This is a low cost way to install a pull-up bar in a standard doorframe. This will put holes in the wood, so you have to be okay with the permanent installation or a bit of patchwork when you want to remove it.
I bought all the materials for this project for $17.13.

What you'll need:
1 iron pipe 3/4" (cut 1/2 inch shorter than doorway)
4 corner braces 3 inch
4 nylon spacers 1/4 inch by 1/2 inch
4 #10 washers
4 #10-32 3/4" machine screws
4 #10 nuts
8 taper head screws 3 inch

Tools:
Hammer
Screwdriver
Adjustable wrench, or 3/8 inch open end wrench
Two tapping blocks
Drill w 5/32 bit

Step 1: Build T- Bracket

Attach two L-brackets together as shown. I use the oval head screw directly through the first brace, then the spacer, then through the second brace, followed by a washer and nut.

Do not fully tighten the screws yet, since the movement will make it easier to insert the assembly into the pipe. The .26" inner diameter of the nylon allows some play, so you will want to get it square before the final tightening

Step 2: Insert T Brackets in Pipe

The T bracket is a very snug fit into the iron pipe, thanks to the 1/4 nylon spacers. You may need to loosen the back screw a little to get it started, but it should fit tightly. Once the first 1/2 inch of the corner braces are into the pipe, straighten the braces and tighten the screw securely.
Put the empty end of the pipe on one tapping block and use the other block with the hammer to drive in the bracket.

Do the same on the other side, but be careful not to bend the bracket (hit it squarely).

Step 3: Install Bar

Mark a spot that is high enough so you won't regularly smack your head and drill the first two pilot holes opposite each other. You can use a level or just measure and hope that the doorway is square and plumb. Make sure to aim towards the center of the doorframe where the studs are.
Make sure that the braces on each end are parallel with each other before mounting.
Secure each side using the 3" screws at the top hole closest to the bar. Align the braces vertically, then drill the other 6 pilot holes. Fasten securely with the remaining 3" screws and it is ready to use!