We present a novel concurrent multidimensional topology optimization approach for beams under torsional loading. The proposed formulation considers the coupling between the one-dimensional beam torsion equation in the longitudinal direction, with the two-dimensional warping function equation in the cross-section. The proposed formulation enables the 3D optimization of non-prismatic beams with variable cross-sections, with significantly reduced computational burden compared to full 3D approaches. The cross-sectional torsional and warping constants are accurately computed utilizing a boundary recognition algorithm, previously developed by the authors. An iterative multidimensional optimization framework is developed in which first, the cross-sectional properties are determined by solving the two-dimensional differential equation. Then, having these properties, the one dimensional beam equation is solved for the rotations along the beam. Three different optimization problems are formulated: minimization of rotation compliance under volume constraint, weight minimization under maximum rotation constraint, and weight minimization under maximum von Mises stress constraint. Results reveal generally smooth convergence in simpler cases and more complex patterns in scenarios with stricter constraints or non-uniform loading. Overall, the proposed algorithm provides a general, flexible, and efficient approach for optimizing 3D beam structures subjected to torsion.