Need to make at 16″oc several (5-6) 1/4″ deep and 1″ wide notches on top of a 2×8 joist (to get some steel bracing flush). The problem is that I need to do this on the middle third of the joist as well.
Is this an absolut no-no or can I can get away with it? The load above is pretty light, a small guest bath with shower, no tub.
Nicoman
Replies
I've seen that much variability in dimensions of 2x8 stock right off the lumberyard rack, especially in PT.
Strength of a beam/joist increases as the square of its depth, IIRC, so you would be reducing your 2x8 dimensional lumber from 7 1/2" deep to 7 1/4" deep, thereby reducing its load capacity by 6.67% to 93.33% of original strength.
Strength of a beam/joist increases as the square of its depth, IIRC, so you would be reducing your 2x8 dimensional lumber from 7 1/2" deep to 7 1/4" deep, thereby reducing its load capacity by 6.67% to 93.33% of original strength.
Bruce,
Let me clarify a few things here. First, bending strength is a cubic (not square) function. (I = 1/12 bh^3 for rectangular sections, where b is the thickness, and h is the depth).
More importantly, a notch in a beam acts as a "stress raiser" and will trigger failure much more rapidly. In other words, a 7-1/2" beam with a 1/4" notch will fail in bending before a 7-1/4" beam with no notches. Think of snapping glass or tile -- that little scratch is a stress raiser and causes the failure.
With that said, a notch at the bottom of a beam is a real no-no, but a notch at the top is not all that bad. The reason is that a well-secured subfloor will sort of make up (somewhat, at least) for the weakness induced by the notch.
Thanks for the clarification. As a cubic function then a 1/4" reduction in depth of a 7" joist reduces load capacity by 11%. Presumably that is also true of a board with a little knot on one edge?Your point about a notch being a "stress raiser" is interesting. If one planed away 1/4", feathering the cut some distance in both directions would that still be a stress raiser?Considering the question further, I can see how a notch would dictate the point of failure, but why would a 1/4" notch in a 7 1/2" beam cause failure at lesser load than an intact 7 1/4" beam? Intuitively I would expect equal performance or perhaps slightly better performance by the notched beam. The "extra" material on the bottom edge would seem to be functionally inert, no longer in tension.I'm not sure your analogy with breaking tile or glass at a scratch seems apt, given that the materials are so different - brittle amorphous solids like glass or tile versus flexible wood with end-to-end grain. Even so, I believe that our scratch mark on glass or tile does little to compromise strength but when we exert breaking force across the scratch it does determine where fracture will occur.
BruceT
The mess that hangs from the top plate will go for sure, but directly on the other side of the wall on the left side (on top of where the overlap will be) there is a furnace and moving it would definitely fall under my intimidating category.Again, not quite following on the stud coming down 5" below the joist. That space is about 6-7" so I would need thick shimming there but the biggest problem is that I need some form of support for the inwall tank. Are you saying I should forgoe the sill because I need something to set it on.Tapcon and PL makes sense, tapcons strong enough? Lag screws overkill?IdahoDon, could you throw me a link to that Simpson strap?
Well shim it then.Tapcons are plnty strong. besides, PL Premium will practicly weld the wood to the block!
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Simply google Simpson strongtie.
Best of luck
Beer was created so carpenters wouldn't rule the world.
"but why would a 1/4" notch in a 7 1/2" beam cause failure at lesser load than an intact 7 1/4" beam?"Again, think of scoring a piece of glass and how it makes it weak. If you take a piece of glass .062" thick and score it with a .002" deep line it will break at that line relatively easy. If you bought a piece of glass that is .060" thick it will still be stronger than that piece of .062" scored glass.Stress risers are bad...ask me some day about a .002" grain of sand caught on the surface of a forged Titanium turbine disk and what that will do!EDIT:
You don't like the glass analogy, fair enough. What about scoring a shim with your razor knife then snapping it? It typically snaps where when you score it??
