Hi @Annette21,
Welcome to the Bunnings Workshop community, it is wonderful to have you with us.
The first thing you should do is confirm the requirements in your area for building approval. In most council areas, any roofed structure, regardless of the size of the structure or weight of the roof sheeting, will require building approval, so understanding your legal requirements before construction planning is important, as they may require you to have a draftsperson or engineer sketch up some plans that would then need to be submitted for approval. If it turns out that you need a draftsperson or engineer to design things for you, then their design will specify what type of beams and rafters are used, which will dictate the spacing of the posts and therefore, how many posts you need.
There are span tables online, such as Woodhouse's Span Tables, which show a variety of timbers and what they are capable of spanning in different situations. The two types of structural members you'll need to look at are beams, which run between the posts and rafters, which run between the beams. You'll note that these span tables are relative to the roof load width and the wind zone of your area.
On a beam, the roof load width is half the length of the rafters that would sit on top of the beam. Using your bedroom pergola as an example, the beams would run along the 6.84 metre side, and the rafters would run perpendicular at 2400mm long. In this situation, the roof load width on the beam would be 1200mm.
Our supplier, Lysaght, has provided this wind classification design guide, which shows how to work out what your wind rating would be.
We would need to know the basic design of the pergolas and the wind classification to accurately calculate how many posts are required and select suitable materials for those spans.
I don't want to discourage you completely, but there is a fair bit of complexity when it comes to designing roofed structures, and things must be designed to these specifications to ensure it passes council inspection.
If you work with the idea that posts are spaced at no more than 2.4 metre intervals along the long side of your pergola, I'd be comfortable saying you would be able to find materials for both beams and rafters that would suit. For the lounge pergola, you would need 5 posts along each long side, for the bedroom pergola, you would need 4 posts, and for the office pergola, you would need 3.
If the plan was to use the house as part of the support structure, then you would absolutely need to consult with an engineer or builder for their assistance.
I understand that it is a lot, so if you have further questions, please don't hesitate to ask, and I'll do my best to clarify.
Jacob
