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01032009, 01:13 PM  #1 
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Sister Board calculation
I am trying to calculate the benefit of sistering 2x's to my 2x10 joist.
Current Joist is 13.5', 2x10, 16" O.C. and I get a deflection of L/420. I am using travertine so need L/720. This means I need around a 70% improvement on my existing joists. The Moment of Inertia (I) for my 2x10 is I = 1/12(1.5)(9.25^3) = 99. So I will need to sister somthing that has I >= 70. I can not easily get 2x10's in the space available. A 2x8 will not give me enough. I calculated the following math for adding two 2x4's at the bottom of the joist as in the pic attached. For one 2x4: I = 1/12(1.5)(3.5^3) + 1.5(3.5)(2.875^2) = 5 + 43 = 48. So the total I = 99 + 48 + 48 = 195. Can anyone confirm this the correct way to calculate this? Thanks Steve 
01032009, 03:40 PM  #2 
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Sister Board calculation
I haven't done structural math like that since college, so I can't speak to whether or not your calc's are correct. But, I do this stuff in the real world and can tell you that adding 2x4's on either side of the bottom of a 2x10 joist will not yield a 70% improvement. To stiffen a framing member, you need to add depth...Like a 2x8 or 2x10 sistered to each joist...Adding 2x4's adds width but not depth and the result will be disappointing.

01032009, 08:17 PM  #3 
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Sister Board calculation
So I found out how to confirm my math. I needed to calculate the centroid differently then I did.
This link can be used by anyone interested in doing the math. http://physics.uwstout.edu/StatStr/S...ms/bdsn51a.htm Look for " Centroids of Composite Areas:" With this new info I found out that using two 2x4's results in I = 159 vs one 2x8 that will result in I = 152, so two 2x4's is slightly better then one 2x8. 
01032009, 10:34 PM  #4 
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Sister Board calculation
What about cross bracing?

01032009, 10:52 PM  #5 
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Sister Board calculation
I don't think your methodology will yield the results you expect. If it did, you could span farther with two 2x4's sistered together as a joist than you can span with a 2x8. Anyone who knows structures will tell you that they'd rather have the 2x8 floor joist over a pair of 2x4's.
Good luck with it. 
01042009, 12:24 AM  #6 
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Sister Board calculation
thekctermite
I added some math to the following link: Floor bounce joist sistering I can't agree with your 2 comments. 1 "If it did, you could span farther with two 2x4's sistered together as a joist than you can span with a 2x8." If you do the math, I for two 2x4's sisterd = 10.7 and I for one 2x8 = 48, so one 2x8 by itself has almost 5 times the inertia of two sistered 2x4's. This is not the same as sistering a 2x8 to the lower portion of a 2x10, or sistering two 2x4's to the bottom of a 2x10. You need to do the math to understand what you are debating. I did not understand it until I learned the math. Check out the links in my other post and you may be plesently surprised. 2. "Anyone who knows structures will tell you that they'd rather have the 2x8 floor joist over a pair of 2x4's." Anyone that knows structures would be an engineer. Engineers are the folks that create the math to represent systems. How can we argue the math? The math proves that sistering two 2x4s to the lower sides of a 2x10 has slightly more moment of inertia then using one 2x8. I think that you may be confusing load bearing with deflection. If you take a perfectly flat joist then the only way you can make it deflect is if you allow the lower surface to go from straight to curved, this requires adding length. By sistering to the lower area or even below it you make it harder to stretch that surface. If you could perfectly apply a flat plate of steel to the bottom of the joist the joist would not deflect at all because steel does not stretch. The best option to use if space is available would to add a 2x4 or 2x6 below the joist like an upside down T. I would be happy to share my spreadsheet with you if you want to see more of the math. Last edited by ijs12fly; 01042009 at 12:31 AM. 
01042009, 12:48 AM  #7 
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Sister Board calculation
I understand your logic about the 2x4's acting in tension and thereby limiting deflection, although I doubt it will give you the anticipated result. I'm not confused about the difference between load bearing and deflection, because they go hand in hand. What you're creating with the 2x4's is commonly called a drag strut. We can agree to disagree, because we definately disagree on the notion that this will work as well as sistering joists.

