GRAPH ALGORITHM ON STABILITY PROBLEM OF REINFORCED CONCRETE COLUMNS

A simplified equilibrium equation is derived by assuming a quadratic parabola distribution of column curvature and using the principle of virtual work to compute the eccentricity due to second order effects. For cross-sectional resistance, the inverse method is conducted to determine the internal force from strain based on the constitutive relationships of steel and concrete. After comparing the precise method with the simplified method in Chinese Code for Design of Concrete Structures (GB50010-2010), a more reasonable and simple formula to determine the ultimate curvature is derived, in which the influence of reinforcement ratio is taken into account. All available solutions, which satisfy the equilibrium equation, can be drawn into a graph by designing and constructing an appropriate coordinate system. For each determining of reinforcement only three basic variables and four auxiliary lines need to be calculated and drawn in the graph respectively. The graph can be used as a simple and efficient tool for concrete reinforcement design.