The roof–column structural system is utilized for many engineering and architectural applications due to its structural efficiency. However, it typically requires column locations to be predetermined, and involves a tedious trial-and-error adjusting process to fulfil both engineering and architectural requirements. Finding efficient column distributions with the aid of computational methods, such as structural optimization, is an ongoing challenge. Existing methods are limited, with continuum methods involving the generation of undesired complex shapes, and discrete methods involving a time-consuming process for optimizing columns’ spatial order. This paper presents a new optimization method to design the distribution of a given number of vertical supporting columns under a roof structure. A computational algorithm was developed on the basis of the optimality-criterion (OC) method to preserve and removed candidate columns pre-embedded with design requirements. Three substrategies are presented to improve optimizer performance. The effectiveness of the new method was validated with a range of roof–column structural models. Treating column locations as design variables provides opportunities to significantly improve structural performance.

Ruled surfaces are widely used for architectural forms, as diverse 3D shapes can be conveniently generated by the movement of a straight ruling. There is vast potential to create a rich variety of new architectural forms by introducing curved rulings into ruled surfaces. This paper presents a new method to generate ruled surface variants by making a fundamental change to existing ruled surfaces through parametric reformulation and the use of curved rulings. A new type of ruled surface composed of curved rulings, the elastica-ruled surface, is proposed. An analytical geometric modelling method is developed based on the transformation of line-ruled surfaces, enabling convenient generation of elegant shapes and forms for architectural applications. In this paper, curved rulings are represented by elastica curves—large, elastic, bending deformations of a straight slender beam. We demonstrate that elastica curve design parameters can completely control the shape of an elastica-ruled surface and define a large set of transformation results. This study classifies elastica-ruled surfaces into five categories based on their shape characteristics. Potential applications of elastica-ruled surfaces that consider elastic bending behaviour are presented, including bending-active structures, robot-assisted manufacturing and kinetic architectural designs. By extension, this study shows that adopting higher-order elastica curves can further enhance the design diversity of novel architectural forms.