FEA question

Hey all, I have a basic question on FEA.

Let's say i want to do an FEA analysis on a rectangular beam (one end of the beam is fixed to a wall) the loads on the beam is its weight and a moment about the beam's longitudinal axis. How does the FEA program go about and determines the value of the high stress region in this problem?

I believe that the stresses will be at its maximum at the connection point between the beam and the wall. Please see if my following prediction is correct.

The stresses will be induced by two thing, the weight of the beam which will create a moment at the beam to wall connection, creating a bending stress (My/I). Second stress will be the shear stress due to the moment about the axis (which will be torque), and this can be calculated by Tr/J. With shear and bending stress, we can use Mohr circle to calculate the principal stress, where sigma x will be the bending stress and Tau will be the shear stress. And the biggest principal stress will be the maximum stress in the system, which will be acting at the connection between the wall and beam.

But how does FEA does the above when the whole beam is split into little elements?? If anyone know where i can find an example of how FEA results are calculated by those programs, it will be very helpful!

Thanks!