flexibility method structural analysis examples pdf

New frameworks have been developed that allow 'exact' formulations irrespectively of the type or nature of the system nonlinearities. However, recent advances in numerical computing have shown a comeback of the force method, especially in the case of nonlinear systems. The upper arguments were valid up to the late 1990s.

In contrast, the procedure of the direct stiffness method is so mechanical that it risks being used without much understanding of the structural behaviors. The main redeeming factor in learning this method nowadays is its educational value in imparting the concepts of equilibrium and compatibility in addition to its historical value. This advantage, however, is a moot point as personal computers are widely available and more powerful. On the other hand, for linear systems with a low degree of statical indeterminacy, the flexibility method has the advantage of being computationally less intensive. For these reasons, the matrix stiffness method is the method of choice for use in general purpose structural analysis software packages. It is also easier to extend for advanced applications such as non-linear analysis, stability, vibrations, etc. It is apparent from the above process that the matrix stiffness method is easier to comprehend and to implement for automatic computation. This is a robust procedure that automatically selects a good set of redundant forces to ensure numerical stability. While the choice of redundant forces in ( 4) appears to be arbitrary and troublesome for automatic computation, this objection can be overcome by proceeding from ( 3) directly to ( 5) using a modified Gauss–Jordan elimination process.

Flexibility method structural analysis examples pdf