Edited 3/18/2007 7:48 pm ET by Buttkickski
Dado it is. That takes care of the whole notch discussion. I'll then bridge midspan, put up some PL glued block with Tapcons to support the studs around the tank, and finally glue the subfloor carefully.Oh, and I'll put a sign on the door "Slim people only, please" for liability.Thanks for all help,
Nicoman
It's been fun!
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It really is an incredible group of people.
You want a ledger on the CMU behind the drain pipe?
If I'm understanding?
Get a long bit & a hammer drill and drill through the existing joist, through the ledger and into CMU.
Don't need an angle drill.
Joe H
I will grant the weakening effect of stress risers in metals, glass and ceramics - all materials of uniform composition - but wood, it seems to me, behaves differently.Wood is not a uniform material but layers of fibers and cell walls "glued" together in the linear orientation of its growth rings that naturally resist fracture across the grain. When a joist fails it does so along the lines of the grain, not across the piece. I would expect that a notch in the bottom edge of a joist would simply reduce its strength to that of a narrower joist but not to less."You don't like the glass analogy, fair enough. What about scoring a shim with your razor knife then snapping it? It typically snaps where when you score it??"I don't like this analogy either. When I score a shim I'm cutting on the face, not the edge, and my cut significantly reduces the thickness at that point, so naturally it breaks easier.
BruceT
That was another really good idea. At first I thought it wouldn't work since I have a gap of about 7", the joist is 1 1/2" and I need to go atleast 2" into the wall, totaling 10 1/2" which leaves room for a 5 1/2" hammer drill between the joists. I've never seen one that small but it would be cute. :-)However, I came to my senses. The equation looks much more favorable if one starts with a short bit through the first joist and then manually insert the long one before it's connected to the hammer drill.At the end of the day though, the metal braces support the whole width of the 2x6 wall whereas a 2x8 ledger would only support a quarter of it so perhaps the braces 16" o.c. is the best solution after all.
Edited 3/18/2007 11:15 pm ET by nicoman
Two weeks and you're still trying to build that wall?
I think you now want to avoid using that joist on the near side of the drain pipe as part of the wall support because you suspect the weight of the wall and the wall mounted toilet and the additional weight of a tile floor will be too much for that one joist to support, resulting in a few ceiling cracks and a failed tile job.
I think we covered the wall part last time. Because most of the wall area behind that joist is occupied with the drain pipe it will be a real pain to drop in a ledger and fasten it to the wall. Just a little problem getting the bolts or lags set when a pipe is in the way.
I suggested an angle iron type of ledger. Lagging or through-bolting the up turned leg of the angle to the wall and using the horizontal component as the base for your 2x6 wall. NOT L-straps across the joist.
Use a single length of angle, maybe 3x3 or better, along the entire length of the new wall, except where you would have to have a break to accomodate the drain upturn. This ledger would be more than strong enough to carry the weight of a simple wall, even with a toilet seating a few hundred pounds of human.
Additional support for the wall, to prevent bowing out, would be provided by attaching 2x's on the flat and nailing or screwing the wall studs to them or by using short lengths of the same ledger angles, bolted to the wall and then lagged to the sides of the studs in the vicinity of the greatest stress, ie., where the toilet hangs.
The bottom plate of your new wall does not have to rest on the floor or joists of the floor. It's totally supported by the angle and to some extent by the number of angles or blocking you attach to the block wall. You can even complete the floor sheathing before you attach the ledger and build the wall.
Now you can forget about the need for and the ramifications of notching the top of that joist.
Regarding the span of your current floor - Unfortunately, you don't want to open up the ceiling below. That would give you an excellent opportunity to use a continuous metal strap, along the length of the bottom of each joist, which increase the factor of tension by a bunch. It has the same effect of increasing the depth of the joist which increases the deflection value necessary for a tile floor.
Looks like you will have to settle for sistering.
