[MUSIC] This is module 17 of Mechanics of Materials part III. Today's learning outcome is to look at inelastic bending. Last time we looked at symmetrical cross sections, this time we're going to look at unsymmetrical cross sections. And so, here's our inelastic beam bending situation. Beams that are symmetric about the y-axis, but unsymmetrical about the x-axis are called unsymmetrical cross-sections. And so here we see where it's symmetric about the y-axis, but about the x-axis I have a larger phalange up here than I do down here. Here's another example of an unsymmetric cross-section, a T-type cross-section. And so for beams that are symmetrical about the y-axis, but unsymmetrical about the x-axis, let's look, what happens is that we go from elastic to fully, or, partially plastic to fully elastic. For fully elastic this is what we look like. None of our locations on our beam have gone to the plastic range. As I go partially plastic, the first place that goes plastic is the furthest location from the neutral axis. And so this has gone plastic. And what happens is, the neutral axis actually shifts up. And then once we go to fully plastic, everywhere along the beam has gone into the plastic region. And so for unsymmetrical beams you'll notice that the neutral axis shifts away from the fibers that first experience the inelastic action. And so in this case, shifts away from this lower section of the beam and migrates further and further away until we get fully plastic. At the fully plastic condition, what happens is that the area above the neutral axis is equal to the area below the neutral axis. And again there is some difference in the stress-strain diagrams for inelastic region of tension and compression. But these differences can be reasonably neglected for most of the real problems and the problems that we'll do in this course. And so the other thing you want to remember is, all of the beam bending assumptions remain the same. We're going to have to work with strain to solve these problems. And strain regardless of material is proportional to the curvature and varies linearly with the distance y from the neutral axis. And so we now know how to approach inelastic beam bending problems and we'll pick up here next module. [SOUND]