Reliability based approach for structural design and assessment 65taking into account their durability during the entire life cycle and their behaviour inaccidental situations. A modern framework for structural design should consider that astructure is a real physical object; it is composed by many elements and components thatinteract with each other and with the design environment and these interactions can leadto strong non-linearities and can be source of different uncertainties. All these requirements are often in contrast with the simplified formulations that arestill widely applied. It is possible to handle these aspects evolving from the simplisticidealisation of the structure as a ‘device for channeling loads’ to the idea of the structuralsystem, intended as a “set of interrelated components working together toward a commonpurpose” (NASA, 2007), and acting according system engineering, which is a robustapproach to the creation, design, realisation and operation of an engineered system.Figure 1 System engineering approach for design PROCESS INPUT Requirements Analysis - Analyze missions and enviroments System - Identify functional requirements Modeling - Define performance and design And constraint requirement Analysis Requirement loop Functional Analysis/ Resources Allocation - Decomposition to lower-level function - Allocate performance - Define functional interfaces - Define functional architecture Design loop Synthesis - Transform architecture Historic Analyses - Define alternative product concepts - Define physical interfaces Evolutive / Innovative Design - Define alternative product PROCESS Risk Management and process solutions OUTPUT Source: Adapted from Bentley (1993)According to the system approach, the design of a generic system is carried out accordingto the three main phases shown in Figure 1 (Bentley, 1993):1 requirements analysis, where the design environment is considered, the functional requirements are identified and design performance and constraints are fixed2 functional analysis and resources allocation, where the task is broken down into lower-level details3 synthesis of the solution.
66 S. ArangioSystem design is an iterative (and non-linear) procedure, so if the first solution is notsatisfactory the design process is iterated; it is possible to note a requirement loopbetween phase 1 and 2, and a design loop between phase 2 and 3. Iterations may berequired for several loops. These phases are carried out by means of an integration of‘soft’ heuristic tools (left bottom side of Figure 1) and ‘hard’ computational techniques(right top side of Figure 1). A key concept of the system approach that can be applied to the structural systems isthe decomposition: for a global understanding of the structural behavior, information onboth the entire structure and the single elements are needed (Figure 2). The structuraldesign should be carried out at different levels of detail and the results of the variouslevels should be properly integrated in order to gain an overall understanding. The whole structural design process can be framed within this system view leading tothe so called performance-based design (PBD) (Smith, 2001, Petrini et al., 2010).Figure 2 Decomposition of a steel structural system Struttura Structural system Substructure Sottostruttura Components Componenti Elements1.1 Structural system qualityAnother key concept related to the system approach is the assurance of the systemquality. In recent years, in order to meet international standards and customer demands,
Reliability based approach for structural design and assessment 67some general standards on system quality, which can be applied also to structuralsystems, have been developed. An important and well known family of standards isthe ISO 9000 series, which represent an international consensus on good qualitymanagement practises. According to the ISO 9000, as synthetically shown in Figure 3,the quality management can be represented as a cycle, set up with the aim of assuringconsistency in the quality of system products and services, combined with continualimprovement in customer satisfaction. A quality management system is a fundamentaltool for achieving the required performance and for checking their accomplishmentduring time.Figure 3 Quality management according to ISO 9000 MANAGEMENT RESPONSIBILITY R S E A C Q T C CONTINUAL U U I U S I MEASUREMENT S S R RESOURCE , Management ANALYSIS F T MANAGEMENT system T E IMPROVEMENT A O O M M C M E E IMPROVEMENT T E R N I R T O S PRODUCT & N INPUTS SERVICE OUTPUTS REALIZATION Source: Adapted from quality-factors.com (2010)1.2 Quality management and EurocodesThe European structural codes (Eurocodes) assume that an appropriate quality policy isimplemented by parties during all stages of the life-cycle. For example, the measureshighlighted in EN 1990 comprise:• accurate definitions of the reliability requirements• organisational measures• control at the stage of design, execution and maintenance.Quality management is an essential consideration in every stage of the life cycle of anyconstruction. The various stages and the associated specific quality assurance activitiesare identified schematically in the quality loop diagram in Figure 4 (Gulvanessian et al.,2009).
68 S. ArangioFigure 4 Quality loop for structural systems Specifications for design Design Demolition New building and recycling 0 90 1 3 Operation and maintenance 15 Maintenance 75 years 25 Maintenance 50 Rehabilitation Source: Adapted from Gulvanessian et al. (2009)2 Criteria for reliability based designThe aim of structural design is to realise structures that meet the expected performance,which can be often represented by a target reliability level (Schneider, 1997). As shownin Figure 5, there are different approaches for reliability verification:a deterministicb probabilisticc semi-probabilistic.The most common deterministic safety measure is the global factor of safety, defined asthe ratio of the resistance over the load effect. The concept of the allowable stresses is atraditional deterministic method, where failure of the structure is assumed to occur whenany stressed part of it reaches the permissible stress. Deterministic verification methodsbased on a single global safety factor do not properly account for the uncertaintiesassociated with strength and load evaluation. The semi-probabilistic approach is based on the limit state principle and makes use ofpartial safety factors for checking the structural safety. These partial factors have beencalibrated so that a structure that satisfies the safety check using a set of designparameters will also satisfy the target reliability level. The semi-probabilistic verification
Reliability based approach for structural design and assessment 69method is still a simplified method but it can much better account for the uncertainties ofsome design parameters. Probabilistic verification procedures are also based on the principle of limit states, bychecking that predefined target structural reliability levels are not exceeded. Thisapproach takes into account explicitly the uncertainties.Figure 5 Reliability verification approaches Safety factors Deterministic Allowable stress Reliability verification approaches Semi- probabilistic Partial safety factors Limit States Analytical and numeric Probabilistic Simulation3 European codes and guidelines for reliability based designMost of the modern codes for constructions have recognised the need of using advancedreliability based design methods that allow taking into account various sources ofuncertainty. To verify whether or not a structural design is acceptable, the uncertaintiesare modelled by using statistical tools and the failure probability is estimated with respectto all relevant limit states. The three main documents that have been drawn on reliability based design, whichare briefly presented in the following sections, are the standard ISO 2394 (1998), theprobabilistic model code developed by the Joint Committee on Structural Safety (JCSS,2001) and the structural Eurocodes.3.1 The international standard ISOThe ISO 2394 – General principles on reliability of structures – is an importantinternational standard that specifies general principles for the verification of thereliability of structures subjected to different types of actions. Reliability is considered inrelation to the performance of the structure throughout its design working life. Thisinternational standard is applicable in all the stages of the construction process as well asduring the use of the structure, including maintenance and repair. The principles are also
