Equivalent Torsional-Warping Stiffness of Cores with Thin-Walled Open Cross-Section Using the Vlasov Torsion Theory

Abstract

In order to calculate the equivalent torsional-warping stiffness of the Reinforced Concrete (RC) cores that have thin-walled open cross-section, a new analytical methodology, which combines the Vlasov torsion theory with the Bernoulli bending theory, is presented herein. As the basis of the calculations, we use the principal elastic reference system of the core from this we consider that is known. Furthermore, we consider that the principal start point of the open cross-section, the core's exact sectorial coordinates, as well as, the warping moment of inertia of the core are all known, also. Moreover, the two above-mentioned theories (Vlasov and Bernoulli) are together combining and in the end, the equivalent torsional-warping stiffness of the core has resulted. This torsional-warping stiffness of the core is very useful in the right simulation of a building that consists of frames, walls, and cores. The present methodology is presented via two special numerical cases of RC cores for illustrative purposes. The present article gives a documented solution in the simulation of the cores and proposes to use an ideal-equivalent column that has to be located on the elastic center of the core. This equivalent column must be provided with a diagonal, lateral-stiffness matrix that represents the properties of the real core and thus this lateral-stiffness matrix of the core is proposed. Finally, in order to check the reliability of the results of various analysis software, the proposed procedure can be used as a benchmark analysis method of cores.