A 3-D Pseudo-Rigid Body Model for Rectangular Cantilever Beams With an Arbitrary Force End-Load

Abstract

This paper presents the first three-dimensional pseudo-rigid body model (3-D PRBM) for straight cantilever beams with rectangular cross sections and spatial motion. Numerical integration of a system of differential equations yields approximate displacement and orientation of the beam’s neutral axis at the free-end, and curvatures of the neutral axis at the fixed-end. This data was used to develop the 3-D PRBM which consists of two torsional springs connecting two rigid links for a total of 2 degrees of freedom (DOF). The 3-D PRBM parameters that are comparable with existing 2-D model parameters are characteristic radius factor (means: γ = 0.8322), bending stiffness coefficient (means: KΘ = 2.5167) and parametric angle coefficient (means: cΘ = 1.2501). New parameters are introduced in the model in order to capture the spatial behavior of the deflected beam including two parametric angle coefficients (means: cΨ = 1.0714; cΦ = 1.0087).