slabs The floor and roof slabs are of composite construction, i.e., prefabricated reinforced concrete ribs interspaced with brick blocks and a 40mm topping slab of cement conglomerate (® Metalstrut). Apparently, two types of slabs have been used in this building – Monotrave ® and Bitrave ® with composite heights of 29cm (25+4) and 24cm (20+4), respectively. 2.3.6 Construction Materials The results of the non-destructive tests on concrete showed the heterogeneity of the tested material and consequently, variability in the resistance values. The results of the destructive tests showed that the compressive strength of concrete was between 15.2 MPa and 20 MPa. A mean value of 18 MPa has been considered for the structural assessment. The yield strength of reinforcement steel has been adopted as 440 MPa. 2.4

Description of the Structure (Building – B)

2.4.1 Introduction The elementary school “Pascoli” is a two-storied reinforced concrete framed structure with masonry infill, prefabricated floor slabs, a small basement floor and sloping roofs (see Figure 2.3 and Figure 2.4). The structure is roofed by sloping reinforced concrete slabs. The building was designed by – design studio of Eng. A. Bagiotti of Viareggio and constructed by the construction firm Lorenzini Pietro of Barga in 1978. The building is approximately squareshaped and symmetrical in plan about one axis. The sides of the building frame measure 41.3 m (X direction) and 35.6 m (Y direction). The structure rises to a height of 8.0 m above the ground level and the foundation extends to a depth of 1.20 m below the ground level. Each floor has a clear height of 3.4 m. The basement room has a clear height of 2.5 m and extends to a depth of 2.6 m below the ground level. The basement room has reinforced concrete columns and reinforced concrete walls. The building has two internal staircases located symmetrically on either sides of a common landing area facing the main entrance on the ground floor. The rear central portion of the building is single-storied. The common landing area of the stairs on the first floor opens onto a terrace. 2.4.2 Foundation The foundation of the structure is composed of continuous, inverted reinforced concrete Tbeams 1200mm deep in the two principal directions. The widths of the web and flange of the

7


T-beam are 400mm and 1000mm, respectively. In few locations these T-beams are interconnected by smaller beams of square cross-section (400mm).

Figure 2.3: View of the front façade of the elementary school "Pascoli" in Barga

Figure 2.4: Rear view of the school building

8


2.4.3 Beams of the superstructure The structure is composed of bidirectional reinforced concrete frames. Most of the beams in the structure are 800mm deep and 400mm wide, 800mm deep and 300mm wide or 600mm deep and 400mm wide. Longitudinal reinforcement bars of diameters 12mm, 14mm, 16mm and 20mm have been used in the beams of the superstructure. 8mm, 14mm, 16mm and 20mm diameter bars have been used for longitudinal reinforcement in the foundation beams. Transverse reinforcement is of 8mm diameter stirrups at a spacing of 200mm, 250mm or 300mm. Some beams have transverse reinforcement of 6mm diameter bars at 200mm and 10mm diameter bars at 100mm. Stirrups in the foundation beams are of 10mm diameter bars at 10 inches or 8mm diameter at a spacing of either 20 or 30 inches depending on their location. 2.4.4 Columns The reinforced concrete columns throughout the building are square-shaped of dimension 400mm. The columns have 4, 6 or 8 longitudinal reinforcement bars of diameters 16mm or 20mm. Since no information on the transverse reinforcement was available, it was assumed that the columns had 8mm diameter bars at 300mm spacing. 2.4.5 Slabs The floor and roof slabs are of composite construction - prefabricated reinforced concrete ribs interspaced with brick blocks and a 40mm topping slab of cement conglomerate. The total height of the slab is 240 mm. 2.4.6 Construction Materials The results of destructive and non-destructive tests showed good quality of concrete in the structure. A mean value of 30 MPa has been considered as the characteristic compressive strength of concrete for the structural assessment. The characteristic compressive strength reported in the structural details and design calculations is 25 MPa. The yield strength of reinforcement steel has been adopted as 440 MPa based on data from the structural drawings and the design calculation report. 2.5 Reference Limit States Adopted for the Seismic Assessments Under the design seismic action, as per § 2.1 of the Italian Seismic Code [OPCM 3274, 2003], buildings (both existing buildings and new constructions) have to satisfy stability criteria and sustain residual stiffness and strength against lateral forces and the entire load carrying capacity for vertical forces, despite severe damage. This is the Ultimate Limit State (SLU). Under a seismic event with a probability of exceedance higher than that of the design seismic action, as per § 2.2 of the Italian Seismic Code [OPCM 3274, 2003], damage has to be prevented in buildings (both existing buildings and new constructions). They should not be severely damaged and should remain functional after the seismic event. This pertains to the Damage Limit State (SLD). As per § 11.2.1 of the Italian Seismic Code [OPCM 3274, 2003], an existing reinforced concrete structure has to be assessed to an additional limit state or, in other words, a total of 9


three limit states of damage or collapse. They are the Limit State of Limited Damage, Limit State of Severe Damage and Limit State of Collapse. The limit states of Limited Damage and Severe Damage correspond to the Damage Limit State (SLD) and the Ultimate Limit State (SLU) defined for new constructions. The Limit State of Collapse corresponds to a higher design seismic action characterised by a lower probability of exceedance. In probabilistic terms, the seismic action corresponding to these limit states are the following:

2.6

•

Limit State of Limited Damage: 50% probability of exceedance in 50 years (return period of 72 years)

•

Limit State of Severe Damage: 10% probability of exceedance in 50 years (return period of 475 years)

•

Limit State of Collapse: 2% probability of exceedance in 50 years (return period of 2475 years) Masses and Loads

2.6.1 Load combinations In accordance with § 3.3 of the Italian Seismic Code [OPCM 3274, 2003], the seismic loads were combined with the dead loads and live loads acting on the structure.

γ I E + G K + PK + ∑i (Ψij QKi )

Eq. 2.1

Where:

γIE

=

Seismic action corresponding to the limit state being examined,

GK

=

Characteristic value of permanent loads,

PK

=

Characteristic value of prestress,

Ψij

=

Ultimate Limit State - SLU (Ψ2i) or Damage Limit State - SLD (Ψ0i) coefficients of combination for variable loads i,

QKi

=

Characteristic value of the variable loads Qi.

The masses corresponding to the two limit states, SLD and SLU, were calculated by the following combination, as per § 3.3 of the Italian Seismic Code [OPCM 3274, 2003]: G K + ∑i (ΨEi QKi )

Eq. 2.2

where, ΨEi is calculated by multiplying Ψij with the coefficient φ. 2.6.2 Coefficients and masses for building A The coefficients applicable in the case of Building A from Tables 3.4 and 3.5 of the Italian Seismic Code [OPCM 3274, 2003] are as follows:

10


Coefficients for destination of use: School:

Ψ0i = 0.70 (SLD) Ψ2i = 0.60 (SLU)

Roofs: Ψ0i = 0.70 (SLD)

Ψ2i = 0.35 (SLU) Coefficients for loads for different floors: Top floor:

φ = 1.0

Other floors: φ = 0.5 Due to the absence of original design calculation documents of the building, standard values have been used to calculate the dead loads and live loads. The volumetric weight of concrete has been assumed as 2500 kg/m3. Weights of the external and internal walls have been assumed as 0.3 t/m2 and 0.2 t/m2, respectively. The live load has been assumed as 300 kg/m2. The slab weights have been assumed as 558 kg/m2 and 382 kg/m2. The live load on the roof (inaccessible roof) has been assumed to be 0.5 KN/m2. 2.6.3 Coefficients and masses for building B The coefficients applicable in the case of the elementary school “Pascoli” from Tables 3.4 and 3.5 of the Italian Seismic Code [OPCM 3274, 2003] are as follows: Coefficients for destination of use: School:

Ψ0i = 0.70 (SLD) Ψ2i = 0.60 (SLU) Ψ0i = 0.70 (SLD)

Roofs:

Ψ2i = 0.35 (SLU) Coefficients for loads for different floors: Top floor:

φ = 1.0

Other floors: φ = 0.5 Dead loads and live loads were determined from the original design calculations of the building. The following are some of the important values used in calculating loads and masses. •

The volumetric weight of concrete used was 25 kN/m3.

11


•

The slab weights used for the first floor were 4.20 kN/m2, 4.10 kN/m2 3.90 kN/m2 or 3.80 kN/m2 depending on the location.

•

The slab weights used for the roof were 4.70 kN/m2, 4.20 kN/m2 or 4.10 kN/m2 depending on the location.

•

The dead loads of external and internal walls were 8.54 kN/m and 5.59 kN/m, respectively.

•

The dead and live loads of the storm water drains and parapet were 5.15 N/mm and 2.45 N/mm, respectively.

•

The live loads used for floor slabs of the building were 3.00 kN/m2 and 5.00 kN/m2 whereas, 2.68 kN/m2 was the live load used for the terrace.

2.7 Seismic Input for Structural Assessment The seismic input in the form of elastic response acceleration spectra have been defined for the three limit states: Limit State of Limited Damage (LS-DL), Limit State of Severe Damage (LS-DS) and Limit State of Collapse (LS-CO), as per § 11.2.5.2, § 3.2.2 and § 3.2.3 of the Italian Seismic Code [OPCM 3274, 2003]. In accordance with the correlation between design and assessment limit states in § 11.2.1, the elastic response spectrum for the Ultimate Limit State (SLU) is the spectrum for the Limit State of Severe Damage (LS-DS). The response spectrum for the Limit State of Limited Damage (LS-DL) is obtained by reducing the spectrum corresponding to the LS-DS by a factor of 2.5 and the response spectrum for the Limit State of Collapse (LS-CO) is obtained by scaling the spectrum of the LS-DS by a factor of 1.5 as per § 11.2.5.2 and § 3.2.6. As per Appendix A (Seismic Classification of the Italian towns) of the “criteria for identification of the seismic zones” of the Italian Seismic Code: Criteria [OPCM 3274, 2003], Building A is situated in Gallicano in the Lucca Province of Tuscany which is categorised as Seismic Zone 2. According to § 3.2.1 of the Italian Seismic Code [OPCM 3274, 2003], the peak horizontal ground acceleration (ag) corresponding to Soil Type A (rock) is 0.25g. As per § 11.2.5.1, § 2.5 and § 4.7 of the Italian Seismic Code: Buildings [OPCM 3274, 2003], the Importance Factor (γI) of the structure which houses a school is 1.2 (i.e. buildings which are important in terms of consequences, in the event of collapse). The soil category at the site of the school building has been considered as Soil Type B (shear wave velocity, Vs,30 = 630 m/s). As per Appendix A (Seismic Classification of the Italian towns) of the “criteria for identification of the seismic zones” of the Italian Seismic Code: Criteria [OPCM 3274, 2003], Building B is situated in Barga in the Lucca Province of Tuscany which is categorised as Seismic Zone 2. According to § 3.2.1 of the Italian Seismic Code [OPCM 3274, 2003], the peak horizontal ground acceleration (ag) corresponding to Soil Type A (rock) is 0.25g.

12


2

Horizontal Spectral Acceleration (m/sec)

1.6 SL di DL

1.4

SL di DS 1.2

SL di CO

1.0 0.8 0.6 0.4 0.2 0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Structural Period (sec)

Figure 2.5: Elastic horizontal acceleration response spectra for the three limit states

Horizontal Spectral Displacement (m

0.4 SL di DL

0.4

SL di DS 0.3

SL di CO

0.3 0.2 0.2 0.1 0.1 0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Structural Period (sec)

Figure 2.6: Elastic horizontal displacement response spectra for the three limit states

As per § 11.2.5.1, § 2.5 and § 4.7 of the Italian Seismic Code: Buildings [OPCM 3274, 2003], the Importance Factor (γI) of the structure which houses a school is 1.2 (i.e. buildings which are important in terms of consequences, in the event of collapse).

13


The soil category at the site of the school building has been considered as Soil Type B (shear wave velocity, Vs,30 = 680 m/s). The acceleration and displacement response spectra pertaining to the three limit states (valid for both buildings A and B) are illustrated in Figure 2.5 and Figure 2.6.

