Flexure-torsion behavior of shear-deformable beams with applications to aircraft wing sections

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Flexure-torsion behavior of shear-deformable beams with applications to aircraft wing sections

Kosmatka, J.B.

The flexure-torsion behavior of a tip-loaded cantilever beam with an arbitrary cross-section is studied using Saint-Venant's semi-inverse method along with a power series solution for the out-of-plane flexure and torsion warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. For complex cross-sections, the calculated coefficients represent a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-section properties including: the torsion constant, shear deformation coefficients, shear correction factors, and the shear center location. A new linear relation is developed for locating the shear center using the Saint-Venant flexure and torsion solutions, where the twist rate is zero about the line of shearcenters (not the centroidal axis). Numerical results are presented for a triangular cross-section and different NACA airfoils.