Center web reinforcing of 21' TJI span

[rchbud]

I have floor that is designed to 1/460 with TJI 360 engineered joist 11-7/8" tall with a 21 foot span, 16" o.c.. I want to increase stiffness to 1/720. I had planned to add reinforcing web sections using 1/2" OSB in the center of each span, but just 8 ft. long, the OSB would be structurally glued and nailed or screwed to the top and bottom flanges of the TJI joist, I was also doing to solid block with 2 x 12s between joist at each end of the web stiffeners. The stiffeners would a 11 7/8' tall by 96" piece of OSB.

However I need to prove this reinforcing is adequate and have not been able to find and formulas for bending or deflection where just the center section of a span is stiffened, not even related to steel beams. Does anyone know where to find these formulas?

 

[msquared48]

Messing with the joists WILL void any warranty. You could consult with Trus Joist too on this (Red Built now for their commercial joists -

http://www.redbuilt.com

or 866-859-6757) Trus Joist still has their residential line though. Either might be able to help you with this.

Might just be better to just space the joists closer together, or double them up to achieve the higher stiffness...

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[MiketheEngineer]

Ditto that

 

[rchbud]

Thanks for the quick responses, but adding more joist is not an option. I already talked to the manufacturer about this configuration and there's not a problem with it, as this is essentially how they tell you to reinforce their joist when cantilevering them. I already convinced myself that adding additional stiffening webs does a lot, calculated the max. deflection from 1/32" to 1/10000" when the webs are added on an 8 ft. section. I would just like to find formulas that address beams that are reinforced in the center section of the span only.

 

[dhengr]

“I already convinced myself that adding additional stiffening webs does a lot, calculated the max. deflection from 1/32" to 1/10000" when the webs are added on an 8 ft. section.”

And, the manufacturer says there’s no problem, so who needs formulas, they just get in the way, and the one’s we might give you would just lie to you. At least, they probably wouldn’t give you ? = 1/32" for those TJI’s on 21' spans at 16" o/c. I used to pay for .0001" tolerances from machine shops and if you are confident enough to do that with TJI deflections, go for it.

 

[rchbud]

just to clarify, I was only able to calculate deflection based upon an 8' long span, unreinforced and then reinforced, only in this span lenght did I come up with the 1/00000", i.e. zero. I just can't actually calculate the deflection of the 21' span with only the center 8' reinforced. Can't find any formulas for wood or steel.

 

[MiketheEngineer]

I am guessing that you want to tile this floor?? If you add 3/8'' DuraRock installed correctly and use latex based cement and grout - I am guessing that you will not have a problem.

I did this on a plain old 2x10 floor system. Two weeks after the install they rolled in a 700 lb refrigerator - no problam.

 

[rchbud]

Thanks for the DuraRock information. Yes it will be tiled, but my tile contractor won't install marble unless he knows the floor deflection is 1/720 or less, even with the DuraRock.

I am also curious to find the formulas that work with partially center stiffened beams. I have been on-line and through numerous structural text books and can't find anything for this particular case which I know is done all the time with wood and steel.

 

[gobsmacked]

One can work out the formula using the unit load method, especially if you can draw the M/(EI) diagram. If you have an 8 foot length glued and screwed at the centre, you would have to decide how much of the ends is 'used up' as a transition zone, rather like the anchorage of a rebar. Perhaps only 6 ft of that can be considered effective?

 

[rchbud]

I was hoping there were some empirical formulas. But at least the method you describe is a way to look at it, which I will investigate. Thanks.

 

[BAretired]

It is easy to generate an empirical formula for this case if you know EI(end) and EI(middle) but if you want to move from a deflection of L/460 to L/720, I don't think it is possible with a couple of 8' long sheets of OSB in the mid-section glued and nailed to the chords.

BA

 

[gobsmacked]

to rchbud, I have worked out a formula, which I attach as a pdf. Nobody has checked it though. But I did an internal check which was OK.

 

[MiketheEngineer]

I suppose you could test it.

L/720 is about .35'' If you are 16'' oc then just put about 67 (.133 x 50 psf) lbs per foot over the joist and measure it. Or a center load of about 700 lbs - gives same moment. Bricks work nicely.

If have access to RISA or other - you could model a beam with three different pieces and two different Inertias but fixed at their connections.

 

[BAretired]

How does E for OSB compare to E for the chord members?

BA

 

[BAretired]

For comparaive purposes, I came up with a formula slightly different from gobsmacked. L is the span and b is the length of reinforced central section. EI is the stiffness of the end sections and k is the ratio of EI(middle):EI(end), in this case, a factor greater than 1.0.

[Δ] = (w/384)*[(L-b)⁴ + 4(L-b)²(L² - b²) + (8/k)*b³(L-b/3) + (12/k)*(L² - b²)b(L-b/2)]

BA

 

[Brad805]

Is there a reason you cannot add to the bottom chord? You can air-nail/epoxy bond a new chord to the bottom far easier and that is more cost effective. Assuming this is an existing structure, adding between the joists is typically problematic if you have any existing elec or mech constraints.

If this reinforcement is for tiling, then I would consider using a product like Ditra also.

Unless you are adding loads above, I cannot follow the logic behind this excercise.

Brad

 

[chicopee]

Attached is a .JPEG file that I copied from a May 1972 "Design News" article on Design of Nonuniform beams. This page is one out of the six in this article. Castigliano's theorem was used to calculate deflection of nonuniform beams.

 

[BAretired]

So that provides a third formula for calculating deflection of a beam with central reinforcement. Does anybody want to check them all out? Hopefully, they all are in agreement, but if not, let us know.

BA

 

[woodman88]

I personally feel that the addition, in the field, of plywood/OSB (due to the critical slip of the connection) has little effect on the deflection. Where asked for my input, I have stated this. My only comment has been that adding additional plywood/OSB would be better at the bearings, as that is the location of highest stress in the web.

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.