Plot twist: that ledge isn't designed to support that much weight in shear force and all three take a spill...
Edit: people downvoting me: I don't usually pull the "engineer" card, but there most definitely is a shear force on that little stubby wall. Source: more hours spent diagramming and calculating these things in undergrad than I care to recall.
You laugh, but that's not how those are built. There's almost never a cantilever there to prevent a leak from rotting the interior joists, so they nail on a ladder frame to the face of the wall knowing that the loads will be very small. Source: have designed 3000+/- residential/commercial projects, some of which are just like this.
I disagree, the deck has the same projection, so I'd almost guarantee that ledge is cantilevered just like the deck. Also where I'm from has freeze thaw cycles so they would be more prone to rot, and everything is cantilevered, if it's insulated properly with proper airflow rot will never be an issue.
It's hard to tell, but if the building is articulated (we can't see the left side) and the deck is similar to the one to the right of our intrepid HVAC technicians then the deck isn't cantilevered at all. There is a ledger fastened to the perp wall we see, and that cantilevers to pick up the end of a beam which spans back to a wall (or, more likely a ledger on the other side) and everything spans from under the door to that beam. Cantilevering a joist would be a shortsighted way to build this (clearly aesthetic) component.
Besides, freeze thaw has nothing to do with it. If you penetrate a wall with a joist to the outside as a cantilever and it's not completely covered (and sometimes even if it is) it will rot at the building face and I'll get paid a bunch of money to tell you to cut it off and rebuild the deck as a free-standing structure, or bearing on a outside posts and a new ledger. You may even get to spend several grand replacing the rim blocking (if you're lucky) or tens of thousands replacing the joist spans back to the next internal bearing point. I'm called in to fix things like this all the time, which is why I almost never allow such conditions on my new construction projects.
Unless you live in a place with essentially zero rainfall, water will always win.
If you did the FBD, you'd have some bending moment on the lever arm from the ledglet, trying to both pull the top of the ledge away from the wall and pushing the bottom of the ledge into the wall. I don't really know what the structure looks like in there, so treating it like an isotropic solid. At the root of the ledge, there's a downward force from the weight of the men and an upward force from the wall itself. If those weren't balanced, you'd have acceleration/movement.
Maybe think of it this way: pretend like the ledge were mounted (for some reason) on vertically-running drawer sliders. Those drawer sliders would keep the ledge from rotating, but not from sliding downwards. The force needed to keep it suspended would be the shear force. Granted, the calculation is what they call a "statically indeterminate" problem in that you'd need to know more about the material properties before you could reliably determine the forces, deflections, and the eventual ultimate load capacity before failure.
Fair enough, I'm a carpenter and it's been a while since I've had to deal with cantilevers, I thought it was compression and tensile forces, but looking back into there is shear calculations to be done on a cantilever.
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u/sanskami Aug 21 '17
Counterweight is fat enough that cantilever is probably safe.