INELASTIC DYNAMIC ANALYSIS OF CONCRETE FRAMES UNDER NON-NUCLEAR BLAST LOADING

Abstract

The blast response of the structure has been drawing attention of engineers and scientists in all over the world for both military and civilian fields. The military engineers so far have focused mainly on the analysis and design of blast resistant shelters for defense establishments. Very little published literature in the area of the blast effect on the framed multistoreyed building are available. The present investigation is therefore aimed to study the response of multistorey reinforced concrete framed structure to ground blast explosive. Explosives when detonate on or above the ground results in a very rapid release of large amounts of energy with in a short time, which generates a pressure wave in the surrounding medium, known as a shock wave, with a sudden increase in pressure at the front known as a shock front. Present state of knowledge has many limitation in assessing the blast loads on the structure, especially the interaction between shock wave and the buildings. In this study, a rational basis for simulation of the blast wave and the blast loads acting on the framed structure has been proposed. Initially the blast wave is defined by two parameters, the potency of the explosive and it's distance from the building. The change of blast wave properties with time and distance is considered, so that, on different elements of the structure, different blast loads are acting with it's own variation with time. The model takes into accounts the time lag in blast loading acting on different elements. Moreover, the 3D nature of blast loading and it's different way of interactions on front, top, sides and rear faces of the structure has been modelled. The reinforced concrete framed building has been modelled using two types of elements, beam-column element and flat shell element for modelling the frame and floor slabs/panels respectively. The stiffness matrix and consistent mass matrix for 3D beam with two rigid ends have been developed and presented in an explicit form. The stiffness and mass matrix for flat shell element have been defined through usual finite element procedure considering the inplane and bending actions uncoupled. vm A computer program has been developed for static and dynamic analysis of 2D and 3D framed building by integrating finite element and stiffness methods. Direct step by step integration is used for dynamic analysis using Newmark's predictor-corrector method for the solution of the resulting equations of motion. The program has been validated for elastic static and dynamic analysis of different type of structures by taking suitable test examples from the published literature. A good agreement between the predicted results obtained using the developed computer program and the published test results has been observed. To extend the analysis into inelastic range, the problem gets further complicated and suitable modelling for r. c. member is required to simulate the actual behaviour of the member at affordable computation cost and time. Different analytical models commonly used in the inelastic dynamic analysis of r.c. frames are discussed. Among these models, the lumped plasticity model has been selected in this study. The concept of plastic hinge has been used to predict the inelastic behaviour of this model. Each beam-column element is represented by an elastic element and the inelastic action is assumed to be lumped at the ends of the element in a form of plastic hinge. For 2D analysis, the interaction of axial force and moment has been considered to develop a plastic hinge. While for 3D analysis the interaction of axial force, bending moments and torsion has been considered. To include the interaction of different forces and moments to develop a plastic hinge, actual analysis of r.c. section has been performed considering nonlinear material modelling. The nonlinear stress-strain relation of concrete and elasto-strain hardening model for steel reinforcement have been used to develop the yield surface for 2D and 3D analysis. The effect of high strain rate associated with blast loading has been considered by increasing the ultimate strength properties of concrete and steel. Third degree polynomials using regression analysis has been fitted to the results obtained from r.c. section analysis to represent the mathematical model of yield surface for each section. There is a good co-relation between the theoretically obtained and the mathematically modelled yield surfaces. Each floor slab has been discretized by a single 4-node flat shell element and assumed to bahave elastically. For panels, the inplane action lx is only considered in the nonlinear nnalysis. Two different layer have been used to simulate concrete and steel assuming full bond between them. Suitable models for different nonlinear phenomena such as cracking, yielding and crushing of concrete and yielding of steel has been adopted from the available models in literature and incorporated in the proposed formulation. The adopted yield surface for concrete in compression include the interaction of different stresses (<r <r <r ). The first stress invariant x y xy and the second deviatoric stress invariant are used to define the yield surface. Semeared crack approach with fixed crack angle is adopted for tensile cracking. Initiation of cracks depends upon maximum tensile stress. Closing and reopening of cracks is allowed in the model following a fictitious path. The shear transfer across crack due to aggregate interlock and dowel action is incorporated by taking a reduced value of shear modulus. The effect of tension stiffness is adopted using simple model. The developed yield surface integrated with the theory of plasticity has been used to develop a general procedure suitable for inelastic static and dynamic analysis for 2D and 3D problems. The inelastic procedure predicts the continuously deteriorating stiffness of the frame and panels due to on-set of plasticity in the frame members and cracking, yielding and crushing of panels. Different 2D and 3D numerical examples have been solved to study the response of r.c. frame and frame-panel system to different potency of explosive charges located on the ground at different distances from the system. From numerical experiments performed throughout this work, it can be concluded that, the proposed computational model, suggested analytical procedures and the developed computer program are able to predict the elastic as well as the inelastic blast response of 2D and 3D r.c. frame-panel system adequately.