DYNAMICAL PROCESSES ANALYSIS IN THE LOAD BEAMS AFTER PARTIAL DESTRUCTION

Abstract eng:
The study of dynamic processes in loaded constructions at sudden changes in their structure and (or) design scheme, due to various reasons, is an urgent task as part of the solution to the problem to ensure reliable and safe operation of facilities. This paper considers the stress-strain state at the ends of a double hinged beam with rectangular cross section in a state of pure bending. It is assumed that at some point the beam is separated from a layer of a certain thickness, which induces a sudden change in the area, moments of inertia and strength of the cross-section. Moreover, the instantaneous partial destruction, changing the calculation scheme of the beam is simulated. Before the formation of the structural damage, the reaction of the construction is defined by a static exposure. The sudden formation of a defect leads to lower overall stiffness of the structure, which no longer provides a static equilibrium of the system. Inertial and dissipative forces, which have suddenly emerged, cause a dynamic response. The beam is set in motion, in which the maximum stresses exceed the stresses developing in a quasi-static layer separation. Mathematically, the problem reduces to the integration of the inhomogeneous differential equation of the 4th order with inhomogeneous boundary conditions for the given initial conditions. The novelty of the approach lies in the fact that the solution is based on the decomposition of the movement on the modes of the natural oscillation of a damaged beam, but the initial conditions are formulated for an undamaged beam. The effect of the layer sudden separation is characterized quantitatively by coefficients such as a ratio of maximum dynamic stress to the maximum static stress and to the stress, developing at the quasi-static transition of a solid beam to a partially damaged one. These coefficients and the time to reach maximum values of stress are determined depending on the degree of damage to a beam (thickness of a separated layer). These quantitative results demonstrate a significant excess (8-fold while reducing by half the height of the cross section) of stresses in a statically loaded beam with a sudden change in the cross-sectional area by reducing its height. The study of the parameters of additional stresses and time of their occurrence can be useful when assessing the vitality of a structure and its elements and time of evacuation in an emergency.

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