Edited 3/18/2007 11:40 pm ET by RalphWicklund
Well, turns out my Bulldog won't fit even without a bit, it's over 17" long.RalphWicklund, guilty as charged, I was wondering when someone would recognise the project from that thread. Well some other issues took priority, but I wasn't sure about the solution either. I did have some followups on the bracing but when I didn't get a response I went for L bracing. These are not Simpsons though, much thicker, and the reason I want them leaning on the joist is more for stiffness than support.Anyhow, I assumed I wanted to support the width of the 2x6 wall if I could, but a 6x6 iron angle felt a bit dramatic.How about attaching the continous metal straps on top instead with PL and continous screws? Or does it have to be below? I assume the joist won't hang on it so even if it isn't as effective, it would still be beneficial?
Edited 3/19/2007 12:15 am ET by nicoman
Your wall is not going to be tasked to hold up the entire side of the building and transfer roof load to the foundation. Just its own weight and a point load where someone plops down on the throne. 6"x6" would be overkill.
You probably don't even need a continuous support along the whole length of the wall but it does help to spread even a small point load around.
You can call (Yellow Pages) a metal fabricator and get just about anything you need.
If you think the angle iron idea is too extreme you can do the same with a 2x4 bolted horizontally above the drain pipe. Then notch the bottom of each 2x6 stud so it fits over the ledger. You will have an inch and a half bearing surface for each stud. Toe nail that to the ledger. A bottom plate would only be for spacing and nailing for the wall covering and the notch is to get the bottom plate to the floor. More 2x4's attached flat and vertically to the block wall with the 2x6 studs screwed or nailed to their sides keeps the wall vertical - no bowing.
There is no force that you or anyone else jumping on a wall hanging toilet can apply that will cause the studs to fail in shear at the notch or along the grain of the lumber. The only concern would be the failure, in shear or pull out, of the bolts or lags into the block wall. This would be like hanging a giant picture frame on better than a gypsum board wall. Have you ever wondered how two thin 3 penny nails can hold up a hundred pound framed picture on a half inch of paper-faced chalk?
The continuous strap along the length of the BOTTOM of a joist is to take up the tension applied to the bottom edge of the joist. That strap in that position will absolutely prevent the normal stretching of the bottom of a joist thereby forcing it to be a stiffer support. The strap is also full of nails along its length not just fastened at each end. Applying a strap to the top does zero.
Thanks, I will look into both of those ideas. The steel ledger gives many advantages; no added pressure on the last joist, the subfloor can rest on it and I won't have to notch the 2x6.So the joists are my problem it seems. No, I would rather not open up the ceiling underneath if it can be avoided and sistering is complicated up there in a cramped space. What about using Ditra to float the tile or would that not help for this type of deflection? I will bridge to atleast spread the possible deflection.
"I suggested an angle iron type of ledger. Lagging or through-bolting the up turned leg of the angle to the wall and using the horizontal component as the base for your 2x6 wall."If the angle iron can be mounted with vertical leg downward, there would be more bearing area for the base of the wall.BruceT
Perhaps a better example would be what happens when you use a chainsaw to cut through a log supported on both ends. If you cut from the top, the log compresses and pinches the blade, and horizontal cracks may appear on both sides. If you cut from below at some point it fails, but as you say, it doesn't leave a vertical cut as glass or tile would. It bends, and the material on both sides of the cut, which are in tension, peel off horizontally.
In all but the most extreme cases joists don't fail in bending, so we are not really worried about "scoring it"so much as reducing its effective height in resisting against excessive deflection. Its going to be way too springy long before it fails.
"I don't like this analogy either. When I score a shim I'm cutting on the face, not the edge, and my cut significantly reduces the thickness at that point, so naturally it breaks easier. "
Face or edge you're still scoring it on the surface that is being loaded, wether it be in tension or compression.
Bruce,
It's been a while since I've done any homework problems on stress concentrations! I reviewed the "stress concentration" chapter in my text, however, to try to answer your questions.
The text states that higher stresses will occur if the cross section of the member undergoes a sudden change. Unfortunately, only two geometries seem to have been studied vigorously enough to generate performance curves and thereby come up with empirical stress concentration coefficients.
