Cantilever beam deflection.

Assuming you have used the correct formula for the specific configuration, your other thinking is also correct. In other words, the deflection produced by the load(s) is less than the allowable deflection, just as it should be.

Thx for your insight. I gave you a GA. I arrived at the 0.264" (DL+LL) deflection by summing the results of that produced by a Beam Overhanging One Support, Uniformly Distributed Load (AISI 2-206, #24), and Beam Overhanging One Support, Uniformly Distributed Load on Overhang (#25).

When I use the pure cantilever, #19, Deflection = (wL^4)/8EI, I get 0.113". Which, from 82/0.113 yields a ratio of 726, > 240 :. ok.

The manufacturer's software does what you recommended, calls it "Alternate Span Loading on Odd # of Spans", resulting in a 0.366" deflection. They use 2L/463 = 0.366" (they use a slightly different L, 84.75").

For "Control", they use 2L/240 = 0.706", vs. L/240 = 82/240 = 0.34".

In conclusion, while their 0.366 passes their 0.706 Control, my 0.264 or 0.113 passes the classical 0.34 Control. Either way, the deflection would be judged ok.

flyinghigh,

In my earlier post, I said:

"If you have a pure cantilever fixed at point B and free at point C, it behaves identically to one half of a simple span."

I should have added:

"if loaded with a concentrated load at the tip or loaded with constant moment (cylindrical bending)."

Under general loading, the statement is not true.

I agree with your conclusion.

Bruce, the load is uniformly distributed on the cantilever; 15 psf DL + 100 psf LL.

In that case, we need to know the spacing between cantilevers, so we can convert to pounds per linear foot on each beam. I would also be nice to know the dimensions of the beams.

Tornado,

I don't think flyinghigh is asking us to check his calculated deflection. He has come up with a value taking into account patterned loading and wants to know if that is in accordance with the code value of L/480. To answer that, we need to know the value of L to be used.

He first proposed 254" for L, the overall length of backspan plus cantilever. I do not agree with that choice. The length of backspan should not control the permissible deflection of the cantilever.

The code does not define what length to use for a propped cantilever, but I would compare the calculated deflection to 2c/480 where c is the cantilever length. In this case, that would be 2*82/480 = 0.342". Since the calculated deflection is less than that, I would interpret that to satisfy the code.

Are you in agreement with that?

I think so. As I have said before, the OP seems to be reasoning correctly, provided the calcs are correct. (Which, lacking the beam choice, we don't yet know.)

I'm only guessing, but I get the idea that some inspector is roadblocking the OP's approach. I may be wrong in this, but we haven't heard whatever conflicting rationales are in contention.

Tornado, thx for your input. Bruce was correct; I was trying to get a better handle on whether my calcs would meet the code's requirements.

First, I ran it thru some software I purchased. It said it was ok.

Second, I thot I might as well run it thru the beam mfr's software, which I had on hand. I kept getting conflicting results. To the unititiated, it is a rather onerous task. While waiting for a response from the mfr, I thot I'd create my own on Excel.

Thirdly, I added the results of the two beam formulas as mentioned previously on Excel.

As Bruce pointed out, I was using the wrong ratio (for simple beam) for a cantilever beam. Interestingly, the result of my purchased software indicated a cantilever length (C) of 7'2"(86") would be ok. But the mfr's software puts C at 6'10"(82"). I would err on the conservative side, i.e., 82".

Tornado, because I didn't intend anyone to check my arithmatic, I purposely left out some data. FWIW, they are 11-7/8 TJI 560 16"oc.

Hi, all,

I'm overhauling/building my house a little at a time. My current project is rather dramatic and I've attached pictures.

There is a 25 ft solid wood beam cantilievered with one end support and one mid support appoximately 14 ft from the end support which leaves 11 ft overhang. There is a roof structure built over this beam consisting of 3 2x8 bundled cieling joists every 16 inches (guilty as charged - it is overbuilt!). The joists are covered with plywood, standard flat roof build-up. The roof structure is 24 ft x 24 ft.

My issue is the beam and any deflection over time. No calculations were performed. I am thinking of adding a steel pole to offset the cantiliever to tie back to the mid-beam support. It would not be as pretty or dramatic, but my concern is shear and deflection over time... Well, and safety.

Any opinions, thoughts, or concerns? (please be nice)

OilyBaby,

I don't know where you live, but in my location, a project such as yours would require a building permit. The authorities would demand engineering approval of the cantilevered beam before granting a permit.

You would be well advised to consult a civil or structural engineer and have him review your design. He can calculate the deflection quite easily if he knows the properties of the beam. No point adding an ugly strut if you don't have to.

This is only an uncalculated guess, but the 11-foot overhang of the beam strikes me as iffy.

Also, how far does the roof overhang past the beam?

Architecturally your place looks great!

Thank you, both of you, the advice.

The only reason for the extra support 2x6 under the cantilever was having additional support in nailing down the plywood. I finished the roofing today and removed the support. The whole roof is very solid when I walk on it but THAT is certainly not proof enough.

Anyway, the conclusion to this is installing a cross steel beam and masking with a wood facade.

I live on a county island, no town in my property. Taxes go to the county, post services in another city, and another city for trash pick-up. Outside structures are not under a permit requirement but left to the owner. The same is true of a pool fence; required in the city, but optional for county islands.

But, hindsight tells me that I should have had this engineered. Anyway, the crossbeam should eliminate any doubts once completed.

Have a great weekend.