Open AccessLIMIT STATE OF ARCHES OF VARIABLE STIFFNESS
Author(s) -
Mykola Soroka
Publication year - 2020
Publication title -
vìsnik odesʹkoï deržavnoï akademìï budìvnictva ta arhìtekturi
Language(s) - English
Resource type - Journals
ISSN - 2415-377X
DOI - 10.31650/2415-377x-2020-81-97-104
Subject(s) - arch , finite element method , bending moment , structural engineering , limit state design , numerical analysis , stiffness , limit analysis , limit load , mathematics , convergence (economics) , boundary value problem , state variable , mathematical analysis , engineering , physics , economics , economic growth , thermodynamics
. An algorithm is proposed for numerically solving the problem of finding the maximum load for flat bar systems having a rectangular section of variable height. The material is elastoplastic; its physical properties are described by the Prandtl diagram. It is assumed that the compressive and tensile strength of the material are different. The modulus of elasticity in tension and compression is the same. The limiting state of a rectangular cross section under the simultaneous action of a longitudinal force and a bending moment is described. Using the proposed algorithm, a program was developed for calculating rod systems by the limit equilibrium. The C++ programming language was used to create a program for the numerical determination of the ultimate load for rod systems. The finite element method was used as the most universal to write a module that performs static analysis of the bar system. Its use makes it easy to design rod systems of arbitrary configuration with arbitrary boundary conditions. As a test example, a hinged circular arch loaded with a uniformly distributed vertical load is considered. Analytical dependences are written, which allow to obtain the ultimate load for an arch of variable section. Examples of calculating the limiting state of the arch and comparing the ultimate loads with and without longitudinal force are considered. The analytical solution is compared with the numerical solution found by the author's program. Good convergence of analytical and numerical solutions is shown. The proposed algorithm for the numerical calculation of the limit states uses the so-called direct method for finding the ultimate load. This allows not only to obtain the value of the ultimate load, but also to establish the order of formation of plastic regions in the sections of the rod system. The calculation algorithm does not imply the use of iterative processes, which has a positive effect on the speed of calculations. Within the accepted assumptions, the calculation methodology is accurate.