The one test case that is somewhat similar to a notched beam is the case where a flat bar has a notch in the top, and a notch in the bottom directly beneath it. Using this curve, it looks like a 2x8 with 1/4" notches at top and bottom would experience about three times as much stress through the reduced section.
It's important to note that the lab test involved a filleted groove -- imagine, for example, the groove produced by a router with a round-nosed bit, as opposed to a regular "straight" bit. Without the fillets, the stress concentratin is MUCH higher. So, I think that a quarter inch notch produced by a saw blade would increase the localized stress by at LEAST a factor of three.
So, to answer your question, an un-notched beam would be able to support at LEAST three times more load than a notched one. That shows the notch is much more influential than a mere 1/4" continuous difference in joist depth.
Your point about a notch being a "stress raiser" is interesting. If one planed away 1/4", feathering the cut some distance in both directions would that still be a stress raiser?
A "feathered" reduction in cross section would also be a stress raiser, albeit a much smaller one. The charts in my book suggest that you'd be looking at a 10% increase in stress if executed ideally.
I'm not sure your analogy with breaking tile or glass at a scratch seems apt, given that the materials are so different - brittle amorphous solids like glass or tile versus flexible wood with end-to-end grain.
The stress concentration coefficient seems to be purely a function of geometry. The test cases in my text were generated with metal bars, and there are no necessary "adjustments" for various materials, etc.
From a stress analysis perspective you just plug in a different value for elasticity when using wood, metal, glass, etc. The big difference between wood and metal (for example) is that a pile of 2x4s have significant variation in grain quality and orientation, number and placement of knots, etc. Steel, by comparison, is a very uniform product. The inherent variation in wood is what makes us overdesign so much (lowering your allowable stress to the lowest common denominator, so to speak) when using wood.
It would be fun to notch a 2x2, set it across a span, and load it until it breaks. By loading an un-notched 2x2, one could test the difference that the notch made.
Regards,
Ragnar
Edited 3/19/2007 1:58 pm ET by Ragnar17
"The stress concentration coefficient seems to be purely a function of geometry. The test cases in my text were generated with metal bars, and there are no necessary "adjustments" for various materials, etc."Once again those analogs in your texts involve very different materials. Homogenous metal versus wood, a product that is naturally sort of laminated. Metal will fracture straight across the piece, whereas wood fractures along the lines of its grain, essentially delaminating its growth rings, so a crack cannot propogate across the grain as it would in the materials studied in stress riser tests."It would be fun to notch a 2x2, set it across a span, and load it until it breaks. By loading an un-notched 2x2, one could test the difference that the notch made."That would be an interesting experiment. Better yet, rip a vertical grain 2x4 at 1 7/8", notch the thicker piece to 1 7/8" and test the two pieces.BruceT
I was able to find a little infomation on the net regarding notched beams:
"In beams having notches, slits or holes with sharp interior corners, large stress concentrations exist at the corners.... As a result, even moderately low loads can cause a crack to initiate at the starp corner and propogate along the grain.... it is generally more economical to avoid sharp notches entirely in wood beams, especially large wood beams, since there is a size effect: sharp notches cause greater reductions in strength for larger beams..." (emphasis added)
http://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr113/ch08.pdf
"Four large glulam beams with notches on the tension side were tested for strength and stiffness....Results quantify the observed behavior of bending beams with notches on the tension side. The strength reduction is so severe for large beams that substituting a beam having the net depth of the notched beam is preferable. Removing material would remove the stress concentrator and would increase the strength up to net section theory prediction..." (emphasis added)
http://www.pubs.asce.org/WWWdisplay.cgi?8602174
You may have noticed that the first quote mentioned specifically failure "along the grain". So if the beam were truly VG, then perhaps the failure would be limited to ONLY the lowest portion affected by the notch, as your intuition seems to be telling you. Of course, in most cases common joists are flat grain (not VG), so that may be a purely academic point.
