How long until my 2x12s sag?

jpearson311

I just installed 2x12x20' southern pine boards in my hip roof garage as joists, with no support above them or below them. Other than a non-insulated garage door, the joists will have virtually no load. Can anyone tell me if the joists will sag over time? Thanks.

Jesse

PS. They are attached to the wall studs with joist hangers and the rafters on top with mending plates. Thanks again.

bill01

You are within the limits for ceiling joists with minimal load in the span tables. You could use 2x8 24 inch on center and still be ok. The table says 2x10 southern pine will go 20ft at at a load that would assume a drywall ceiling. The key function of the joist is to prevent spreading of the walls. You really should have the joist nailed to the rafters. Hard to say mending plates are not a rated to perform this function... but it may work. I suspect you would see the joist hanger pulling away from the walls if you had a issue.

tony.g

Any joist will sag, even under its own weight and regardless of the span; it's a question of how much deflection you are prepared to tolerate. For domestic floors, your local code will probably put a limit on the deflection; typically it's about 0.003 of the span. For unloaded ceiling joists in a garage, the deflection allowance will obviously be greater.
What is more of an issue here is what bill01 has pointed out - the fixing between the ceiling joists and rafters. As he stated, strictly,they should be nailed together (or bolted). If your plates are big enough, though, you should be OK.

jpearson311

Yeah, I think I should use ties instead of mending plates. I've read about deflection before. What exactly is it? Oh, and the span is about 22.5". Thanks.

Jesse

bill01

The math gets complex very fast when you want to calculate the actual deflections. The tables just make sure you do no exceed a value but do not tell the actual value just that you are less. The common one to use is x/240 so in your case you have 20ft which 20/240 = .083 ft or about 1 inch. But that would assume you use 2x8 or 2x10. With 2x12 it will be less. I bet about 1/2 inch.

If you mean hurricane ties those won't do the job either. The actual force is also a complex calculation that is dependent on many thing like the slope of the roof and the snow loads. I would bet you have 500lbs of force you have to transfer from the top of the wall to the joist. If you were going to nail it they would want 5 3 inch nails. When you start using using metal side plates especially when they meet at a angle you need to be a structural engineer to calculate if they will work.

They do make long coils of steel strapping that you can run the complete length to hold the rafter ends together. You could then not worry about the joist. I think you can do them every other joist rather than everyone.

tony.g

There are equations to work out the actual deflection of beams, and as a matter of interest I tried it on yours. If your span is 270"; your joists are @16" c/s; they are only supporting their own weight and a plasterboard ceiling; and your timber is 1,000 psi grade, then the natural deflection (sag) will be about 0.2 inches at maximum (at midspan), which is nothing. The natural warp/twist of the timber will probably be more than this.

Over time, the timber will gradually sag a litle more because timber is subject to long-term creep under load, but it still won't add up to much.

As pointed out before, your main concern is to make sure that the joists are firmly fixed to the rafters.Without an adquate fixing, the rafters will tend to push the walls out of plumb, and then deflection of the ceiling joists would be the least of your worries!

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tony.g

(You were quicker off the mark with your figures than I was, though I got sidetracked by the sketch!)

jpearson311

Good point. I'm going to return my mending plates and replace them with ties. Something like these. Right now, the top of each joist at the end has a slope cut in it so they sit flush against the bottom of each rafter. Then, there are 2x10 joist hangers underneath them, nailed into the wall stud. With the hangers and the ties at the ends, I think I'm good there. I just don't want them to sag in the middle so I think what I'm going to do is tie a 2x4 from the top middle of each joist to the rafter directly above them with perpendicular ties. It's a hip roof so it's going to be a little challenging for the middle one, but I think I can pull it off. Thanks!

Jesse

GBrackins

did you install ceiling joists, or is this a cathedral ceiling?

__________________
Gary

"You get what you pay for, and sometimes free costs more!"

jpearson311

I installed the joists. There were only 4 before and they were 2x8x20s nailed to the sides of the wall studs.

jpearson311

Here is a pic I snapped yesterday in case anyone wants to see. Thanks.

Jesse

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Yoyizit

The wood sags immediately on being loaded.

Whether the Modulus of Elasticity of wood increases or decreases with time is another question.

jpearson311

It must barely sag because I hung on one the other day after I installed it and it didn't move at all. And I'm 230 lbs.

Jesse

Yoyizit

Meaning, "It sagged an amount imperceptible to the eye". A sixteenth of an inch, perhaps?

If you dangled off the center of the span or even elsewhere you can use the deflection plus the formulas in the Engineering Toolbox to figure all the parameters of this beam.
The formulas are not complicated but they are tedious.

tony.g

Assuming timber is Douglas Fir or equiv., with E = 1,000,000 psi (for a single beam acting alone) on a span of 270", 230lbs at centre, using d = 1/48 x WL3/EI, gives max deflection around 0.5" - as you say,probably too small to see on that span.