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Joined: Dec 2006
Location: virginia beach VA
I guess it depends on many factors. If you put hinges on a toy chest, they really need very little strength - when the hinge is closed it is supporting no weight, and as you open it , it only has to carry the weight of the top in compression - which even the tiniest of hinges can do, no matter how thin. The length of the hinge will help resist twisting, so longer would be better, though I have never seen any ratio of length of a piece to length of a top. It is likely that if you bought a 3/4" long hinge, and mounted two of them on a 4 foot long top, you would have issues with twisting, though they would probably easily work with a top that was 18 inches.
Now, if you were making hinges for a cabinet door, or a secretary bookshelf, the hinge will have a totally different set of stresses. As you open the door, the door will have to resist the tension force of gravity at the top hinge, and some gravity, but more likely compression at the bottom hinge, since the hinge will have to support the weight of the door. Even when closed, if it not rubbing on the bottom of the frame, that means that the hinge is carrying the weight of the door. You have the same issues with length - longer means less likely that the door will twist.
In addition to the hinge, you have to consider the size of the screw. If you used a 1/2 inch screw to install a door hinge, I am pretty sure the door hinge would not fail, but it will probably pull out of the frame.
So my guess is that you size hinges by eye, if it looks right, it will probably work, especially for hinges that open up. For hinges that open out, and hold more weight, I would go beefier. For screws, I don't have any suggestions, other than that longer and thicker are better, especially for hinges that open out.