14

Chapter 3. Structural Modelling

3. STRUCTURAL MODELLING 3.1 Knowledge Levels and Permissible Analyses In accordance with § 11.2.3.3 and Table 11.1 (see Table 3.1 and Table 3.2) of the Italian Seismic Code: Buildings [OPCM 3274, 2003], on the basis of the information available about the structure, the lower middle school “Puccetti” has been graded as belonging to the ‘Adequate Knowledge Level’ (LC2). The geometry of the building were available from original design drawings verified by subsequent site survey. The structural details were available from original blue prints verified by a limited site survey of the main structural members. The structural details available from the drawings are not complete. Nominal values of material properties were obtained from the original design and limited in-situ destructive and non-destructive testing. About 14 drilled cores from ground floor and first floor columns were tested to determine the quality of concrete and this, approximately, makes up 25% of the total number of columns. In accordance with § 11.2.3.3 and Table 11.1 (see Table 3.1 and Table 3.2) of the Italian Seismic Code: Buildings [OPCM 3274, 2003], on the basis of the information available about the structure, the Elementary school “Pascoli” has been graded as belonging to the ‘Adequate Knowledge Level’ (LC2), as well. The geometry of the building was available from original design drawings verified by a successive site survey. The structural details were available from original blue prints verified by a limited site survey of the main structural members. The structural details available from the drawings are not complete. Nominal values of material properties have been obtained from the original design and limited in-situ destructive and non-destructive testing. With reference to Table 3.1 and Table 3.2, if a rigorous classification is to be applied, the absence of information on the present condition of the reinforcement steel in both the buildings should prompt a classification of Buildings A and B in the “Limited Knowledge Level” (LC1) category. But considering the quality and adequacy of the remaining information available and, acknowledging that the variability properties of steel is generally lesser than concrete, the buildings have been categorised in LC2 (i.e. adequate knowledge level). All methods of analysis (linear or non-linear and static or dynamic) are permitted as the structure belongs to the category LC2. No partial safety factors for materials (γm), have to be used in the analyses. 15


Table 3.1: Knowledge levels as a function of the information available and the consequent methods of the analyses permitted and partial material safety factors (Table 11.1translated from OPCM 3274: 2003)

Knowledge level LC1

Geometry From original design drawings with sample visual survey or complete new survey

LC2

LC3

Structural details Design simulated with norms pertaining to construction period of the structure and limited in-situ verification Incomplete construction details + limited in-situ verification or extensive in-situ verification Complete construction details + limited in-situ verification or exhaustive insitu verification

γm

Material properties Normal values in construction practice of the period of structure and limited in-situ tests

Methods of analysis Linear static or dynamic analyses

Increased

From original design specifications + limited in-situ tests or extensive in-situ tests From original test certificates + limited in-situ tests or exhaustive insitu tests

All

Constant

All

Decreased

Table 3.2: Definition of the survey and material test levels for buildings in reinforced concrete (Table 11.3a translated from OPCM 3274: 2003)

Limited verification Extensive verification Exhaustive verification

Survey (construction details) Tests (materials) For every type of primary element (Beam, column, etc.) Quality and layout of reinforcement 1 test on concrete specimen per steel is verified at least for 15% of the building floor, 1 reinforcement elements specimen per building floor Quality and layout of reinforcement 2 tests on concrete specimen per steel is verified at least for 35% of the building floor, 2 reinforcement elements specimen per building floor Quality and layout of reinforcement 3 tests on concrete specimen per steel is verified at least for 50% of the building floor, 3 reinforcement elements specimen per building floor

16


3.2

Structural Modelling of Building A

3.2.1 Lumped plasticity modelling A three dimensional, linear elastic, finite element model of the school building was created with a lumped plasticity approach using the structural analysis code SAP2000 (CSI, Berkeley). The model developed on SAP2000 was used to analyse the structure under a gravity load combination, to perform modal analysis and multi-modal response spectrum analyses for the three limit states. Plans of the all the levels and elevations of the frames are illustrated in Figure 3.2 through Figure 3.9.

Figure 3.1: 3D view of the SAP2000 model of the lower middle school "Puccetti"

The main assumptions made in the modelling and issues addressed are enumerated below: •

The compressive strength of concrete, f’c, was assumed to be 18 MPa and the yield strength of reinforcement steel, Fy, was assumed to be 440 MPa without any partial safety factors.

•

The uncracked (initial) stiffness of concrete, Ec, was calculated as using the formula proposed by Mander et al. [1988]: E c = 4700 f c' MPa

Eq. 3.1

The formula has been successively multiplied by a factor of 1.2 to account for ageing of concrete in the structure. The value of the initial stiffness has been estimated as 23928.5 MPa. The cracked concrete stiffness was considered to half of the value of the initial stiffness, i.e. 11964.25 MPa, in accordance with § 4.4 of the Italian Seismic Code: Buildings [OPCM 3274, 2003].

17


•

Three dimensional beam elements with six degrees of freedom were used to model columns and beams in the frame and shell elements with full shell behaviour were used to model the floor and roof slabs. The lengths of the elements correspond to the actual lengths of the members (i.e. they have not been sub-divided).

•

Soil-structure interaction has not been considered in the structural assessment and therefore the structure was analysed with base fixity.

•

Masses were lumped at the nodes of the model.

•

The internal dog-legged staircase has been incorporated as lumped masses at appropriate nodes.

•

The floor and roof slabs were incorporated in the model using shell elements. An equivalent section of the composite slab was estimated based on the geometry and material characteristics to define a flexible diaphragm. The equivalent thickness of the slab is calculated as

t=

X + mY A

Eq. 3.2

m=

Gs Gc

Eq. 3.3

where m is the modular ratio,

Gs and Gc are the shear modulus of steel and concrete, respectively. Xm3 is the actual volume of concrete in the slab from the topping and ribs and Ym3 is the volume of steel in the slab from the reinforcement steel of the ribs and the reinforcement mesh of the topping. The equivalent thickness of the slab with double ribs (Bitrave ®: 250 + 40 mm) and the slab with single ribs (Monotrave ®: 200 + 40 mm) have been estimated as 75 mm and 41 mm, respectively. •

The new classroom, which was an addition in 1980, has not been incorporated in the model because the structure is isolated from the original frame with construction gaps and a separate foundation. Neglecting the new structure would be a conservative measure, as the presence of beams immediately outside the new structure at the periphery of the original frame (at the same level of the new floor slab) would assist in a rather smooth transfer of lateral forces.

•

An external staircase, which is isolated from the main structure by means of construction gaps and a separate foundation, has also been neglected from the modelling.

18


Figure 3.2: Plan at -3030 mm level

Figure 3.3: Plan at ±0 mm level

19


9X

8X

6X

7X

5X 4X

3X

2X

1X 3Y 1Y

2Y

4Y

5Y

6Y

7Y

8Y

9Y

10Y

11Y

12Y

Figure 3.4: Plan at + 3170 mm level and frame numbering

Figure 3.5: Plan at + 6430 mm level

20




21


Figure 3.8: Section at y = 0 mm (Frame No: 1Y)

Figure 3.9: Section at x = 0 mm (Frame No.: 1X)

3.2.2 Distributed plasticity modelling A 3D, non-linear fibre element model of the building was developed on SeismoStruct (SeismoSoft, 2003) to perform the static non-linear pushover analysis. 3D, inelastic, beamcolumn elements have been used to model the frame. Steel cross braces have been used to model the flexible slab. The material of the braces is chosen so as to ensure that they remain elastic under lateral loading (Modulus of elasticity 9000 MPa, Yield strength – 105 MPa). The lateral elastic stiffness of the flexible diaphragm of equivalent thickness described in § 3.2.1 would be the axial stiffness of the brace. This is true only for square or nearly square slabs. Once the axial stiffness is calculated, the area of cross section and hence the diameter of a circular brace can be determined. The braces are connected to the nodes by means of joint elements to avoid moment transfer. An example is

22


illustrated in Appendix A showing the calculation of the equivalent thickness of a slab and consequently the brace diameter.

Figure 3.10: SeismoStruct model of the lower middle school "Puccetti"

3.3

Structural modelling of Building B

3.3.1 Lumped plasticity modelling A 3D, linear elastic, finite element model of the school building was developed using the structural analysis code SAP2000. The model developed on SAP2000 was used to analyse the structure under a gravity load combination, to perform a modal analysis and multi-modal response spectrum analyses for the three limit states. Plans of the all the levels and elevations of the frames are illustrated in Figure 3.12 though Figure 3.16. The main assumptions made in the modelling and issues addressed are enumerated below:

•

The compressive strength of concrete, f’c, was assumed to be 30 MPa and the yield strength of reinforcement steel, Fy, was assumed to be 440 MPa without any partial safety factors.

•

In a procedure similar to that described in § 3.2.1, the value of the initial stiffness has been estimated as 30891.55 MPa. The cracked concrete stiffness was considered to half of the value of the initial stiffness, i.e. 15445.78 MPa, in accordance with § 4.4 of the Italian Seismic Code: Buildings [OPCM 3274, 2003].

•

Three dimensional beam elements with six degrees of freedom were used to model columns and beams in the frame and shell elements with full shell behaviour were used to model the floor and roof slabs. The lengths of the elements correspond to the actual lengths of the members (i.e. they have not been sub-divided).

23


•

Soil-structure interaction has not been considered in the structural assessment and therefore the structure was analysed with base fixity.

•

Masses were lumped at the nodes of the model.

•

The two internal dog-legged staircases have been incorporated as lumped masses at appropriate nodes.

•

The parapets and storm water pipe masses were considered appropriately as distributed loads and moments in the model.

•

The equivalent thicknesses calculated for the various slabs in the structure are 174mm, 164mm, 78mm and 84mm, following the procedure described in § 3.2.1.

•

The reinforced concrete structural walls of the basement room have been modelled with shell elements (full shell behaviour) of thickness 200mm.

•

Since the structural mode periods were found to be closely spaced, the CQC (Complete Quadratic Combination) method was used for the modal combination in the multi-modal response spectrum analysis.

Figure 3.11: SAP2000 model of the elementary school "Pascoli"

24


Figure 3.12: Plan at 0mm level 3Y

8Y

9Y

14Y

11X 10X 9X 8X

7X 6X

5X 4X

3X 2X

1X

1Y

2Y

4Y

5Y

6Y

7Y

10Y

11Y

12Y

13Y

15Y

16Y

Figure 3.13: Plan at 3700mm level and frame numbering

25


Figure 3.14: Plan at 7400mm level

Figure 3.15: Section at Y = 6900mm

Figure 3.16: Section at X = 10200mm

26


3.3.2 Distributed plasticity modelling A 3D, non-linear fibre element model of the building was developed on SeismoStruct to perform the static non-linear pushover analysis. A plan view and a 3D view of the model are illustrated in Figure 3.17 and Figure 3.18. 3D, inelastic, beam-column elements have been used to model the frame. Every member was subdivided into four elements with shorter elements at the ends to accurately capture the inelastic behaviour of the structural components. The basement structural walls were modelled using frame elements rigidly connected to the adjacent nodes. Steel cross braces have been used to model the flexible slab. The material of the braces is chosen so as to ensure that they remain elastic under lateral loading (Modulus of elasticity – 30891.55 MPa, Yield strength - 105 MPa). The lateral elastic stiffness of the flexible diaphragm of equivalent thickness described in § 3.3.1. would be the axial stiffness of the brace. This is true for square or nearly square slabs. Once the axial stiffness is calculated, the area of cross section and hence the diameter of a circular brace can be determined. The braces are connected to the nodes by means of joint elements to avoid moment transfer. An example is presented in Appendix-1 showing the calculation of the equivalent thickness of a slab and consequently the brace diameter.

Figure 3.17: Plan view of SeismoStruct model of elementary school "Pascoli"

27


Figure 3.18: 3D view of the SeismoStruct model of elementary school "Pascoli"

28

Chapter 4. Discussion of Results

4. DISCUSSION OF RESULTS 4.1 Capacity Calculations Flexural and shear capacities of the beam and column sections (at the two ends and the middle), were computed from considerations of section equilibrium (refer to Appendix 2) and according to § 11.3.3 of the Italian Seismic Code: Buildings [OPCM 3274, 2003]. Flexural and shear capacities of the sections are a function of the axial load in the members. Axial forces due to gravity loads alone were considered to compute the capacity of the column sections. The capacities of the columns have been estimated in two orthogonal directions as there the layout of reinforcement is not symmetrical about both the horizontal axes. Each member is classified as either a “ductile” or “brittle” member based on the following logic:

•

The shear force obtained from the moment capacity at the ends of the member is compared with the shear capacity of the section.

•

If the shear capacity is found to be greater than the shear demand due to flexure, then the member is classified as a ‘ductile’ member. This implies that the member is capable of reaching its flexural capacity before failing in shear.

•

On the other hand, if the demand due to flexure is greater than the shear capacity of the section, the member is classified as ‘brittle’. This implies that the member will fail in a brittle fashion before reaching its flexural capacity.

