ᐅ Carport structural calculation for verification – Thank you!

Hello dear members,

I have planned a green roof for my carport. Unfortunately, the seller at the trade fair exaggerated a bit and said the saturated dead load is about 40 kg/m² (8.2 lb/ft²). After reading the planning documents, it turns out to be 80 kg/m² (16.4 lb/ft²).

To avoid overloading the carport, I tried to calculate the structural load. Since this is my first time and I don’t want to make any mistakes, I would appreciate it if someone could check my calculations:

Here are the figures I came up with:

EPDM membrane 1.5 kg/m² (0.3 lb/ft²)
Green roof 80 kg/m² (16.4 lb/ft²)
Wooden boards, spruce, 1.2 cm (0.5 inch) thick, 6 kg/m² (1.2 lb/ft²), larch C24
Rafters 6 x 12 cm (2.4 x 4.7 inches), spacing 80 cm (31.5 inches), span 2.84 m (9.3 ft), 4.5 kg/m² (0.9 lb/ft²), larch C24

When I enter this into the well-known online calculator with a snow load of 85 kg/m² (17.4 lb/ft²), the result shows it is just sufficient. To be on the safe side, I would reduce the substrate weight by 25%, lowering the load by 20 kg/m² (4.1 lb/ft²).

Is my calculation correct, or are there major mistakes?

The support beams (7 meters (23 ft)) should be fine, 8 x 24 cm (3.1 x 9.4 inches), larch C24, 12 kg/m² (2.5 lb/ft²).
The posts (8 pieces, 2.5 meters (8.2 ft) high) with 12 x 12 cm (4.7 x 4.7 inches), larch C24, 3 kg/m² (0.6 lb/ft²) as well.

Thanks if someone could take a quick look over a coffee and let me know if my calculations roughly make sense or if there are any significant errors.

Thank you!