70 S. Arangioapplicable to the structural appraisal of existing constructions or assessing changes ofuse.3.2 The JCSS probabilistic model codeThe probabilistic model code developed by the Joint Committee on Structural Safety(JCSS, 2001) represents an important step in the direction of the necessarystandardisation of the reliability based method. In 1971, the Liaison Committee, whichcoordinates the activities of six international associations of Civil Engineering (FIB, CIB,ECCS, IABSE, IASS, and RILEM), created a Joint Committee on Structural Safety(JCSS) with the aim of improving the general knowledge in structural safety. In 1992, theJCSS set as a long term goal the development of a probabilistic model code for new andfor existing structures. The JCSS code gives guidance on the modelling of the randomvariables in structural engineering and it is intended as the operational part of codes likethe ISO 2394 (1998), the Eurocodes and other national codes that allow for probabilisticdesign but do not give any detailed guidance. The code consists out of three main parts that deal with general requirements,modelling of loads and modelling of structural properties. The code gives no information,however, on mechanical models like buckling, shear capacity, foundation failure and soon. Little or no information is given on other modelling aspects, like for example thewind pressure coefficients.3.3 Structural EurocodesThe idea of common modern structural specifications for the countries of the Europeaneconomic area was born in 1975, when the Commission of the European Communitydecided on an action programme in the field of construction based on Article 95 of theTreaty of Rome. The objective of the programme was the elimination of technicalobstacles to trade and the harmonisation of technical specifications.Figure 6 Links between the Eurocodes EN 1990 Basis of Structural Design EN 1991 Action on structures EN 1992 EN 1993 EN 1994 Design and detailing EN 1995 EN 1996 EN 1999 Geotechnical and EN 1997 EN 1998 Seismic DesignThe Eurocodes are used for the design of new structures but they also cover engineeringprinciples that could be used to form the basis of assessment of existing structures. The
Reliability based approach for structural design and assessment 71ten structural Eurocodes are linked as shown in Figure 6. The first one, EN 1990 – Basisof Structural Design is the head code, which gives the basis of structural design adoptedby the whole suite and needs to be used alongside of the remaining standards. Thesecond one (EN 1991 – Actions on structures) gives actions. Then, there are sixstandards for design and detailing, grouped by material (EN 1992 – Concrete,EN 1993 – Steel, etc.), and two standards for Geotechnical (EN 1997) and Seismic (EN1998) design. The Eurocodes are being implemented by each member country troughnational standards which comprise the full text of the Eurocode and may be followed by anational Annex.3.4 The Italian approachIn Italy a new structural code is in force from July 2009 (Norme Tecniche delleCostruzioni (NTC) – passed with D.M. 14/01/2008). This code has been written inaccordance with the principles of the Eurocodes. Many parts have been quoted from theEurocodes, others have been modified, according to the Italian needs. The NTCrepresents an important step in the Italian approach: for the first time the national code isbased on a modern probabilistic approach (that actually in most of the cases can bebrought to a semi-probabilistic approach with the use of the partial factors). It deals withboth design of new structures and assessment of existing ones.Part II Existing structures4 Structural assessment processThe assessment of existing structures aims at producing evidence that they will functionsafely over a specified residual service life. It is mainly based on estimating the materialproperties and strength capacity of the members taking into account the present state ofthe structure, and evaluating its ability to withstand anticipated hazards and future loads. Nowadays, this problem is particularly important in the case of infrastructures. Infact, the rate and extent of the deterioration of existing bridges have lately significantlyincreased. Indeed, the current low funding in the infrastructure sector of many Europeancountries has forced highway agencies to postpone necessary investments in new roadand bridges and consequently stretch the service life of their existing old stock. Theprioritisation of the distribution of funds among maintenance, repair and rehabilitationactivities is a major problem that bridge authorities everywhere are facing (Frangopol andDas, 1999; Casas, 2006). The structural assessment is assuming a key role in the management of existingstructures and different approaches exist. The most commonly used method is the socalled condition rating method, where, on the basis of visual inspections, a grade isassigned to the structure. The grade can be either numerical ranging for example betweenone for very poor condition to ten for excellent condition, or descriptive by classifyinginfrastructures as poor, acceptable, good, etc. The main drawback of this approach is thatoften it lacks of objectivity because it is based on the sensibility of the engineer, so thesame structure, assessed by two different engineers, can be rated with different grades.
72 S. Arangio In the past three decades, a new measure for the assessment of existing structures hasbeen developed within the probabilistic framework based on the reliability index(Melchers, 1999). According with the decomposition approach previously discussed, the most efficientprocesses are based on the verification of the reliability at different levels. Looking at theexample in Figure 7 (Bontempi et al., 2009), the verification can be carried out at a globallevel (called 4th level in the figure), at the level of the single structural element(3rd level), on the section of the element (2nd level), and at the material level (1st level).For each level appropriate methods and tools are available.Figure 7 Reliability verification levels in the limit states approach Source: Adapted from Bontempi et al. (2009)It is also important to note that the choice of the assessment method and level of accuracyis strictly related to the specific phase of the life-cycle and to the complexity andimportance of the structure (Bontempi, 2006). The use of advanced methods is notjustified for all structures; the restriction in terms of time and cost is important(Arangio et al., 2010): for each structural system a specific assessment process, whichwould be congruent with the available resources and the complexity of the system, shouldbe developed. In Bontempi et al. (2008) for example, the structures are classified formonitoring purposes in the following categories: ordinary, selected, special, strategic,active and smart structures. The information needed for an efficient monitoring,shown in Figure 8 by means of different size circles, increases with the complexity of thestructure.
