Heuristic catenary-based rule of thumbs to find bending moment diagrams

There are numerous nature-inspired curves representing certain structural behaviour being utilised in form-finding process by some famous architects. By closely scrutinising these forms, some interrelated morphological analogies between different structural forms and functions, such as the similarity between free-standing tension-only elements and the shape of bending moment diagram of a beam under the same load condition, can be explored. Most studies in the field of statics principles have only focused on developing numerical and mathematical approaches which are not suitable for practitioners who prefer quick access to the general forms. This paper first gives a brief overview of the most common archi-structural forms through the history of the architecture, and attempts to find the shape of bending moment diagrams through a new simple heuristic method based on drawing an analogy between natural tension-only forms and the diagrams. The purpose of this research is to propose a shortcut to diagram drawing substituting the general time-consuming methods as well as enhance the architects’ perception of bending behaviour of a structural element. A holistic approach is utilised, integrating the natural curves, bending moment diagrams and some rule of thumbs used to define the tapered beam or portal frame general shapes. This simple non-computational method can ease the design process. It will also be useful for educational purposes as well as pre-design phase conception including identification of the critical points of bending elements as well as designing tapered beams and portal frames.