Design with Regard to Explosion - Response of a structural system and equivalent 2DOF model

Abstract

Structural elements subjected to explosion loads are often transformed to simplified Single Degree of Freedom (SDOF) mass-spring system in order to facilitate and expedite their design. This simplification has showed good results for single vibrating elements, i.e. beams or slabs on stiff supports. However, if a structural system consisting of a beam supported on two beams is considered, a 2DOF mass spring system is needed to capture the response of the structure. Models were created in the commercial FE software ADINA, and several parametric studies were carried out for structures with various stiffness and mass ratios. First, a beam on spring supports was studied as an intermediate step between a simple beam and a structural system. Then, the beam-on-beam structural systems were modelled and the equivalent 2DOF system was created and verified so that its response was agreeing with the one obtained from Finite Element Method. Modification of ordinary SDOF systems was carried out, resulting in the systems being capable of describing the behaviour of each part of the structural system approximately. It was discovered, that the response of the structure with an intermediate stiffness ratio (between 3 and 8) is too complex to be described by a SDOF simplification, and there an equivalent 2DOF system must be used. Outside of this range, both 2DOF and modified SDOF systems give reasonable and acceptable results. After a detailed study, it was found that treating the element as a part of a structure can result in its displacements being reduced up to 40-50 %, i.e. it may be very conservative to assume a single vibrating element in such a case.