Reliability based approach for structural design and assessment 73Figure 8 Relationship between classification of structures and characteristics of the monitoring process Source: From Bontempi et al. (2008)Another hierarchical model, based on six levels of assessment, is proposed in variousguidelines (e.g., SAMARIS, 2006; Rücker et al., 2006 for bridges). The various levels aresummarised in Figure 9 and Table 1. They are numbered from 0 to 5 withlevel 0 (informal qualitative assessment) being the simplest and level 5 (full probabilisticassessment) the most sophisticated.Figure 9 Structural assessment levels Structural Assessment Qualitative Quantitative Assessment Assessment Measurement based Model based Assessment Assessment Level 0 Level 1 Level 2 Level 3 Level 4 Level 5 Experience Direct Assessment of Assessment of Adaptation of Probabilistic based subjective assessment of safety and safety and target reliability assessment of assessment of serviceability serviceability serviceability methods ad safety and deterioration values from using simple using refined assessment of serviceability effects and other measured load model based model based safety and values damage after effects methods methods serviceability visual inspection with modified Data from test, Data from Data from test, structure- monitoring, etc. documents monitoring, etc specific values Source: Adapted from Rücker et al. (2006)
74 S. ArangioTable 1 Structural assessment levels Assessment Strength and load Calculation models Assessment methodology level models Strength and load Simple linear elastic LFRD-based analysis, 1 models as in design code calculation load combinations and Material properties Refined, load partial factors as in the based on design redistribution is design code 2 documentation and allowed, provided standards that the ductility 3 Material properties can requirements are be updated on the basis fulfilled LRFD-based analysis, of in situ testing and modified partial factor are 4 observations using allowed Bayesian approach Strength model Probabilistic analysis including probability 5 distribution for all variables Source: Adapted from Rücker et al. (2006)It is important to note that there are some substantial differences between the design ofnew structures and the assessment of existing ones. Consider for example the followingaspects:• the structural codes for design consider generic situations and the inputs of the design process are established according to standard rules. On the other hand, the assessment of existing structures is carried out case by case, evaluating the real actions• in the assessment of existing structures the real constraints are uncertain• the required performance are easier to be accomplished in the design phase than in the assessment• some structures could have adequate performance even if they have exceeded their nominal life.The probabilistic framework for assessment of existing structures can thus be seen as anextension of the probabilistic framework for the design of new structures, providing arational and consistent basis for the inclusion of new information and uncertainties. Anexample is schematically illustrated in the JCSS document (Figure 10). The assessmentof existing structures by using methods of modern reliability theory is seen as asuccessive process of model building, consequence evaluation and model updating byintroduction of new information or by modification of the structure. The analysis to beperformed involves various steps:• formulation of a priori uncertainty models• formulation of limit state functions• establishing posterior probabilistic models• setting acceptable levels for the probability of failure.
Reliability based approach for structural design and assessment 75The issue of setting acceptable levels for probabilities of failure, that is setting targetreliability levels, assumes a key role. In the following sections some strategies suggestedby different guidelines and codes for the selection of the target reliability indices arepresented.Figure 10 Probabilistic approach for structural assessment Probabilistic modeling Uncertainty Limit state equation Modeling Consequence Modify design Introduce new information Change use of structure Actions Source: Adapted from JCSS (2001)5 European codes and guidelines for structural reliability assessmentGuidelines for evaluating the safety of existing structures are available in some countries.For example, in Canada, Germany, Slovenia, the Netherlands, Switzerland, and in somestates of the USA they have been prepared with a careful attention to details. In the UK, aconsiderable amount of guidance on the design, management and assessment of bridgestructures is provided in the Design Manual for Roads and Bridges (DMRB) (HMSO,2001). A good example of evaluation code is the recently developed Danish BMSDANPRO+ (Bjerrum et al., 2006). In Italy, the recently issued structural code (NTC,2008) includes an entire chapter on the assessment of existing constructions. Even ifsome countries in Europe are using specific guidelines or standards for structural safetyassessment, many European countries still do not have specific methods. While for the design of new structures there are common European specifications(the Eurocodes), there are no common standards for the assessment of existing structures.As already said, some indications are given in the Eurocodes but they are not enough. Inthe light of the development of common European standards, there is a need to harmonisethe various existing specifications. For example, a report by the European Convention forConstruction Steelwork (ECCS) and the Joint Research Center has been prepared to
76 S. Arangioprovide technical insight on the way existing steel structures could be assessed and theremaining life could be estimated (Kühn et al., 2004). These recommendations follow theprinciples of the Eurocodes. It is important to note that, even if all the mentioned specifications provide aphilosophical basis and a theoretical framework for the assessment of structures, most ofthem propose procedures based on deterministic approaches. There have been a numberof applications of reliability based assessment in some countries (Frangopol and Strauss,2008) but the probabilistic approaches are not yet commonly used in practise, mainly dueto the lack of information and standardisation. A remarkable exception is presented forexample in the work by Biondini et al. (2004a). Some important documents that havebeen drawn up in this sense are the standards ISO 2394 and 13822, and the JCSSProbabilistic Code. Also various research projects [e.g., Rücker et al. (2006) and BRIME(2003)] have proposed guidelines on monitoring and reliability-based assessment.5.1 The international standard ISOThe already mentioned ISO 2394 – General Principles on Reliability of Structures, andthe ISO 13822 – Assessment of Existing Structures – deal with reliability assessment ofexisting structures. The general principles for the verification of the reliability areintroduce in clause 10 of ISO 2394, where it is explained how the basic variables, such asloads, material properties and model uncertainties, shall be taken. This approach allowsdrawing conclusions with respect to the bearing capacity of single tested members, to thecapacity of other non-tested members and other load conditions as well as to thebehaviour of the entire system. The International Standard ISO 13822 provides generalrequirements and procedures for the assessment of existing structures (buildings, bridges,industrial structures, etc.) based on the principles of structural reliability andconsequences of failure. It is intended to serve as a basis for preparing national standardsor codes of practise in accordance with current engineering practise and the economicconditions.5.2 The JCSS probabilistic model codeAn important step in the direction of the necessary standardisation of the reliability basedmethod is the probabilistic model code developed by the Joint Committee on StructuralSafety (JCSS, 2001). The JCSS document includes general guidelines on reassessment,methodologies for reliability updating, acceptability and safety criteria, with examplesand case studies. This document was created because the classical code approaches wereoften not suited to address questions such as the evaluation of the risk of structures, andthe choice of the adequate type of inspection. Thus, the document was created with thefollowing basic goals:a to standardise methods and terminologyb to be operational for the consulting engineersc to be generally applicable for various materials and various structural typesd to build the basis of future codes and standards.
Reliability based approach for structural design and assessment 775.3 Structural EurocodesAs specified above, the structural Eurocodes deal with the design of new structures butthey also cover engineering principles that could be used to form the basis of structuralassessment. For example, according to UNI EN (1990), a concrete structure shall bedesigned in such a way that deterioration of concrete and/or steel should not impair thedurability and performance of the structure. In other words, an adequate maintenancestrategy is part of the design concept of the structural Eurocodes. However, clause 1.1(4)does recognise that additional or amended rules and provisions might be necessary whereappropriate.5.4 The Italian approachItaly represents a particular case in the field of structural assessment because of the hugenumber of historic and valuable existing structures. There are numerous typologies ofstructures, built in various historic epochs and by using different methods. For thesereasons it was very difficult to define standards able to deal with the issue of structuralassessment in a general way. Another important aspect is that, in Italy, the indicationsgiven in the structural codes are compulsory, so the existing guidelines cannot be usedand, even if the Eurocodes are standards for all the member states, they need a specificdocument, approved as a law, for their effective application in Italy. In the last Italian structural code (NTC, 2008) an entire chapter is devoted to theexisting structures. The indications regarding the assessment are mainly oriented toward aperformance based approach: few rules and general indications are given and theengineer is free to choice the method to guarantee the required performance. In this codeit is noticeable the introduction of two new concepts related to the performance approach:the so called knowledge levels and confident factors. Both are used to modify thecapacity parameters. Three different levels of knowledge (Livelli di conoscenza, LC) aredefined:• level of knowledge 1 (LC1): limited knowledge• level of knowledge 2 (LC2): adequate knowledge• level of knowledge 3 (LC3): accurate knowledge.For each level of knowledge a confident factor, which is used together with the otherpartial factors, is assigned (Table 2). The aspects that are considered in order to classifythe level of knowledge are:• the geometrical characteristics of the structure• the mechanical properties of the materials, obtained from both project documents and specific tests• the geotechnical characterisation.More details are available in the code and in specific publications (see for exampleFranchin et al., 2010).
