Cantilever and Tributary Area

Aaron Hayward · 10-05-2009, 03:39 PM

Cantilever and Tributary Area
Situation, Canadian code requires that

cantilevered floor joist extend 6 times the length of the cantilever to a double header joist when loaded by a roof.

The loading in this case when it is most severe is when the truss run in the same direction as the joist i.e. to ward the front of the home..

I think this distance could be less if say the cantilever was supporting only a gable end and not all the trusses. Tributary area is significantly less in the second case and therefore so is the load.

Any thoughts?

Aaron

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**Gunnar Alquist** · 10-05-2009, 04:20 PM

Originally Posted by Aaron Hayward

Cantilever and Tributary Area
Situation, Canadian code requires that cantilevered floor joist extend 6 times the length of the cantilever to a double header joist when loaded by a roof. The loading in this case when it is most severe is when the truss run in the same direction as the joist i.e. to ward the front of the home.. I think this distance could be less if say the cantilever was supporting only a gable end and not all the trusses. Tributary area is significantly less in the second case and therefore so is the load. Any thoughts? Aaron

Seems reasonable to me, except that in the case of a sloped/"vaulted" ceiling, the cantilevered joists are going to be taking a large amount of the roof load because the ridge beam will be directed down through that gable-end wall.

I would think that any modification of the code would be beyond the scope of a home inspector and I would defer to a licensed structural engineer.

Richard A Hetzel · 10-05-2009, 05:20 PM

A ridge "beam" is not a beam at all usually...it is just a nailer for the rafters, and carries no load. Therefore, probably half the roof load is coming down on the end of the cantilever. The cantilever MUST be designed assuming full live load on the roof, and ZERO live load on the floor. That is a condition that can easily occur, or someting close to it...an empty room, and a hefty snow on the roof. Depending on the source of whatever plans might have been used to construct the house, the cantilever may or may not have been so designed

If the ridge is a structural ridge, when an actual ridge BEAM would be present, then yes, the roof load at the end of the cantilever is only a quarter of full load, but a true ridge BEAM is rarely seen in residential construction, unless vaulted ceilings are present.

So, just call it what it its...simply a RIDGE, not a RIDGE BEAM. Some old-timers call it a "ridge pole"...which recognizes its structural non-entity. In fact, one COULD just nail the rafters together and omit the ridge altogether, although this is not modern preferred practice. It was done occasionally in the old days.

Aaron Hayward · 10-05-2009, 05:37 PM

Gunnars,

good point about the ridge in that particular situation. I would think that in that case a cantilever would not even be advisable (concentrated point load on a cantilever), unless calculations were shown to prove otherwise. The reason i brought it up was because of mechanical runs. I have seen a few cases were the change in direction of the joist has caused portions of the mechanical systems to be surface mounted to the underside of the joist and hence require a drop or t-bar ceiling be installed. The ultimate problem here was poor house design with respect to mechanical runs.

Your right to about a Building Inspector making or allowing changes to code. In the situation i mentioned though the loading patterns are completely different. A house 30 x 30 from eave to eave. roof load 52 lbs per square foot, 900 square feet x 52 = 46800 total roof load. the front wall would carry half that load or 23,400 lbs and the back wall the other half , gables on the side of the home would actually take a small portion of that load too. 30' of wall divided by 23400= 780 that's the weight per foot transferred to the floor ignoring cladding and windows and other wall weight although i think you can agree that the 52 lbs per foot is conservative. The moment generated on the cantilever is then counteracted by say 50 lbs per foot of floor load 6 times the length of the cantilever. 2' cantilever times the 23400 = 46800 ft-lbs. The floor 6 x 2 = 12' of joist beyond inside wall multiplied by say 26' (distance between walls interior) of floor width = 312 square feet then multiply by 50 lbs\square feet you get 15600 lbs. going in the opposite direction of the moment acting on the floor joist directly under the roof at approximately a distance of 6' from the inside of the wall. 6' x 15600 lbs = 93600 ft lbs. This is the cumulative torques created along the outside of the home (front) and the interior floor. So you can see that there is a considerable moment in the other direction about the outside wall below the floor.

Now consider the gable end at the front with floor joist remaining the same. the roof load carried by the gable is the total eave or overhang and half the distance between the gable and the next truss usually 1' if the truss are placed 2' o.c.. so the distance is say 1' + 2' for overhang. 30'x 3' = 90 feet square then x 52 lbs 4680lbs. 4680lbs x 2' cantilever is 9360 ft-lbs. The torque here or moment is then only about 20% or 1/ 5 of the case above. Hence it would require less than the normal required distance inside the wall.

If it takes 6 times the distance to counteract 46800 ft-lbs then it would stand to reason that the 6 times distance would not be necessary to counteract the 9360ft-lbs generated by the gable wall.

this reasoning makes sense to me although i am not an engineer. I realize this is not a complete consideration but i think it is a reasonable one.

Thoughts?

Aaron

Aaron Hayward · 10-05-2009, 05:44 PM

Richard,

can you explain the conditions for zero live load on the floor and how that applies?

Aaron

Aaron Hayward · 10-05-2009, 05:46 PM

Just so you guys know too i do not practice things like this during work, its just typical of the situations that cross my mind in the run of a day.

Aaron

Richard A Hetzel · 10-05-2009, 07:25 PM

Richard,

can you explain the conditions for zero live load on the floor and how that applies?

I thought I did...imagine an empty bedroom. with its floor joists cantilevering, and a roof with full live load (lots of snow) coming down on the end of the cantilever. One cannot assume that the full design live load, or even ANY of it, will exist on the main span.

Same goes for decks with cantilevered joists: "Hey, everone, come and watch the kids in the pool", and the whole party runs to the end of the deck, on the cantilever, leaving almost ZERO live load on the main span.

So, the cantilever must be designed for full live load, or in the case of the roof, full live load on IT, and no load on the main span, which will probably result in uplift forces at the inner end of the joists. However, unless conditions are extreme, most joist hangers installed in the conventional position, also have sufficient uplift capability to resist the forces. Still has to be checked, though.