Physical-mathematical model to determine the structural efficiency of sections shaped as ellipses and parallelograms when used in reinforced concrete columns
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MARQUEZ-PEÑARANDA, JORGE FERNANDO | 2021-06-09
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.
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