78 S. ArangioTable 2 Level of knowledge and confident factor Level of knowledge Confident factor LC1 – limited knowledge 1.35 LC2 – adequate knowledge 1.20 LC3 – accurate knowledge 1 Source: Adapted by NTC (2008)6 Acceptability and target criteria for the reliability indexFor the assessment of existing structures, target reliability levels different than those usedin the design must be considered (Vrouwenvelder and Scholten, 2010). The differencesare based on the following considerations (ISO 13822).• economic consideration: the cost between accepting and upgrading an existing structure can be very large, whereas the cost of increasing the safety of a structural design is generally very small; consequently conservative criteria are used in design but should not be used in assessment• social considerations, as the consequences of disruption of ongoing activities• sustainability considerations: reduction of waste and recycling, which are considerations of lower importance in the design of new structures.Table 3 Target reliability indices for the reference period of 50 years and 1 year and ‘moderate’ relative costs of safety measures Codes Consequences EN 1990 Low Normal High ISO 9324 Small Some Moderate Great JCSS Minor Moderate Large EN 1990 – 50 years - 3.3 3.8 4.2 ISO 9324 – life time 1.3 2.3 3.1 3.8 JCSS – 50 years - 2.5 3.2 3.5 EN 1990 – 1 year - 4.2 4.7 5.2 ISO 9324 – 1 year 2.9 3.5 4.1 4.7 JCSS – 1 year - 3.7 4.2 4.4Target values are given in several codes and guidelines (e.g., Moses, 2001; CAN/CSA-S6-00, 2000; COWI, 2007; JCSS, 2001; UNI EN, 1990, 2002). For the definition of thereliability indices various factors are considered as for example consequences of failure(e.g., low, normal, high for EN 1990), reference period, relative cost of safety measures(e.g., small, moderate, great for ISO 9324), importance of structure (bridges, publicstructures, residential buildings, etc.) and so on. In Table 3, some target reliability levelsproposed by international codes for design and assessment are shown. They vary with theconsequences of failure and the reference periods (in the table 50 years for design and
Reliability based approach for structural design and assessment 791 year for assessment). The proposed values consider ‘moderate’ relative costs of safetymeasure The target limits are obtained from different procedures. For example, the CanadianStandards Association (CSA, 2000) has adopted the following life-safety criterion forbridge assessment. To take into account that some failures are much less likely to resultin death or injury than others, they define the conventional probability of failure: A⋅ K Pconventional = W⋅ nwhere Pconventional is defined as the target annual probability of failure based on life-safetyconsequences, K is a constant based on calibration to existing experience which is knownto provide satisfactory life safety, A is the activity factor which reflects the risk to humanlife associated with activities for which the structure is used, W is the warning factorcorresponding to the probability that, given a failure, a person at risk will be killed orseriously injured, and n is the importance factor based on the number of people n atrisk if failure occurs. The CAN/CSA-S6-00 (2000) proposes also to adjust the target reliability indices forbridges according to the consequences of failure of one element. For example, if thefailure of one element does not lead to collapse because of redundancy then the risk tolife is reduced; if an element fails gradually, then the failure is likely to be noticed beforecollapse takes place. Table 4 provides some examples of adjustments for single elementsand for the entire system.Table 4 Reliability index adjustment for bridge assessment β = 3.5 − ( Δ E + Δ S + Δ I + Δ PC ) Adjustment for element behaviour ΔE Sudden loss of capacity with little or no warning 0.0 Sudden failure with little or no warning but retention of post-failure capacity 0.25 Gradual failure with probable warning 0.5 Adjustment for system behaviour ΔS Element failure leads to total collapse 0.0 Element failure probably does not lead to total collapse 0.25 Element failure leads to local failure only 0.5 Adjustment for inspection level ΔI Component not inspectable – 0.25 Component regularly inspectable 0.0 Critical component inspected by evaluator 0.25 Adjustment for traffic category ΔPC All traffic category except PC 0.0 Traffic category PC 0.6 Source: Adapted from CAN/CSA-S6-00 (2000)
80 S. ArangioPart III Structural system robustness and dependability7 Structural robustnessThe traditional approach for structural design and assessment aims at the verification ofthe safety of the structure under assigned loads and boundary conditions, but it does nottake into account some advanced aspects: for example the fact that also a small initialfailure could result in a disproportionate structural damage as shown by several cases ofbuilding collapses in the past (see for example Crowder et al., 2008). Such behaviour iscommonly interpreted as a lack of structural robustness (Starossek, 2009; Giuliani, 2009). To clarify the role assumed by structural robustness, it is necessary first to clarify itsmeaning. The term robustness appears often in the structural engineering literature and ithas been widely discussed in international scientific conferences (see for example thespecial sessions on structural robustness organised at the IABMAS Conferences (2008,2010) by Bontempi and Starossek, and the Conferences ‘Handling the Exceptions’ inRome (HE, 2008; 2010). Even so, it is used differently by the various authors and there isno general agreement today about its precise meaning. A set of definitions has beenselected in a recent work by Starossek and Haberland (2010). Two qualitative definitionsare the following:• ability of a structure to withstand actions due to fires, explosions, impacts or consequences of human error, without suffering damages disproportionate to the triggering causes (EN 1991-1-7: 2006)• insensitivity of the structure to local failures (Starossek et al., 2007).The main difference in these definitions, which reflects also a certain dispute in recentliterature (Starossek and Wolff, 2005; Faber, 2006), consists in the identification of thecause a structure should withstand in order to be considered robust. According to the firstdefinition, a structure is robust if a disproportionate collapse is not triggered inconsequence of an accidental action, while the second definition of robustness refersdirectly to the ability of a system to tolerate structural damages, apart from the actionsthat could have determined them. In the latter case, the robustness is intended as a property inherent to the structuralsystem and can represent a direct measure of the susceptibility of a structure todisproportionate collapses. According to the first definition instead, the robustness of astructure would depends on the accidental action considered. Summing up the different definitions, it is possible to say that robustness refers to theability of a structure not to respond disproportionately to either abnormal events or initiallocal failure. It is important to point out that it is not to be expected that the structure willresist all the possible occurrences without any damage: not only is practically impossiblethe foreseeing of any possible critical event, but hardening a structure to resist perfectlyinteger to hazards that have such a low probability of occurrence, would be noteconomically feasible. More detail can be found in Starossek (2009), Giuliani (2009),Bontempi et al. (2007) and Brando et al. (2010). The robustness of a structure strongly influences its reliability but it very difficult tomeasure the contribution. In most of the existing codes and guidelines the subject ofstructural robustness in treated in a general way and only indirect design criteria areprovided. The task of the quantitative evaluation of robustness, and consequently the
