Risk-Based Approach – Explosions and Structural Response

This manuscript introduces the Single Degree Of Freedom (SDOF) approach for predicting the response of structures being impacted by an explosion. The concept of pressure-impulse diagrams is introduced and identified as a valuable tool to be used during the analysis of results generated during the development of a risk-based quantitative assessment.


The interaction with a structure and a blast wave involves establishing the design of blast loads, setting the structural performance requirements and evaluating the structure to ensure that can withstand these loads within the required performance limits. For practical design purposes and in a risk-based quantitative assessment framework, it is convenient to adopt approximate methods which permit rapid analysis of even complex structures with reasonable accuracy. These methods usually require that both the structure and the loading be idealized in some degree. It is frequently possible to reduce the system to a Single Degree of Freedom (SDOF), a system in which only one type of motion is possible such that the position of the system at any instant can be defined in terms of a single coordinate. Structural elements can be represented by an equivalent SDOF and even though such elements which are parts of a complete structure, it is often permissible to treat them independently.

For the idealized system to perform in the same way as an actual structure, it is only necessary to make a proper selection of the system parameters. Transformation factors can be applied to obtain the equivalent mass, spring constant, load and resistance functions. The ideal spring mass system is selected such that the deflection of the mass is the same at some point of significance on the structure. The key point is that an idealized system which behaves timewise in exactly the same fashion as the actual structure can be constructed and then analyzed with relative ease.

The proposed method should not be regarded as merely a crude approximation. Problems in structural dynamics typically involve significant uncertainties, particularly with regard to loading characteristics. Complex methods of analysis are often not justified and are extremely time consuming and expensive. It is not practical to employ methods having precision much greater than that of the input of the analysis.

This paper proposes a detailed elasto-plastic SDOF numerical dynamic analysis for evaluating each structural element that conforms a blast-loaded closed rectangular building. The proposed methodology maximizes the most reliable criteria by balancing the required level of detail with the inherent uncertainties present in the problem definition. The method of analysis used is optimized because the loading effects of explosions cannot be precisely specified. Based on criteria and assumptions established in referred bibliography below, more detailed efforts would not be justified based on the mentioned inherent uncertainty of the input data analysis.

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