ALGORITHMS FOR DETERMINING PLANAR AREA PROPERTIES FROM PERIPHERAL POINTS

The determination of planar properties-cross sectional areas, centroids, moments of inertia, and so forth-plays a central role in the solution of many diverse engineering problems. Despite the increasing availability of computational power to engineers and students alike in recent years with the advent of small desktop computers, however, the traditionally laborious and error-prone methods of making these determinations, involving area decomposition or strip integration, are still being taught to the present generation of engineering students, mostly due to a lack of suitable alternative techniques. These classical methods are found to be particularly difficult to adapt to general computational algorithms. This work presents a novel approach, requiring only the peripheral points of any planar area as inputs, and is ideally suited for numerical methods. It is shown that all planar properties of technical interest can be generated, once and for all, with straightforward algorithms that are readily programmed in any scientific computing language, or adapted to typical spreadsheet formats. These algorithms are fully general and require no decision-making on the part of the user. Various worked examples are presented.