According to § 11.2.2 and § 11.2.6.2, ductile members are verified in terms of deformation capacity, whereas the strength verification is carried out for brittle members. The verification for the Limit State of Collapse is performed in terms of ultimate deformations for the ductile members and in terms of ultimate strengths for brittle members (§ 11.2.2). The expression used to compute the ultimate deformation capacity in terms of chord rotation is equation A.1 from Eurocode 8 [prEN 1998-3:2003]:

29


θ um

⎡ max(0.01, ω ' ) ⎤ = 0.0172 ⋅ (0.3 ) ⎢ fc ⎥ γ el ⎣ max(0.01, ω ) ⎦ 1

0.175

υ

0.4

⎛

⎜ αρ sx ⎜ ⎛ LV ⎞ ⎜ ⎟ 25 ⎝ ⎝ h ⎠

f yw ⎞ ⎟ f c ⎟⎠

(1.3100 ρ d )

Eq. 4.1

Where, γel is 1.5 for primary and 1.0 for secondary elements; h is the depth of the cross section;

ν=

N bhf c

Eq. 4.2

Where, b is the width of the compression zone, N is the axial force positive for compression;

ω and ω’ are the mechanical reinforcement ratios for tension and compression of the longitudinal reinforcement, respectively;

fc is the estimated value of concrete compressive strength in MPa;

ρsx=Asx/bwsh is the ratio of transverse steel parallel to the direction x of loading (sh is the stirrup spacing);

LV is the shear span (LV =M/V);

ρd is the steel ratio of diagonal reinforcement, if any, in each diagonal direction; α is the confinement effectiveness factor that may be calculated as: s s ∑i⎟ α = ⎜⎜1 − h ⎟⎟⎜⎜1 − h ⎟⎟⎜⎜1 − ⎟ ⎝ 2bc ⎠⎝ 2hc ⎠⎝ 6hc bc ⎠ ⎛

⎞⎛

b ⎞

⎞⎛

Eq. 4.3

Where, bc and hc are the dimensions of the confined core inside the hoops; bi is the centre to centre spacing of longitudinal bars laterally restrained by a stirrup corner or a cross-tie along the perimeter of the cross section. In members without detailing for earthquake resistance the value given by the equation A.1 is divided by 1.2. Moreover, if stirrups are not closed with 135° hoops α is equal to zero. In the case of the lower middle school “Puccetti” building, adequate detailing is not provided. Stirrups are not closed with 135° hoops and neither is diagonal reinforcement provided, therefore the equation simplifies to:

θ um

⎡ max(0.01, ω ' ) ⎤ = fc ⎥ 0.0172 ⋅ (0.3 ) ⎢ γ el ⎣ max(0.01, ω ) ⎦ 1

υ

0.175

⎛ LV ⎞ ⎜ ⎟ ⎝ h ⎠

0.4

Eq. 4.4

For the Limit State of Severe Damage the chord rotation capacity is assumed as ¾ of that obtained for the Limit State of Collapse, as stated in § A.3.1.2 of the Eurocode 8, part 3. Capacities for the Limited Damage Limit State used in the verification are expressed in terms of yielding bending moments and chord rotation at yielding θy, evaluated as:

30


θ y = φy

0.2ε sy d b f y LV + α el + α sl 3 (d − d ' ) f c

Eq. 4.5

Where, the first two terms account for flexural and shear contributions, respectively and the third for anchorage slip of bars. αel = 0.00275 for beams and columns, d and d’ are the depths to the tension and compression reinforcement, respectively; and fy and fc are the estimated values of the steel tensile and concrete compressive strengths, respectively. 4.2 Modal Analysis The modal information pertaining to the structural model of Building A is reported in Table 4.1. The periods of vibration corresponding to the initial (uncracked or elastic) stiffness of concrete and cracked stiffness of concrete have been reported in the table along with the modal mass participation factors. Cumulative mass participation of above 85% (for Ux and Uy) is achieved in the first five modes. The third mode of vibration is strongly torsional. The first four mode shapes are shown in Figure 4.1. Table 4.1: Mode periods and mode mass participation factors of Building A

Mode

1

Period of vibration (sec) Uncracked Cracked concrete concrete stiffness stiffness 0.441 0.623

Modal participation mass ratios (%)

Cumulative participation mass ratios (%)

UX

UY

RZ

UX

UY

RZ

5.23

54.00

28.47

5.23

54.00

28.47

2

0.385

0.545

66.00

17.00

5.71

71.00

70.00

34.18

3

0.346

0.489

18.00

15.00

54.57

89.00

85.00

88.75

4

0.208

0.294

0.03

0.00

0.01

89.00

85.00

88.76

5

0.141

0.199

1.48

7.96

2.17

91.00

93.00

90.94

6

0.134

0.190

7.81

3.29

0.01

98.00

97.00

90.94

7

0.126

0.179

0.25

1.71

7.55

99.00

98.00

98.50

8

0.119

0.169

0.50

0.51

0.63

99.00

99.00

99.13

9

0.118

0.167

0.27

0.43

0.59

99.00

99.00

99.72

10

0.102

0.144

0.24

0.06

0.00

100.00

99.00

99.72

31


Mode shape (in plan)

3D view of mode shape

Figure 4.1: Fundamental mode shapes (1-4) of Building A from SAP2000

32


The modal information pertaining to the structural model of Building B is reported in Table 4.2. The periods of vibration corresponding to the initial (uncracked or elastic) stiffness of concrete and cracked stiffness of concrete have been reported in the table along with the modal mass participation factors. The mode periods are closely spaced. Cumulative mass participation of above 90% (for Ux,Uy and Rz) is achieved in the first three modes. Apparently none of the modes shapes are strongly torsional. The first three and sixth mode shapes are shown in Figure 4.2 and Figure 4.3. Table 4.2: Mode periods and mode mass participation factors of Building B

Mode

1

Period of vibration (seconds) Uncracked Cracked concrete concrete stiffness stiffness 0.373 0.527

Modal participation mass ratios (%)

Cumulative participation mass ratios (%)

UX

UY

RZ

UX

UY

RZ

50.00

0.03

43.00

50.00

0.03

43.00

2

0.351

0.496

0.06

91.00

0.00

50.00

91.00

43.00

3

0.340

0.481

42.00

0.03

50.00

92.00

91.00

92.00

4

0.206

0.292

0.00

0.02

0.00

92.00

91.00

92.00

5

0.177

0.251

0.02

0.00

0.20

92.00

91.00

92.00

6

0.143

0.202

4.72

0.74

1.57

97.00

92.00

94.00

7

0.142

0.201

0.88

5.12

0.12

98.00

97.00

94.00

8

0.136

0.193

1.95

0.03

5.59

100.00

97.00

100.00

9

0.135

0.191

0.00

2.28

0.00

100.00

99.00

100.00

10

0.121

0.171

0.00

0.00

0.00

100.00

99.00

100.00



Figure 4.2: First mode shape of Building B from SAP2000

33




Figure 4.3: Fundamental mode shapes (2, 3 and 6) of Building B from SAP2000

34


4.3

Methods of Analysis for Building A

4.3.1 Introduction In accordance with § 11.2.5.4 and § 4.5 of the Italian Seismic Code: Buildings [OPCM 3274, 2003], broadly, four methods of structural analysis are applicable in this case as the structure belongs to the “adequate knowledge level”. They are: static linear analysis, dynamic modal analysis, static non-linear and dynamic non-linear analysis. 4.3.2 Linear Static Analysis A static linear analysis is applicable only if the structure satisfies the ‘regularity’ criteria outlined in § 4.3.1 of the Italian Seismic Code: Buildings [OPCM 3274, 2003].

A building is considered to be “regular in plan” if the following conditions are met: 1. the configuration is compact and approximately symmetric in the two orthogonal directions, with regard to distribution of mass and stiffness; 2. the ratio between the sides of the rectangle circumscribing the building is less than 4; 3. any existing re-entrant corners or protrusions do not exceed 25% of the total length of the building in the direction concerned; 4. the floor slabs are considered to be infinitely rigid in their own plane with respect to the vertical elements. A building is considered to be “regular in height” if the following conditions are fulfilled: 5. all vertical resisting elements of the building (walls and frames) extend over the entire height of the structure; 6. mass and stiffness remain constant or reduce gradually, without abrupt changes, from the base to the top of the building (the variation from one floor to another must be within 20%); 7. the ratio between the capacity and the demand should not be significantly different for different floors (the ratio between the capacity and demand calculated for a generic floor should not vary by more than 20% for the same ratio calculated for another floor); 8. any reduction of section of the building has to be gradual and within the limit: the reduction in section at any floor can neither exceed 30% of the corresponding dimension of the ground floor, nor 10% of the corresponding dimension of the floor immediately below. The school building (in terms of its mass and rigidity) is not symmetrical about either of its horizontal axes and hence does not satisfy the criterion of ‘regularity in plan’ (criterion 1). Not all vertical load resisting systems in the structure extend till the top of the building and 35


hence the structure fails to satisfy the criterion of ‘regularity in height’ (criterion 5). Therefore, a static linear analysis is not applicable in the case of the lower middle school “Puccetti” building. Nevertheless, the structure has been analysed for a combination of gravity load as explained in the following section of this report § 4.3.3. 4.3.3 Gravity Load Assessment For the ultimate limit state the structure has been assessed for the following gravity load combination (obtained from § 2.3.2 and § 2.3.3 of Eurocode 2 UNI ENV 1992-1-1):

γ G G k + γ Q Qk

Eq. 4.6

Where:

γ G = partial safety factor for permanent load Gk = permanent action (or dead load)

γ Q = partial safety factor for the variable load Qk = variable load (or live load)

The partial safety factors applicable in the case of this building are γ G = 1.4 and γ Q = 1.5. On the whole, most of the structural members of the building are safe under the gravity load combination (i.e. capacity is greater than demand). There are very few elements for which the demand is greater than the capacity. Flexural demand is greater than flexural capacity for the first floor beam Y30403 and column C10603D and C40304 (structural elements are identified in building sections in Appendix C). Shear demand is greater than the shear capacity for the ground floor beam X20604, the first floor beams Y30504A, B, Y30106A and ridge beams Y50403A, B (refer Appendix C). 4.3.4 Dynamic Modal Analysis Dynamic modal analyses (linear multi-modal response spectrum analyses) have been carried out for the three limit states – Limited Damage, Severe Damage and Collapse. In accordance with § 4.5.3 of the Italian Seismic Code: Buildings [OPCM 3274, 2003], the response spectrum analysis has been performed by the first ten modes of vibration (cumulative modal mass participation factor greater than 85% and all modes with individual mass participation factor greater than 5%). The complete quadratic combination (CQC) rule has been utilised for modal combination as per the same section (§ 4.5.3) of the code, as the mode periods are closely spaced (in the range of a 10% difference between modes). Directional combination of the seismic action has been performed in accordance with § 4.3.3.5.1 of the Eurocode 8 [prEN 1998-1:2003], using the sum of the square root of squares rule.

36


Flexural demands at two ends and centre of each member is compared with the flexural capacities to determine the ρ ratios. As per § 11.2.5.4, the ratio (ρmax/ρmin) between the maximum and minimum values of ρ for ρ >1, has to be less than 2. The ρmax/ρmin value should not exceed 2. The ρmax vales and ρmax/ρmin values for the three limit states analysed here are tabulated in Table 4.3. From the reported values, it is evident that the modal dynamic analysis is not applicable in the case of the lower middle school “Puccetti” as the ρmax/ρmin values exceed 2 for all the limit states and the ρmax values are higher than 7 for the Limit States of Severe Damage and Collapse. At this point, it is important to mention that the maximum values of ρ and the maximum of the ρmax/ρmin ratio occur in the columns of the ground floor. Barring a single beam of the first floor slab only in the Limit State of Collapse, all the beams of the structure have ρ values less than 1. Table 4.3: ρmax/ρmin ratios for the three limit states

ρmax

ρmax

(beams)

(columns)

Limited damage

1, has to be less than 2. The ρmax/ρmin value should not exceed 2. The ρmax vales and ρmax/ρmin values for the three limit states analysed here are tabulated in Table 4.8. From the reported values, it is evident that the modal dynamic analysis is not applicable in the case of the elementary school “Pascoli” as the ρmax/ρmin values and the ρmax values for all the limit states are excessively high. Table 4.8: ρmax/ρmin ratios for the three limit states

ρmax

ρmax

(beams)

(columns)

Limited damage

5.9

8.8

8.8

Severe damage

15.6

21.9

21.4

Collapse

22.0

32.0

32.0

Limit State

ρmax/ρmin

4.4.4 Non-Linear Pushover Analysis According to § 4.5.4.1 of the Italian Seismic Code: Buildings [OPCM 3274, 2003], the static non-linear analysis is a procedure where a set of increasing horizontal forces are applied onto the structure up to its ultimate capacity. As per § 4.5.4.2, two different lateral load distributions are applied to the centre of gravity of the structure and they are:

•

Load distribution proportional to the mass (distribution 1)

•

Load distribution proportional to the product of the mass and the modal deformation of the first mode of vibration of the structure (distribution 2)

The total lateral load that has been used for the load distribution is 10,000 KN. The load has been distributed in height and the corresponding load at each floor is then distributed in plan at the beam-column joints proportional to the tributary mass at these nodes. Table 4.9 shows the mass proportional load distribution which is the same for both the horizontal directions – x and y. Table 4.10 and Table 4.11 tabulate the load distribution proportional to the product of the masses and mode shapes of the first mode of vibration for the x-direction and y-direction respectively. In this case of this building, the modal coordinates are the same in both directions therefore the same mass distribution was used for the pushover in each direction.

