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I recently made a tabletop for a rolling tool cart using 2x4's jointed and pocket-screwed. When I set the table upon the cart I noticed a very serious bow, almost like I was starting to make a barrel!
What methods are there to prevent this from happening during a fastening or glue-up scenario?
A common solution is to alternate your clamps between top and bottom:
Another solution is to clamp boards down across the panel as Drew suggested, although an even better variation on this solution is to use cauls, which start out curved but evenly distribute the pressure across the surface as they are flexed flat against both sides of the panel.
Read more about cauls: http://www.familyhandyman.com/woodworking/how-to-clamp/view-all#step2
But even if you use both of the above solutions, your panel can still bow and warp with changes in humidity, so it's important to let it acclimate first, as Matt suggested, by letting it sit for at least a week or two, assuming the lumber was already kiln-dried or adequately air-dried. If possible, let it acclimate to the environment in which it will ultimately be used--for example, if it will be in your dining room, let it acclimate inside your house.
You can also minimize movement by using quartersawn lumber and cutting out the pith. If you're stuck using the typically low-quality lumber from a home center, the best you can do may be to look at the grain direction and alternate it every other board, so one board will cup downward, the next will cup upward, the next downward, etc.
I always clamp jointed boards with some good, straight hardwood boards across their faces. This way, you'll use long clamps across the face of the jointed boards to keep your joints together, and shorter clamps to clamp your truing boards to the face. Use a pair of boards with the work piece between them. When it sets up, it should not be bowed at all.
No one has mentioned your jointer technique. If the jointer fence is not perfectly 90° then any small deviation get multiplied by the number of boards you have and you get a curve. The solution to this is NOT to try to get your jointer fence exactly 90° (although close is good). Instead, lay out your boards how you want them to be glued up, and draw a giant "V" across the table top with a pencil, marking every board. The V should span the entire top. Now flip every other board over. Now label the top face of each board with an "F". Now joint each board with the face labeled "F" towards the fence of the jointer. Now lay out your boards again, flipping every other board so that you reconstruct the original "V" you drew. The result is that the deviations from 90° alternate direction, and so cancel one another out, and viola! Flat top, not a barrel. If the deviation from 90° is extreme, the clamping pressure might tend to make the boards slip out of plane with one another, and so cauls, as others suggest, are still a good idea. But honestly, if you're anywhere close to 90° and have true joints you should require minimal clamping pressure and slipping shouldn't be a problem. YMMV.
An alternative is to make T-braces (my name). Screw two inch boards into a T shape. If the board edges are straight and the screws long enough, the brace will stay straight under very great pressure. Its the same principle as a torsion box. Then clamp 2 of them face to face with the table between them.
look at the grain direction and alternate it every other board(as mentioned by rob) is a vital part of any of the answers provided.