Minimum design bending moment for systems of equivalent stiffness

Abstract

In this article, the minimum design bending moment of concrete slender columns is studied by assuming a system of equivalent stiffness. For concrete structural parts such as slender columns, their stiffness is dependent on the loading, originated from lumped and distributed masses, and the rheological behavior of the material. The latter alters the concrete's modulus of elasticity, introducing changes over time. Basically, the desired transformation is from a one-dimensional non-prismatic system to another prismatic one which exhibits an equivalent bending stiffness. As the bending stiffness changes due to the change of the problem's independent variables, the geometric characteristics of the transformed system reflect the same dependence as the original system. This implies changes in the minimum design moment since it is linked to the dimensions of the equivalent section. To assess the hypothesis proposed, a numerical simulation is conducted over a real structural system using a vertical loading ranging from zero up to the critical buckling force, taking into account the change in the modulus of deformation of concrete and assuming a certain level of cracking of the material. The results obtained showed that the strategy of using a system of equivalent stiffness simplifies the analysis of non-prismatic elements because the problem is reduced to a prismatic element of equivalent properties. Besides that, due to the incorporation of the concrete creep in the problem, the maximum moment obtained in the equivalent system needs to be multiplied by a factor of 2.94 in order to equal the maximum moment occurring in the original system.