Center of Stiffness, Principal Axes and Principal Start Point of Thin-Walled Open-Sections of Cores: A New Modified Calculation Technique Based on Vlasov Torsion Theory

Abstract

The present paper deals with the exact calculation of the Principal Elastic Reference System of R/C Cores, which have thin-walled open section. A new modified technique based on Vlasov torsion theory is developed that examines the warping phenomenon of cores. The exact position of the elastic center (or shear center) of a core and the orientation of the principal axes of elasticity, as well as the exact calculation of warping constant, are special parameters since, on the one hand it strongly affects the in plan stiffness distribution of the building members, and on the other hand it affects the values of the building eigen-frequencies and mode-shapes. These parameters are particularly critical in seismic design of asymmetric multistorey buildings. Based on Vlasov torsion theory of cores with thin-walled open sections, a repetitive mathematical procedure about the calculation of the location of the elastic center of core and the principal start point of the section is proposed. This new modified technique can be applied to cores of any shape. Afterwards, the exact diagram of sectorial coordinates of the section, as well as the warping constant, are calculated. All the above-mentioned parameters are very useful in the simulation of the cores in numerical models that are going to use in linear and nonlinear seismic analysis of the structures. Knowing all mentioned parameters, the numerical accuracy of the finite element method on cores can be checked. Finally, a numerical example, where the proposed new modified technique is applied on a fully asymmetric core, is presented.