A new mixed-dimension coupling method is formulated for members with (bi-symmetric) wide flange cross sections based on the idea of least squares transformations between two sets of point clouds. This coupling method imposes the minimum number of constraint equations required to link the displacement, rotation, and torsion-warping degrees-of-freedom of the dependent node. At the heart of the formulation is the solution of a 4 x 4 eigenvalue problem and the deduction of torsion-warping deformations. The proposed method is implemented and validated for nonlinear finite element analysis and the source code is made publicly available. Examples demonstrate that the proposed coupling method can improve interface stress distributions over alternative methods and is suitable for the coupling of elastic continuum finite elements.