Derivation of P-I diagrams for axially preloaded beams using graphical method

Pressure-impulse (P-I) diagram method is used for the preliminary design and assessment of structures subjected to extreme events such as gas and bomb explosions. The P-I diagrams are sensitive to loading/supporting conditions and structural parameters, and need to be rebuilt to account for any changes in loads, supports and/or geometry. The present paper proposes a new graphical approach that enhances the efficiency of the P-I diagram method in the described situation. This approach is based on the extension of the P-I diagram by the addition of the complementary diagrams defining the position of each P-I curve. The graphical approach is developed in the dimensional and normalised forms. The dimensional approach provides efficient means for derivation of new P-I curves while the normalised approach for assessment of a structure in different structural states. The effectiveness of the proposed graphical approach (in both of its forms) is demonstrated using an axially preloaded beam subjected to transverse pressure load as a case study. The complementary diagrams are formulated as the force-impulse (F-I) and force-pressure (F-P) diagrams. The F-I relationship corresponding to the analysed structural system is obtained based on curve fitting as a parabolic function, while the F-P relationship as a linear function. The unique advantages of the proposed graphical approach are demonstrated and discussed. It is suggested that the new approach (especially in its normalised form) represents a convenient tool for rapid preliminary assessment of multiple typical structures exposed to blast loads and can be readily incorporated into the existing codes for design of structures subjected to extreme loads.