The logical extension of discrete mass systems is one of an infinite number of masses. In the limit, this is a continuous system. Take the generalized beam-column as a generic representation:
Previously saw (in Unit 19)that a multi degree-of-freedom system has the same basic form of the governing equation as a single degree-of-freedom system The difference is that it is a matrix equation
For a number of cross-sections we cannot find stress functions. However, we can resort to an analogy introduced by Prandtl(1903) Consider a membrane under pressure p, Membrane\. structure whose thickness is small compared to surface
Thus far have considered only static response. However, things also move, this includes structures Can actually identify three \categories\ of response A.(Quasi)-Static [quasi because the load must first be applied
Thus far, we have concentrated on the bending of shell beams. However, in the general case a beam is subjected to axial load. F · bending moments,M · shear forces,S torque(torsional moments)
Now consider the case of compressive loads and the instability they can cause. Consider only static instabilities (static loading as opposed to dynamic loading [ e.g., flutter) From Unified, defined instability via a system becomes unstable when a negative stiffness overcomes
