How to design barge for load 20tonnes excavatoror

We can agree to disagree on this point, no problem at all.
If a teacher always gives a detailed SOR he is always testing just the application of (mostly mathematical in this case) knowledge, never the integration of said knowledge.
In real life the customer walks in and says just that, "I need a barge for my excavator". Then it's up to the NA to ask enough of the right questions to define a meaningfull SOR. If he has never done it before and has no ideea how to do it the result will not be great. How to best train for it, implicitly or explicitly, is something teachers can argue about.

 

There have been several students posting in the forum asking for a solution for their homework. In your last semester of university, students should have the basic knowledge, or the ability to search for it. A barge is the simplest of hulls, so the assignments is not ridiculously difficult. I agree that the SOR ( also called Statement Of Needs in some schools) has to be the starting point. The dimensions of the barge will be determined by it. This students wants numbers to solve a problem he is not defining. For example, he needs the center of gravity of the crane with the boom at different positions, the maximum reach of the crane and the maximum load it will lift.

 

It depends on many things. There are barges whose hulls are tremendously difficult, and studying their stability under various load conditions can be very difficult and very cumbersome. But, in fact, a barge can go, from something similar to a shoe box, to hulls with hoppers, doors at the bottom to discharge waste, legs to anchor the barge to the sea bed, ...
Before crying out to the four winds how easy it is for me to design a barge, we should know what barge it is.

 

Maybe it is expected that the OP consider all these variables, given that he is in his last year. I wish I had studied NA when I still had the chance. I'm limited to self study.

Lift capacity and length of boom as gonzo mentioned are critical factors. These will probably be quite similar amongst 20t excavators. They are usually long boom versions as well in this application. Calculate the leverage of the boom length using lift capacity. I won't comment on stability calculations as a boatbuilder, many here are much more knowledgeable and trained in this specific field. With the required displacement calculated shape the shoebox according to the stability required. I guess.