Analysis of Thin-Walled Straight Beams with Generally Shaped Closed Sections Using Numerically Determined Sectional Deformation Functions

This investigation presents one-dimensional static and eigenvalue analyses of thin-walled straight beams with generally shaped closed single-cell or multicell sections. For accurate beam analysis, sectional warping and distortional deformations should be considered in addition to the standard Timoshenko displacement field, but it is difficult to obtain the deformation functions analytically for arbitrarily shaped sections. Thus, a numerical method is proposed to obtain sectional deformations for any arbitrarily shaped sections. Once the deformations are identified, they can be integrated over a cross section to yield one-dimensional higher order beam equations. For the numerical determination, the cross section of a thin-walled beam is modeled as a beam frame, where the warping and distortional deformation functions of the section are identified as the eigenmodes of the frame model; the lowest few energy mode sets of in-planar and out-of-planar modes are selected as the distortional and warping deformation functions, respectively. The validity of this approach is checked by comparing the present results with shell finite-element results. For numerical tests, several thin-walled closed sections, including those with flanges or varying wall thicknesses, are considered. The effect of the number of selected warping and distortion sets on solution convergence is also investigated.