Have dealt, thus far, with perfect columns, loading eccentricities, and beam-columns. There are, however, many more issues in buckling/(static) structural instability, most of which will try to touch on a) Buckling versus Fracture Have looked at columns that are long enough such that they buckle

Thus far have considered separately beam - takes bending loads column -takes axial loads Now combine the two and look at the beam-column (Note: same geometrical restrictions as on others

We have looked at basic in-plane loading. Lets now consider a second\building block of types of loading: basic torsion There are 3 basic types of behavior depending on the type of cross-section

We have thus far looked at In-plane loads torsional loads In addition, structures can carry loads by bending. The 2-D case is a plate, the simple 1-d case is a beam. Let's first review what you learned in Unified as Simple Beam Theory

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

Thus far we have discussed mechanical loading and the stresses and strains caused by that We noted, however, that the environment can have an effect on the behavior of materials and structures. Let's first consider:

There are many structural configurations where we do not have to deal with the full 3-D case. First let's consider the models Let's then see under what conditions we can apply them A. Plane Stress

We do not characterize materials by their E mnpq The Emnpa are useful in doing transformations, manipulations, etc. We characterize materials by their \ENGINEERING CONSTANTS\ (or, Elastic Constants)

Let's first review a bit... from Unified, saw that there are basic considerations in elasticity: 1. Equilibrium 2. Strain-Displacement 3. Stress- Strain Relations (Constitutive Relations)