Maybe I'll be able to do that little experiment someday; I've actually done stuff like it before out of curiosity. Based on what I read, however, it seems like a 2x2 would be a poor indicator; it seems it would be better to test something that would proportionately look more like a 2x8 or more.
Ragnar
Thanks for digging up those data. I am amazed at the magnitude of the effect of a little notch.BruceT
Thanks to Ragnar17, BruceT999 and Buttkickski for the structural dialog. Notching turned out to be quite interesting.
Yes and no - in most cases go for it.
If these are already overspanned and carrying more than average loads, then no
but it is just as likely that they are plenty fine already and won't sufffer. Knowing the span would help.
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The span is 13' but the joist's physical size is 7", it's from the 50's.
"the joist's physical size is 7inches, it's from the 50's.."
Chances are real good that that joist is thicker than todays (1-1/2inch) joists. Probably at least 1-3/4 thick if not 1-7/8ths? Extra thickness helps out.
Looking at my book of span tables for floor joists, at 16inch OC, 13 ft is pretty much the maximum that (todays) modern 2X8s can safely span, and that's only if using "select structural" grade lumber.
Doubling up your existing joists as earlier mentioned is not a bad idea.
Davo
Edited 3/18/2007 3:56 am ET by Davo 304
Better to notch the top than the bottom.
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just be sure to dbl them all up and use a steel flitch plate bolted every 6"!!!
kidding : )
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but a true friend will be sitting next to you saying,
"Damn... that was fun!"
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6" staggered top and bottom ...
so that'd really be every 3".
Jeff Buck Construction
Artistry In Carpentry
Pittsburgh Pa
yer right..sorryI didn'tclarify
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Ouch, not the answer I was hoping for. The joists are exactly 1 1/2" wide so no luck there either.Since I'm planning to tile I will thinset and add an additional layer of 3/4" plywood on top, will that stiffen up and help my case or cause more stress/deflection? Risk my floor tiling will crack even?
Since they are already on the vedrge of being overspanned, notching tops is an open question. especially for tile. While adding ply underlayment may help some with localized movement and improve some of the some load sharing, it will also add more weight to work against the deflection.More info ---What are these braces you are letting in doing? Would glued plywood do the same?
Are you openning the ceiling below?If you have elevation to add plywod sheathing, then you may be able to lay the bracing profile above the joists and then glue shims to top of joists.If open below, you can add strapping in such a way that it improves the floor systems load capacity by making a diaphragm of the whole thing
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or just use epoxie grout...Wars of nations are fought to change maps.
But wars of poverty are fought to map change.
Need to make at 16"oc several (5-6) 1/4" deep and 1" wide notches on top of a 2x8 joist (to get some steel bracing flush). The problem is that I need to do this on the middle third of the joist as well.
What exactly is the steel bracing for? Are you trying to stiffen the bathroom floor?
I'm reading that you've got 2x8s at 16" centers on a 13' span. I'd agree with others here by saying that the joists are somewhat undersized. That was the span at my own house, and even though it was built with good lumber (back in 1912), there was a certain springiness that I was never comfortable with. It didn't help that previous owners had badly notched or otherwise cut up a number of the joists, either.
Since it was important to me to minimize the springiness, I bit the bullet and sistered on 2x10s to stiffen the floor. (Note that a 2x10 is about 2.1x stiffer than a 2x8.) It was a major PITA (since I had to temporarily disconnect a lot of wiring and plumbing, and then drill dozens of holes and reconnect), but for me it was worth the effort.
Since a springy floor and tile do not go together well, maybe there's a simple way to stiffen or otherwise support the floor in your case. What's under the bathroom -- crawl space? - basement?
Edited 3/18/2007 1:57 pm ET by Ragnar17
FWIW..My Opinion.
I have read where "In The Old days" any loose or suspect knots that occurred along the top of a joist were cut out and replaced with a block so prevent failure.
