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Calculating Increase in Joist Stiffne…

| Posted in General Discussion on April 6, 2001 02:09am

*
Is there any straightforward way to estimate the improvement in floor joist stiffness I would get, by gluing another member underneath the existing joist, to form a _|_ cross section? (This seems much easier than sistering a deeper joist).

What improvement in deflection could be expected from a 1×3 as 2×4 vs something else?

How much improvement if I do every joist (ugh), as opposed to alternate joists?

And finally, is there any structural or stiffness advantage to jacking up the joists slightly, before gluing & nailing the member? I guess that would pre-stress the member into tension when the jack is removed, if that matters. The sub floor is adequately flat right now.

Right now, the joists are doug-fir, 2×6, 16″ OC, that span about 9-10 feet. I recall this is marginal for L/360 deflection (40 lbs live load). The subfloor is 5/8 T&G plywood, nailed but not glued.

Thx in advance.

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  1. Mike_Maines_ | Mar 27, 2001 06:19pm | #1

    *
    Tom, the engineering calculation for stiffness boils down to multiplying the base times the height^3 of the section. A 2x6 on edge has a relative stiffness of (1.5)x(5.5)^3=250.

    A 2x6 on the flat has a relative stiffness of (5.5)x(1.5)^3=18.5

    Add these together and you have 278.5, or a relative increase of 11%

    If you could attach the two pieces so there is NO slippage between the two (glue and lots of nails?) you would get more of a true I-beam effect, but the equations are trickier--

    It's probably easier to just sister another joist, you'll get much more stiffness, and it's not as important if there's slippage between the two members. At least from a calculation point of view.

    MM

    1. tom_herman | Mar 27, 2001 06:35pm | #2

      *Mike,Seems like there is negligible benefit using a _|_ section, even though others on this Forum have suggested it.I take it the benefits of an engineered I-joist are mainly because of it's depth (?). Sounds like I may have to struggle with gluing & nailing a 2x8 or 2x10 onto the existing 2x6.

      1. Jon_M. | Mar 27, 2001 06:38pm | #3

        *Tom,You can roughly decrease the deflection by a half using a 2x4. But you have to be careful attaching the 2x4 to the joist. Glue would not do it for you. You would have to lag or screw, and lagging into the 2-inch side of a 2x6 is kind of hard. The lags would have to transfer horizontal shear to make sure the inverted 'T' acts as a member. This can be calculated by an engineer. (v = VQ/Ib)A 1x3 will decrease deflection by roughly a quarter, again assuming that it is properly fastened to the joist.Obviously, sistering a 2x6 would halve the deflection also. Frankly, I think it would still be easier to do this rather than an inverted T with a 2x4 and lagging.I would not recommend doing alternate joists, since this would give you "soft spots" in your floor.You can camber your floor by jacking it, then attaching the flange you are proposing. Calculate the dead load deflection only and jack this amount. Actually, if your floor is already flat, I don't know if I'd bother with this, unless the dead load on the floor is going to be significantly higher.Hope this helps.Jon

        1. Art_B | Mar 27, 2001 07:03pm | #4

          *Just finished adding a 16ft by 3/16 by 4" steel plate to 6X12 over son's garage door to double the strength to allow use of above truss floor space for storage. Like Mike and Jon say, NO SLIPPAGE ALLOWED for this to work - Used 148 each (no typo, over a gross) 3/8" 6 " long lag bolts for the above. As Jon says, lots more work (and expense if you have to buy the bolts)than sistering, but was only option for aesthetics and door space for this case.The classic text, "Elements of strength of materials", Timoshenko and Young, Van Nostrand, 1964, has all the calculation methods on pgs 124-149 for the built up beam method.

          1. tom_herman | Mar 27, 2001 08:07pm | #5

            *Seems like some of you are suggesting screws, a major pain.WHY can't a _|_ or sister joist simply be glued and nailed? Wouldn't a quality grade of adhesive (like subfloor glue, or construction polyurethane, or Epoxy) ensure a "non-slip/ non-moving" connection to absorb the horizontal shear ?? After all, isn't that how commercial I-joists are assembled, mainly glue?

          2. Art_B | Mar 27, 2001 08:55pm | #6

            *If the glue will take the shear and not be subject to creep (you need the glue specifications to be sure, subfloor glue or polyurethane or drywall adhevise definetely will NOT work because of creep, 2 part epoxy or polyester resin probably would), you need to do the jacking trick (with nails or lots of jacks)like Jon said AND LEAVE THE JACKS IN PLACE UNTIL THE GLUE IS FULLY CURED. You will help prevent further sag or bouncing by holding it with nails while the glue sets (don't walk across the floor while the glue cures or you will disturb the bond), but you could not get enough nails in to prevent the longitudinal shear from disturbing the glue joint during cure if you are trying to correct any existing sag. You can always try one joist first and test the results. good luck.

