Methodology for determining progressing ultimate states based on the displacement method

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Abstract

Solving of calculation problems for building structures is currently based on the principle of minimum total energy of structures deformation. However, it is not possible to determine the remaining bearing capacity of the structure using this principle. In the study it is proposed to use the criterion of critical levels of deformation energy to solve this problem. As a result, the ultimate state conditions of a design are formulated on the basis of extreme values of generalized parameters of designing over the whole area of their admissible values, including the boundary. The task is solved as a problem of eigenvalues for the stiffness matrix of the system. The extreme values of design parameters that correspond to critical energy levels are found, which are used to find the maximum possible value of the energy of deformation for the considered structure. The residual bearing capacity is calculated by the value of residual potential energy, which, in turn, is equal to the difference between the maximum possible value of the deformation energy of the structure and the work of external forces. A gradual methodology for investigating the progressive ultimate limit state is proposed, which is based on the sequential exclusion of those elements where the onset of the ultimate limit state is expected firstly. An example of the practical use of the proposed methods is given on the example of calculating a simple but visual design - a statically indeterminate truss.

About the authors

Leonid Yu. Stupishin

National Research Moscow State University of Civil Engineering

Email: lusgsh@ya.ru
ORCID iD: 0000-0002-1794-867X

Doctor of Technical Sciences, Professor, Department of Structural and Theoretical Mechanics, Institute of Industrial and Civil Engineering

Moscow, Russian Federation

Konstantin E. Nikitin

National Research Moscow State University of Civil Engineering

Author for correspondence.
Email: niksbox@yandex.ru
ORCID iD: 0000-0002-8003-4299

PhD, Associate Professor, of the Department of Structural and Theoretical Mechanics, Institute of Industrial and Civil Engineering

Moscow, Russian Federation

Maria L. Moshkevich

Southwest State University

Email: mmoshkevich@mail.ru
ORCID iD: 0000-0001-8749-2252

PhD in Economics, Associate Professor, Department of Industrial and Civil Engineering, Faculty of Construction and Architecture

Kursk, Russian Federation

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