How can you determine that an object will break, when the result in it's maximum stress exceeds the ultimate strength of the material while the displacement result is only 8.8mm that obviously shows that the object can still resist the load...

Your maximum stress appears to be concentrated in a very small area. I'm not an expert on stress analysis, but a model defect, or mesh error can cause such a concentration and lead to a failure.

This may be a good example of the software telling you something (there is an error), Instead of telling the answer you anticipated.

Could you upload the beam models? Then someone who is great at analysis could look at the problem area instead of guessing from the screenshots.

How do you have the stress applied onto the beam? (Area where stress is being applied) I see your image showing it on the end but it looks like its just on the edge of the beam.

I think I may have found one of your problems. In the model, you have this made as one whole part which can create problems with readings, even if they are solid bodies. You also have the vertical beam and horizontal beam all as one entity rather than separate parts. It is best to make each individual part and then put them in an assembly. It looks like this is all welded together so when you make the assembly, each part should then come out with a proper bonded contact. Once you make this an assembly and constrain it all properly, your readings will be much more accurate.

The reason for this is that these readings of course are completely different. Von Mises measures where the impact of where the force is taking place. Basically, its showing you where the force being applied is having the most impact on the part. The displacement is the resulting physical change that force is actually having on the part.

Here is a link to a tutorial I wrote up during college on how to do stress analysis/FEA. Its for inventor but should explain things a little clearer to you if you are having trouble.

Autodesk Inventor FEA Analysis Tutorial