          3. Jon_M. | Mar 27, 2001 09:37pm | #7

            *Tom,For a 'T' section, the moment-of-inertia equation is a little trickier because you also have to add the area times the distance from area center to the combined centroid squared to the quantities Mike mentioned. For the T with a 2x4, this portion actually accounts for 95% of the net increase in stiffness.To answer your question about gluing, what you are essentially trying to do is build a half of a pre-engineered wood I-beam. But the key word here is "pre-engineered." The wood I-beams are engineered products and manufactured in a controlled environment. They are also rigorously tested to determine their allowable loads and deflections. In your case, you must assume that the glue essentially takes no shear. I would bet that your local building official will only allow shear values for mechanical fasteners, not glue. You can probably use nails, but I wouldn't. I'd use lags.I still think you are better off sistering the floor joists. With calculations, you probably don't need to have them bear on a beam. If you are just trying to control deflections, I would have an engineer check if you can just sister a 2x4 to the bottom part of your 2x6 (but installed with the 4-inch side vertically). This is in essence the same as building a inverted 'T' at least structurally. It will actually look like an 'L.' This way you spike or lag into the side of the 2x6 with a 2x4.Good luck.Jon

          4. Darrell_Hambley_PE | Mar 28, 2001 01:38am | #8

            *Tom,Even if you could convince the inspector that the equations are valid, the type of glue you'd need is the kind they make i-joists out of..heat-cured epoxy. Can't get this at HD. Sounds easier to take 50 bucks and buy a few more 2x6's.DH

          5. tom_herman | Mar 28, 2001 02:53am | #9

            *You guys have convinced me! Sistering deeper joists seems to be the way to go. Thanks.

          6. Mike_Maines_ | Mar 28, 2001 04:40am | #10

            *Tom, on the OTHER hand, I'm a carpenter and not an engineer, and don't have the span tables handy, but if your floor passes code (or code isn't an issue) and you just feel like experimenting, you could try what you wanted to. Glue the two members together with Resourcinol or Urea Resin glue, which are commonly used in furniture laminations because they creep less than yellow glue. Lots of big spikes to clamp it all up, pre-stress the assembly with some floor jacks or studs cut too long, and let it set a good long time. Some creep over the long term won't hurt too much as long as the joint holds. Guaranteed to make the floor stiffer, just can't get an engineer's stamp on it. Probably easier to just sister on something, though. Lots of bolts near the ends for shear. Good luck,MM

          7. Tim_Kline | Mar 28, 2001 05:32am | #11

            *b WBA At Your ServiceOne of our structural engineers has taken a liking for this T type of repair in certain situations. Like when the joists have about 50 wires and pipes running through them rendering sistering out of the question. (Happens EVERY time !) As a result, I have made several repairs just as described above with great results. We have done the repairs according to the engineers specs (always been a common sense kind of guy). A 2x6 is glued to the bottom of each joist after it has been sanded with a belt sander to clean it up. The 2x6 is glued with PL Premium adhesive and then screwed through predrilled holes with 3 1/2 inch drywall screws on 3" centers. Your calculations may show only 11% stiffness increase, but I can assure you these floors felt a whole lot more than 11% tighter. I never would have believed it if I hadn't seen it myself.

          8. SamD_ | Mar 28, 2001 02:46pm | #12

            *3 1/2" drywall screws? Hmm...................Sam

          9. Jon_M. | Mar 28, 2001 03:41pm | #13

            *My estimation is that if you have a 2x8 floor joist with a 2x6 attached to the bottom like an inverted 'T', the increase in stiffness is about 340%. In layman's terms, the joist would deflect about 3-1/2 times less than just a 2x6. A 2x6 with a 2x4 (as Tom has) would yield about a 100% increase in stiffness, or halve the deflection.I also agree with Mike that if there are no code compliance issues (i.e., stresses or loads), then you can probably convince your local building official that what you are doing is just a owner-requested enhancement. If there are heavy loads, you have to be careful about compressive stresses at the upper edge of the web.There are certainly instances where doing this may be necessary (as Tim has pointed out), but the prep work necessary to get a good glue bond is still a lot of work.

          10. tom_herman | Mar 28, 2001 04:41pm | #14

            *MNow maybe, I'm back to undecided!The floors in question are to code, so it is not a structural issue, nor should I need an inspector's OK. The desired stiffening is more of an "enhancement". I might just try a section with each technique (_|_ vs Sistering) and give it a "bounce test".

          11. Art_B | Mar 28, 2001 05:17pm | #15

            *One more:You can also get an improvement in "apparent" stiffness (eg bounce from walking across floor as opposed to deflection from full loading) with multiple bridging, such as on 4 ft spacing. The metal types are real easy to install.

          12. Darrell_Hambley_PE | Mar 28, 2001 06:17pm | #16

            *Since the floor's already to code I would do the "enhancement" thing. Since most floors never have a constant 40psf live load, the creep would be negligable and I'd use normal construaction adhesive. The only time this glue would have a load is when you walk or bounce on it so there's not enough total time for creep.

