Biaxial bending of RC rectangular column sections: Improved ‘load contour’ formulation

Abstract

AbstractIn design practice, the safety of any given rectangular reinforced concrete column section is checked by ensuring that all possible combinations of axial compression (Pu) and biaxial moments (Mux, Muy) at the ultimate limit state lie within its three‐dimensional load–moment interaction failure surface. Although such a check is facilitated by commercial software packages, it is traditionally carried out with the help of an approximate formulation of the ‘load contour’ at any given axial load level, first proposed by Bresler. The present study proposes an efficient algorithm, using a ‘modified thick layer integration’ approach and a ‘nested bisection’ method, to generate the ‘exact’ load contour (and thereby, the complete interaction surface) for any symmetrically reinforced column section, complying with the strength design requirements of ACI 318 (or EC2 or IS 456). The algorithm also generates a measure of the safety margin, called ‘demand‐to‐capacity ratio’ (DCR), defined as the ratio of the resultant design moment (Mu) to the moment capacity (Muθ) at a given axial load level (Pu). For an optimal code‐compliant design, the peak value of DCR generated from various factored load combinations (obtained from frame analyses) must be close to 1.0. The extent to which the peak DCR is less (or greater) than 1.0 provides a measure of over‐design (or under‐design) in a given context. After validating the algorithm, a parametric study was carried out on a spectrum of 36 different cross‐sections having different aspect ratios, bar arrangements and reinforcement percentages. The study reveals that the exponent in the approximate load contour formulation depends not only on the axial load (as currently assumed in ACI: SP17, EC2 and IS 456), but also on the percentage of longitudinal reinforcement. Accordingly, modifications have been suggested to improve the accuracy in these code‐prescribed approximate formulations of the load contour, for more economical and safe design.