43


The pushover analysis is performed using the non-linear programme SeismoStruct (version 3.0) where the lateral load is increased step-by-step until a target displacement is reached. The pushover analysis was performed separately in the x-direction and the y-direction. The pushover analyses were performed to different maximum displacements and they have been reported in Table 4.12. Table 4.9: Load distribution 1 - Mass proportional Load distribution proportional to the mass (1) SLU Floor

Mass (Tonnes)

Floor mass/Total mass

Lateral Force (N)

Second Floor

937.34

0.44

4366402.25

Ground Floor

1209.37

0.56

5633597.75

Σ

2146.71

1.00

10000000

Table 4.10: Load distribution 2 - Proportional to product of mass and mode shape (X direction) Load distribution proportional to the mode - X direction (2a) SLU miφi miφi2 m i φ i 2 /m i φ i Lateral Force (N) Mass (Tonnes) m i Modal Coordinates φ i Floor Second Floor 937.34 1.00 937.34 937.34 0.58 5762285.36 Ground Floor 1209.37 0.57 689.34 392.92 0.42 4237714.64 Σ 2146.71 1626.68 1330.26 1.00 10000000.00 Γ 1.22

Table 4.11: Load distribution 2 - Proportional to product of mass and mode shape (Y direction) Load distribution proportional to the mode - Y direction (2b) SLU miφi miφi2 m i φ i 2 /m i φ i Lateral Force (N) Mass (Tonnes) m i Modal Coordinates φ i Floor Second Floor 937.34 1.00 937.34 937.34 0.58 5762285.36 Ground Floor 1209.37 0.57 689.34 392.92 0.42 4237714.64 Σ 2146.71 1626.68 1330.26 1.00 10000000.00 Γ 1.22

The pushover analysis was performed for the following cases: Table 4.12: Summary of pushover analyses performed Maximum Direction

Load

Displacement (mm)

X Y

Displacement (actual pushover curve) corresponding to Limit State (mm) Limited

Severe

Damage

Damage

Collapse

Distribution 1

400.35

34.2

85.5

128.2

Distribution 2

343.99

37.9

94.8

142.2

Distribution 1

351.72

32.9

82.1

132.2

Distribution 2

337.00

37.7

94.3

141.5

44


It must be noted here that since the masses corresponding to the two limit states SLD and SLU and the structural mode periods of the models with these two masses were very close, the model with SLU mass was used to perform all the pushover analyses. A comparison of the pushover curves (MDOF system) for load distributions 1 and 2 in the xdirection is shown in Figure 4.7. The procedure of obtaining the forces in the structure corresponding to the three limit states using the capacity curves is demonstrated for one of the cases: pushover in the X-direction and load distribution 1. The procedure involves the estimation of equivalent SDOF and bilinear systems from the capacity curve to determine the yield and maximum displacements. 8000000 7000000

Total Base Shear (N)

6000000 5000000 4000000 3000000 2000000 SLU_X_1

1000000

SLU_2_X 0 0

50

100

150

200

250

300

350

400

450

Displacement of Node 301 (mm)

Figure 4.7: Comparison of capacity curves for load distributions 1 and 2 applied in the x-direction

The coefficient of participation, Γ factor is computed using the equation 4.7 of § 4.5.4.3 of the Italian Seismic Code: Buildings [OPCM 3274, 2003]. Table 4.13: Parameters required to compute Γ factor SLU Mass (Tonnes) m i Modal Coordinates φ i Floor Second Floor 937.34 1.00 Ground Floor 1209.37 0.57 Σ 2146.71

miφi

miφi2

m i φ i 2 /m i φ i

937.34 689.34 1626.68 Γ

937.34 392.92 1330.26 1.22

0.58 0.42 1.00

From the capacity curve for the multi degree-of-freedom (MDOF) system, the coordinates for the capacity curve of the equivalent single degree-of-freedom (SDOF) is obtained by

45


factoring the displacements and base shears by Γ as per equation 4.8 of § 4.5.4.3 of the code. Here F* and d* represent the force and displacement of the equivalent SDOF system. The capacity curve of the equivalent SDOF system is illustrated along with the capacity curve of the MDOF system in Figure 4.8. 8000000 7000000


6000000 5000000 4000000 3000000 2000000 MDOF

1000000

SDOF 0 0

100

200

300

400

500


Figure 4.8: Comparison of the MDOF and SDOF capacity curves for the structure

The next step involves the construction of an idealised elastic-perfectly plastic forcedisplacement relationship (procedure adopted from ANNEX B of Eurocode 8 [prEN19981:2003]. The maximum base shear of the equivalent SDOF system ( Fy* ) and the corresponding displacement ( d m* ) are identified. The yield displacement, d *y is computed using the equation 4.9, where E m* is computed from the area under the equivalent SDOF system curve. The equivalent bilinear curve is illustrated in Figure 4.9. Fy* = 5834158 N, d m* = 69.81 mm, E m* = 3133935908.17 Nmm and d *y = 32.18 mm.

The period of vibration of the equivalent SDOF system, T * is calculated by equation 4.8 in § Fy* 4.5.4.3, where m * is Σmiφi , (i.e. 1626.68) from Table 4.13, k * is * therefore, T * = 0.59 dy seconds. This T * is compared with Tc of Table 3.1 of § 3.2.3 of the code. The value of Tc for soil category B is 0.5 seconds, and since T * > Tc , maximum displacement of the equivalent system according to equation 4.10 of § 4.5.4.4 is calculated as follows for the different limit states.

46


7000000

5000000

4000000 3000000

Yield displ.

2000000

1000000

d*m


6000000

0 0

50

100

150

200

250

300

350


Figure 4.9: Equivalent SDOF and bilinear systems

The same equivalent period T * is used to read the values of S De (T * ) from different displacement spectra for the three limit states: Limit States of Limited Damage, Severe Damage and Collapse for the SDOF system. Therefore, * d max = 28.0 mm for Limit State of Limited Damage, * d max = 69.9 mm for Limit State of Severe Damage and * d max = 104.8 mm for Limit State of Collapse

The maximum displacement of the equivalent SDOF system is then converted to the maximum displacement of the MDOF system by multiplying with the factor Γ (equation 4.12). Therefore,

d max = 34.2 mm for Limit State of Limited Damage, d max = 85.5 mm for Limit State of Severe Damage and d max = 128.2 mm for Limit State of Collapse For the structural verification of the elements, all the member actions except shear forces are obtained at the maximum displacement d max corresponding to each limit state. If the maximum displacement of a given limit state is before the peak of the pushover curve, then the shear force corresponding to the maximum displacement of that limit state is used. . If the 47


maximum displacement of a given limit state is beyond the peak of the pushover curve, then the shear force corresponding to the peak is used. 4.5 Discussion of Results of Static-Non-Linear Analyses – Building A The results of the non-linear, static pushover analysis performed using the code SeismoStruct is discussed in this section. The classification of structural elements into “ductile” and “brittle” for each limit state is elaborated in the appendices.

It is important to mention here that the pushover analysis in the y-direction could not be performed up to the displacement limit required by the code, i.e. 150% of d max due to the apparent failure of some structural elements. Therefore, in the global Y-direction the structure could not be verified for the severe damage (SL-DS) and collapse limit states (SL-CO) for either of the load combinations. 4.5.1 Limit State of Limited Damage (SL-DL)

4.5.1.1 Pushover direction: X, Load distribution: 1 Foundation level: Some beams of this level do not comply with the requirement of the limit state for flexural capacity with a maximum flexural demand to capacity ratio of 1.2. All brittle beams and ductile beams comply with limit state requirements for shear capacity and rotation capacity, respectively. All the columns comply with the limit state requirements for flexural capacity. All the columns are ductile and comply with the limit state requirements of rotation demand. Ground floor level: A number of beams of this floor fail to meet the criterion for flexural capacity. The maximum flexural demand to capacity ratio is 2.0. The maximum ratio for rotation demand to capacity for ductile beams is 1.83 and the maximum shear demand to capacity for brittle beam is 1.43.

A number of columns of the ground floor do not comply with the requirements for flexural and rotation capacities for the limit state. The maximum flexural demand to capacity ratio is 1.6. All the columns are ductile and the maximum ratio for rotation demand to capacity for ductile columns is 1.78. First floor level: A few beams of this level do not comply with the flexural capacity requirements for the limit state with a maximum flexural demand to capacity ratio of 1.1. The maximum ratio of rotation demand to capacity is 1.06. Few columns of this level do not comply with the limit state requirements of flexural capacity. The maximum flexural demand to capacity ratio is 1.2. All the columns are ductile and few columns fail to comply with the limit state requirements for rotation capacity with a maximum rotation demand to capacity ratio of 1.71. Roof level 1: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Few columns are brittle.

48


Roof level 2: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Except for two, all columns are brittle.

4.5.1.2 Pushover direction: X, Load distribution: 2 Foundation level: A couple of beams of this level do not comply with the requirement of the limit state for flexural capacity with a maximum flexural demand to capacity ratio of 1.1. All brittle beams and ductile beams comply with limit state requirements for shear capacity and rotation capacity, respectively. All the columns are ductile and they comply with the limit state requirements of flexural and rotation capacities. Ground floor level: A number of beams of this floor fail to meet the criterion for flexural capacity, rotation capacity and shear capacity. The maximum flexural demand to capacity ratio is 2.0. The maximum ratio for rotation demand to capacity for ductile beams is 2.09 and the maximum shear demand to capacity for brittle beam is 1.44.

A number of columns of the ground floor do not comply with the requirements for flexural capacity, rotation capacity and shear capacity for the limit state. The maximum flexural demand to capacity ratio is 1.6. All the columns are ductile and the maximum ratio for rotation demand to capacity for ductile columns is 1.75. First floor level: A few beams of this level do not comply with the flexural capacity requirements for the limit state with a maximum flexural demand to capacity ratio of 1.3. All the brittle beams comply with the limit state requirements for shear capacity. The maximum rotation demand to capacity ratio is 1.29.

A number of columns of this level fail to satisfy the limit state requirements of flexural capacity with the maximum flexural demand to capacity ratio being 1.3. All the columns are ductile with many of them having rotation capacity to demand ratios greater than one (maximum ratio of 1.74). Roof level 1: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Few columns are brittle. Roof level 2: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Except for two, all columns are brittle.

4.5.1.3 Pushover direction: Y, Load distribution: 1 Foundation level: All beams and columns are ductile and comply with the requirements of the limit state for flexural capacity and rotation capacity. Ground floor level: A number of beams of this floor fail to meet the criterion for flexural capacity, rotation capacity and shear capacity. The maximum flexural demand to capacity ratio is 2.0. All the brittle beams comply with the limit state requirements for shear capacity. A number of ductile beams do not satisfy the limit state requirements for rotation capacity with the maximum rotation demand to capacity ratio being 4.22. 49


A number of columns of the ground floor do not comply with the requirements for flexural capacity for the limit state. The maximum flexural demand to capacity ratio is 1.3. Two columns are brittle and the maximum ratio for shear demand to capacity for brittle columns is 1.02. A number of ductile columns do not comply with the limit state requirements for rotation capacity with the maximum rotation demand to capacity ratio being 3.71. First floor level: All beams of this level comply with the flexural capacity requirements for the limit state excepting two (flexural demand to capacity ratio of 1.5). All the brittle beams comply with the shear capacity requirement of the limit state. A few ductile beams do not comply with the limit state requirements of rotation capacity with the maximum demand to capacity being 3.48. A few columns of this level do not comply with the limit state requirements of flexural capacity with the maximum ratio of flexural demand to capacity being 1.3. All the columns are ductile. A number of ductile columns do not comply with the limit state requirements for rotation capacity with the maximum rotation demand to capacity ratio being 3.73. Roof level 1: All the beams of this level meet the limit state requirements for flexural, rotation and shear capacities. All columns except one comply with the limit state requirements for flexural capacity (demand to capacity ratio: 1.1). Excepting one, all columns are brittle and they satisfy the limit state requirements for rotation or shear capacity. The rotation demand to capacity ratio for the ductile column is 1.23. Roof level 2: All columns except one comply with the limit state requirements for flexural capacity (demand to capacity ratio: 1.0). Excepting one, all columns are brittle and they satisfy the limit state requirements for rotation or shear capacity. The rotation demand to capacity ratio for the ductile column is 1.

4.5.1.4 Pushover direction: Y, Load distribution: 2 Foundation level: All beams and columns are ductile and comply with the requirements of the limit state for flexural capacity and rotation capacity. Ground floor level: A number of beams of this floor fail to meet the criterion for flexural capacity, rotation capacity and shear capacity. The maximum flexural demand to capacity ratio is 2.1. All the brittle beams comply with the limit state requirements for shear capacity. A number of ductile beams do not satisfy the limit state requirements for rotation capacity with the maximum rotation demand to capacity ratio being 5.01.

