Biaxial bending of slender HSC columns and tubes filled with concrete under short- and long-term loads: I) Theory

An analytical method that calculates both the short- and long-term response of slender columns made of high-strength concrete (HSC) and tubes filled with concrete with generalized end conditions and subjected to transverse loads along the span and axial load at the ends (causing a single or double curvature under uniaxial or biaxial bending) is presented. The proposed method, which is an extension of a method previously developed by the authors, is capable of predicting not only the complete load-rotation and load-deflection curves (both the ascending and descending parts) but also the maximum load capacity. The columns that can be analyzed include solid and hollow (rectangular, circular, oval, C-, T-, L-, or any arbitrary shape) cross sections and columns made of circular and rectangular steel tubes filled with HSC. The fiber method is used to calculate the moment-curvature diagrams at different levels of the applied axial load (i.e., the M-P-φ curves), and the Gauss method of integration (for the sum of the contributions of the fibers parallel to the neutral axis) is used to calculate the lateral rotations and deflections along the column span. Long-term effects, such as creep and shrinkage of the concrete, are also included. However, the effects of the shear deformations and torsion along the member are not included. The validity of the proposed method is presented in a companion paper and compared against the experimental results for over seventy column specimens reported in the technical literature by different researchers