Engineering Which is the strongest of these 3 beam cross sections?

[Kalle]

Homework Statement

The 3 metre long butcher block is loaded to 30KN/m.There are three cross-section options.
1. 45x 220 rectangular cross section (vertical).
2. T-shaped cross-section formed by two 45 x 220 cross-sections.
3. I-shaped cross-section formed by three 45 x 220 cross-sections.
Find the internal forces and draw the internal force curves.Check which of the three cross sections is the most suitable(meets the requirements with minimum material consumption).Submit the calculations for all variants(fm 16N/mm2)For the most suitable variant, draw the normal stress epoxy and the shear stress epoxy principle shape. I solved points 1 and 2. Please check if it is correct.
I attach the solution steps.

Relevant Equations

V = ql/2; M=ql2/8

Added solutions. Check if there is a correct solution.