A number of columns of the ground floor do not comply with the requirements for flexural capacity for the limit state. The maximum flexural demand to capacity ratio is 1.2. Two columns are brittle and the maximum ratio for shear demand to capacity for brittle columns is 1.01. A number of ductile columns do not satisfy the limit state requirements for rotation capacity with the maximum rotation demand to capacity ratio being 4.39. First floor level: All beams of this level comply with the flexural capacity requirements for the limit state excepting two (flexural demand to capacity ratio of 1.6). All brittle beams comply with the shear capacity requirements of the limit state. A few ductile beams do not 50


comply with the limit state requirements of rotation capacity with the maximum demand to capacity being 4.39. A few columns of this level do not comply with the limit state requirements of flexural capacity with the maximum ratio of flexural demand to capacity being 1.3. All the columns are ductile. A number of ductile columns do not comply with the limit state requirements for rotation capacity with the maximum rotation demand to capacity ratio being 4.42. Roof level 1: All the beams of this level meet the limit state requirements for flexural, rotation and shear capacities. All columns except two comply with the limit state requirements for flexural capacity (demand to capacity ratio: 1.1). Excepting one, all columns are brittle and they satisfy the limit state requirements for rotation or shear capacity. The rotation demand to capacity ratio for the ductile column is 1.36. Roof level 2: All columns except one comply with the limit state requirements for flexural capacity (demand to capacity ratio: 1.0). Excepting one, all columns are brittle and they satisfy the limit state requirements for rotation or shear capacity. The rotation demand to capacity ratio for the ductile column is 1.95. 4.5.2 Limit State of Severe Damage (SL-DS)

4.5.2.1 Pushover direction: X, Load distribution: 1 Foundation level: Some beams of this floor fail to meet the limit state requirement for flexural capacity with a maximum flexural demand to capacity ratio of 1.6. All the ductile beams comply with the limit state requirements of rotation capacity. Some columns of this floor fail to meet the limit state requirement for flexural capacity with a maximum flexural demand to capacity ratio of 1.3. All the columns are ductile and the maximum rotation demand to capacity ratio is 1.03. Ground floor level: A large number of beams of this floor fail to meet the criterion for flexural capacity. The maximum flexural demand to capacity ratio is 2.6. The maximum ratio of rotation demand to capacity for ductile beams is 1.52. All the brittle beams comply with the limit state requirements for shear capacity except one with a shear demand to capacity ratio of 1.64.

A number of columns of the ground floor do not comply with the limit state requirements for flexural capacity. The maximum flexural demand to capacity ratio is 1.7. All the columns are ductile and a number of them do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 1.60. First floor level: Most of the beams of this level comply with the flexural capacity requirements for the limit state. The maximum flexural demand to capacity ratio for the beams is 1.6. All the beams satisfy the conditions for rotation and shear capacity.

A number of columns of this level do not comply with the limit state requirements of flexural capacity with the maximum flexural demand to capacity ratio being 1.6. All the columns are ductile and a number of them do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 1.50. 51


Roof level 1: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Few columns are brittle. Roof level 2: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Except for two, all the columns are brittle.

4.5.2.2 Pushover direction: X, Load distribution: 2 Foundation level: Some beams of this floor fail to meet the limit state requirement for flexural capacity with a maximum flexural demand to capacity ratio of 1.6. All the ductile beams comply with the limit state requirements of rotation capacity. Some columns of this floor fail to meet the limit state requirement for flexural capacity with a maximum flexural demand to capacity ratio of 1.2. All the columns are ductile and comply with limit state requirements for rotation capacity. Ground floor level: A large number of beams of this floor fail to meet the criterion for flexural capacity. The maximum flexural demand to capacity ratio is 2.6. A number of ductile beams fail to comply with rotation requirements of the limit state and the maximum ratio of rotation demand to capacity is 1.53. All the brittle beams comply with the limit state requirements for shear capacity except one with a shear demand to capacity ratio of 1.61.

A number of columns of the ground floor do not comply with the limit state requirements for flexural capacity. The maximum flexural demand to capacity ratio is 1.7. All the columns are ductile and a number of them do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 1.62. First floor level: Most of the beams of this level comply with the flexural capacity requirements for the limit state. The maximum flexural demand to capacity ratio for the beams is 1.6. All the brittle beams satisfy the conditions for shear capacity. The maximum rotation demand to capacity ratio is 1.09.

A number of columns of this level do not comply with the limit state requirements of flexural capacity with the maximum flexural demand to capacity ratio being 1.6. All the columns are ductile and a number of them do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 1.58. Roof level 1: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Few columns are brittle. Roof level 2: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Except for two, all the columns are brittle.

4.5.2.3 Pushover direction: Y, Load distribution: 1 Foundation level: All the beams meet the limit state requirement for flexural capacity except for one with a flexural demand to capacity ratio of 1.3. All the ductile and brittle beams comply with the limit state requirements of rotation and shear capacity, respectively. Some columns of this floor fail to meet the limit state requirement for flexural capacity with a

52


maximum flexural demand to capacity ratio of 1.1. All the columns are ductile and meet the limit state requirement for rotation capacity. Ground floor level: A large number of beams of this floor fail to meet the criterion for flexural capacity. The maximum flexural demand to capacity ratio is 2.7. The maximum ratio of rotation demand to capacity for ductile beams is 2.49. All the brittle beams comply with the limit state requirements for shear capacity except one with a shear demand to capacity ratio of 1.64.

A number of columns of the ground floor do not comply with the limit state requirements for flexural capacity. The maximum flexural demand to capacity ratio is 1.3. A number of ductile columns do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 2.85. Out of two brittle columns one of them does not comply with the limit state requirement of shear capacity with a demand to capacity ratio of 1.53. First floor level: Most of the beams of this level comply with the flexural capacity requirements for the limit state. The maximum flexural demand to capacity ratio for the beams is 2.0. One beam does comply with the requirements of shear capacity with a demand to capacity ratio of 1.19. A single beam does not comply with the limit state requirement of rotation capacity with a demand to capacity ratio of 1.92.

A number of columns of this level do not comply with the limit state requirements of flexural capacity with the maximum flexural demand to capacity ratio being 1.4. All the columns are ductile and a number of them do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 2.65. Roof level 1: A few beams do not comply with the limit state requirements of flexural capacity with a maximum demand to capacity ratio of 1.1. All the beams and columns of this level meet the limit state requirements for rotation and shear capacities. Except for one column, all are brittle. Roof level 2: All the beams of this level meet the limit state requirements for flexural, rotation and shear capacities. Except for a single column all the columns meet the limit state requirements for flexural capacity. The maximum flexural demand to capacity is 1.1. Except for two, all the columns are brittle. All the ductile and brittle columns comply with the limit state requirements for rotation and shear capacity, respectively.

4.5.2.4 Pushover direction: Y, Load distribution: 2 Foundation level: Except for one beam all the beams meet the limit state requirement for flexural capacity with a maximum flexural demand to capacity ratio of 1.1. A single column of this floor fails to meet the limit state requirement for flexural capacity with a flexural demand to capacity ratio of 1.0. All the columns and beams are ductile and meet the limit state requirement for rotation capacity. Ground floor level: A large number of beams of this floor fail to meet the criterion for flexural capacity. The maximum flexural demand to capacity ratio is 2.8. The maximum ratio 53


of rotation demand to capacity for ductile beams is 2.53. All the brittle beams comply with the limit state requirements for shear capacity. A number of columns of the ground floor do not comply with the limit state requirements for flexural capacity. The maximum flexural demand to capacity ratio is 1.3. A number of ductile columns do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 2.91. Out of two brittle columns one of them does not comply with the limit state requirement of shear capacity with a demand to capacity ratio of 1.26. First floor level: Most of the beams of this level comply with the flexural capacity requirements for the limit state. The maximum flexural demand to capacity ratio for the beams is 2.1. One beam does not comply with the requirements of shear capacity with a demand to capacity ratio of 1.27. A couple of beams do not comply with the limit state requirement of rotation capacity with a demand to capacity ratio of 2.16.

A number of columns of this level do not comply with the limit state requirements of flexural capacity with the maximum flexural demand to capacity ratio being 1.4. All the columns are ductile and a number of them do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 2.71. Roof level 1: A couple of columns do not comply with the limit state requirements of flexural capacity with a maximum demand to capacity ratio of 1.1. All the beams and columns of this level meet the limit state requirements for flexure, rotation and shear capacities. Except for one column, all are brittle. Roof level 2: All the beams of this level meet the limit state requirements for flexural, rotation and shear capacities. Except for a single column all the columns meet the limit state requirements for flexural capacity. The flexural demand to capacity of this column is 1.1. Except for two, all the columns are brittle and all comply with the limit state requirements for shear capacity. A single ductile column does not comply with the limit state requirement for rotation capacity with a demand to capacity ratio of 1.14. 4.5.3

Limit State of Collapse (SL-CO)

4.5.3.1 Pushover direction: X, Load distribution: 1 Foundation level: Some beams of this floor fail to meet the limit state requirement for flexural capacity with a maximum flexural demand to capacity ratio of 1.7. All the brittle and ductile beams comply with the limit state requirements for shear and rotation capacity, respectively. Some columns fail to meet the limit state requirement for flexural capacity with a maximum flexural demand to capacity ratio of 1.4. All the columns are ductile and the maximum rotation demand to capacity ratio is 1.03. Ground floor level: A large number beams of this floor fail to meet the criteria for flexural capacity, rotation capacity and shear capacity. The maximum flexural demand to capacity ratio is 2.8. All the brittle beams comply with the limit state requirements for shear capacity

54


except one brittle beam with a shear demand to capacity ratio of 1.64. The maximum rotation demand to capacity for ductile beams is 1.57. A large number of columns of the ground floor do not comply with the limit state requirements for flexural capacity. The maximum flexural demand to capacity ratio is 1.7. All the columns are ductile and a number of them do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 1.56. First floor level: Most of the beams of this level comply with the flexural capacity requirements for the limit state. The maximum flexural demand to capacity ratio for the beams is 1.7. All the beams satisfy the conditions for rotation and shear capacity.

A number of columns of this level do not comply with the limit state requirements of flexural capacity with the maximum flexural demand to capacity ratio being 1.6. All the columns are ductile and comply with the limit state requirements for the rotational capacity. Roof level 1: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Few columns are brittle. Roof level 2: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Except for two, all the columns are brittle.

4.5.3.2 Pushover direction: X, Load distribution: 2 Foundation level: Some beams of this floor fail to meet the limit state requirement for flexural capacity with a maximum flexural demand to capacity ratio of 1.7. All the brittle and ductile beams comply with the limit state requirements for shear and rotation capacity, respectively. Some columns fail to meet the limit state requirement for flexural capacity with a maximum flexural demand to capacity ratio of 1.3. All the columns comply with the requirements of the limit state for rotation capacity. Ground floor level: A large number beams of this floor fail to meet the criterion for flexural capacity. The maximum flexural demand to capacity ratio is 2.8. A number of ductile beams fail to meet the limit state requirements for rotation capacity with a maximum rotation demand to capacity ratio of 1.56. All the brittle beams comply with the limit state requirements for shear capacity except one brittle beam with a shear demand to capacity ratio of 1.61.

A large number of columns of the ground floor do not comply with the limit state requirements for flexural capacity. The maximum flexural demand to capacity ratio is 1.7. All the columns are ductile and a large number of columns fail to comply with the limit state requirements for rotation capacity with a maximum rotation demand to capacity ratio of 1.64. First floor level: Most of the beams of this level comply with the flexural capacity requirements for the limit state. The maximum flexural demand to capacity ratio for the beams is 1.8. All the brittle beams satisfy the conditions for shear capacity. The maximum rotation demand to capacity ratio for ductile beams is 1.07.

55


A large number of columns of this level do not comply with the limit state requirements of flexural capacity with the maximum flexural demand to capacity ratio being 1.6. All the columns are ductile and a number of columns fail to comply with the limit state requirements for rotation capacity with a maximum rotation demand to capacity ratio of 1.54. Roof level 1: All the beams of this level meet the limit state requirements for flexural, rotation and shear capacities. A single column fails to comply with the limit state requirement for flexural capacity with a demand to capacity ratio of 1.1. Few columns are brittle. All the ductile or brittle columns comply with the limit state requirements for rotation or shear capacity, respectively. Roof level 2: All the beams and columns of this level meet the limit state requirements for flexural, rotation and shear capacities. Except for two, all the columns are brittle.

4.5.3.3 Pushover direction: Y, Load distribution: 1 Foundation level: A single beam of this floor fails to meet the limit state requirement for flexural capacity with a flexural demand to capacity ratio of 1.3. All brittle and ductile beams comply with the limit state requirements for shear and rotation capacity, respectively. Some columns fail to meet the limit state requirement for flexural capacity with a maximum flexural demand to capacity ratio of 1.0. All the columns are ductile and comply with the limit state rotation requirements. Ground floor level: A large number beams of this floor fail to meet the criteria for flexural capacity. The maximum flexural demand to capacity ratio is 2.8. All the brittle beams comply with the limit state requirements for shear capacity. A number of ductile beams fail to meet the limit state requirements. The maximum rotation demand to capacity for ductile beams is 2.68.

A large number of columns of the ground floor do not comply with the limit state requirements for flexural capacity. The maximum flexural demand to capacity ratio is 1.3. A number of them do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 2.99. Two columns are brittle and one of them does not comply with the limit state requirements for shear capacity. The shear demand to capacity ratio is 1.53. First floor level: A number beams of this level do not comply with the flexural capacity requirements for the limit state. The maximum flexural demand to capacity ratio for the beams is 2.1. Except for two beams all the others comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 2.07. One beam fails to comply with the limit state requirements of shear capacity with a shear demand to capacity ratio of 1.19.

