On the torsion constant of multicell profiles and its maximization with respect to spar position

A closed form expression for the torsion constant of thin-walled multicell profiles is derived based on a simple algorithm to generate the coefficient matrix of the system of linear algebraic equations for the shear flows. New explicit results are given for the three-cell profiles with either two or three internal walls, and for the two-cell profiles. They are applied to derive the optimal location of the internal walls which maximizes the torsion constant of triangular, rectangular, elliptical and deltoidal thin-walled profiles. The condition is also derived for the inner wall to carry a prescribed portion of the shear flow in a two-cell profile, with the application to thin-walled trapezoidal and rectangular profiles.