Dimensionless Pressure-Impulse Diagrams for Elastic Plastic and Elastic Plastic with Hardening Structural Members for SDOF Structural Systems

A pressure-impulse (P-I) diagram provides a quick tool to assess the resistance of a structural system to blast loads, based on a nonlinear single-degree-of-freedom (SDOF) analysis. Thus, instead of performing many SDOF analyses, the P-I diagram is the limit curve representing the combination of pressure and impulse for which the designed damage of the structure is achieved (commonly defined by the allowed maximum displacement). In this paper, nonlinear SDOF equations are represented in a dimensionless form for linear-elastic, elastic-plastic, and elastic plastic with hardening systems. Dimensionless P-I diagrams are derived for triangular blast load, and they are represented by the dimensionless parameters of the problem. Based on regression analysis, simplified empirical equations are developed to quickly calculate the dimensionless and absolute P-I diagram for a given case without performing any additional structural or numerical analysis. The accuracy of the suggested method is proved by statistical parameters and by a case study showing its capabilities. The study is limited to a solution of a classical SDOF system but may be extended to a more realistic scenario in which an equivalent SDOF equation is commonly adopted.