A large number of columns of this level do not comply with the limit state requirements of flexural capacity with the maximum flexural demand to capacity ratio being 1.4. A large number of columns fail to meet the limit state requirements for rotation with the maximum rotation demand to capacity being 2.79. 56


Roof level 1: All the beams of this level meet the limit state requirements for flexural, rotation and shear capacities. Two columns fail to meet the limit state requirements for flexural capacity with a maximum demand to capacity ratio of 1.1. Except for one column, all are brittle and they comply with limit state requirements for shear and rotation. Roof level 2: All the beams of this level meet the limit state requirements for flexural, rotation and shear capacities. One column fails to meet the limit state requirements for flexural capacity with a demand to capacity ratio of 1.1. Except for one column, all are brittle and comply with limit state requirement for shear. The ductile column fails to comply with the limit state requirement for rotation with a demand to capacity ratio of 1.01.

4.5.3.4 Pushover direction: Y, Load distribution: 2 Foundation level: A single beam of this floor fails to meet the limit state requirement for flexural capacity with a flexural demand to capacity ratio of 1.1. All the beams are ductile and comply with the limit state requirements for rotation capacity. All the columns meet the limit state requirement for flexural and rotation capacity. Ground floor level: A large number beams of this floor fail to meet the criteria for flexural capacity. The maximum flexural demand to capacity ratio is 2.8. All the brittle beams comply with the limit state requirements for shear capacity. A number of ductile beams fail to meet the limit state requirements. The maximum rotation demand to capacity for ductile beams is 2.70.

A large number of columns of the ground floor do not comply with the limit state requirements for flexural capacity. The maximum flexural demand to capacity ratio is 1.3. A number of them do not comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 3.02. Two columns are brittle and one of them does not comply with the limit state requirements for shear capacity. The shear demand to capacity ratio is 1.24. First floor level: A number beams of this level do not comply with the flexural capacity requirements for the limit state. The maximum flexural demand to capacity ratio for the beams is 2.2. Except for two beams all the others comply with the limit state requirements of rotation capacity with a maximum rotation demand to capacity ratio of 2.27. One beam fails to comply with the limit state requirements of shear capacity with a shear demand to capacity ratio of 1.27.

A large number of columns of this level do not comply with the limit state requirements of flexural capacity with the maximum flexural demand to capacity ratio being 1.4. A large number of columns fail to meet the limit state requirements for rotation with the maximum rotation demand to capacity being 2.81. Roof level 1: All the beams of this level meet the limit state requirements for flexural, rotation and shear capacities. Two columns fail to meet the limit state requirements for flexural capacity with a maximum demand to capacity ratio of 1.1. Except for one column, all are brittle and comply with limit state requirements for shear and rotation. 57


Roof level 2: All the beams of this level meet the limit state requirements for flexural, rotation and shear capacities. One column fails to meet the limit state requirements for flexural capacity with a demand to capacity ratio of 1.1. Except for one column, all are brittle and comply with limit state requirement for shear. The ductile column fails to comply with the limit state requirement for rotation with a demand to capacity ratio of 1.19. 4.6 Discussion of Results of Static-Non-Linear Analyses for Building B The results of the non-linear, static pushover analysis performed using the code SeismoStruct is discussed in this section. The classification of structural elements into “ductile” and “brittle” for each limit state is elaborated in the Appendix D.

Table 4.14 reports the maximum values of demand to capacity ratios in flexure, shear and rotation for ground and first floor beams and columns for all the three limit states. The elements that have not conformed to the limit state requirements of shear and rotation capacity are identified in Appendix E of this report. From Table 4.14 and illustrations in Appendix E, the following inferences can be drawn:

•

For all the three limit states and for pushover analyses in both x and y directions, a number of beams and columns fail to meet the limit state requirements of flexural capacity, the maximum ratio of flexural demand to capacity for beams and columns being 6.53 and 5.24 (for the LS-CO), respectively.

•

All the brittle beams conform to the all limit state requirements for shear capacity for pushover in the x-direction. In the y-direction pushover, brittle beams conform to the shear capacity only for the limit state of Limited Damage. Two beams do not conform to the shear capacity requirements for the limit states of Severe Damage and Collapse.

•

All beams conform to all the three the limit state requirements of rotation capacity for pushover in both directions.

•

All the ductile columns conform to the Limited Damage and Severe Damage limit states requirements of rotation capacity for the pushover in the x-direction (load distributions 1 & 2). All the ductile columns conform to the rotation capacity for the limit state of Collapse for the pushover in the x-direction with load distribution 2.

•

8 (out of 72) columns on the ground floor fail to meet the limit state requirements for rotation capacity for the limit state of Collapse for the pushover in the x-direction with load distribution 1.

•

30 columns on the ground floor (out of 72) and 28 columns of the first floor (out of 60) fail to meet the limit state requirements for rotation capacity for the limit state of Limited Damage for the pushover in the y-direction (load distribution 2).

•

25 of 72columns on the ground floor fail to meet the limit state requirements for rotation capacity for the limit state of Limited Damage for the pushover in the ydirection (load distribution 1).

58


Pushover LS

direction & load X-1

X-2

DL Y-1

Y-2

X-1

X-2

DS Y-1

Y-2

X-1

X-2

CO Y-1

Y-2

Element

Table 4.14: Summary of maximum demand to capacity ratios for all elements and all limit states in flexure, shear and rotation (Building B) Maximum Demand/Capacity ratios -

Maximum Demand/Capacity ratios -

Ground floor elements

First floor elements

Flexure

Shear

Rotation

Flexure

Shear

Rotation

B

3.53

< 1.00

< 1.00

1.59

< 1.00

< 1.00

C

4.62

-

< 1.00

< 1.00

-

< 1.00

B

3.68

< 1.00

< 1.00

1.66

< 1.00

< 1.00

C

4.58

-

< 1.00

1.18

-

< 1.00

B

3.05

< 1.00

< 1.00

3.83

< 1.00

< 1.00

C

4.56

-

1.02

-

< 1.00

B

3.36

< 1.00

3.81

< 1.00

< 1.00

C

4.52

-

1.21

-

B

5.42

< 1.00

< 1.00

1.73

< 1.00

< 1.00

C

4.90

-

< 1.00

1.22

-

< 1.00

B

6.27

< 1.00

< 1.00

2.28

< 1.00

< 1.00

C

4.89

-

< 1.00

1.38

-

< 1.00

B

4.98

1.16 (2)$

< 1.00

4.00

< 1.00

< 1.00

C

5.08

-

1.25

-

< 1.00

B

5.70

1.08 (1)$

< 1.00

5.70

< 1.00

< 1.00

C

5.14

-

< 1.00

1.46

-

< 1.00

B

5.29

< 1.00

< 1.00

1.92

< 1.00

< 1.00

C

4.99

-

1.21

-

< 1.00

B

6.53

< 1.00

< 1.00

2.35

< 1.00

< 1.00

C

4.93

-

< 1.00

1.52

-

< 1.00

< 1.00

3.88

< 1.00

< 1.00

1.22

-

< 1.00

1.20 (25/72)* < 1.00 1.15 (30/72)*

1.06 (15/72)*

1.05 (8/72)*

$

1.20 (28/60)*

B

4.74

1.16 (2)

C

5.11

-

B

6.12

1.17 (2)$

< 1.00

5.83

< 1.00

< 1.00

C

5.24

-

< 1.00

1.50

-

< 1.00

1.08 (37/72)*

* Number of columns failing to meet limit state rotation capacity requirement $ Number of beams failing to meet the limit state shear capacity requirement B – Beam; C - Column

59


•

15 columns (out of 72) on the ground floor fail to meet the limit state requirements for rotation capacity for the limit state of Severe Damage for the pushover in the ydirection (load distribution 1).

•

32 of the 72 columns on the ground floor fail to meet the limit state requirements for rotation capacity for the limit state of Collapse for the pushover in the y-direction (load distribution 1).

60

Chapter 5. Concluding Remarks

5. CONCLUDING REMARKS 5.1 Building A Despite the absence of in-situ tests on the current condition reinforcement steel, considering the quality and adequacy of the information on material properties (concrete), geometry and structure details of the building available for the seismic verification, lower middle school Puccetti in Gallicano has been classified in the adequate knowledge level. Such a classification of the building in the adequate knowledge class has permitted all types of structural analysis, viz. static or dynamic, linear or non-linear analyses, as per the Italian Seismic Code [OPCM 3274, 2003].

The structure was assessed under a gravity load combination, by a multi-modal response spectrum analysis and a static, non-linear pushover analysis. The results of the multi-modal response spectrum analysis have not been used in the structural verification of the elements as the ρmax/ρmin values exceed the code stipulations. Therefore, the results of the pushover analysis have been used for the assessment of the structural elements. A number of columns and beams of the ground storey possess lesser flexural capacity than the demand corresponding to the three limit states. A relatively lesser number of columns and beams of the first storey fail to comply with the limit state requirement for flexural capacity. This implies that the ground storey is structurally the weakest link in the structure. For the pushover analysis in the x-direction, the maximum flexural demand to capacity ratio is 2.8 and this is noticed for the Limit State of Collapse in a ground storey beam. The maximum flexural demand to capacity ratio noticed for a ground storey column is 1.7 for the Limit State of Collapse. For the pushover in the y-direction, the maximum flexural demand to capacity ratio is 2.1 and is noticed for the Limit State of Limited Damage in a ground storey beam. The maximum flexural demand to capacity ratio noticed for a first storey column is 1.6 for the Limit State of Limited Damage. For the pushover in the y-direction, it is noticed that a number of beams and columns on the ground and first floor have very high rotation demand to capacity ratios.

61


The two columns of the main entrance portal have been found to be brittle for the pushover in the y-direction and one of them fails to comply with the limit state requirements for shear capacity. Otherwise brittle columns have been identified only at the roof level. The structure turns out to have a “weak column-strong beam” system, a feature typical of buildings where design for gravitational forces dominates design for lateral forces. From the structural assessment using the results of the pushover analysis it is seen that most of the structural elements of the building remain “ductile” across all the three Limit States of Limited Damage, Severe Damage and Collapse. This, in a sense, is favourable for the structure from the point of view of energy dissipation. Nevertheless, excessive ductility coupled with a “weak column-strong beam” layout and rotational demand exceeding rotational capacity in a number of elements can imply excessive deformations under seismic action. The structural frame of the new classroom added within the double-height space near the entrance to the building in 1980 could on the one hand reduce the vulnerability of the portal columns but on the other pose a problem of pounding between adjacent elements. The new structure was not modelled and studied in the structural assessment. Considering the fact that a large number of beams and columns fail to satisfy limit state requirements under seismic action and given that the quality of concrete in the structure is not exceptionally high, a project of seismic retrofit of the school building may turn out to be ineffective in terms of cost and time. 5.2 Building B Considering the quality and adequacy of the information on material properties, geometry and structure details of the building available for the seismic verification, and despite the absence of in-situ tests on the current condition reinforcement steel, the elementary school Pascoli in Barga has been classified in the adequate knowledge level. This classification of the building in the adequate knowledge class has permitted all types of structural analysis, viz. static or dynamic, linear or non-linear analyses.

The cracked fundamental mode period of the structure is 0.53 seconds just off the plateau of the elastic pseudo-acceleration response spectrum for soil category B, PGA 0.25g on rock and a structure of importance factor 1.2. The structure was assessed under a gravity load combination, by a multi-modal response spectrum analysis and static non-linear pushover analyses as per the Italian Seismic code – Technical norms for seismic design, assessment and retrofit of buildings (version - 25/03/03). The results of the multi-modal response spectrum analysis have not been used in the structural verification of the elements as the ρmax/ρmin values exceed the code stipulations. The results of the pushover analysis have been used in the verification. Most of the structural elements in the building are classified as ‘ductile’. There are only eight beams (six on the ground floor and two on the first floor) that are ‘brittle’. All the columns of

62


the ground and first storey are ductile. This could be considered to be a positive feature for the building from the point of view of energy dissipation. The structure is apparently more resistant in the x-direction (as seen from the results of the pushover in the x-direction) than in the y-direction. With the exception of 8 ground storey columns unable to satisfy the limit state of Collapse requirements for rotation demand, all the elements satisfy limit state (Limited Damage and Severe Damage) requirements for rotation demand. A large number of ground storey columns apparently fail to meet the limit state requirements of rotation demand. This is pronounced in the assessment for the limit states of Limited Damage and Collapse where the rotation capacities of the elements are based on yield rotation and ultimate rotation, respectively. It is apparent that a concentration of damage can be expected in the ground storey columns. An observation similar to that made for Building A is possible here. Since a large number of ground storey columns fail to satisfy limit state requirements for rotation demand, ductile response of the frame can imply excessive deformation under seismic action. From the results of the non-linear static analyses and seismic verification, it can concluded that though not all structural elements in Building B satisfy the code requirements, considering the good quality of concrete in the building, it would be favourable to carryout a programme of seismic retrofit to retain the structure and its function.

