ANALYSIS OF POSSIBLE CAUSES AND MECHANISMS OF DESTRUCTION OF BUILDING STRUCTURES

Abstract

In order to better understand the wave properties of the Timoshenko equation, the derivation of the refined equation from the equations of the plane elasticity problem for a long band is carried out. The simple iterations method is used for the derivation. It includes known methods: the semi-inverse method of Saint-Venant and Picard operator. In accordance with the semi-inverse method, a part of the unknowns is defined, which are interpreted as the values of the initial (zero) approximation. Proceeding from them, a sequential computation is carried out using a sequence of the four Picard operators in such a way that the outputs of the one operator are the inputs for the next. Calculating in this way all the unknowns in the zeroth approximation by the direct integration over the transverse coordinate, the values of the initial approximation are calculated in the first approximation. These quantities are small of the second order with respect to the dimensionless thickness. Expressions for the unknowns are obtained as power functions of the transverse coordinate and as a function of the deriva-tives along the longitudinal coordinate. By the Banach fixed point theorem, the computation process is asymptot-ically convergent one. After this, boundary conditions on the long sides are satisfied by means of the derivatives of the arbitrariness, depending only on the longitudinal coordinate. This gives us the ordinary differential equations for the determination of these arbitrary functions. In turn, the integration constants of the last equations can be found from the conditions on the short sides of the strip. The ordinary differential equations are split into equations for slowly varying and quickly varying quantities. The slowly changing values give the classical solu-tion of the beam oscillations. The quickly varying solutions give the perturbed solutions describing high-frequency oscillations and singularly perturbed wave solutions for time-concentrated effects. Some of these soluions are absent in the Timoshenko equation. It is assumed that the selected shear waves provoke in the buildings subjected to the rapid impacts (shock by airplane, explosions, and seismic movements of the base) the interruptions of interlayers between the floors and subsequent progressive collapse.