Reliability based approach for structural design and assessment 81modification of the reliability indices have been treated by several authors. Four mainapproaches exist: risk based (Faber, 2006), topology based (Agarwal et al., 2003), energybased (Starossek and Haberland, 2008) damage based (Biondini and Frangopol, 2008;Yan and Chang, 2006; Bontempi et al., 2007). A summary of the main quantitativedefinitions proposed in the past few years is given in Giuliani and Bontempi (2009).7.1 Robustness and the EurocodesThe topic of robustness is essentially covered by two Eurocodes, EN 1990 – Basis ofStructural Design, which provides the high level principles for achieving robustness andEN 1991: Part 1-7 – Accidental Actions (EN 1991-1-7), which provides strategies, andmethods to obtain robustness and the actions to consider. The leading principle is that, in case of accidental actions, local damage is acceptable,provided that it will not endanger the structure, and that the overall load-bearing capacityis maintained during an appropriate length of time to allow necessary emergencymeasures to be taken (Gulvanessain and Vrouwenvelder, 2006).Figure 11 The arrow indicates the point where the rock impacted the pile, (a) impacted point (b) rock (c) maximum height of the debris flow during the event (d) height of debris at the end of the landslide (see online version for colours) Messina – Catania Highway Racinazzo Torrent Source: From Ortolani and Spizuoco (2009)An example of lack of structural robustness in an accidental situation is shown inFigure 11. The highway bridge in the picture is located at the entrance of the city ofMessina (Sicily Island, Italy) where in October 2009 a large landslide occurred; thedebris flow impacted the bridge and a big rock (visible in Figure 12) strongly damagedone of the piers. The traffic was interrupted for entire days causing trouble to thecirculation of the entire city. In Figure 11, the arrow indicates the point where the rock
82 S. Arangioimpacted and the marked surface represents the volume of the debris flow. In Figure 12the zone is viewed from the other side. In such a case, it would have been necessary toquantify the structural robustness and evaluate the residual life of the structure beforereopening the bridge to the normal traffic. In fact this structure was designed to carrymainly vertical loads and the sudden impact with the heavy rock changed its structuralbehavior. A robust design approach of bridges located in hazardous areas should properlytake into account accidental situations in order to avoid disruption of the service or eventhe collapse of the structure. Other examples of structural behaviour under accidentalscenarios are given for example in Crosti (2009) and Gentili et al. (2010).Figure 12 The arrow indicates the damaged pier (see online version for colours) Damaged pier Messina – Catania HighwayNotes: On the right it is possible to see the big rock that impacted on the bridge. Source: From Ortolani and Spizuoco (2009)7.2 Redundancy in Eurocodes and NCHRPAccording to the Eurocodes, redundancy is the availability of alternative load-carryingcomponents and alternative paths for a load to be transferred from a point of applicationto a point of resistance. This implies the absence of critical components whose failurewould cause the collapse of the structure (Frangopol and Curley, 1987). There is a strong connection between redundancy and robustness (Starossek andHaberland, 2010). Redundancy is a key factor for robustness: a redundant structure hasalternative load carrying components; if one or more components fail, the remainingstructure is able to redistribute the force originally carried by the failed components intoalternative load paths. However, the terms robustness and redundancy denote differentproperties of the structure and they should be clearly distinguished (Biondini et al., 2008;Starossek, 2009). Using them as synonyms obscures the fact that redundancy is not theonly means to achieve robustness. Both concepts should be considered in a reliabilitybased assessment of structures. It is important to note that the definitions given above are generally used in Europe;the term redundancy is used in a different way in the literature of the USA: the concept ofredundancy is mainly related to the ability of a structure to withstand the failure of asingle structural member without collapsing. For example, NCHRP 406 defines bridgeredundancy as “the capability of a bridge to continue to carry loads after the damage orthe failure of one of its member (the first member to fail)” (Ghosn and Moses, 1998). In asense, their definition of redundancy is equivalent to the definition of the robustness
Reliability based approach for structural design and assessment 83given in the Eurocodes. Thus, the methods proposed in USA (as for example in theNCHRP Report 406, 1998) for the assessment of the reliability taking into account theredundancy, in the European point of view, could be applied for reliability assessmenttaking into account the robustness. Actually, this is the same concept called in differentways (Arangio and Ghosn, 2010). NCHRP Report 406 (Ghosn and Moses, 1998) developed a process for quantifyingredundancy (i.e., robustness according to the European view) in bridge super structures.Subsequently, this approach was extended to substructures (Liu et al., 2001). A bridge isconsidered safe if:• it provides a reasonable safety against first member failure• it provides an adequate level of safety before it reaches its ultimate limit states• it does not deform excessively under expected loads• it is able to carry some traffic loads after damage or loss of members.Accordingly four limit states are defined as:• member failure, which is a check of individual member safety using elastic analysis• ultimate limit state, which is defined as the ultimate capacity of the bridge system or the formation of a collapse mechanism• functionality limit states, which is defined as the capacity of the structure to resist a main member live load displacements of specified magnitude• damaged condition limit state, which is defined as the ultimate capacity after removal of one main load carrying component.The four limit states should be checked to ensure the satisfactory safe performance of thebridge system under extreme and regular conditions. ‘Adequate’ safety margins can bedetermined using reliability based techniques. A reliability index can be defined for eachlimit state, thus there will be βmember for the member failure, βu for the ultimate limit state,βfunct for the functionality limit state, and the system reliability index βdamaged for damagedconditions. To study the redundancy of a system, it is useful to examine the differences betweenthe reliability indices of the system expressed as βu, βfunct, and βdamaged and the reliabilityindex of the most critical member as βmember. The relative reliability indices are definedas: Δβ u = β u − β member Δβ f = β func − β member Δβ d = β damage − β memberThese relative reliability indices give measures of the relative safety provided by thebridge system compared with the nominal safety of first member failure. On the basis ofanalyses of typical bridge configurations, a direct redundancy evaluation procedure hasbeen proposed in the NCHRP reports. It is based on satisfying minimum values of therelative reliability indices. According to these analyses, a bridge will provide adequatelevels of redundancy if all three following conditions are satisfied:
84 S. Arangio Δβ u ≥ 0.85 Δβ f ≥ 0.25 Δβ d ≥ −2.708 Structural systems dependabilityFor the purpose of the evaluation of the overall quality of structural systems a newconcept has been recently proposed: the structural dependability. It can be introducedlooking at the scheme in Figure 13, where the various aspects discussed in the previousparagraphs are ordered and related to this concept. It has been said that a modernapproach to structural design requires evolving from the simplistic idea of structure to theidea of structural system, and acting according to the system engineering approach. Inthis way it is possible to take into account the interaction between the different structuralparts and between the whole structure and the design environment. The grade ofnon-linearity and uncertainty in these interactions determines the grade of complexity ofthe structural system. In case of complex structural systems, it is important to evaluatehow the system works as a whole, and how the elements behave singularly. In thiscontest, dependability is a global concept that describes the aspects assumed as relevantto describe the quality of a system and their influencing factors (Bentley, 1993). It hasbeen originally developed in the computer science field but it can be reinterpreted in thecivil engineering field (Arangio et al., 2010). The dependability reflects the user’s degreeof trust in the system, i.e., the user’s confidence that the system will operate as expectedand will not ‘fail’ in normal use: the system shall give the expected performance duringthe whole lifetime.Figure 13 Roadmap for the analysis and design of complex structural systems Interaction among different structural parts Interactions are characterized by STRUCTURAL SYSTEM strong nonlinearity Interaction between and uncertainty the whole structure and the design environment DECOMPOSITION SYSTEM APPROACH COMPLEXITY STRATEGY ATTRIBUTES QUALITY of the whole structural THREATS system: DEPENDABILITY MEANS PERFORMANCE BASED DESIGN
