Limitations of the Standard Interaction Formula for Biaxial Bending

摘要

This paper illustrates the limitations and crudeness of the standard interaction formula for biaxial bending when compared to the analytical method in structural analysis. The comparison can now be made because the analytical method in predicting the ultimate strength of reinforced concrete circular and rectangular sections have been made available by the author in his book entitled 'Analytical Method in Reinforced Concrete'. The standard interaction formula assumes equilibrium of internal and external forces without actually demonstrating it. Thus, it cannot satisfy the basic requirement in any structural analysis mandating that summation of forces and moments are equal to zero. It also relates the external loads to the internal capacity of a section by a formula expressing the rations of these moments not to exceed unity. The analytical method can predict the capacity of a concrete section at any position of the capacity axis from zero to π/2. This is not possible with the interaction formula for biaxial bending. The analytical method shown by the author in his book precludes using this formula which was copied over and over again in codes of practice. In this age of computers number of equations to solve a problem is no longer a problem. It is time to implement the analytical method instead of continuing the status quo of the standard interaction formula. To this end this paper will demonstrate the justification of discarding the standard interaction formula by using the results of the analytical method and applying the interaction formula to the results. The comparison will show that the interaction formula underutilised the capacity of a concrete and steel section.