63

References

REFERENCES Computers and Structures, Inc., [2004] “SAP2000 Nonlin/Adv – Integrated Finite Element Analysis and Design of Structures, Version 8.2.3, Berkeley, California, CA, USA. Eurocode 2 “Design of concrete structures – Part 1-1: General rules and regulations for buildings” Pr-EN 1992-1-1. UNI ENV 192-1-1:1993. Eurocode 8 “Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings” Pr-EN 1998-1. Final draft. December 2003. Eurocode 8 “Design of structures for earthquake resistance – Part 3: Strengthening and repair of buildings” Pr-EN 1998-3. Draft no.4. July 2003. Grant, D. Bommer, J.J., Pihno, R., Calvi, G. M., Goretti, A. and Meroni, F. [2007] “A prioritization scheme for seismic intervention in school buildings in Italy,” Earthquake Spectra, Vol. 23, No. 2, pp. 291-314. Mander, J. B., Priestley, M. J. N. and Park, R. [1988] “Theoretical stress-strain model for confined concrete”, ASCE Journal of Structural Engineering, Vol. 114, no. 8, pp. 1804-1825. Ordinanza del Presidente del Consiglio dei Ministri n. 3274 del 20 Marzo 2003. “Primi elementi in materia di criteri generali per la classificazione sismica del territorio nazionale e di normative tecniche per le costruzioni in zona sismica”. GU n. 72 del 8-5-2003. Ordinanza del Presidente del Consiglio dei Ministri n. 3316 del 2 Ottobre 2003. “Modifiche ed integrazioni all’ordinanza del Presidente del Consiglio dei Ministri n. 3274 del 20 Marzo 2003”. GU n. 236 del 10-10-2003. SeismoSoft [2003] "SeismoStruct - A computer program for static and dynamic nonlinear analysis of framed structures" [online]. Available from URL: http://www.seismosoft.com.

64

Appendix A

APPENDIX A

A1

Appendix A

ILLUSTRATIVE

EXAMPLES

FOR

CALCULATION

OF

EQUIVALENT

THICKNESS OF FLEXIBLE DIAPHRAGM EXAMPLE 1: The procedure adopted for estimating the equivalent thickness of the flexible diaphragm (for SAP2000) is illustrated for a square slab of side dimension 3500mm existing in building A:

Ec, Elastic modulus of the concrete = 1.2 × 4700 f c' , E c = 1.2 × 4700 18 = 23928.5 MPa ν, Poisson’s ratio of concrete = 0.2 Gc, Shear modulus of concrete =

E 23928.5 , = 9970.2 MPa 2(1 + ν ) 2(1 + 0.2)

Es, Elastic modulus of steel = 200000 MPa ν, Poisson’s ratio of steel = 0.3 Gs, Shear modulus of steel =

Modular ratio: m =

200000 = 76923.08 MPa 2(1 + 0.3)

G Steel 76923.08 = 7.72 = GConcrete 9970.2

Calculating, the total volume of steel and concrete present in the slab: Concrete: 3500 × 3500 ×3 40 + 5(3500 × 22544mm 2 ) = 908430303mm3 144 244 144424443 Topping

Ribs

⎡ ⎤ π 62 2 Steel: ⎢2 × 108mm × 3500 + 14 × × 3500⎥ = 2141442mm 3 4 ⎣ ⎦

Equivalent thickness, t =

908430303 + 7.72 × 2141442 = 76mm 3500 × 3500

The procedure adopted for estimating the dimensions of the brace (for SeismoStruct) using the equivalent thickness of the square slab of side dimension 3500mm is illustrated. The lateral elastic stiffness of the flexible diaphragm is K =

1 3

( L' ) ( L' ) + 12 EI AS G

L’:

Length of the slab perpendicular to the seismic action,

E:

Elastic modulus of the concrete,

I:

Inertia of the section,

, where,

A2

Appendix A

G:

Shear modulus,

L:

Length of the slab in the direction of the seismic action,

As:

Shear area.

L’ = 3500mm, E = 23928.5 MPa, I=

3500 3 × 76 = 2.7x1011 mm4 12

As =

5 × A = 5/6 x 3500x76 = 220226.7 mm2 6

Gc = 9970.2 MPa K=

1 3

3500 3500 + 11 220226.7 × 9970.2 12 × 23928.5 × 2.7 x10

= 465667.7 N/mm

The lateral stiffness of the slab would be the axial stiffness of the braces, i.e. k A =

EAb , l

where, kA:

Axial stiffness of the brace

E:

Elastic modulus of the brace

Ab:

Area of the brace

l:

Length of the brace

For square or nearly square slabs the lateral stiffness of the slab is equal to the axial stiffness of the braces. kA = 465667.7 N/mm, E = 23928.5 MPa, l = Ab =

3500 2 + 3500 2 = 4949.75 mm,

465667.7 × 4949.75 = 96324mm2 23928.5

Considering a circular cross section for the brace, the diameter of the brace would be 350mm.

A3

Appendix A

EXAMPLE 2: The procedure adopted for estimating the equivalent thickness of the flexible diaphragm (for SAP2000) is illustrated for a square slab of side dimension 6800mm existing in building B:

Ec, Elastic modulus of the concrete = 1.2 × 4700 f c' , E c = 1.2 × 4700 30 = 30891.55 MPa

ν, Poisson’s ratio of concrete = 0.2 Gc, Shear modulus of concrete =

30891.55 E , = 12871.48 MPa 2(1 + ν ) 2(1 + 0.2)

Es, Elastic modulus of steel = 200000 MPa

ν, Poisson’s ratio of steel = 0.3 Gs, Shear modulus of steel =

Modular ratio: m =

200000 = 76923.08 MPa 2(1 + 0.3)

G Steel 76923.08 = 5.98 = GConcrete 12871.48

The slab has 2 ribs per metre run. Calculating, the total volume of steel and concrete per millimetre run present in the slab: Concrete: 6800 40 + 0.002(250 × 240) = 1088000mm3/mm 142×4 3 1442443 Topping

Ribs

Steel: ⎡ π 62 ⎤ π 12 2 π 14 2 π 12 2 π8 2 × × 6800 + 1 × × 4533 + 1 × × 3400 + 1 × × 3400 + 1 × × 3400⎥ × 0.002 ⎢ 4 4 4 4 4 ⎣ ⎦ 3 = 3952.12 mm /mm Equivalent thickness, t =

1088000 + 5.98 × 3592.12 = 163.47mm 6800

The procedure adopted for estimating the dimensions of the brace (for SeismoStruct) using the equivalent thickness of the square slab of side dimension 6800mm is illustrated. The lateral elastic stiffness of the flexible diaphragm is K =

1 3

( L' ) ( L' ) + 12 EI AS G

L’:

Length of the slab perpendicular to the seismic action,

E:

Elastic modulus of the concrete,

I:

Inertia of the section,

, where,

A4

Appendix A

G:

Shear modulus,

L:

Length of the slab in the direction of the seismic action,

As:

Shear area.

L’ = 6800mm, E = 30891.55 MPa, I=

6800 3 × 163.47 = 4.28x1012 mm4 12

As =

5 × A = 5/6 x 6800x163.47 = 926349 mm2 6

Gc = 12871.48 MPa K=

1 3

6800 6800 + 12 926349 × 12871.48 12 × 30891.55 × 4.28 x10

= 1301532.43 N/mm

The lateral stiffness of the slab would be the axial stiffness of the braces, i.e. k A =

EAb , l

where, kA:

Axial stiffness of the brace

E:

Elastic modulus of the brace

Ab:

Area of the brace

l:

Length of the brace

For square or nearly square slabs the lateral stiffness of the slab is equal to the axial stiffness of the braces. kA = 1301532.43 N/mm, E = 30891.55 MPa, l = Ab =

6800 2 + 6800 2 = 9616.65 mm,

1301532.43 × 9616.65 = 405171.8 mm2 30891.55

Considering a circular cross section for the brace, the diameter of the brace would be 718mm.

A5

Appendix B

APPENDIX B

A6

Appendix B

YIELDING AND ULTIMATE FLEXURAL CAPACITY CALCULATIONS

EQUILIBRIUM AT YIELDING

Tension

Ainf ⋅ Fy

reinforcement Compression

Asup Fy

reinforcement Concrete Axial Load

0.5 ⋅ B ⋅

yy − c H − yy − c Fy ⋅ E c

E y ⋅ (H − y − c )

⋅ y2

P

Equilibrium is given by:

⎛ 1 Ec ⎞ ⎜ ⋅ Fy B ⎟ ⋅ y 2 + (Asup + Ainf ) ⋅ FY + P ⋅ y + (c(Ainf − Asup ) − Ainf H ) ⋅ FY + (c − H ) ⋅ P = 0 ⎜2 E ⎟ y ⎝ ⎠

[

]

[

hence the depth of neutral axis is given by y y1, 2 =

]

− β ± β 2 − 4αγ , 2α

⎛1 E ⎞ where α = ⎜ ⋅ c Fy B ⎟ , β = (Asup + Ainf ) ⋅ FY + P and ⎜2 E ⎟ y ⎝ ⎠

γ = (c(Ainf − Asup ) − Ainf H ) ⋅ FY + (c − H ) ⋅ P and the yielding moment is

(y y − c ) ⎛ H ⎞ Ec ⎛H ⎞ 1 Fy ⎛H 1 ⎞ M y = Ainf Fy ⎜ − c ⎟ + B y y2 ⋅ ⎜ − y y ⎟ + Asup Fy (H − y y − c ) ⎜⎝ 2 − c ⎟⎠ ⎝2 3 ⎠ ⎝2 ⎠ 2 E y (H − y y − c )

A7

Appendix B

EQUILIBRIUM AT ULTIMATE

Tension

Ainf ⋅ f y

reinforcement Compression

a) Asup ⋅

ε cu y

⋅ ( y − c) ⋅ E y

Reinforcement

b) Asup ⋅ f y

Concrete

(0.85 ⋅ 0.8 ⋅ B ⋅ f cc ) ⋅ y

Axial Load

P

ε cu

a) If compression steel is not yielded, then

y

( y − c) ≤ ε y


(0.85 ⋅ 0.8 ⋅ B ⋅ f cc ) ⋅ y 2 + [Asup ⋅ E y ⋅ ε cu − Ainf ⋅ f Y

]

− P ⋅ y − c ⋅ Asup ⋅ E y ⋅ ε cu = 0 ;

hence the depth of neutral axis is given by y u1, 2 =

[

− β ± β 2 − 4αγ , 2α

]

where α = (0.85 ⋅ 0.8 ⋅ B ⋅ f cc ) , β = Asup ⋅ E y ⋅ ε cu − Ainf ⋅ f Y − P and

γ = −c ⋅ Asup ⋅ E y ⋅ ε cu ; The ultimate moment is

ε ⎛H ⎞ ⎛H ⎞ ⎛H ⎞ M u = (0.85 ⋅ 0.8 ⋅ B ⋅ f cc ) ⋅ y ⋅ ⎜ − 0.4 y ⎟ + Ainf ⋅ f y ⋅ ⎜ − c ⎟ + Asup ⋅ cu ⋅ ( y − c ) ⋅ E y ⋅ ⎜ − c ⎟ y ⎝2 ⎠ ⎝2 ⎠ ⎝2 ⎠ b) If compression steel is yielded,

ε cu y

( y − c) ≥ ε y


(0.85 ⋅ 0.8 ⋅ B ⋅ f cc ) ⋅ y + [(Asup − Ainf )⋅ f Y

]

−P = 0;

hence the depth of neutral axis is y u =

(A

inf

− Asup ) ⋅ f Y + P

(0.85 ⋅ 0.8 ⋅ B ⋅ f cc )

;

The ultimate moment is ⎛H ⎞ ⎛H ⎞ ⎛H ⎞ M u = (0.85 ⋅ 0.8 ⋅ B ⋅ f cc ) ⋅ y ⋅ ⎜ − 0.4 y ⎟ + Ainf f y ⋅ ⎜ − c ⎟ + Asup f y ⋅ ⎜ − c ⎟ ⎝2 ⎠ ⎝2 ⎠ ⎝2 ⎠

A8

Appendix C

APPENDIX C

A9

Appendix C

ELEMENTS WITH DEMAND GREATER THAN CAPACITY UNDER GRAVITY LOAD COMBINATION – BUILDING A Frame

Frame

No.

C20303

C20603 Y20301

3Y

C10303D

C10603D

C10303C

C10603C

C10303B

C10603B

C10303A

C10603A 138

Section at x = 4980mm

117

Flexural demand greater than capacity

Y30403

4Y

103

113

18

F1

39

46

50



A10

Appendix C

C40304

3X

115

116 117

120

18

17

121

122

123

124

125

19

Section at y = 6620mm


X20604

6X 136

137 138

39

40



Y30106A

1Y 101

112

115

135

136

144

148

Section at x = 0mm

Shear demand greater than capacity

A11

Appendix C

Y50403A

Y50403B

4Y 103

113

18

F1

39

46

50



Y30504A

Y30504B

5Y

4

11

18

26

40

47

51



A12

Appendix D

APPENDIX D

A13

Appendix D

CLASSIFICATION OF ELEMENTS AS DUCTILE/BRITTLE FOR DIFFERENT LIMIT STATES – BUILDING A

Note: In the figures, all the elements shown with dotted lines indicate “brittle” members, whereas all the bold, running lines indicate “ductile members. A.D.1 X-direction Pushover Frame

Frames in the Y-direction

No.

