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Perpendicular / Sideways Studs, Thin Partition Walls, Math and Soundproofing

Perpendicular / Sideways Studs, Thin Partition Walls, Math and Soundproofing

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  #1  
Old 08-27-14, 08:55 PM
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Perpendicular / Sideways Studs, Thin Partition Walls, Math and Soundproofing

This is my first post, please be kind.

When you're tight on space and it doesn't take long to consider turning the 2x4's sideways so that the studs are now rotated 90-degrees and perpendicular to the adjacent wall--you gain 2 precious additional inches of room or closet space doing this. So when is this space saving/gaining thin-walled construction a good idea and more importantly when is it bad?

Walls with doors seems to be a no-go, and certainly exterior or any interior load bearing walls are clearly out (against code as well). But I was not finding any rules of thumb that helped to decide when thin-wall construction can work well--the only obvious choice would be for closets, and beyond that I didn't know. if anyone knows of a good source for some rules of thumb then please reply.

The thin wall (sideway studs) will pass more noise through them, not because the sheetrock is closer together, it's because the studs are not as rigid sideways and you have more direct connection of the stud to the sheetrock; if you can add 1/4" of styrofoam or other soundproofing material then it would help. If you really need the thinest wall possible and it must be soundproof, then consider draping plastic inside and then fill it up with DRY play sand; to dry the play sand you have to spread it out on the floor with plastic and indirectly blow the air around with fans, and rack the sand a few times a day for a few days, but you'll have maximum soundproofing with you thin walls! You fill the walls by laying sheetrock sideways, and filling it up 4-feet, then 1 or 2 feet at the top. Filling to the top is not as bad as you think, especially the last foot, and you're already a stubborn determined DIYer who demands those 2 extra inches while refusing to give up an inch (or would that be decibel) on soundproofing! If you want decent soundproofing, don't want to spend big bucks on materials, fear the thought of racking sand on the floor for days, then cut a sheet of firerock almost as big as the inside of your stud, then drill a hole in each corner, about 6" inward left/right and about 24" from the bottom or top; place a rubber grommet inside each hole and run a wire in the bottom holes and feed up to the top hole, loop through that and tie onto a hook at the top of the middle of the stud. This extra mass will help stop sound waves. and will not vibrate with the studs of the wall. If you like you can seal around the edges with caulking and that will also not pass sound waves. The very best soundproofing methods require making walls thicker, so I've limited my focus here on thin walls.

If you are considering thin partition walls they are obviously structurally weaker so you have to check your local codes, especially in earthquake and severe weather zones (FEMA has some nice recommendations). One key item FEMA mentions is to take care where you or someone later might desire to attach heavy shelving or cabinets to your thin wall.

I'm not an engineer, I don't want to misrepresent myself, with that said I played with the math and found some interesting things. I'll show my homework at the end so that an engineer can chime in here correct any errors if I made them.

Let's first compare the rigidness of 2x4 studs as they get longer than 8', I used the maximum deflection formula where a weight is placed on the center of the beam to measure how much it bows (deflects).

We all know that longer boards flex more than shorter ones, so how much more?
Compared to an 8' 2x4 a 9-footer will flex 42.4% more--this is true regardless if the long side or short side is holding most of the weight). Let's compare flex for the short side holding the weight of 250 Lbs at the center of the board; an 8' flexes down 1.77", add that extra 12" in length and now we're dropping down 2.52". 10' bends 3.46" (95.3% more than the 8'), 11' bends 4.61" (160% more), and the 12' bends (if it doesn't crack/snap) 5.98" (237.5% more).

The same weaknesses of tall walls do not hold as true for span width of the walls provided that you secure the 2x2 header with a second header above the ceiling that is now a standard width 2x4, and then secure it firmly to the floor with a 2x2 sill, and obviously secure them on both sides of a room's wall or corner. I would not recommend a thin-wall that just ends in the middle of a room, it really needs to be attached to another wall or corner to give it lateral strength.

While it has been shown that longer studs do flex more, the ratio of their flexing is the same if you compare apples to apples. For example, a 8' 2x4 will flex 444.44% more when a weight is pressed on the thin side of the board vs. the wider side of the board. using our 250 Lbs example, it will flex 1.77" if pressing on the center of the with the thinnest part holding the weight; and it will only flex 0.33" if the wider part of the board is holding the weight. While longer board will flex more, the percentage when comparing wide (normal framing) to thin (sideways thin wall construction), the percentages will always be 444.44% more flex from the thinner board.

What this shows is that you would want to add more 2x4's or at this rate throw in some 2x8s or 2x12x to save the day! What I found was very interesting, if you made the entire wall of 2x4s, 2x12's, 2x60's, whatever, the entire wall was solid wood 2" thick (technically 1.5" thick), you would still not equal the strength found with standard 2x4s framed 16" on center. A solid "thin wall" of wood it would still flex 19% more than the standard 2x4 frame construction.

Now I also found that to be good news. 19%! Hey, that's not bad, just how strong do I need the back of my closet to be anyway?! So there is hope where you can tighten up the spacing and/or use some wider boards to increase the rigidity a bit.

I did not go into the use of steel, this was getting long enough, I'd be curious how much advantage some thin-wall steel construction would offer and how soundproof it would be; I don't have experience with it.

