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Old 01-04-2009, 12:03 AM   #16
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Floor bounce joist sistering


Nester,

Here is a where I learned how to calculate the Inertia: http://darkwing.uoregon.edu/~struct..._lecture28.html
http://darkwing.uoregon.edu/~struct...xample28-4.html.

You will then have to learn how to calculate the location of the centroid. This link will explain that:
http://physics.uwstout.edu/StatStr/...ams/bdsn51a.htm

And one more good source I found for deflection is http://books.google.com/books?id=yZo...um=6&ct=result

With this theory I came up with the following:
Moment of Inertia (I) : Support
99 : 2x10
198 : Two 2x10's
159 : 2x10 with two 2x4's
153 : 2x10 with one 2x8
167 : 2x10 with two 2x6's
210 : 2x10 with one T 2x4
250 : 2x10 with one T 2x6

So you can see that using a 2x4 T will give you a 2.1 benefit and a 2x6 will give you a 2.5 benefit if you start with a 2x10.

Let me show you how I did the T with a 2x4.

First I = bh^3 / 12.
2x10, b = 1.5, h = 9.25. A = bxh = 13.88
2x4: b = 3.5, h = 1.5. A = bh = 5.25
Assuming the bottom of the 2x4 on an x,y plot is y = 0, then the centroid of the 2x4 is y = 0.75". For the 2x10, its center is 4.625, but its sitting on the 2x4 so its centroid distance is 4.625+1.5 = 6.125. Now to combined centroid you will use Yct = (A1*y1 + A2*y2)/(A1 + A2) = (13.88*6.125 + 5.25*.75) / (13.88 + 5.25) = 4.65. Now we need to determine the distance from each center to the combined centorid. The 2x4 is 4.65 - .75 = 3.90 and for the 2x10 its 6.125 - 4.65 = 1.475.

Now we calculate I = Ia + Aad^2 + Ib + Abd^2
I = 1/12(1.5)(9.25^3) + 13.88(1.475^2) + 1/12(3.5)(1.5^3) + 5.25(3.9^2) = 210

So you can see that the moment of inertia for a 2x4 added to a 2x10 takes it from 99 up to 210, or a 2.1 multiplier.

Deflection is proportional to 1/I. So if you double I, you reduce deflection by half.

Here is a link to my major problem that I have not yet solved on another forum: http://www.johnbridge.com/vbulletin/...445#post744445

Regards

Steve

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Old 01-04-2009, 02:54 PM   #17
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Floor bounce joist sistering


Steve:

Your U of Oregon links don't seem to work for me, so I wasn't able to follow your calculation because I forget how to calculate the effective moment of inertia of a composite beam. However, I know this to be a valid way of calculating the effective Moment of Inertia because I did these calculations in the 2nd year of Mechanical Engineering at the U of Manitoba.

Also, the results you're getting are in good agreement with the results I get when calculating the effective I of a 2X10 if you glue and screw a 2X3 to the bottom of it to effectively make it into a 2 X 12. (Almost the same thing as making a 2X10 "grow" into a 2X12, really.) The built up beam will have an I value of about twice the 2X10, or you get about the same increase in strength from that 2X3 as sistering the 2X10 with a second 2X10.

So, you're preaching to the choir. I agree that gluing wood to the bottom of a beam will increase the effective value of I, and therefore reduce the deflection of the beam under any given load.

The problem rears it's ugly head in this thread from last September: (can you skim it over?)

joist sistering

Specifically, when thekctermite says:

"Sorry Nestor, but that is not a factual statement unless you've devised a way to grow 2x12's from 2x10's. Tensile stress will occur at the bottom of the loaded beam, and lumber added to the bottoms of joists would have to be fastened in a way that would resist the tensile stress to lower the joists' tensile chord...Not easily done. I've seen and inspected hundreds upon hundreds of engineers' designs and fixes for damaged joists and excessive deflection, and not one of them included the addition of wood to the underside of a joist. Nearly all incorporated addition of wood to the sides.

The linked thread was muddied by engineering gobbledy-gook that doesn't necessarily hold water in the real world, and generally isn't promulgated on a DIY site because it really isn't of benefit to the average poster. We need to give out advice that is practical and usable. I spent 5 years in college dealing with theory of structures, and assure you that trying to loosely educate most DIYers (and a lot of carpenters for that matter) is not going to accomplish anything but to frustrate them."

What thekctermite is saying is: "Every plan to increase joist strength I've seen involves adding wood to the side(s) of the joists, and therefore your gameplan to add wood to the bottoms of the joists won't work. If it did, people would do it. And don't bother with the technical gobbeldy-gook, we're supposed to be giving practical advice in here, not trying to confuse the natives."

My position is that as long as:

A) the wood you add is as strong or stronger than the wood the joist is made of, and

B) the glued joint between the new wood and old wood is as strong or stronger than the joint would be if it were made of solid wood, then

the modified joist is stronger than the original joist by the ratio of their moments of inertia, and will deflect proportionately less under any given load.

