Peer-reviewed by international ex- perts and accepted for publication by SEI Editorial Board Paper received: June 28, 2011 Paper accepted: September 21, 2011 Structural Engineering International 1/2012 Scientific Paper 99 Assessing the Consequences of Building Failures Victoria Janssens, PhD Student; Dermot W. O’Dwyer, Senior Lecturer; Trinity College, Dublin, Ireland; and Marios K. Chrys- santhopoulos, Prof., University of Surrey, Guildford, UK. Contact: janssenv@tcd.ie DOI: 10.2749/101686612X13216060213473 At present, the recommended strat- egy 2 leading to an acceptable level of robustness for CC3 structures involves the undertaking of a systematic risk assessment, taking into account both foreseeable and unforeseeable events. The risk assessment can be either qualitative or quantitative but in either case, the acceptable risk ought to be considered through a consideration of the likelihood of undesirable events and associated consequences (typi- cally in the form of a risk matrix). This paper focuses on the explicit modelling and quantification of consequences, as a necessary component in a risk-based robustness evaluation. Risk-based Robustness Within a risk-based framework for the evaluation of robustness 3, 4 , the risk R E associated with a particular event E may be assessed through the following product: E E E R pC = (1) where p E is the probability of the (adverse) event and C E are the conse- quences arising from the occurrence of the event. As formalised in EN 1991- 1-7, 2 a scenario approach with respect to potential hazards, direct damages and follow-up failures can be adopted, thereby expressing the risk related to a particular structure through the fol- lowing equation: ( ) ( | ) ( | ) ( ) S D N N i j i k k j ij PH PD H PS D C S R = i=1 H N ∑ j=1 k=1 ∑∑ (2) where it is assumed that the structure is subjected to N H different hazards (corresponding to single or multiple events), that the hazards may dam- age the structure in N D different ways (which can be dependent on the con- sidered hazards) and that the perfor- mance of the damaged structure can be discretised into N S adverse states S k with corresponding consequences C(S k ). Moreover, P(H i ) is the prob- ability of occurrence (within a refer- ence time interval) of the ith hazard, P(D j |H i ) is the conditional probability of the jth damage state given the ith hazard and P(S k |D j ) is the conditional probability of the kth adverse overall Abstract The consequences of structural failures, as a result of a hazard, can take several forms: from material/structural damage and human injuries/fatalities to func- tional downtime and environmental impact. Within a risk-based robustness framework, consequence modelling is an important step in estimating risk, both in determining the robustness of a building and in assessing the benefit of pos- sible robustness-improving measures. This paper highlights the principles to be adopted in estimating consequences arising from potential building failures. The multi-dimensional and variable aspects of the “cost of failure” are discussed, and the various types of consequences arising from building failure are examined. In this respect, a categorisation of failure consequences is presented, together with associated models for quantifying their magnitude. Keywords: robustness; consequences; buildings; collapse; risk assessment. Introduction Consideration of failure conse- quences is essential in structural design and assessment, including reli- ability differentiation 1 and robust- ness evaluation. 2 Table 1 highlights the consequence classes currently adopted in the Eurocode suite; as can be seen, consequences are assumed to be dependent on the building type and function. For the purpose of robustness evaluation, these classes are further elaborated with respect to the size of the building (number of storeys, floor area), function and occupancy. The distinction between consequence classes, particularly between CC2 and CC3, is inevitably subjective to a degree. The collapse of a ten-storey building (currently classed as CC2) could result in high loss of human life, depending on the nature and time of the accident. In this regard, a classifica- tion based on quantitative thresholds for human and other consequences, rather than indirect indicators, would enable a rationalisation of acceptable risks and of the benefits from specific mitigation measures. Class Description Examples CC1 Low consequence for loss of human life, and economic, social or environmental consequences are small or negligible Agricultural buildings where people do not normally enter (e.g. storage buildings, greenhouses) CC2 Medium consequence for loss of human life, economic, social or environmental consequences are considerable Residential and office buildings, public buildings where failure consequences are medium (e.g. office building) CC3 High consequence for loss of human life, or economic, social or environ- mental consequences are very great Grandstands, public buildings where the consequences of failure are high (e.g. concert hall) Table 1: Consequence classes adopted in EN 1990 1 SEI Authors Copy