SHOWING MY HOMEWORK
The maximum deflection formula is D = (WL^3)/(192EI), this would be: (Weight Lbs x Inches of Length) / (192 x Modulus of Elasticity for the Wood x Moment of Inertia). Moment of Inertia for a Rectangle describes the cross-sectional area of the stud but gives more weighted average to the depth that is being pressed against, therefore the thinner 1.5" is what gets cubed rather than the 3.5" for standard framing; it really makes a big difference when you are taking a number to the 3rd power. The formula for Moment of Inertia is I = BD^3/12, where B is the Beam width and D is the Depth that is holding the weight. For standard framing this would be 1.5 x 3.5^3 / 12 = 5.359375; for thin wall design it would be 3.5 x 1.5^3 / 12 = 0.984375. The Modulus of Elasticity (E) is a number used to define stiffness, for imperial calculations use the PSI (Pounds Per Square Inch) version of this number, often call EPSI.

Harder woods with large PSI number will be stiffer and flex less, but when you are comparing the same board turned sideways versus the regular way, it actually does not effect the percentage relationship. Having said that, it helps to have some numbers to play with, I used 660,000 for a nice quality Southern Pine; a Northern Douglas is 690,000. Click here for source The EPSI will alter how much flexing occurs with the math, but it will not have impact when comparing apples to apples, like how much does it bend this way vs. that way, or if I'm using 8' or 12'... the ratios end up being the same because you are not changing the EPSI when comparing numbers.
 
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Old 08-27-14, 09:15 PM
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i have wired some 1 1/2 inch walls.......it is harder

to meet code you would have to sleeve the wires in EMT
 
  #3  
Old 08-27-14, 09:51 PM
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Welcome to the forums.

Is this a book report for extra credit. Couldn't sleep.

One question for you on your wall studs on the flat..... what do you attach them to top and bottom and how ?

In "normal" construction the sill plate and the top plate are flat for a place to nail the studs to.
The only place studs on the flat will work is when you can fasten them directly to a wall.... like in a basement.
 
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Old 08-28-14, 03:01 AM
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I agree, Pete. This has to be a final exam for school. Mark Main, welcome to the forums! You are thinking too much on this. It doesn't require formulas and all that math. It is building a simple wall. As Pete mentioned, how are you attaching your walls top and bottom, and why do you want them to be flat? Your dissertation was too long and I lost interest. Building a wall in a conventional manner would give better support, easier to install, easier to run periphery, and better lateral support front to back.
 
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Old 08-28-14, 05:52 AM
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Mark Main,
If I ever build a tree house, I want you there

Just picking on you, that's a lot of work for a closet wall.

Engineers are needed and it sounds like you may go far.
 
  #6  
Old 08-28-14, 11:38 AM
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LOL! I like math and when I played with the numbers I was shocked to find that you could build a solid wall of wood studs sideways back-to-back and still not meet the strength of standard 16" OC. And that got me playing around until I'd done so much math that I might as well post what I found.

The other surprise to me was the fact that wall height would impact the rigidity but wall width did not increase the problem noticeably more (assuming you secure it top and bottom to something solid).; said differently, an 8' or 12' wide wall can be secured to be just as strong as a 4' wall secured the same way. Ok, a 1' or 2' is probably going to be stronger because you are lending from the strenght of the attached walls and they are really close together, but really, other than this extreme, the width of the wall can be controlled by securing it top and bottom, this leave only the height as the rigid issue here with these 1-1/2" walls.

I was asked about this and so I'll answer that here. If your studs are sideways then here are the only ways that I know to secure them so the wall is rigid:

FOOTER/SILL
You can use 2x2 pressure treated wood, drill into the floor with 1/2" wedge screws.
Alternatively you can lay a 2x3 or 2x4 flat and center it between your sideways studs; the 1x3's will protrude half an inch on both sides, the sheetrock can lay perfectly on top of this--now you just need to cut some 6" long 2x2's and nail them onto the footer in between your studs so that you can nail your sheetrock to that at the bottom. It's cut to 6" assuming you need some room for the wedges screw's bolt in the center to clear it.

HEADER
Use a 2x2 at the header for the sheetrock to screw into;
now you just need to figure out how to tie this weak 2x2 to something strong. If your wall runs perpendicularly across an bunch of ceiling joists then you can just tie into that for strength; if instead it runs parallel then you can add a 2nd header that is a 2x4 and just ensure that the 2x4 is taller than the ceiling height, then just anchor this stronger 2x4 header to the walls and the ceiling joists.
If there are no ceiling joists to tie into at all, then just run this 2nd 2x4 header along the top and secure it to the walls, the height of this 2nd header must be taller than the ceiling because it protrudes out. Then just add ceiling joists for your ceiling.
 
  #7  
Old 08-28-14, 02:50 PM
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Get some sleep, hoss. It's too easy to do it right. All your support at the top and bottom plates must carry through, and cannot be choppy as your 2x2 will do.

Math is fun. My wife knows I am educated, but I am a naildriver, who threw away the cape and "S" years ago. She asks how I make things square. I show her the Pythagorean theorem. Throw back days, but you use it daily and it becomes part of you. Everything else is common sense, level, square and plumb.
 
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