COMPRESSED ELEMENTS WITH A VARIABLE IN LENGTH STIFFNESS EQUILIBRIUM FORM STABILITY DETERMINATION
DOI:
https://doi.org/10.26906/znp.2019.53.1886Keywords:
equilibrium form, compressed reinforced concrete columns, software complex, stability loss equationAbstract
One of the most powerful modern methods of calculating complex building structures is the finite element method in the
form of a displacement method for discrete systems, which involves the creation of a finite element model, that is, splitting
the structure into separate elements within each of which the functions of displacements and stresses are known. On the basis
of the displacement method and the methods of iterations and half-division, an algorithm for stability calculation of the first
kind equilibrium form of compressed reinforced concrete columns with hinged fixing at the ends, considering the stiffness
changing has been developed. The use of the above methods enables to determine the minimum critical load or stress at the
first bifurcation and their stability loss corresponding form. The use of matrix forms contributes to simplification of high order stability loss equation. This approach enables to obtain the form of stability loss that corresponds to the critical load.
References
Hartmann, F. (1985). The Mathematical Foundation of Structural Mechanics. Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-642-82401-2
Lacarbonara, W. (2013). Nonlinear Structural Mechanics. Boston: Springer. https://doi.org/10.1007/978-1-4419-1276-3
Hjelmstad, K.D. (2005). Fundamentals of Structural Mechanics. Boston: Springer. https://doi.org/10.1007/b101129
Hulse, R. & Cain, J. (1991). Structural Mechanics. London: Palgrave. https://doi.org/10.1007/978-1-349-11897-7
Shkurupiy, O., Mytrofanov, P. & Masiuk, V. (2018). Calculation of The Stability of the Form of Equilibrium of Discrete Systems. International Journal of Engineering & Technology, 7(3.2), 401-407. http://dx.doi.org/10.14419/ijet.v7i3.2.14561
Shkurupiy, O.A. (2015). Stability of equilibrium and dynamics of discrete systems. Poltava: PoltNTU.
Kyselev, V.A. (1980). Structural mechanics. Special course. Moscow: Stroyizdat.
Smyrnov, A.F., Aleksandrov, A.V. & Lashchenikov, B.Y. & Shaposhnikov N.N. (1981). Structural mechanics. Dynamics and stability of structures. Moscow: Stroyyzdat.
Bazhenov, V.A., Perel'muter, A.V. & Shyshov, O.V. (2008). Structural Mechanics. Computer Technology. Kyiv: Karavela.
Faddeev, D.K. & Faddeeva, V.N. (1960). Computational methods of linear algebra. Moscow: Fyzmatlyt.
Bazhenov, V.A. Dekhtyarnik, V.A. & Dekhtyarnik, Ye.S. (1998). Structural Mechanics. Dynamics of structures. Kyiv: IZMN.
Smith, P. (2001). An Introduction to Structural Mechanics. Palgrave Macmillan.
Severyn, V., Pashchenko, A. & Mytrofanov, P. (2018). Probabilistic Analysis of Structures Under Snow Load.
International Journal of Engineering & Technology, 7(3.2), 339-342.