Reliability based approach for structural design and assessment 85The assessment of dependability requires the definition of three elements (Figure 14):• the attributes, i.e., the properties that quantify the dependability• the threats, i.e., the elements that affect the dependability• the means, i.e., the tools that can be used to obtain a dependable system.In structural engineering, relevant attributes are reliability, safety, security,maintainability, availability, and integrity. Not all the attributes are required for all thesystems and they can vary over the life-cycle. They are essential to guarantee:• the ‘safety’ of the system under the relevant hazard scenarios, that in current practise is evaluated by checking a set of ultimate limit states (ULS)• the survivability of the system under accidental scenarios, considering also the security issues; in recent guidelines, this property is evaluated by checking a set of ‘integrity’ limit states (ILS)• the functionality of the system under operative conditions (availability), that in current practice is evaluated by checking a set of serviceability limit states (SLS)• the durability of the system.These attributes can be divided in high level or active performance (reliability,availability, and maintainability) and low level or passive performance (safety, security,and integrity) (Petrini et al., 2010). The threats to system dependability can be subdivided into faults, errors andfailures. According to the definitions given in Avižienis et al. (2004), an active ordormant fault is a defect or an anomaly in the system behaviour that represents a potentialcause of error; an error is the cause for the system being in an incorrect state; failure is apermanent interruption of the system ability to perform a required function underspecified operating conditions. Error may or may not cause failure or activate a fault. Incase of civil engineering constructions, possible faults are incorrect design, constructiondefects, improper use and maintenance, and damages due to accidental actions ordeterioration. The problem of conceiving and building a dependable structural system can beconsidered at least by four different points of view:1 how to design a dependable system, that is a fault-tolerant system2 how to detect faults, i.e., anomalies in the system behaviour (fault detection)3 how to localise and quantify the effects of faults and errors (fault diagnosis)4 how to manage faults and errors and avoid failures (fault management).
86 S. ArangioFigure 14 Dependability: attributes, threats and means RELIABILITY MAINTAINABILITY AVAILABILITY ATTRIBUTES INTEGRITY SAFETY SECURITY FAULT DEPENDABILITY THREATS ERROR FAILURE FAULT TOLERANT DESIGN FAULT DETECTION MEANS FAULT DIAGNOSIS FAULT MANAGING Source: Arangio et al. (2010)The task of fault management includes the so called fault forecasting, that is the set ofmethods and techniques for performing evaluations of the system behaviour with respectto fault occurrence or activation. These evaluations have two aspects:a qualitative, aimed at identifying the possible failure modes or hazardous scenariosb quantitative, aimed at evaluating in terms of probabilities some of the attributes of dependability.A system is taken as dependable if it satisfies all requirements with regards to variousdependability performance and indices, so the various attributes, such as reliability, safetyor availability, which are quantitative terms, form a basis for evaluating the dependabilityof a system. The evaluation of the dependability is a complex task because this is a termused for a general description of the quality of a system and it cannot be easily expressedby a single measure. The approaches for dependability evaluation can be qualitative orquantitative and usually are related to the phase of the life cycle that it is considered(design or assessment). In the early design phase a qualitative evaluation is moreappropriate than a detailed one, as some of the subsystems and components are notcompletely conceived or defined. Qualitative evaluations can be performed, for example,by means of failure mode analyses approaches, as the failure mode effects and criticalityanalysis (FMECA) or the failure tree analysis (FTA), or by using reliability block
Reliability based approach for structural design and assessment 87diagrams. Note that these models assume independence among modeled components. Onthe other hand, in the assessment phase, numerous aspects should be taken into accountand all of them are affected by uncertainty and interdependencies, so quantitativeevaluations, based on probabilistic methods, are more suitable. It is important to evaluatewhether the failure of a component may affect other components, or whether areconfiguration is involved upon a component failure. These stochastic dependencies canbe captured for example by Markov chains models, which can incorporate interactionsamong components and failure dependence. Others methods are based on Petri Nets andstochastic simulation. At the moment, most of the applications are on electrical systems(e.g., Nahman, 2002) but the principles can be applied in the civil engineering field.When numerous different factors have to be taken into account and dependability cannotbe described by using analytical functions, the use of linguistic attributes by means of thefuzzy logic reasoning can be helpful (Ivezić et al., 2008; Biondini et al., 2004b).9 ConclusionsIn this work a state of the art about the European reliability based approach for the designand assessment of civil engineering systems is presented. The first part deals with theissues related to the design phase, while the second part considers the reliability basedassessment of existing structures. In the last part the concept of structural robustness isdiscussed showing the difference between the European point of view and the US one.Looking at the recent literature and structural standards, it is possible to notice that thereis an increasing interest in the reliability based approach. However it has been shown thatmost of the regulations are still based on over simplified approaches that are not able totake into account the intrinsic complexity of the modern structural systems and theconcept of robustness. The existing measures are mostly local indices whereas thereliability of a structural system should be evaluated in global way, taking into accountthe possible non-linearities and the various sources of uncertainties. For the purpose ofthe evaluation of the overall quality of structural system a new concept has been recentlyproposed and it is discussed in the last part of the paper: the dependability. It is a globalconcept that describes the aspects assumed as relevant and their influencing factors. It hasbeen originally developed in the computer science field but it can be applied to civilengineering systems.AcknowledgementsThe present paper is a result of a work conducted within a collaboration with the TaskGroup 2 of the SEI-ASCE Technical Council on Life-Cycle Performance, Safety andReliability and Risk of Structural Systems. Prof. Franco Bontempi and his teamwww.francobontempi.org from Sapienza University of Rome, and Prof. Michel Ghosnfrom CUNY of New York are gratefully acknowledged for their suggestions. Prof. Casasof the UPC, Prof. Malerba of the Polytechnic of Milan and Dr. Starnes of the TRB arealso acknowledged. The opinions and conclusions presented in this paper are those of theauthor and do not necessarily reflect the views of the sponsoring organisations.