And, just as you calculated the effective I of the composite beam, it would also be possible to calculate the effective EI of a composite joist reinforced with steel plates on the sides, or with a square cross section steel channel glued and screwed to the underside of the joist.

It's reassuring to have someone else in this forum that understands that the strength of a joist can be increased OTHER than by sistering it. Adding material to the bottom is a far more cost effective method of strengthening the joist.

And yet, I am at a loss to explain why architects and engineering firms don't suggest doing this as a quick and cheap method for strengthening joists.
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Old 01-04-2009, 03:37 PM   #18
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Floor bounce joist sistering


Try this link:

http://darkwing.uoregon.edu/~struct/...lecture28.html

the address after the http:// is

darkwing.uoregon.edu/~struct/courseware/461/461_lectures/461_lecture28/461_lecture28.html

This would be such an easy test to setup for someone who is in the business. Take two 2x10's, seperate by 16", attach some blocking to prevent joists from rotating, add 300 lb load to the middle of it. Measure deflection. Glue and Screw two 2x4's and measure again.

If this test shows that D is not reduced by around a factor of 2, then post the results and edjucate us math type people.

I don't have the room for a T beam config, one thing I am considering is using a steel plate rather then a wood beem fixed to the bottom of the joist. I have been told that adding a 3/16" x 1.5" steel plate would take my "I" from 99 to 216, or a 2.1 multiplier. I need to find the math to prove this so I can show it to my town inspector.

Any ideas on the math?

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Old 01-05-2009, 01:17 AM   #19
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Floor bounce joist sistering


I graduated from Mechanical Engineering in 1974, so it's been a long time.

I did, however, find that your US military has already investigated the effectiveness of using steel strapping to strengthen floor joists in the following report entitled: "Evaluation of Expedient Techniques for Strengthening Floor Joist Systems in Residential Dwellings. By: Michael S Black."

The web location of that report is supposedly at:

http://stinet.dtic.mil/oai/oai?verb=...fier=ADA013987

but, that link doesn't work for me. Maybe contact the Army Corps of Engineers and see if they'll send you a photocopy of that report.

It'll be depressing, it found only a 10 % improvement in the deflection of 2X10 joists after NAILING 1/8 inch thick steel strapping to the bottoms of the joists.

The effectiveness of this method was found to be SMALL. That is, it wasn't very effective in strenthening the joists. However, my understanding is that the steel strapping was NAILED to the floor joists rather than being glued and screwed. If it wuz me, I'd use a strong construction adhesive like LePage's PL Premium moisture cure polyurethane adhesive to glue the steel strapping to the joists. Using nails allows the joists to deflect without the benefit of the steel strapping reinforcement until the tolerance between the hole drilled in the steel strapping and the nail is accomodated by deflection of the joist.

The other thing to consider is that joists are made of SOFT wood, like spruce, fir and pine. The result is that deflection of the nails holding the strapping to the joist would result simply because the wood around the nails would compress on one side. Wood is a very accomodating material.
Thus, SOME nails would compress the wood while others wouldn't even be carrying a load.

This study needs to be redone with the steel strapping bonded to the bottom of the joist, not just nailed to it.

If one were to GLUE the steel strapping to the joists, then the joist and steel strapping would behave as a single composite beam with the steel carrying it's share of the tensile force deflecting the beam right from the start. That is, I'd like to see your Army Corps of Engineers redo this study with the steel strapping glued and screwed to the bottoms of the joists with PL Premium construction adhesive.

http://ths.gardenweb.com/forums/load...002328620.html

http://ths.gardenweb.com/forums/load...531723856.html

THE MOST IMPORTANT aspect of composite beams is that there can be NO relative movement between the different sections of the beam. That is, if you simply screw steel strapping to the bottom of a floor joist, there is no bond between the wood and the steel, and there is the possibility of the two acting as two seperate beams, independant of one another. In order to ensure that they act together as one beam, it is necessary to GLUE (with construction adhesive like LePage's PL Premium) the steel strapping to the bottom of the joist. Without that, any clearance between the screws holding the strapping to the joists and the holes drilled to accomodate those screws is going to allow the steel and wood to act independant of one another. Thus, until the clearance between hole and screw is taken up, there will be virtually no benefit from the steel strapping.

However, by gluing the steel strapping to the bottom of the joist, then the steel strapping begins to stretch as soon as the joist begins to bend, and that means that you get more resistance to deflection right from the get go.

The only concern I'd have is to ensure that the glue layer was as thin as possible to minimize the "slack" attributable to deformation of the glue layer thickness as the joist bends.

