# Ultimate Capacity of Biaxially loaded R.C. Columns of Arbitrary cross-section using parametric mapping

**Ferdinand F. Bengusta**

Thesis (MS Civil Engineering)--University of the Philippines Diliman-2003

**Abstract**

A numerical analysis for the determination of the ultimate strength of reinforced concrete columns of arbitrary cross-sections subjected to biaxial bending is presented. In satisfying equilibrium of forces and bending moments at a cross-section, the magnitude and location of the stress block normal to the member cross-section and the location of the neutral axis must be determined. In locating the neutral axis, a procedure akin to the initial stress method in finite element analysis of non-linear continua is adopted. This iterative procedure calculates the non-linear response to loading through a series of iterations, assuming elastic response in each step. In determining the magnitude and location of the stress block, parametric mapping is used. Parametric mapping of non-dimensionalized local coordinates and Cartesian coordinates which define the square and the rectangular hexahedronal domain and two and three-dimensional isoparametric element with curved boundaries, respectively, was adopted. In this technique, evaluation of the transformed integral equations was conveniently carried out by the Gaussian integration scheme.

Subject Index : Reinforced concrete,