Did you ask the person that designed the house?

Where is a picture of the rooms. Where are the windows, a fireplace if there is one? Is it a build a remodel? If a build? Where is the floor plan? A remodel? Where is that plan?

As posed, there is nowhere near enough information in your question.

Where will you get a 22' faux beam and on what method of semi transport?

You need to post what you have and what you are doing: )

You don't need a semi to transport a 22' box beam. LOL Sometimes there is a nearby source and they handle getting it to the house; other times they are ordered from an online source and they handle shipping (surprisingly inexpensive sometimes.) Or if you live near me, I could bring it to you on the simple flatbed trailer we get horse hay on. All the roadblocks to avoid just answering a simple question. For a 22' foot living room about 17' high at the peak, a beam size of 8" x 12" looks right. Entry hall...this is where knowing the total size of the foyer and what is in it matters to what beams will look best. In general for 10' ceilings, 6" x 8" is a good proportion. Some will argue that the narrow side down looks more "real" but if you only want two or three, putting the 8" side down can look good.

It's not to avoid the question, It is to PUT CONTEXT around the question.

What source and where the 22' FAUX beam? It isn't coming UPS lol

IMO faux beams always look fake and to just add them in different areas with not idea if they would have actually been there is awful IMO so is a17' ceiling but that is done .To add on beam to abig space and 3 to a small space IMO never going to look right. Post pics of the space here in comments DO NOT start another post . Is this house being buillt or are these addons for some reason. Yes a 22' beam can come delivered the issue is how it gets installed if this is not under condtruction INFO is needed and the pics all in comments here The very first pic in your idea book is exactly the wrong look for that ceiling so think before doing