I'd check that study by the Corps of Engineers to see if they actually glued and screwed the steel straping to the bottoms of the joists, or only screwed it to the bottoms of the joists. The former would be far more effective than the latter.
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Old 01-05-2009, 05:11 AM   #20
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Floor bounce joist sistering


Quote:
Originally Posted by Nestor_Kelebay View Post
Steve:

And yet, I am at a loss to explain why architects and engineering firms don't suggest doing this as a quick and cheap method for strengthening joists.
Most engineers would see it as, You will be Loosing Head Room by adding wood to the bottom of the beam. but you have my attention on gluing and screwing strapping to the bottom of the beam. BOB

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Old 01-21-2009, 02:41 AM   #21
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Hi

Any one have any information on how to strengthen TGIs?

Thanks Gary
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Old 01-22-2009, 10:43 AM   #22
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You can also create a similar effect by glueing and nailing/screwing 1/2" or 3/4" plywood across the entire ceiling. It creates a nice box beam configuration and significantly reduces bounce.

I'd suggest adding blocking (use glue to prevent squeeks), and see if that's enough before going further.

By the way, if you have no windows down there you are likely violated code egress requirements for finished space.
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Old 05-10-2009, 01:19 PM   #23
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Floor bounce joist sistering


With this theory I came up with the following:
Moment of Inertia (I) : Support
99 : 2x10
198 : Two 2x10's
159 : 2x10 with two 2x4's
153 : 2x10 with one 2x8
167 : 2x10 with two 2x6's
210 : 2x10 with one T 2x4
250 : 2x10 with one T 2x6

So you can see that using a 2x4 T will give you a 2.1 benefit and a 2x6 will give you a 2.5 benefit if you start with a 2x10.

Regards

Steve[/quote]

Very interesting Steve,

I'm wondering if you'd calculate for my situation in order to install tile.

My kitchen =
Thank you for using the John Bridge Forums Deflect-O-Lator :-)
For joists that are Unknown wood, but in good condition, 7.25 inches tall, 1.5 inches wide, 12 inches on center, and 12 feet long between supports, the deflection calculated is 0.468 inches.
This translates to a deflection of L / 307.
Since the maximum deflection for tile is L / 360, and for natural stone is L / 720, your floor is rated for Sheet Vinyl or wood.


My bath =

For joists that are Unknown wood, but in good condition, 7.25 inches tall, 1.5 inches wide, 16 inches on center, and 11 feet long between supports, the deflection calculated is 0.457 inches.
This translates to a deflection of L / 289.
Since the maximum deflection for tile is L / 360, and for natural stone is L / 720, your floor is rated for Sheet Vinyl or wood.

My current flooring is 3/4" thick.

Making the "T" is a matter of installing the 2X4 flat against the bottom of my existing joist with glue and screws?

Thanks, Tom
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Old 05-10-2009, 01:42 PM   #24
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The issue of excessive floor flexing is quite different from the issue of beam strength. The 2x10 joists are sufficiently strong by code for 15 foot spans, however strength refers to the ability to carry load without breaking. It is not the same as deflection, which usually controls, since excessive deflection can occur on a beam (joist) which is considered adequately strong.

The purpose of X bracing is to increase the lateral stiffness of a beam, to prevent sideways buckling under unusual loading conditions. The X bracing has the additional benefit of transferring a small portion of the load from one joist to adjacent joists, however this is not the main purpose of the bracing. The bracing adds virtually no moment capacity to the joists, so it does not make the joists "stronger", however your joists appear to be sufficiently strong by code anyway.

So, on to the deflection problem. I don't think additional X-bracing is going to do much to solve your problem, although it certainly will not hurt, just cost you time and money. Your original idea about stiffening the joists by sistering lumber onto the side of them is good, and will certainly work. Since you do not have a strength issue, there is no reason you need to run full length sistered joist. The post recommending centering the sistered joist was correct, you should have a continuous beam across the center of the span, where the deflection will be the greatest.

The important thing is to make sure the sistered joist is adequately secured to the existing joist. This can be done using an adequate number of nails or screws. The idea is to make the two pieces of wood act as a single unit by transmitting the shear from one joist to the other (hence the nails or screws). I don't have the tables for your particular application, but in similar circumstances I have driven three inch structural screws every six inches, installed about 1 inch from the top and bottom, staggered. In other words, when you are done, there will be a row of screws along the top, about 1 inch from the top of the joist, and a row at the bottom, about 1 inch above the bottom of the joist, with the screws six inches on center. The two lines of screws are offset three inches from each other, that way the screws do not line up vertically, reducing the potential for splitting the wood.

The additional stiffness of a sistered beam would reduce your floor flex substantially. By the way, you could also add wood to the bottom of each joist, however this is rarely done because of headroom clearance issues.
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Old 05-10-2009, 01:50 PM   #25
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I'm not so much concerned about the head clearance as it is in the garage side of a walkout basement and there is the additional duct work that falls much lower. The good news to my situation is that the joists run parallel with the length of the upstairs bathroom floor. Being a small bathroom, I should only require sistering a couple of the joists. There are also double joists already under each wall of the bathroom.

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