Page History

...

Sigma-theta, the bending stress, is a function of r only as expected from theory. It is tensile (positive) in the top part of the beam and compressive (negative) in the bottom part. There is a neutral surface axis that delineates separates the tensile and compressive regions. The bending stress, Sigma-theta, is zero on the neutral surface. We will use the probe to locate the region where the bending stress changes from tensile to compressive. In order to find the neutral axis, lets let's first enlarge the geometry. Do this by clicking the Box Zoom tool then click a and drag a rectangle around the area you want to magnify. Now, click the probe tool in the menu bar This will allow you to hover the cursor over the geometry at see the stress at that point. Hover the cursor over the geometry until you have a good understanding of where the neutral axis on the beam is. To zoom out, click "Zoom to Fit"

...

Looking at the distribution, we can see that the stress varies only as a function of r as expected. The magnitude of Sigma-r is quite a bit lower than Sigma-theta (this is why Winkler-Bach theory assumes Sigma-r =0). Also, we can see that there is a stress concentration in the area where the moment is applied. In the theory, this effect is ignored. In order to further examine the Sigma-r, let's look at the variation along the symmetry line. Click on Solution > Sigma-r along symmetry. This solution is the normal stress in the r-direction at the midsection of the beam.

...

Looking at the color bar again, we can see that the maximum r-stress is -.110 psi, and the minimum r-stress is -82.302 psi. At r=a and r=b, Sigma-r ~ 0 as one would expect for the free surface.

Tau-r-theta

In the details window, click Solution > Tau-r-theta to bring up the stress distribution for shear stress.

...