The theory being that the top 1/2 of the board is in compression and by placing a "compression block that fit tight to the notch that the board would be stronger than having a loose or split knot. It can't develop the needed "bend" to place undue stress on the bottom of the board that is in tension and is the part that ultimately fails.
I see the same thing applying here, cut the notches very tight so the board cannot fold or compress, glue(with a non creeping glue) and screw the subfloor and and you should be good to go .
The project is a small bath (shower no tub) on the third floor over a bedroom in a small townhouse. The picture is taken from the door looking into what was previously a walk-in closet with cabinets on the block wall and some interesting framing basically hanging on the rafter. I'm now looking to install a wall-mount toilet on this wall roughly where the PVC drain pipe stops, which needs a 2x6 encasing. The trick is that I don't have any real support for a new 2x6 frame and the toilet. As you can see there isn't a joist against the wall, the room below has plaster directly on the block wall. Ceiling rests on this in the corner.Lag bolting a 2x6 against the CMU wall is awfully tight, not more than 6-7", so I have trouble getting even an angled drill in there. I was given the advice to mount either a ledger or steel bracing, so my plan has been to use 8" steel L braces 16"oc where the horizontal leg then rests on the joist to make the braces stiff. The notch needed is less than a 1/4" actually, more like 3/16". On top I will then place a 2x6 that primarily will be supported by the lag-bolted braces.I do see the point of scoring of glass but at the other hand I think the well-secured, glued subfloor is a good argument as well. I'm now more worried that the joists aren't strong enough to begin with. Sistering on 2x10s does not feel all that tempting to be honest so I hope I can get away with it without it coming to that, I wouldn't know how to even get new joists in there. Much more feasable would to bridge the existing ones midspan but the question is if that would be enough?Is Ragnar possibly a Swedish name?
Edited 3/18/2007 3:17 pm ET by nicoman
Rather than noching those for angle brackets, I think it would be relatively easy to secure your new 2x6 framing directly to the firewall if that is legal in atownhouse in your jurisdiction, and to double up the 2x8s with sistering from above there.Your other option for merely securing the new wall framing is just to glue and fasten the new subfloor, extending beyond that joist, then frame up from it to the rafters, replacing the hodge-podge there now.
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I'm not sure I'm following you, how would I relatively easy secure them to the firewall? By toenailing?The sistering also confuses me, with overlap I need to squeeze in atleast 14-15' joists there and there just isn't room to manuevre withour extensive demolition.Your last suggestion would obviously be the easiest, but the whole reason for the bracing/ledger was that I felt the subfloor would deflect if I started to build a 2x6 wall on top without any support underneath? Do I misunderstand you or do you mean in combination with securing against the wall? Since this wall will harbor the in-wall toilet tank and the toilet itself there is downward pressure, although I assume most will be torque and the sides of the inwall tank will be bolted to the studs.
Yes you might need to demo a bit more to slide joists in to sister.What I think of as easy because we do it all the time might be more intimidating to yourself.To fasten to the firewall, I would remove the mess that hangs from the top plate at rafter now and frame new all all the way to base with the 2x6s. Then use scrap blocks to attach to the wall with PL pemium and tapcons.But that might not be legal. Another option around that would be to use steel studs in contact with the firewall.Here is another - you main concern here is stability where the wall mount toilet hangs. You could run studs there from that top plate to fit about 5" down behind that floor joist - notched to fit if need be for plumb. Then with each stud fastened at top to plate and at bottom to the back side of that joist, they won't flex.There's lots of ways to skin this cat.
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Had I waited one more minute for you to post first, it would have saved some typing! *chuckle*
Beer was created so carpenters wouldn't rule the world.
Well, like I said - lots of ways to skin this cat - I wasn't even thinking of the ledger you explianed. I was putting scrap blocks to the wall. Ledger probably easier.'course, he has all those scraps up therea lready, and keep in mind this is three stories up in the air...I hate all that hiking!
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'course, he has all those scraps up therea lready, and keep in mind this is three stories up in the air...I hate all that hiking!
