Keywords: multi-story building failure, premeditated destructive events, failure modes, fault tree, fuzzy logic, fuzzy sets.

Civil engineers now are faced with addressing Premeditated Destructive Events (PDEs) in the design and construction of structures. Of greatest concern is the politically motivated PDE such as terrorist activities. In the light of the latest terrorist activities aimed at buildings, it has become clear that anti-social activities seem to be focused at prominent structures. These unfortunate incidents have made it a necessity to anticipate such occurrences in the design of structures so as to enable it to withstand such a mishap.

This paper presents the germinal work towards developing a system that enables the user to identify the "hot spots" of a designed building and hence correct the design so as to eliminate such points. The study focuses on the initial steps towards accomplishing a multi-story building safer from PDEs.

A structure is designed to withstand loads applied to it like dead load and live load. Depending on where the structure is built, design also takes into consideration wind load, snow load, and in extreme cases earthquake loading. But in light of the new incidents, a designer has to take into consideration other unlawful activities like a PDE while designing a prominent structure. But do we have such design methodology that takes into consideration these factors. The answer is both "Yes" and "No". Yes because there are some designs that try to minimize the chances of an external agent gaining access to a prominent structure to cause harm to it. But little work has been done that addresses the design criteria to aid the structure withstand the shock of, for example, a bomb blast.

The purpose of this study is to analyze the failure modes of structural components and develop design features aimed at delaying, if not nullifying, the partial or complete failure of the structure. This can be achieved, in short, by making every part of a structure strong enough to withstand anticipated loads including loads due to unprecedented events such as bomb blasts. Failure of the weak points of the building can cause consequent collapse of the remaining part of the structure. Hence, making the entire structure equally strong will eliminate "hot spots" of the building and subsequently prevent or delay partial or entire failure. In the worst scenario, if the design is such that the failure is "held off" for a few more minutes or hours, that by itself would make a difference in saving hundreds of lives by permitting people to escape from the structure before its collapse.

The analysis method used by the authors incorporates subjective judgment of structural performance from experts in the fault tree model. Fault tree analysis is used as a diagnostic method by relating component failure to failure of the structure. Contributing events are categorized into enabling events, triggering events, and loss of support events. Enabling events are due to internal problems and are designated as inadequate performance of designs, substandard materials, and poor workmanship. Triggering events are external events, such as explosion and fire. Loss of support events are due to the failure of the supporting component, for example, a slab cracks because one of the supporting columns has collapsed.

The authors use fuzzy fault-tree analysis as the basis for development of software that permits engineers to evaluate the structural components performance with PDE as a triggering event and building collapse at the top event. The rotational model is used to evaluate fuzzy expressions. Blockley's model and Baldwin's curve are incorporated in the software written using MS Excel macros. The software is based upon the method of partial matching, the angular model, the fuzzy set concept and fuzzy fault tree analysis.

For all of the concepts detailed above, a program is developed using Visual Basic and Macros in Microsoft Excel spreadsheets. The hidden rows of the spreadsheets have the detailed steps involved. Each of the spreadsheets is provided with a form button that pops up as user interface form for the entry of variables. The software processes the input variables and gives a corresponding output curve/angle/graph. The following software are available for the evaluation of the fault tree: (1) Assessment of the fault tree performance using fuzzy set concepts, (2) Method of partial matching using modus ponens deduction, (3) Fuzzy logic operations using angular models, and (4) Fuzzy fault tree analysis. The last method of analysis, namely fuzzy fault tree analysis, evaluates the whole fault tree to give a resultant curve for the top undesired event.

The software presented in this paper forms the basis for developing a system that enables the user to identify building vulnerability to PDEs. It permits these flaws to either be corrected in the design phase or in the case of existing structures, it permits effective retrofit design of the building to protect the structure and its occupants from PDE. This study takes the initial steps towards accomplishing a design and construction of a multi-story building that is safer from PDEs.

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