Physical – mathematical model to determine the structural efficiency of sections shaped as ellipses and parallelograms when used in reinforced concrete columns

Abstract

Current practice of structural design of reinforced concrete columns uses mainly rectangular and circular sections. Among other reasons, this preference is linked to its ease of construction and spatial efficiency, and the historical inertia of civil works processes. Nowadays, modern design and construction techniques make possible to study the structural beahviour of sections distinctively shaped. If typical sections are extended from circular to elliptical and from rectangular to parallelogram shaped, it is possible to compute mathematical and physical parameters needed for the structural analysis. This work presents a physical–mathematical model to determine the structural efficiency in terms of relative strength and stiffness of sections shaped as ellipses and parallelograms when used in reinforced concrete columns. To solve the model, a Matlab® code for drawing the column interaction diagram of each studied section was written. Each diagram describes, in terms of mechanical physics, the relation between the uniaxial bending and the compression load that defines safety conditions as a mathematical limiting curve. The governing equation has the form P(m, g)=f(M(m, g) in which P describes the axial load strength function, M the bending moment strength function, m the material properties, and g the geometrical characteristics function. Structural efficiency has been expressed as the relative behaviour of each section with respect to comparable rectangular sections. To obtain the results of the model, a Matlab® code was written.