A theoretical and experimental investigation of a family of minimum-weight simply-supported beams

Space and force diagrams are presented for a family of simply-supported minimum-weight beam structures. The analytical methods, used to determine volume and displacements for a structure with different strength in tension and compression, are reviewed using the simplest circular arc beam example. The full design of a non-trivial symmetrical beam is described. The use of power series solutions and a matrix operator numerical method, developed for plane-strain slip-line field theory, are described to determine the beam layouts. The results of testing beam models, manufactured using both laser free-form sintering of nylon powder and CNC milling of aluminum alloy plate, are compared to the theoretical predictions of stiffness and maximum load capability. The theoretical predictions are shown to provide excellent agreement with both the isotropic aluminum test structure, and with the strongly bi-modulus nylon test structures.