In use, the apparatus squeezes hard on the door frame, the same way a clamp would do. This means most of your weight is held by friction on the door frame.
There is not anything inherent in the function of a door frame that means it must be able to survive clamping, friction, or weight. But in practice, a lot of door frames are made that way: they can withstand clamping friction and weight, because whoever makes walls frames the door with solid timber.
Anyway. It pretty much just hangs on the lintel until you put weight on it. It’s working for my kid.
What didn’t work is those things that expand to fill a door frame, with a screw thread/bolt. Which aren’t clamped on both sides. That works for laundry (unless you fill it up with wet denim). Softwood timber framing isn’t hard enough or stiff enough to support a grown youths weight on one of those – and, from observation, he didn’t like it when he suddenly was dropped to the floor.
The bar is on one side of the door, and the hook is on the other, pressing against wall above the lintel.
The load is directly down on the bar, but with the contact points on each side of the door, this load is off-center. This creates a moment - a rotational force about the center of the bar (the whole pull-up bar structure). It is this moment that pulls the bar into the frame on one side, and the hook into the frame above the lintel on the other. The combination of these moments under load create the force that holds the bar securely against the structural framing supporting the door.
The geometry of the device means that this squeezing action assures that the rectangular crossbar (see images at OP’s link) won’t easily become disengaged from the lintel once the user is hanging their weight on the handles. But the entire weight of the user and the device are borne by that rectangular crossbar pulling down on the lintel. Friction doesn’t enter into this. If you zoom in on those pics you’ll see that the parts of the round bars that make contact with the vertical door trim are covered with soft foam rubber, which would require a relatively large amount of shear distortion before exerting any frictional load on the door trim. The lintel (and the rectangular bar that engages it) will hardly distort at all, meaning the lintel will be carrying pretty much all of the weight here.
as k9bfriender notes, it’s probably kind of a coin toss as to whether your builder used enough finishing nails to enable a typical residential lintel to bear your weight.
I’ve seen bars like what you describe using the rotational force but I don’t see that happening with the bar the OP linked to. The guy is hanging down directly from the brace bar with a downward force causing no rotation of the fixture. The downward force looks like it’s being transferred directly to the lintel brace.
It’s seems to get any rotation the guy would have to be hanging off the end of those nubs or a second horizontal bar should be attached to the end of those nubs.
This would be an interesting experiment to do in a physics lab. Put some sensors at the contact points and see where the force is distributed.
Typically the ends of the top piece of molding is cut at a 45 and sits on the ends of the vertical pieces. It may be more accurate to think that the bar is hanging from the essentially rectangular frame made by all 3 pieces of molding. It would be an interesting experiment to have just the top piece of molding without the vertical pieces and see how well that can support the user’s weight.
If the user were hanging directly below the lintel brace, there would be no moment. But the lintel brace is on one side of the doorway and the user is on the other side of the doorway - a horizontal offset of maybe six inches when using the grips that are closest to the door frame (as in the picture at the OP’s Amazon link). 180 pounds of weight from the user, at a half-foot horizontal offset from the lintel brace, makes for a moment of 90 lb-ft.
The vertical offset between the lintel brace on the far side of the doorway and the cross brace on the user-side of the doorway also looks to be about six inches - meaning that when the user is suspended from the grips, there’s about 180 pounds of force pushing the lintel brace horizontally against the lintel, assuring that it won’t disengage (unless the user gets really jerky at the top of a rep).
As noted in my previous post, the lintel brace is the only thing that’s transferring a vertical load (i.e. the user’s weight) to the door frame.
That’s not a lintel, it’s just the door head casing. The structural header (if there is one, such as if the door is in a load-bearing wall) is buried behind the casing and drywall. Lintel is a term generally reserved for masonry construction, either for a steel angle holding the brick, stone, or block above, or a very heavy piece of stone or reinforced concrete. In a non-load-bearing wall, the rough door frame is made of a single 2x4 or 2x6 depending on the wall thickness. The door frame/jamb is usually 3/4" poplar or pine, with a 1/4" to 1/2" gap to the rough framing for shims. The casing then covers the gap and is nailed to both the jamb and drywall, plus hopefully through to the rough framing as well.
The offset Machine Elf describes seems to be the special sauce here. While you could simply hang a bar with a couple of clamps over the casing on both sides of the door, that would likely damage the casing at the point of contact due to all the loads being concentrated into just a couple of small spots. Also as filmore mentions, the head and jamb casing is mitered together, so it provides a little bit of extra strength that’s not dependent entirely on the finish nails.
In the OP’s apparatus, the rectangular brace rests on top of the casing on the back side of the door to keep it from falling when it’s not in use, but when someone puts their weight on it, a lot of the weight/moment goes into the jamb casings on near side via those foam “rollers” for lack of a better term. The rectangular brace on the other side then presses into the drywall and against the framing buried in the wall since it’s trying to rotate. The bar’s large surface area helps distributes that load so it doesn’t damage the drywall. It gets pulled down onto the casing by gravity as well. Some of the reviews show, however, that those “rollers” don’t really distribute the load on the near side very well, leading to black marks and dented trim.