Fully stressed frame structures unobtainable by conventional design methodology

A structure is said to be fully stressed if every member of the structure is stressed to its maximum allowable limit for at least one of the loading conditions. Fully stressed design is most commonly used for small and medium size frames where drift is not a primary concern. There are several potential methods available to the engineer to proportion a fully stressed frame structure. The most commonly used methods are those taught to all structural engineering students and are very easy to understand and to implement. These conventional methods are based on the intuitive idea that if a member is overstressed, it should be made larger. If a member is understressed, it can be made smaller, saving valuable material. It has been found that a large number of distinct fully stressed designs can exist for a single frame structure subjected to multiple loading conditions. This study will demonstrate that conventional methods are unable to converge to many, if not most, of these designs. These unobtainable designs are referred to as ‘repellers’ under the action of conventional methods. Other, more complicated methods can be used to locate these repelling fully stressed designs. For example, Newton’s method can be used to solve a non-linear systemof equations that deAnes the fully stressed state. However, Newton’s method can be plagued by divergence and also by convergence to physically meaningless solutions. This study will propose a new fully stressed design technique that does not have these problems