Naming Normal and Tangential Stresses


This screencast will describe how to name
stresses, and the type of stresses we have are normal stresses, and the most common one
that we know of is pressure. We indicate those stresses with a sigma. The second type of
stress that we have is a tangential stress and we negate that with a tau. Remember that
stresses are a force per unit area. So lets define our coordinate system; x,y, and z.
Every stress has 2 subscripts. The first subscript indicates the normal to the plane the stress
is acting on. The second subscript is the direction it is acting, and these subscripts
are z, y, or z. So if we have a normal force that acts in this direction. Its sigma normal
to the plane it is acting on is in the x-direction, and the direction acting is also x. You can
see that all normal forces are going to have the same 2 letters as subscripts. Now lets
look at our tangential forces. So in order to do that we need to look at a face. So here
we have a face. We call this tau, and the first thing you have to do is determine the
normal to the plane it is acting on. In this case that normal is x, and if it is acting
this way the direction it is acting on is z. We could also look at one that goes this
way. Again the normal of the plane it is acting on is x. However the direction it is acting
is y. So in addition to naming stresses. We also have to have a sign convention. So the
sign convention is that the positive direction is in the direction of the outward normal,
and we base our coordinate system on that. Lets give an example by again using the bottom
of a cube. Lets say that we have a normal force that acts in this direction or here
is our outward normal. In that case our coordinate system is going to look like this, were these
are the positive directions. So our normal force in this direction is sigma zz, and its
positive because of our coordinate system. If we look at a tangential that goes this
way the normal to that plane is x, and it is in the positive y direction, because that
is how we set up our coordinate system.

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