Given the level of questions you've already posted about designing/building an arbor/patio cover, you should probably consult with a licensed landscape contractor before you go any further. It makes more sense to design and build the structure to meet your local building codes, and a contractor can come out, take a look at your site, and advise you on the process with getting a building permit, designing it to last, and getting it built. You don't seem to realize that putting a wood post in contact with soil and not properly anchoring it to protect it from rot and also to make sure it lasts and is stable requires quite a bit more thought than you're aware of. A good locensed contractor should be able to set you straight, look for local listings or talk to friends who've used one to get recommendations for your area.

Alternatively you can check out a library book by Ortho books or Sunset on landscape structures and construction so you can get up to speed on best design/construction methods, so you can better evaluate the advice you'll get when you interview/select a contractor.

If you want a patio cover a landscape architect, structural engineer or general or landscape contractor can design, do the calculations of load for you and may even submit the plans to your building department for permit for you.
They will also do all the necessary code research for you before laying pencil to paper.

The above mentioned professionals are those who normally get involved with the design of an overhead patio structure.

A licensed building contractor is the professional who builds the structure.
Your designer may also be involved in project management.
Depending on the materials that you choose you may have two different types of tradesmen working on the overhead structure, - as an example you may have wood posts but a metal roof , or you may have the arbor outfitted with solar panels which involves another type of tradesman.

You can trust the type of professionals mentioned above once thoroughly interviewed and vetted to do a quality job.
Putting the plans out to bid to 2 or 3 licensed building contractors is the norm for competitive pricing.

An architect / landscape architect can determine the most desirable architectural style that will marry well with your architecture and installation budget.

Below are some samples of overhead structures from our office:
Basic plain jane:
{{gwi:33404}}From Smith Project

with solar panels added
{{gwi:33406}}From Smith Project

with a little more detail on the rafter wings
{{gwi:33407}}From Oranje project

Cast concrete columns and metal overhead structure.
{{gwi:33408}}From portfolioMay08.jpg

All metal:
{{gwi:33409}}From portfolioMay08.jpg