"INTRODUCTION Stress analysis and rigid body motion are just two of the fields of mechanics in which area and area moment properties are frequently required. Such properties. where distances are measured from some moment axis to the elemental area and the integration is applied over the whole of the area of interest (the zeroth moment when n = 0gives the area). In the numerous text books that derive the various moments@ a cartesian approach is invariably taken whereby the shape of interest is decomposed into essentially rectangular elements in order for the integration to be applied. This approach is perfectly acceptable for the relatively simple shapes that are normally considerd but becomes less so when the shape is complex. The approach becomes particularly messy when shapes with re-entrant boundaries are to be analysed. In this note an alternative@ pseudo polar@ approach is developed in which a triangular ""slice"" element is used for the required integration. It is demonstrated that such an approach leads to easily implemented computational algorithms that are general and can cope with shapes of arbitrary complexity. Having obtained the area and moment properties@ the mass-based properties can be easily calculated for a real shape@ or plate@ of finite thickness."
TM 119-2002 history
2002TM 119-2002 Calculation of planar area and moment properties – theoretical background