Summarizing what we've looked at in elasticity, we have: 15 equations in 15 unknowns 3 equilibrium -6 strains -6 strain-displacement -3 displacements

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:

Return to the simplest system the single spring-mass This is a one degree-of-freedom system with the governing equation

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

Have considered the vibrational behavior of a discrete system. How does one use this for a continuous structure? First need the concept of..... Influence Coefficients

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

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

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)

Outline Multiple Sequence AlignmentCarillo-& Lipman, Clustal(W) Position-Specific Scoring Matrices(PSSM) Information content, Shannon entropy Sequence logos Hidden Markov Models Other approaches: Genetic algorithms, expectation maximization, MEME, Gibbs sampler