It makes my hurting hip hurt even more thinking about stairs! It never seemed like our profession required a lot of climbing until you add it up.
Beer was created so carpenters wouldn't rule the world.
I thought for a couple of years that I was heading for a hip replacement early in life.Then when I fionally tended to my back, the hip pain disappearred. They had also x-rayed itwhen assessing the back and said there was no damage to the hip anyhow. All the arthritis was in the spine.So My hip pain was all referred from an aggravated nerve. I wonder if a chiropractor and some physical therapy would help your hip
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Did you reply to the wrong thread or is that an allegory for my problematic ledger?
No, did you notice that Idaho Don mentioned hip pain...?
I responded to that.We are freinds here, not just entities, so we tend to diverge and wander a bit sometimes chasing these rabbits.
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No, I didn't notice that. My brother in law has hip pain as well, and that too turned out to be related to the back. He now has a bench that he can rotate to almost vertical, and fixate his feet into, so that he can stretch his back. It has made a big difference in his life and he now uses it less and less.
I wonder if a chiropractor and some physical therapy would help your hip
You are probably right. A fishing buddy is a chiropractor so it's just been stuborness keeping it from being looked at.
Early last year I strained a muscle in my left hip on a multistory finish job and I was almost convinced that it was the start of bursitis or arthritis, but completely went away when the next job started and we were climbing far fewer stairs.
The current hip pain is in a muscle slightly farther back, but otherwise feels similar. It seems hard to slow down enough for it to completely heal, but that's probably what it needs.
The good news is years of back strains and pains have gone away as I've been more careful with lifting and bending!
I'll be turning 40 a week from today and it has me thinking of ways to keep from wearing out joints prematurely.
Beer was created so carpenters wouldn't rule the world.
Young kids like you....;)I was in the prime of my life about 36 to 40 YO.
Had a physical for my fortieth birthday 'cause wife said I ought to...
Doc said, "You are the healthiest man on the island!"It was all downhill starting the next day...LOL
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Nice clean looking gut job though. :)View Image
The picture helps a great deal!
You would be much better off getting a ledger against the concrete blocks and it won't be hard to do.
Take the drain pipe and the 2x spacer behind it out. Also demo the X bracing at the first joist bay and the wall directly above it.
The first full length joist to go next to the wall has 18" Simpson straps prenailed to the back side every 16". Check out the fastener specifier's guide at Fastenal's website for sheer ratings for concrete screws and CMU's. It's then an easy task to drill and secure the exposed section of the prenailed joist straps.
Block between the first few joists at each wall hanger to prevent rotation of the joist hanging off the straps. I'd slip in another joist between the existing joists, but it's a good idea to add new tight blocking to the whole works.
If you need to screw into the CMU's directly to pass inspection, pick up a 6" long drill extension to get the drill chuck out of the way for the best angle and put the top Tapcons in at an angle, probably no closer than 2" from the edge of the board. For the lower bolts drill a 3/8" hole in the middle of the 1st existing joist at an angle and use a 6" extension (or two 6" extensions if needed) to drill and secure the lower concrete screws. This is probably how I'd attach the whole works and forgo the straps on the wall altogether.
There are other more elaborate methods of holding up a floor joist next to the wall using simpson sheer brackets and threaded rod, but that seems like more work and money than it's worth. This method can also provide real numbers for the inspector if he has an open mind since the Simpson brackets and threaded rods are all rated in various ways.
An even more elaborate way of doing the same is securing the studs to the wall and using even more Simpson brackets to hold the floor assembly tight to the studs. This is even more money and time, not to mention it looks strange and requires an even more open minded inspector. In many ways it's like the previous method, but different.
Your problem is rather simple so don't over think it. Also, add those extra joists if at all possible and your tile will last much longer.
Best of luck
Beer was created so carpenters wouldn't rule the world.
Rather than notching, could you surface mount the steel and furr the joists?
Or dado the back ofr the sheathing over the metal bracing
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