Need help with floor joists in transformed garage

I am setting up my woodworking shop in a newly walled off garage and I'd like to put a wood floor in over the concrete floor. Currently, the floor is the original concrete floor and has a considerable slope to a centrally located drain. I'd estimate the fall to be as much as 4 inches from edge to center (about 10 feet). The floor drains from all sides and this really complicates cutting floor joists as I have to calculate for slope from two sides. The floor has to run from nothing at the edge, in other words, I can't raise the floor more than 3/4" from the highest grade, which is the edge. At first, I thought I could just cut a 1" X 6" on an angle to match the fall, but now it seems like each joist will have to be custom cut.
Any suggestion about how to approach this and end up with a level floor?
John Doh!
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John Doe wrote:

Your 1x6 idea should work. Set it up and level it, then scribe it so the scribe line is at the bottom at the low point. Then cut on the line. Does that make sense to you?
--
Joseph E. Meehan

26 + 6 = 1 It's Irish Math
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On Wed, 20 Oct 2004 00:14:45 GMT, "Joseph Meehan"

The old fashioned way to level a situation like this is to level the joists with shingles. Push the narrow tapered end in from both sides till you get the thickness you need. A bit of construction adhesive on the shingles will ensure they stay in place. No need to make this overly complicated. If two shingles aren't enough, just use more.
Dan
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In alt.home.repair on 20 Oct 2004 00:14:38 GMT John Doe

The top surface of the floor or the bottom? If the top, how thick is the floor going to be?

You're trying to get the whole joist to rest on the floor, aren't you?
I'm not sure if this is what Joe said or not:
Check to make sure that your 4 edges are level. I think you can use a level for a couple places and a taut string for the rest, or a good excuse to buy a laser level. If they're not level, you'll have to add another step to this process:
First set the joist(s?) that pass over the drain in place and level. Measure the exact distance from the drain to the bottom of the joist. (or if the drain is below the cement, the distance to the cement on either side.) Assume for this post that it is 3 3/4 inches exactly.
Then set all joists in the exact places they will go. (Or you can do them one at a time.) Leveling each joist like Dan says is ok by me. Make some little tool that will rest on the floor and will slide along it on its rounded point, and which will have a hole 3 3/4 inches from the bottom end, directly above the point, and through which your pencil point will stick out (either the pencil has to be firm in the hole so it remains horizontal, or it should only stick out enough for the point to make the lines you need. The point has to stay 3 3/4 inches from the floor.
Then with each joist in place, start at one end of the room and use the tool to make a line 3 3/4 inches above the floor from one end of the joist to the other. When you pick up each joist after it is marked, or earlier, you should probably number them.
Since the edge end of each joist can't be more than 3/4 of an inch higher than the cement at the edges, assuming you were talking above about the height of the *bottom* surface of the floor, I guess that's why you plan to use joists 6 inches high, actually 5 1/2 iirc. 5 1/2 - 3 3/4 is 1 3/4 inches. This will raise the bottom surface of the floor at the edge by 1 3/4 inches, an inch more than you allow. So I guess, before you cut them on the line you made. you would have to rip an inch off the whole length of each one, or more, if you don't want to reach your maximum on this first step. If the first distance you measured was 4 inches, like your estimate, instead of 3 3/4, you would only have to rip 3/4 inch.
How do you plan to attach the joists, and to what? If you plan to connect them to the walls somehow, you can't let them get to narrow (short) at the ends.
Meirman If emailing, please let me know whether or not you are posting the same letter.
Change domain to erols.com, if necessary.
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John Doe wrote:

I went through something similar a few years ago. I was going to make a small apartment in my 2 car garage for my Mother-in-law. My garage does not have a center drain, but it tapers from the back wall, where the entrance to the rest of the house is, to the overhead garage doors with perhaps a 3" drop. I must have gone over every step of the building of the floor a hundred times in my mind. How to put a flat floor with a minimum joist thickness at the door to the rest of the house. I also thought of shaving it down to the 3/4" so there wouldn't be a step up into the garage. I also reminded myself not to use long underlayment nails at that end of the joists lest they hit the concrete underneath. I have a lally column right in the middle of the garage that had to be considered in the floor planning. Another consideration was how to secure the floor joists to the concrete. I thought I would just use some sort of panelling glue and let the new interior walls do the rest of the holding down. It would be more or less, a floating floor, except glued down. I also thought of just having some concrete delivered and float a level floor, then install a floating laminate floor over that, but I didn't want to make this a permanent thing that couldn't be removed with minimum work and expense, in case I wanted to sell the house. I could tear down walls and rip up the floor and get the garage back to what it was, but jackhammering concrete would be a little more work and expense than I wanted. As it turned out, nature eliminated the need for the apartment, so I never got to build it. However, maybe some of my ideas will help. Maybe the concrete idea since you are going to cover the drain anyway?
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If you had enough vertical space to use actual joists, then you could just level them with shims and blocks of wood every 2 feet or so. But with only 3/4" to play with, you pretty much have to use sleepers that are continuously supported, and so you should do it by scribing them individually to match the slope of the floor. On the other hand, if it's a single-car garage, it's what, 10x20? so how many do you actually need? 16?
--Goedjn
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38.144.126.103:

highest

1" X

Thanks to all for excellent suggestions. I think that the right approach for me is to set up level line(s), scribe them individually and then just rip away. While it somewhat bigger than the suggested 10x20, it is only a few boards. I'm assuming that I have to scribe only half of the full joist length (since the deepest part of grade is in the middle of the floor) leaving me with two boards for each full length joist. Any suggestions about joining these two butt ends together?
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John Doe wrote:

Since they will be laying on the concrete and not really supporting the floor, just a couple of pieces of plywood sandwiching the butt ends together so they don't move when nailing down the underlayment.
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