I checked again and the beams are not Glulams, they are Versalam, which is a better material for this application. They are sheathed in Hardiboard. I measured, and on the east and north sides they are 18" x 5 1/4" and on the West side, over the garage doors, they are 24" x 5 1/4".
The posts under the beams are 14' tall, 15' 6" on the west side where the garage is. They are 6" x 6" pressure treat. The stone-sheathed post bottoms are 26" and 44" tall. Under the stone is 12" x 12" hollow cinderblock, concrete filled. The piers are 4' x 2' with lots of rebar and 4 pieces of #4 bar coming up the interior of the block. Galvanized post bases and caps.
The west side is where the tiles are coming loose the most, on the north side, they are almost perfect, and very little deterioration on the east side.
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The contractor was out this morning and what he wants to do is take up the tile in a 20' x 10' section on the west side, let it dry for about a month, and test the polyurethane grout in this section. He thinks he can tell just by examining it whether it will last through the winter.
My cost is only going to be $300 - $400 on the test section, maybe even less.
Right now my inclination is to let him go ahead and do that. The biggest reason is that he told me he has insurance which covers failures like this and if we can't get a good resolution, he feels he can just turn it over to his insurance. If I tell him how to do the job instead of of just making suggestions, the insurance is not going to cover it, so I have to tread lightly. OTOH, he is a very sensible guy and we are both in agreement on how to proceed.
If the test section doesn't look good, then I will suggest expansion joints in the concrete underneath the mortar.
The insurance adds a whole new dimension to the problem, especially since the contractor is willing to help me if it gets to that. We would both prefer not to have to use the insurance, but at least no one is going to go bankrupt if worse comes to worse.
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Some of the things that make me feel good is that last year the efflourescence on the bottom of the headers was much, much worse than this year. Almost continuous along the bottom of the headers. The cause of these deposits is water coming through the tile, down the back of the headers, and evaporating from the bottom of the header.
Also, last year the grout was missing, as in totally gone, not just deteriorated, from about half the deck area, this year it is much better. And the efflourescence on the surface of the deck is much, much less than last year.