Roll-over stability as a problem of high-rise buildings’ designing

Roll-over stability of tall buildings under wind loads is considered. The nonlinear nature of the problem is taken into account, including geometric, physical, and structural non-linearity. The problem is solved on the base of a system of linearized incremental equations of structural mechanics that describes the behavior of a system tall building - foundation soil. Several methods are examined for solving nonlinear problems of roll-over stability, specifically: 1) deformation method of systems equilibrium states tracing; 2) method of linearization of nonlinear equations and systems equilibrium states tracing; 3) method of linearization of nonlinear physical relations of a systems with constructive, static, geometric nonlinearity; 4) method of linearization of nonlinear physical relations of a system with constructive nonlinearity based on nonlinear incremental structural mechanics; 5) method of the deformation process tracing for a physically nonlinear soil base, given the increase of discharge zones and constructive nonlinearity. Each of these methods is used to solve a model task. These tasks take into account roll-over stability of high structures under action of wind loads. In general, the problem of roll-over stability of a high object can be represented as repeatedly nonlinear one with various types of non-linearity. In this regard, in the practice of high-rise buildings designing, it is necessary to develop scientifically and methodically substantiated methods of assessing roll-over stability, considering non-linear factors. Taking these factors into account will make it possible to assess the roll-over stability of a high-rise object more accurate.

THE ELASTOPLASTIC CALCULATION OF FRAMES USING THE DISPLACEMENT METHOD

We proposed a method for calculating statical indeterminacy frames taking into account plastic defor­mations, which is based on the use of a schematized diagram of material with hardening. Two types of standard beams with supports are used during the implementation of the displacement method (DM) and the elastic solu­tion of the problem: “fixed” - “pinned” and “fixed” - “fixed”, but unlike the elastic solution, standard beams con­tain plastic zones (PZs). So as the stresses in these zones did not exceed the limit of yielding in the nonlinear frame calculation, we took measures to transform the PZs into equal strength plastic zones (ESPZ). The calcula­tions were made for both types of beams for all single and load impacts. The frame calculation consists of two stages (elastic and plastic). At the elastic stage, we determine an elastic moment diagram and the corresponding load. For a practical use of the DM in a nonlinear frame calculation, we introduced a simplifying prerequisite sup­plementing the well-known hypotheses of the classical version of the method, and formulated a Statement of the limiting load. According to the Statement, each length of the PZ can correspond to the lower boundary of the lim­iting load. The plastic stage of the calculation is performed at a given length of the PZ using the method of se­quential loadings. At each loading stage, incremental equations are written using the DM equations, which estab­lish relations between incremental moments and the incremental load, that allows you to get the resulting moment diagram. This diagram represents a sum of the elastic diagram and the diagrams of incremental moments at all previous loading stages. According to the resulting diagram, we calculate the length of the PZ, together with the limiting load. The calculation is considered complete if the length of the PZ does not exceed the specified value within the margin of error.

Hybrid Natural Element Method for Elastic Large Deformation Problems

Elastic large deformation analysis based on the hybrid natural element method (HNEM) is presented in this paper. The natural neighbor interpolation is adopted to construct the shape functions for the HNEM. The incremental formulation of Hellinger–Reissner variational principle is used to derive discrete system of incremental equations under the total Lagrangian formulation. And the Newton-Raphson iteration is applied to solve these incremental equations. Compared with the natural element method (NEM), the HNEM can directly obtain nodal stresses of higher precision, which will bring advantage in the iteration process and improve computational efficiency in solving elastic large deformation problems. Some numerical examples demonstrate the validity of the HNEM for elastic large deformation problems.

A Beam Element for Geometric Nonlinear Dynamical Analysis

In this paper, a three-dimensional beam element is developed for geometric nonlinear dynamical analysis. This element is based on the co-rotational formulation, in which the displacements of beam element are subdivided into rigid body movements and elastic deformations. The formulations are derived from the continuum mechanics based Updated Lagrangian incremental equations. The element can undergo large deflections and rotations, but small strains are assumed in the deduction. The validity of this element is confirmed by comparing with the numerical results in other literatures.

A Study on Modelling the Plane Strain Behaviour of Sand and its Stability

The plane strain behaviour of sand is studied using, previously proposed, incremental model describing its pre-failure deformations. Original model has been formulated for the tri-axial configuration, and then generalized for 3D conditions. This 3D model was subsequently adapted to study deformations of sand in the plane strain conditions, in the x1; x3 plane. There are three unknowns in such a configuration, namely the principal strains "1; "3 and the principal stress σ2. Respective equations were derived, and then applied to study deformations of sand for chosen stress paths. The governing incremental equations were integrated numerically, and it was shown, for some loading paths, that σ2 epends linearly on the other principal stresses, so introduction of apparent Poisson’s ratio is justified, as a kind of approximation. Subsequent analysis of deformations of sand was performed using this concept, as well as using full system of governing equations.