88 S. ArangioReferencesAgarwal, J., Blockley, D., Woodman, N. (2003) ‘Vulnerability of structural systems’, Structural Safety, Vol. 25, No. 3, pp.263–286.Arangio, S. and Ghosn, M. (2010) ‘Non deterministic approaches in current structural codes for assessing the safety and reliability of bridges’, Proceeding of IABMAS Conference, 11–15 July 2010, Philadelphia, USA.Arangio, S., Bontempi, F. and Ciampoli, M. (2011) ‘Structural integrity monitoring for dependability’, Structures and Infrastructures, Vol. 7, Nos. 1–2, pp.75–86, DOI: 10.1080/ 15732471003588387.Avižienis, I., Laprie, J.C. and Randell, B. (2004) ‘Dependability and its threats: a taxonomy’, 18th IFIP World Computer Congress, Toulouse, France, Vol. 156, pp.91– 120, Kluwer Academic Publishers.Bentley, J.P. (1993) An Introduction to Reliability and Quality Engineering, Longman, Essex.Biondini, F. and Frangopol, D.M. (2008) ‘Structural robustness of deteriorating systems’, Proceedings of Handling Exceptions in Structural Engineering (HE08), 13–14 November, Rome, Italy.Biondini, F., Bontempi, F., Frangopol, D. and Malerba, P.G. (2004a) ‘Reliability of material and geometrically non-linear reinforced and prestressed concrete structures’, Computer & Structures, Vol. 82, Nos.13/14, pp.1021–1031.Biondini, F., Bontempi, F. and Malerba, P.G. (2004b) ‘Fuzzy reliability of concrete structures’, Computers & Structures, Vol. 82, pp.1033–1052.Biondini, F., Frangopol, D.M. and Restelli, S. (2008) ‘On structural robustness, redundancy and static indeterminacy’, ASCE/SEI 2008 Structures Congress, Nos. 13–14, ASCE, SEI, Vancouver, BC, Canada.Bjerrum, J., Larsen, E., Bak, H. and Jensen, F. (2006) ‘Internet-based management of major bridges and tunnels using DANPRO+’, Conference on Operation, Maintenance and Rehabilitation of Large Infrastructure Projects, Bridges and Tunnel, Copenhagen.Bontempi, F. (2006) ‘Basis of design and expected performances for the Messina Strait Bridge’, Proceedings of BRIDGE 2006, Hong Kong (on CD-ROM).Bontempi, F., Crosti, C., Giuliani, L. and Petrini, F. (2009) ‘Principi fondamentali ed applicazioni dell’approccio prestazionale’, (in Italian), Antincendio, pp.106–119, May, ISSN E012421.Bontempi, F., Giuliani, L. and Gkoumas, K. (2007) ‘Handling the exceptions: robustness assessment of a complex structural system’, (invited lecture) Proceedings of the 3rd International Conference on Structural Engineering, Mechanics and Computation (SEMC), pp.1747–1752, Cape Town, South Africa.Bontempi, F., Gkoumas, K. and Arangio, S. (2008) ‘Systemic approach for the maintenance of complex structural systems’, Structure and Infrastructure Engineering, Vol. 4, No. 2, pp.77–94.Brando, F., Testa, R.B. and Bontempi, F. (2010) ‘Multilevel structural analysis for robustness assessment of a steel truss bridge’, IABMAS 2010, The Fifth International Conference on Bridge Maintenance, Safety and Management, 11–15 July, Philadelphia, USA.Bridge Management in Europe (BRIME), Deliverable D6 (2003) ‘Experimental assessment methods and use of reliability techniques’, Demands and Longer Lives, Project start and end date: 2003-12-01–2007-11-30.CAN/CSA-S6-00 (2000) Canadian Highway Bridge Design Code and Commentary, Canadian Society for Civil Engineering (CSCE).Casas, J.R. (2006) ‘Bridge management: actual and future trends’, in Bridge Management, Life Cycle Performance and Cost, pp.21–30, Taylor and Frances, London.
Reliability based approach for structural design and assessment 89COWI (2007) ‘Guidelines for load and resistance assessment of existing European railway bridges’, Report of the WP4 of the integrated research project ‘Sustainable Bridges – Assessment for Future Traffic Demands and Longer Lives’ funded by the European Commission within 6th Framework Programme.Crosti, C. (2009) ‘Structural analysis of steel structures under fire loading’, Acta Polytechnica, Vol. 49, No. 1, pp.21–28.Crowder, B., Stevens, D.J., Hall, B. and Marchand, K.A. (2008) Unified Progressive Collapse Design Requirements for DOD and GSA, 2008 Structures Congress – Crossing Borders, Vancouver, Canada, 24–26 April 2008.Faber, M. (2006) ‘Robustness of structures: an introduction’, Structural Engineering International, SEI, May, Vol. 16, No. 2, pp.101–107.Franchin, P., Pinto, P.E. and Rajeev, P. (2010) ‘Confidence factor?’, Journal of Earthquake Engineering, Taylor and Francis, Vol. 14, No. 7, pp.989–1007.Frangopol, D. and Das, P. (1999) ‘Management of bridge stocks based on future reliability and maintenance cost’, Current and Future Trends in Bridge Design, Construction and Management, pp.45–58, Thomas Thelford.Frangopol, D.M. and Curley, J.P. (1987) ‘Effects of damage and redundancy on structural reliability’, Journal of Structural Engineering, Vol. 113, No. 7, pp.1533–1549.Frangopol, D.M. and Strauss, A. (2008) ‘Bridge reliability assessment based on monitoring’, Journal of Bridge Engineering, Vol. 13, No. 3, pp.258–270.Gentili, F., Crosti, C. and Giuliani, L. (2010) ‘Performance based investigation of structural systems under fire’, 4th International Conference on Structural Engineering, Mechanics and Computation (SEMC’10), September 2010, Cape Town, South Africa.Ghosn, M. and Moses, F. (1998) NCHRP Report 406 Redundancy in Highway Bridge Superstructures, Transportation Research Board, Washington DC.Giuliani, L. (2009) ‘Structural integrity: robustness assessment and progressive collapse susceptibility’, PhD thesis, University of Rome “La Sapienza”.Giuliani, L. and Bontempi, F. (2009) ‘Numerical strategies for structural robustness assessment’, Proc. of the 2nd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2009), 22–24 June 2009, Island of Rhodes, Greece.Gulvanessian, H. and Vrouwenvelder, T. (2006) ‘Robustness and the eurocodes’, Journal of the International Association for Bridge and Structural Engineering (IABSE), Structural Engineering International, Vol. 16, No. 2, pp.167–171.Gulvanessian, H., Calgaro, J-A. and Holický, M. (2009) Designers’ Guide to EN 1990 – Eurocode: Basis of Structural Design, Thomas Telford, London.Handling Exceptions in Structural Engineering (HE20 08) (2008) Bontempi, F. (Ed.), Sapienza University of Rome, available at http://www.francobontempi.org/handling.php (accessed on 02 February 2010), 10.3267/HE2008.Handling Exceptions in Structural Engineering Workshop, Rome (2008) DOI: 10.3167/HE2008.Handling Exceptions in Structural Engineering Workshop, Rome (2010) DOI: 10.3267/HE2010.HMSO (2001) Design Manual for Roads and Bridge (DMRB), UK.IABMAS 08 (2008) ‘Special session: structural robustness’, organized by Bontempi, F. and Starossek, U., 13–17, July, Seoul, Korea.IABMAS 10 (2010) ‘Special session: advances in structural robustness: dependability framework’, organized by Starossek, U. and Bontempi, F., 11–15 July 2010, Philadelphia, USA.ISO 13822 (2001) Bases for the Design of Structures – Assessment of Existing Structures.ISO 2394 (1998) General Principles on Reliability for Structures.
