Securing Door in Stucco House

I've always heard one should use 3" screws to secure the door hinges to the studs behind the door frame. The screws used in my hinges are 3/4" and there doesn't appear to be a stud behind the frame (stucco house in Florida).
If this is true, is there any way to better secure the door? Thanks for any advice.
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you actually think theres no wood behind that stucco?
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I suspect the old door was shimmed in place and there was a gap between the old door frame and house stud. OP really needs to take off interior moldings and some sheetrock to see what is going on. If not replacing door he can just remove one screw at a time from each hinge and replace it with a long screw being careful not to warp frame out of shape by overtightening.

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How are you so sure about that?
If there is no stud behind the frame, I'd move out and sell the house before it falls down. Building codes call for certain framing measures at openings for doors and windows and that includes the 2 x 4 stud.
The rough opening can be 1/2" wider than the frame of the door, thus you may drill or screw through the 3/4" frame and find a gap. Beyond that, there should be the 2 x 4 framing. You may be able to remove the inside door trim and see how the door frame and wall studs are in there behind the sheetrock, or at leas poke the sheetrock with a nail and feel the solid framing.
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Use tapcon screws.

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Your stucco house may be wood framed with a stucco exterior. It may also be cement block, CMU, with a stucco finish. Either way, there is wood under that door frame. It would be possible to have close to an inch gap between your casement and the sub framing. Use a small drill bit to go through the jamb. If you are worried about it showing, remove a hinge and drill where it will be concealed. I suspect you will feel the stud.
There is a chance that the termites have removed it or the water has rotted it. If you truly cannot find the stud, then remove a piece of trim from either the inside or outside to see the space in question.
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