Keywords: cross-section analysis, biaxial bending, reinforced concrete.

It is very difficult to determine the inner forces and the tangent modulus matrix of a reinforced concrete section subjected to axial force and biaxial bending. Mari et al. [1] and Tsao et al. [2] have developed the most popular fiber method. In 2001, Fafitis [3] transformed the double integration over the compressed concrete region into the integration along the cross section boundary using Green's theorem. In 2007, Sousa Jr. et al. [4] presented an analytical procedure based on a piecewise polynomial stress-strain relationship assumption.

This paper presents a general analytical integration for the evaluation of section resistant forces and tangent modulus of arbitrary polygonal reinforced concrete sections subjected to axial force and biaxial bending, no matter what kind of stress-strain relationship is supposed. In the procedure, a section is subdivided into a few number of quadrilaterals at first, corresponding to each of the contour sides. The inner forces and the sectional tangent modulus matrix of each quadrilateral then are calculated through analytical equations for any given deformation, based on the definition of several concrete constitutive integral functions. These constitutive integral functions are only dependent on the constitutive law equation only if it is a continuous function. Therefore, the procedure is analytically exact and computationally efficient. A nonlinear analysis of a cantilever was also conducted to verify its exactness, in which the section properties at the numerical integration point are calculated according to equations presented in this paper, and very good results were provided.

1

A.R. Mari, "Nonlinear geometric, material and time dependent analysis of three dimensional reinforced and prestressed concrete frames", Report No. USB/SESM-84/12, Department of Civil Engineering, University of California, Berkley, California, USA, June 1984.

2

W.H. Tsao, T.C. Hsu, "A nonlinear computer analysis of biaxially loaded L-shaped slender reinforced concrete columns", Computer and Structures, 49, 579-588, 1993. doi:10.1016/0045-7949(93)90062-I

3

A. Fafitis, "Interaction surfaces of reinforced-concrete sections in biaxial bending", J Struct Eng, 127(7), 840-846, 2001. doi:10.1061/(ASCE)0733-9445(2001)127:7(840)

4

J.B.M. Sousa Jr., C.F.D.G. Muniz, "Analytical integration of cross section properties for numerical analysis of reinforced concrete, steel and composite frames", Engineering Structures, 29, 618-625, 2007. doi:10.1016/j.engstruct.2006.06.002

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