I can't find the answer to this question in my old textbooks or online! Please see the image at the following link. http://tinypic.com/r/20qjt60/5 It is a small stepped stem in a cantilever beam position. If I have a force F at the end of the beam, the bending stress will be My/I correct? How can I calculate I and y correctly? Is I about an x-axis at the fixed end? Also, will cantilever beams exceed yield strength in bending before failure in shear in this case? Are there significant stress concentrations at the step? I really appreciate any help you may give. Thanks!
Answers to your questions in order: 1. My/I is stress at any point along the beam. You use the values of I and Y at each x location. In your case you will have two regions to compute y and I. M will have to be calculated at each point of interest along the beam as well. 2. At each x location of interest find the cross section and compute I and y in the usual manner. 3. No. see answer 2. 4. Shear failure is only an issue if the beam is very short in comparision to its cross section. 5. Yes the step creates stress concentrations. It is significant if the material of the beam is brittle or it is subject to fatigue loading.
You may also consider referring to a book such as Roark's Forlumas for stress and strain. There are detailed considerations and tables for such load cases and many more.
Without knowing the application of the beam, I can't say if this is feasible, but the stress concentration could be reduced to negligible levels if a fillet were to be added to the step to create a more gradual change in diameter.
