Estimating Interaction Diagrams for Arbitrarily Shaped Concrete Sections by Interpolating Stationary Points

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Estimating Interaction Diagrams for Arbitrarily Shaped Concrete Sections by Interpolating Stationary Points

Kim, Han-Soo

In this paper, a new interpolation method for developing full 3-dimensional (3D) interaction diagrams for arbitrarily shaped reinforced concrete columns subjected to an axial force and biaxial bending is proposed. The interpolation method uses six stationary points that can be determined by searching unconstrained nonlinear optimization solutions or through manual calculations. The weighted sum of a quadratic and linear equation along the meridian and parallel directions is used to preserve the convexity of the interaction diagrams. A coordinate transformation is applied to asymmetrical sections wherein the vertical axis of the meridian diagram is tilted. The proposed interpolation method is applied to various reinforced concrete sections to evaluate the full 3D interaction diagrams. The error ratios of the interpolated diagrams are less than 5% when optimum weighting factors are used. A weighting factor of 0.7 is recommended for the meridian and parallel interpolations of rectangular and asymmetrical sections.