Exterior doors go through a lot of wear and tear in addition to being exposed to all kinds of weather. Wooden doors and door jambs expand in the presence of rain or even high humidity, which can make your door refuse to open. Sagging hinges or a malfunctioning latch assembly can also keep a door stubbornly closed, so it's important to figure out what's wrong before you can find the appropriate solution.
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Identify the Problem
Examine the door closely. This is usually easier to do from the inside, especially if you've got either harsh weather or glaring sunlight outside. If there are no gaps anywhere around the door, you may have swollen wood or frozen hardware. Gaps along the top of the door on the doorknob side and along the bottom on the hinge side are probably due to sagging hinges. Either way, your first step is to get the stubborn door open.
Getting the Door to Open
Every door is different, so there isn't one fool-proof way to coax them open. This is largely a matter of trial and error, and may require muscle and a bit of teamwork. Make sure that the lock is not frozen shut. If it is, you will have to remove the doorknob assembly, remove the hinges and wiggle the entire door out of its frame.
If the latch assembly is working just fine but the door is still stuck, try squirting a little bit of all-purpose lubricant between the door and the frame. Use a spatula or putty knife to get a little space between the door and the frame, then use a combination of wiggling and brute force to get the door open. Don't try to kick or smash it open because this could damage the door and injure you. You can try bracing one foot against the frame and pulling hard. Do not have one person push and the other pull because if the door releases suddenly, the one pulling can get hurt.
Fixing a Swollen or Warped Door or Jamb
Once the door is open, you should be able to more easily spot the problem. A warped or swollen door or frame can be sanded down using coarse-grit sandpaper. Follow this with a finer grit to get the door or frame as smooth as possible. Do not try to plane a door smooth unless you are experienced at this. Planing removes much more wood than sanding does. If you take off too much, you'll have permanent gaps between your door and your frame.
Once the door is opening and closing smoothly, repair the finish by painting or staining as necessary. Let it dry completely before closing the door.
Repairing a Hardware Problem
Examine the hinges on your door, especially the ones at the top. If they are loose and out of true, simple remove the screws holding them in place and replace them with screws that are at least 3 inches long. It is best to remove the door first so that you don't have to fight its weight while reattaching to hinge to the frame.
Fix a doorknob assembly that is sticking by spraying some graphite inside of it. If you can't loosen it that way, remove it from the door and take the entire thing to a locksmith shop. They will be able to figure out what's wrong with it, and bringing the assembly to them will cost far less than a house call.