As RTCool points out: straight beams and curved beams carry similar loads “in beam” if the ends of the curved beam are not constrained and/or the curvature ratio: height/span is very low: 1/20 etc. In my most recent designs I use parabolic arched columns to support a curved roof, but the height/span is approx 2/3 and I restrain the ends of the columns so the curved arch supports are mostly carrying the gravity snow loads in arch compression, which is very, very efficient. Wind side loads against my columns somewhat depend on “in beam” strength but they are less severe loads than snow loads for my structure. In my climate in the NW corner of the United States, snow loads in our mountains are significant: 120-lbs per square foot (with safety factor of 1.6 as is common in the ASCE building codes).
As mentioned in my first post above, I am not a structural engineer, so my opinions are only “amateur mixed with a bit of experience” and must be evaluated in that light. That said, I have spent the past 2 years working on residential home designs in an effort to devise more affordable structures, using materials more efficiently and even more important: reduce the time to manufacture and assemble the dwelling to the greatest extent possible. To that end, I will gladly spend more for a particular material choice, if in using it, time to construct is reduced even more.
SkyCiv FEA stress analysis tools have helped these efforts tremendously and given me some insight about various roof structures and the beams employed to support them. As others have mentioned: 9m is a serious span for a residential structure, but not as difficult if the loads your roof will see in the future are primarily wind loads (uplift is usually the worst case for nearly flat roofs) and not snow loading in your case. Perhaps in your location snow loads are non-existent or very modest. If this is the case my guess is your biggest roof loads as mentioned will likely be wind uplift. Depending on the shape of your house and the surrounding topography (high on a mountain escarpment ?, on a flat plain but with few trees to protect it ? …etc) wind uplift on a flat roof can generate loads (in imperial units) of 8 - 20 pounds/sqft acting upwards against gravity, depending on the calculated wind speed for your area in a gusting wind storm. -20psf may not sound like a lot but multiplied over the large surface area of your roof it generates substantial forces that work to rip the roof off your house. Your roof beams and all the parts of the roof that connect to them will need to resist this upward force in a wind storm. Normally your roof will work in the other direction to hold the weight of the roof and it’s materials from moving closer to the ground, but it is the unexpected forces, like wind uplift which must be thoroughly dealt with to keep the inhabitants inside the house safe.
Sometimes roof beams also need to resist what are called “moment forces”. These forces, for example, can act to push a wall over in an earthquake, but the roof beams working together with other structural members, add stability, shear resistance and what you might think of as torque resistance so that sideways forces to the house are resisted. Properly setup, SkyCiv can evaluate these forces against the house and the ability of the structural members to react safely.