I don't know about "sturdy enough", but it looks too tall and not being about to move your wrists seems like a pain in the arse when doing pull ups, but I'm no expert.
>>5167 The wooden beam itself is easily strong enough to take your weight as long as it's not rotten.
If it doesn't go "through" the walls, it's hard to see what else is holding it up. It looks like it's physically resting on top of the breeze-blocks on the right hand side and is mortared in, I'd assume it's fitted the same on the left hand side with some plasterwork just boxing it in.
So as long as it's more than a couple of inches inside the blockwork it'll easily hold your weight.
As others have said though the biggest problem is being comfortable holding it. If you can get one, I'd try and find one of those over-door-frame pull up bars, and perhaps bodge it a little to mount onto that beam.