90 S. ArangioIvezić, D., Tanasijević, M. and Ignjatović, D. (2008) ‘Fuzzy approach to dependability performance evaluation’, Quality and Reliability Engineering International, Vol. 24, No. 7, pp.779–792, doi: 10.1002/qre.926.Joint Committee on Structural Safety (JCSS) (2001) Diamantidis, D. (Ed.): Probabilistic Assessment of Existing Structures, RILEM Publications, Bagneux-France, ISBN: 2-912143- 24-1.Kühn, B. et al. (2004) ‘Review by questionnaire on guidelines and standards on the assessment of existing structures’, Report WGA-0604-06 of ECCS Technical Committee 6 “Fatigue”, Working Group A, available at http://icom.epfl.ch/ECCSTC6/.Liu, W.D., Neuenhoffer, A., Ghosn, M. and Moses, F. (2001) NCHRP Report 458 Redundancy in Highway Bridge Substructures, Transportation Research Board, Washington DC.Melchers, R.E. (1999) Structural Reliability Analysis and Prediction, 2nd ed., Wiley & Sons Ltd., Baffins Lane, Chichester, England.Moses, F. (2001) ‘Calibration of load factors for LRFR bridge evaluation’, NCHRP Report 454, National Cooperative Highway Research Program, Transportation Research Board, National Research Council, Washington, DC.Nahman, J. (2002) Dependability of Engineering Systems, Springer-Verlag, Berlin.Norme tecniche per le costruzioni (NTC) (2008) D.M. Infrastrutture 14 gennaio 2008 (in Italian).National Aeronautics and Space Administration (NASA) (2007) Systems Engineering Handbook, available at http://www.nasa.gov (accessed on 16 October 2011).Ortolani, F. and Spizuoco, A. (2009) ‘Alluvione del messinese del 1 Ottobre 2009’, La colata fangoso-detritica del Torrente Racinazzo che ha devastato Scaletta Zanclea Marina, available at http://www.scomunicando.it/cronaca-provinciale/alluvione-del-messinese-del-1-ottobre- 2009 (accessed on 20 February 2011).Petrini, F., Manenti, S., Gkoumas, K. and Bontempi, F. (2010) ‘Structural design and analysis of offshore wind turbines from a system point of view’, Wind Engineering, Vol. 34, No. 1, pp.85–108, Multi-Science Publishing Company: Brentwood, UK, ISSN 0309-524X, DOI: 10.1260/0309-524X.34.1.85.Rücker, W., Hille, F. and Rohrmann, R. (2006) ‘F08a guideline for the assessment of existing structures’, SAMCO Final Report, Federal Institute of Materials Research and Testing (BAM), Berlin.SAMARIS (2006) ‘Guidance for the optimal assessment of highway structures’, Final Report to the European Commission, deliverable D30, doc. SAM-GE-DE30.Schneider, J. (1997) ‘Introduction to safety and reliability of structures’, IABSE – AIPC – IVBH.Smith, I. (2001) ‘Increasing knowledge of structural performance’, Structural Engineering International, Vol. 12, No. 3, pp.191–195.Starossek, U. (2009) Progressive Collapse of Structures, Thomas Telford Publishing, London.Starossek, U. and Haberland, M. (2008) ‘Approaches to measures of structural robustness’, 2008 Structures Congress – Crossing Borders, 24–26 April 2008, Vancouver, Canada.Starossek, U. and Haberland, M. (2010) ‘Disproportionate collapse: terminology and procedures’, ASCE, Journal of Performance of Constructed Facilities, Vol. 24, No. 6, pp.519–528.Starossek, U. and Wolff, M. (2005) ‘Design of collapse-resistant structures’, Workshop on Robustness of Structures, JCSS & IABSE WC 1, 28–29 November 2005, Garston, Watford, UK.Starossek, U., Smilowitz, R., Waggoner, M., Rubenacker, K.J. and Haberland, M. (2011) ‘Report of the terminology and procedures sub-committee (SC1): recommendations for design against disproportionate collapse of structures’, in Ames, D., Droessler, T.L. and Hoit, M. (Eds.): Proceedings of the Structures Congress 2011 – ASCE, Las Vegas, Nevada, USA, 14–16 April, pp.2090–2103.
Reliability based approach for structural design and assessment 91Swiss-code SIA 263 (2003) Steel Structures, Swiss Society of Engineers & Architects.UNI EN (1990) Eurocode: Basis of Design, European Committee for Standardization (CEN), Brussels, EN 1990, 2002.Vrouwenvelder, T. and Scholten, N. (2010) ‘Assessment criteria for existing structures’, Structural Engineering International, Vol. 20, No. 1, pp.62–65.Yan, D. and Chang, C. (2006) ‘Vulnerability of long-span cable-stayed bridges under terrorist event’, Proceedings of the International Conference on Bridge Engineering – Challenges in the 21st Century, Hong Kong.