Shape factors for beams with misaligned loads

Abstract Shape factors have been recently developed for the optimal design of load-bearing beams. The shape factors so far developed assume that the loading is ideally aligned, i.e. that the load is exactly perpendicular to a section of beam. However, misalignment of loads is very common in real industrial applications. This paper extends the methodology of shape factors by developing shape factors for misaligned loads. The paper shows that misalignment as small as 1 or 2° can cause significant reductions in efficiency of sections, especially for ‘optimal’ sections such as I-beams. In addition, it is essential for designers to identify the extent of load misalignment, as the most efficient sections for a small misalignment of load can be very different to the most efficient sections for an aligned load.