1X 101

102

103

106

4

107

108

109

110

111

122

123

124

125

5

Section at y = 0mm

2X 113

112

11

12


3X 115

116 117

120

17

18

121

19


A14

Appendix D

4X 129

26

130

131

132

133

134

27


5X 135

FB


6X 136

137 138

39

40


A15

Appendix D

7X 141

142

143


8X 144

145

46

47


9X 148

149

50

51


A16

Appendix D

Frame

Frames in the X-direction

No.

1Y

101

112

115

135

136

144

148

145

149

Section at x = 0mm

2Y

102

137

116

Section at x =3800mm

3Y

138


117

A17

Appendix D

4Y 103

113

18

FB

39

46

50


5Y

4

11

18

26

40

47

51


6Y

8

12

19

27


A18

Appendix D

7Y 106

121

129


8Y 107

122

130


9Y 108

122

130


A19

Appendix D

10Y 109

124

132

141


11Y 110

125

133

142


12Y 111

126

134

143


A20

Appendix D

A.D.2 Y-direction Pushover

Frame

Frame

No.

1X 101

102

103

106

4

107

108

109

110

111

122

123

124

125

5

Section at y = 0mm

2X 113

112

11

12


3X 115

116 117

120

17

18

121

19


A21

Appendix D

4X 129

26

130

131

132

133

134

27


5X 135

FB


6X 136

137 138

39

40


A22

Appendix D

7X 141

142

143


8X 144

145

46

47


9X 148

149

50

51


A23

Appendix D

Frame

Frame

No.

1Y

101

112

115

135

136

144

148

145

149

Section at x = 0mm

2Y

102

116

137


3Y

138


117

A24

Appendix D

4Y 103

113

18

FB

39

46

50


5Y

4

11

18

26

40

47

51


6Y

8

12

19

27


A25

Appendix D

7Y 106

121

129


8Y 107

122

130


9Y 108

123

131


A26

Appendix D

10Y 109

124

132

141


11Y 110

125

133

142


12Y 111

126

134

143


A27

Appendix E

APPENDIX E

A28

Appendix E

IDENTIFICATION OF ELEMENTS THAT FAIL TO CONFORM TO LIMIT STATE REQUIREMENTS OF SHEAR AND ROTATION IN BUILDING A

In the following tables, all elements that fail to conform to the limit state requirements of shear or rotation demand have been identified for different cases of the pushover analyses. Elements represented by bold, continuous lines indicate those which conform to the limit state requirements for shear and rotation demand, whereas, those elements that fail to conform are represented by dotted lines. A.E.1 Limit State of Limited Damage – X-direction Pushover, Load distribution 1

Frame

Frame

No.

1X 101

103

102

106

4

107

108

109

110

111

124

125

5

Section at y = 0mm

2X 113

112

11

12


3X 115

116 117

120

17

18

121

122

123

19


A29

Appendix E

4X 129

26

130

131

132

133

134

27


5X 135

FB


6X 136

137 138

39

40


A30

Appendix E

7X 141

142

143


8X 144

145

46

47


9X 148

149

50

51


A31

Appendix E

Frame

Frame

No.

1Y

101

112

115

135

136

144

148

145

149

Section at x = 0mm

2Y 102

137

116


3Y

138


117

A32

Appendix E

5Y

4

11

18

26

40

47

51


7Y 106

121

129


8Y

107

122

130


A33

Appendix E

9Y

108

123

131


10Y 109

124

132

141


11Y 110

125

133

142


12Y 111

126

134

143


A34

Appendix E

A.E.2 Limit State of Limited Damage – Y-direction Pushover, Load distribution 1

Frame

Frame

No.

1X 101

103

102

106

4

107

108

109

110

111

5

Section at y = 0mm

3X 115

116 117

120

17

18

121

122

123

124

125

131

132

133

134

19


4X 129

26

130

27


A35

Appendix E

6X 136

137 138

39

40


7X 141

142

143


9X 148

149

50

51


A36

Appendix E

Frame

Frame

No.

1Y

101

112

115

135

136

144

148

145

149

Section at x = 0mm

2Y

102

137

116


3Y

138


117

A37

Appendix E

4Y 103

113

18

FB

39

46

50


5Y

4

11

18

26

40

47

51


6Y

8

12

19

27


A38

Appendix E

7Y 106

121

129


8Y

107

122

130


9Y

108

123

131


10Y 109

124

132

141


A39

Appendix E

11Y 110

125

133

142


12Y 111

126

134

143


A40

Appendix E

A.E.3 Limit State of Severe Damage – X-direction Pushover, Load distribution 1 Frame


No.

2X 113

112

11

12


3X 116 117

115

120

17

18

121

122

123

124

125

19


5X 135

FB


A41

Appendix E

6X 136

137 138

39

40


7X 141

142

143


8X 144

145

46

47


A42

Appendix E

9X 148

149

51

50


Frame


No.

1Y

101

112

115

135

136

144

148

145

149

Section at x = 0mm

2Y

102

137

116


3Y

138


117

A43

Appendix E

4Y 103

113

18

FB

39

46

50


5Y

4

11

18

26

40

47

51


6Y

8

12

19

27


A44

Appendix E

7Y 106

121

129


9Y

108

123

131


10Y 109

124

132

141


A45

Appendix E

11Y 110

133

125

142


12Y 134

126

111

143


A.E.4 Limit State of Severe Damage – Y-direction Pushover, Load distribution 1

Frame

Frame

No.

1X 101

102

103

106

4

107

108

109

110

111

5

Section at y = 0mm

A46

Appendix E

3X 115

116 117

120

17

18

121

122

123

124

125

131

132

133

134

19


4X 129

26

130

27


5X 135

FB


A47

Appendix E

6X 136

137 138

39

40


7X 141

142

143


9X 148

149

50

51


A48

Appendix E

Frame

Frame

No.

1Y

101

112

115

135

136

144

148

145

149

Section at x = 0mm

2Y 102

137

116


3Y

138


117

A49

Appendix E

4Y 103

113

18

FB

39

46

50


5Y

4

11

18

26

40

47

51


6Y

8

12

19

27


A50

Appendix E

7Y 106

121

129


8Y

107

122

130


9Y

108

123

131


A51

Appendix E

10Y 109

124

132

141


11Y 110

125

133

142


12Y 111

126

134

143


A52

Appendix E

A.E.5 Limit State of Collapse – X-direction Pushover, Load distribution 2 Frame


No.

1X 101

103

102

106

4

107

108

109

110

111

124

125

5

Section at y = 0mm

2X 113

112

11

12


3X 115

116 117

120

17

18

121

122

123

19


A53

Appendix E

4X 129

26

130

131

132

133

134

141

142

143

27


5X 135

FB


6X 136

137 138

39

40


7X


A54

Appendix E

8X 144

145

47

46


9X 148

149

51

50


Frame


No.

1Y

101

112

115

135

136

144

148

145

149

Section at x = 0mm

2Y

102

116

137


A55

Appendix E

3Y

138

117


4Y 103

113

18

FB

39

46

50


5Y

4

11

18

26

40

47

51


A56

Appendix E

7Y 106

121

129


8Y

107

122

130


10Y 109

124

132

141


12Y 111

126

134

143


A57

Appendix E

A.E.6 Limit State of Collapse – Y-direction Pushover, Load distribution 2

Frame

Frame

No.

1X 101

103

102

106

4

107

108

109

110

111

5

Section at y = 0mm

3X 115

116 117

120

17

18

121

122

123

124

125

131

132

133

134

19


4X 129

26

130

27


A58

Appendix E

5X 135

FB


6X 136

137 138

39

40


7X 141

142

143


A59

Appendix E

9X 148

149

51

50


Frame

Frame

No.

1Y

101

112

115

135

136

144

148

145

149

Section at x = 0mm

2Y

102

137

116


3Y

138


117

A60

Appendix E

4Y 103

113

18

FB

39

46

50


5Y

4

11

18

26

40

47

51


6Y

8

12

19

27


A61

Appendix E

7Y 106

121

129


8Y

107

122

130


9Y

108

123

131


A62

Appendix E

10Y 109

124

132

141


11Y 110

125

133

142


12Y 111

126

134

143


A63

Appendix F

APPENDIX F

A64

Appendix F

CLASSIFICATION OF STRUCTURAL “BRITTLE” IN BUILDING B

MEMBERS

AS

“DUCTILE”

AND

In the following table, all the columns and beams of every frame of the structure have been classified as “ductile” or “brittle” elements. Ductile elements have been represented with bold, continuous lines whereas brittle elements have been represented with dotted lines. The classification is presented for 12 frames in the y-direction (Frames 1X, 2X, etc.) and 16 frames in the x-direction (Frames 1Y, 2Y, etc.).

102

101

103

104

105

106

114

115

116

123

124

Frame 1X at Y = 0 mm

107

108


110

109

111

112

113


117

118

119

120

121

122

125

126


A65

Appendix F

127 128

129

130

131 132

133 134

135

136

137

138


139

140

39

141

142

40

Frame 6X at Y =21600 mm

143

145

144

146

147

148

45


149

150

49

50

151


A66

Appendix F

152

153

52

53

154


155 156

157

158

159

160

161

171

172

162

58


163

164

63

64

165

166


167

168

169

170


A67

Appendix F

101

109

117

Frame 1Y at X = 0 mm

127

143

155


118

128

156

167


102

110

119


A68

Appendix F

111

103

120

129

144

157

168


139

145

149

152

158

163 169

130

39

45

49

52

63

58


107

112

121

131


140

150

153

164

132

40

50

53

64


A69

Appendix F

133

165

141


108

213

222

234


135

142

146

151

154

159 166

170

160

171


104

114

123

136

147


A70

Appendix F

105

115

124


125

137

161

172


138

148

162


106

116

126


A71

Appendix G

APPENDIX G

A72

Appendix G

IDENTIFICATION OF ELEMENTS THAT FAIL TO CONFORM TO LIMIT STATE REQUIREMENTS OF SHEAR AND ROTATION IN BUILDING B

In the following tables, all elements that fail to conform to the limit state requirements of shear or rotation demand have been identified for all the cases of the pushover analyses. Elements represented by bold, continuous lines indicate those which conform to the limit state requirements for shear and rotation demand, whereas, those elements that fail to conform are represented by dotted lines. All elements of the structure under the X-direction pushover (for both load distributions, 1 and 2) conform to the limit state requirements of shear and rotation for the Limit States of Limited and Severe Damage and hence are not shown here. Only those frames with elements that do not conform to shear and rotation demand are illustrated. A.G.1 Limit State of Limited Damage: Y-direction Pushover, Load distribution 2

102

101

103

104

105

106


117

118

119

120

121

122

123

124

125

126


127

128

129

130

131 13

133

134

135

136

137

138


A73

Appendix G

157

155 156

158

159

160

161

162

58


163

164

165

166

64

63


167

168

169

170

171

172


101

109

117


A74

Appendix G

127

143

155


118

128

156

167


102

110

119


103

111

120

129

144

157

168


A75

Appendix G

145

139

149

152

158

163 169

130

39

45

49

58

52

63


107

112

121

131


150

140

153

164

132

50

40

53

64


133

141

165


A76

Appendix G

108

213

222

234


135

142

146

151

154

159 166

170


11

104

123

13

147

160

171


105

115

124


A77

Appendix G

125

137

161

172


138

148

162


106

116

126


A78

Appendix G

A.G.2 Limit State of Severe Damage: Y-direction Pushover, Load distribution 1

102

101

103

104

105

123

124

106


117

118

119

120

121

122

125

126


163

164

63

64

165

166


167

168

169

170

171

172


A79

Appendix G

101

109

117


118

128

156

167

157

168


102

110

119


103

111

120

129

144


A80

Appendix G

145

139

149

152

158

163 169

130

39

45

49

58

52

63


107

112

121

131


133

141

165


108

213

222

234


A81

Appendix G

135

142

146

151

154

159 166

170


104

114

123

136

147

160

171

161

172


105

115

124


125

137


A82

Appendix G

106

116

126


A83

Appendix G

A.G.3 Limit State of Collapse: X-direction Pushover, Load distribution 1

102

101

103

104

105

106


11

109

11

111

113

114

115

116


103

120

111

129

157

144

16


107

112

121

131


A84

Appendix G

108

113

122

134


11

10

123

136

147

16

17


105

115

124


106

116

126


A85

Appendix G

A.G.4: Limit State of Collapse: Y-direction Pushover, Load distribution 1

102

101

103

104

105

106

114

115

116


110

109

111

112

113


11

11

119

120

121

122

123

124

125

126


127 128

129

13

131 132

13

134

135

136

137

138


A86

Appendix G

139

140

39

141

142

40


145

144

143

146

147

148

45


155 156

157

158

159

160

161

162

58


163

164

63

64

165

166


A87

Appendix G

168

167

169

170

171

172


101

109

117


127

143

155


118

128

156

167


A88

Appendix G

110

102

119


111

10

12

120

15

144

168


139

145

152

149

158

163 169

130

39

45

49

52

58

63


107

112

121

131


A89

Appendix G

150

140

164

153

132

50

40

64

53


133

165

141


108

113

122

134


135

142

146

151

154

159 166

170


A90

Appendix G

114

10

123

13

147

160

171


115

105

124


125

137

161

172


138

148

162


A91

Appendix G

106

116

126


A92