The paper presents results of the preliminary strength design using the method of statically admissible discontinuous stress fields (SADSF) of two new and interesting thin-walled structures based on double-tee sections. Although these constructions are intended to carry torsion moment loads, all their surfaces are accessible from outside. The paper is completed with the selected results of linearly-elastic FEM analyses of the presented solutions. They show surprisingly good strength properties and significantly higher load-carrying capacity comparing to structures designed in an intuitive way. The objectives of the paper, among other things, are as follows: popularization of the SADSF method, presentation of its new solutions and confirmation of practical usefulness in the design of thin-walled structures.