Your approach is sound. I wouldn't bother toeing screws in from top/bottom. I would drill through both the stud and the filler board and attach with nuts/bolts/washers (as opposed to threading a screw into the stud). Two bolts above the bar and two below.
Alternatively you can attach horizontal 2x4's across your studs with recessed lag bolts and then mount the pull-up bar to those. Since the 2x4's will be attached to the studs the same way the pull-up bar would have been attached you won't lose much connective strength.
- Note: I am not an engineer, and I haven't done any kind of load calculations on the recommendations below. I did some somewhat related research on how to hang a 100LB heavy bag (punching bag) from a wall (just one wall). Initially I was thinking about using pipe and a pipe floor flange, but I decided that a pipe attached to a wall was not going to be sufficient to deal with the forces exerted by a 100LB bag swinging. Most heavy bag hangers (aka wall mounts) use tube steel construction, with the tube fastened to the wall at multiple points, which is a lot stronger.
This question is a little different because you'll be able to support both ends of the pipe, so the pipe should be able to support more weight.
I think it would be helpful to break this down into parts:
A. Hardware/Mount to attach the pipe to
B. Fasteners for attaching the mount to the wall
A. Hardware / Mount
i) You could use different pipe fittings (like a 'pipe floor flange', google that to see what it looks like if you are not familiar) and threaded pipe to build a good, strong setup.
The problem with the flange is that the holes that they provide for fasteners/screws are pretty small. More on this in part B because this is about fasteners
ii) You could just get a thick block of wood (e.g. 4x material, so 3.5" thick ), and drill 1.75" holes into it to accommodate the pipe, and then attach the block of wood to the wall with fasteners of some kind (see part B). If you wanted to be able to remove the bar from the block, make one hole deeper than the other
iii) You could get 2x wood material, and create a channel for the pipe. Imagine something in the shape of a U, so you would put the bar/pipe in from the top. It wouldn't be secured but if you wanted it to be you could probably figure an easy way to secure the top of the U (e.g. a sliding block). Similar to the above, you would make sure that the wood material is large enough that it gives you space to drill fasteners through it into the concrete/brick wall
B. Fasteners
For attaching things to concrete/brick, you can use things like:
i) Anchors
ii) Tapcon screws
iii) Threaded rods, bolts/nuts, epoxy, like the Simpson Adhesive Anchoring System:
http://www.strongtie.com/products/anchorsystems/adhesives/adhesive_anchoring_install.html
So I think the best thing to do is figure out:
a) how big a pipe you will use, making sure that they have a pipe floor flange in that size
b) how big the fasteners are that will fit in the pipe flange, and if you think they'll be strong enough
c) if you don't want to attach the flange directly to the concrete/brick wall, you could go with the wood mounting options, which would give you a lot more area to install whatever fastener you want
long answer, but hope it helps
Best Answer
Much better to go with screws for several reasons, especially that they can be adjusted tight and will stay there, while nails will only set until the head hits the surface of the metal flange and also they have low withdrawal strength. Yes, most of your force is shear but because there is not much preventing the nails from pulling out, over time the nails will tend to loosen.
I suggest using a structural lag screw with around 2" of embed into the wood after accounting for the thickness of the flange. I suggest Simpson SDS x 2-1/2". A good quality #8 or #10 screw would work too. I strongly suggest not using cheap or low strength screws such as those used for dry wall.