01042009, 10:20 AM  #8 
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Sister Board calculation
thekctermite
Its more then just acting in tension. Do you understand that by adding the 2x4s to the bottom you move the centroid of the system from the midpoint of the 2x10 (9.25/2) = 4.625" from the bottom to a new position that is only 3.38" from the bottom. And that gives the 2x10 by itself more "I = moment of inertia" taking it from a static value of 99 up to 120. If you sister a 2x8, the centroid barely moves so I goes from 99 to 102. Not sure if you are saying you understand all the math and agree with the math, but in practice the math does not replicate how it works in the field? 
01042009, 10:57 AM  #9 
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Location: Illinois
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Sister Board calculation
I am not a structural engineer but I do deal with floor deflection because of tile installations. I see what both are saying. It's hard to argue with math and the calculations. I don't think anyone would disagree with your math.
HOWEVER, the point is that no matter what math you are using, you still need to back it up with real world testing. The manufacturers of the joist are really the only ones that can tell you what might happen with changing the original specifications of their joists. They did the math but they've also put their products to the test....probably a lot of testing. I'm sure the liability of writing a spec that fails is huge. So while I'd have no doubt your math is correct, the ultimate say should probably come from the manufacture of the joists. I call them all the time. If I have a deflection ratio that's questionable, I just call the technical support department and talk with an engineer. Maybe try that????? 
01042009, 11:11 AM  #10 
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Sister Board calculation
Angus,
This thread is completely regarding deflection for my kitchen I am getting ready to tile with Travertine. Not sure what contacting a joist manufacture will do except have them agree that the joist span will give too much deflection for natural stone and I need to support it. Since I first started this post I found some the math that now shows me I have 3 options if I want to make sure I exceed L720 for my 13'4" span. 1. I can sister with a 2x10 (the 2x4 ides does not give enough support, neither does a 2x8). 2x10 sister is very hard for me to get into place but may be my best option. Need to relook at how to make this work out. 2. Use steel plate under or a new support beam/wall to reduce the span. This would be the easiest to install. I checked with my town and even though its not a code concern they want to see an engineering estimate of how the steel reinforcement bolted to bottom of joist would work for me to use it. So far I can not find any technical info that quantifies how it works. 3. Use a support wall or beam requires 2x2x2 footings which seems like a big mess and a lot of work. Breaking the slap, etc. I am just trying to find the best way to reduce deflection before I begin my renovation. Thanks 
01042009, 11:17 AM  #11  
K&B Remodeler/Tile Guy
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Location: Illinois
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Sister Board calculationQuote:
My advice is to call the manufacturer of your joists and ask them to recommend a procedure. What can it hurt? If they give you one, that's better than any math you have. I'm not questioning your theory, I'm just trying to give you the possibly easiest solution. 

01042009, 11:36 AM  #12 
Licensed P.E./Home Insp
Join Date: Dec 2008
Location: New Jersey
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Sister Board calculation
I'm a licensed engineer, and a contractor to boot. It's not as simple as you're portraying, especially if you're trying to prevent a travertine floor from cracking. Plus as a contractor I'd never just do the 2x4 thing, personally. In theory you think it adds up, but there are stronger more elegant solutions out there. Unfortunately I get paid for these sorts of questions, so my advice is to call a licensed engineer in your area and put it by them. I know that's a frustrating thing to read, but if you're at this point asking that question, you are far better off contacting a pro.

01042009, 04:13 PM  #13 
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Sister Board calculation
Aggie,
Where in NJ are you. I am in Somerset Cty. 
01042009, 04:19 PM  #14 
Licensed P.E./Home Insp
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Location: New Jersey
Posts: 587

Sister Board calculation
Sir, I live in Branchburg, and if you're the gentleman around the corner on Oriole, I'm going to freak out. How small of a world would that be?

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