          13. The_Tennis_Court_Builder_...on_t | Mar 28, 2001 06:59pm | #17

            *Most everyone who posted has totally overthought your question Tom...You are looking for less bounce and an easy fix.Your solution is the easiest, the cheapest, and the will hugely effect the bounce and the short term load strength...Creep is a non issue for temporary loads.And do not try to push the floor up. Total waste of time as the bounce component does not depend on that and in fact may be worse...Kinda like a spring held dampened verses one with no dampening.near the stream agreeing with Darrel and Jon,ajThe rest of you flunked the quiz 'cause you read more into the question than was there!OK...I'll buy all your sorry butts the next round of beer at the tavern!

          14. Mike_Maines_ | Mar 30, 2001 02:17am | #18

            *Tom, since your question was "is there a straightforward way to estimate the improvement in stiffness," it seems like everyone agrees that what you propose will help. Worst case, there is slippage, and you gain 11% stiffness. Best case, add all the lags the engineers recommend and get 340% improvement. Average the two and you get 175% improvement. To do the calculations you have to assume one situation or the other. AJ's right though, exactly how much it will help probably isn't important in your case, the fact is it will help.AJ, thanks for the beer. Next one's on me.MM

          15. The_Tennis_Court_Builder_...on_t | Apr 03, 2001 01:53am | #19

            *Sorry Mike...no lags needed...just screws and glue...No creep in the picture...Bounce does not give glue creep time. The short term bounce strength will be as high as the best case scenario...That is as if the pieces grew together.Ya all need to study with a farmer and at college and in the field,near the stream,ajBeer time again...On me again for being so friggin arrogant and American.

          16. Scott_Hitchcock | Apr 03, 2001 02:29am | #20

            *AJ, Mike, Darrell.......Would 2 x 4's on flat, every 2' or so, perpindicular to the joists, glued and screwed take some of the bounce out of the floor?If so can any of the engineers out there tell us how much?Scott

          17. Mike_Maines_ | Apr 03, 2001 03:41am | #21

            *Ahem...grew up on a farm, degree in civil/architectural engineering, work as a carpenter and cabinetmaker...but I defer to your experience, AJ. You want to take Scott's new question? I seem to have trouble just letting the last word go....Mike

          18. The_Tennis_Court_Builder_...on_t | Apr 03, 2001 04:22pm | #22

            *Scott...It would help by reducing some of the harmonics but not add nearly as much to the temporary carrying capacity...Do it the parallel, glued and screwed way...It will go faster than lickity split and will do as posted above.near the stream,ajps...IF yaa did all methods mentioned, then the foundation would give way first! Yaa could drive Abhrams tanks in and park em overnight.

          19. The_Tennis_Court_Builder_...on_t | Apr 03, 2001 04:26pm | #23

            *Mike...yaa got all "the right stuff" but...Maybe you were practicing your sociology 101 class instead trying to be nice to those that really missed the point of the question.Now stick to your guns boy and I'll back you up yaa fellow edumacated farmer boy,near the stream,aj

          20. Ryan_C | Apr 06, 2001 12:08pm | #24

            *Sorry Mike, doesn't work that simply. If you had a simple rectangel , that would work but once you joit two to make a "T", you have to do your calculation around the "neurtal plane" which is sort of the center of the shape. A 2x6 on flat that sits alone is nothing like a 2x6 in flat that is way out at the far end of this new shape.Adding a 2x6 to make a "T" would be a significant improvement but only if you can keep the two pieces of wood from slipping against each other. Most glue will creap over time, and if you use screws you'll need alot of them. The shear forces between the two pieces is huge.

          21. Mike_Maines_ | Apr 06, 2001 01:42pm | #25

            *Ryan,Yah, I know, the centroid is close to the bottom of the existing joist, IF there is a perfect connection between the two. What Tom originally asked for was a way to estimate the amount of improvement. That's why my first answer was to assume slippage, that's one way to estimate. The other way is to assume no slippage and get a perfect connection. Apparently Tom, there is no EASY way to calculate...we just know it'll work for you.Mike

          22. The_Tennis_Court_Builder_...on_t | Apr 06, 2001 02:09pm | #26

            *Ryan....We are trying to stop bounce...There is not enough time for glue to creep...Glue does not creep in a hundreth of a second. So there would be a huge change in bounce.near the creeping stream,aj

  2. tom_herman | Apr 06, 2001 02:09pm | #27

    *
    Is there any straightforward way to estimate the improvement in floor joist stiffness I would get, by gluing another member underneath the existing joist, to form a _|_ cross section? (This seems much easier than sistering a deeper joist).

    What improvement in deflection could be expected from a 1x3 as 2x4 vs something else?

    How much improvement if I do every joist (ugh), as opposed to alternate joists?

    And finally, is there any structural or stiffness advantage to jacking up the joists slightly, before gluing & nailing the member? I guess that would pre-stress the member into tension when the jack is removed, if that matters. The sub floor is adequately flat right now.

    Right now, the joists are doug-fir, 2x6, 16" OC, that span about 9-10 feet. I recall this is marginal for L/360 deflection (40 lbs live load). The subfloor is 5/8 T&G plywood, nailed but not glued.

    Thx in advance.

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