Earlier looked at Simple Beam Theory in which one considers a beam in the x-z plane with the beam along the x-direction and the load in the z-direction Figure 14.1 Representation of Simple Beam Now look at a more general case Loading can be in any direction

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

Before we look specifically at thin-walled sections, let us consider the general case (i.e, thick-Walled) Hollow thick-walled sections Figure 12.1 Representation of a general thick-walled cross-section 中=c2 on one boundary φ=c1 on one boundary This has more than one boundary(multiply-connected do=0 on each boundary

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:

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

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

As we've previously noted, we may often want to describe a structure in various axis systems. This involves... Transformations (Axis, Deflection, Stress, Strain, Elasticity Tensors) e.g., loading axes material principal axis Figure 7.1 Unidirectional Composite with Fibers at an Angle

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)

Sources of Stresses and Strains Depends on type of structure Aircraft

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)