I-Joist Web Hole Reinforcement 2

[phamENG]

Got a call from a developer I work with - their plumber did a minor hack job on an I joist. Long rectangular hole - about 10"x4" 3' from bearing on a 24' span. 16" deep joist. Violates the manufacturer's allowable hole dimensions.

I'm trying to work up a repair, but I'm having a hard time finding good resources on this. The ASCE Journal of Structural Engineering has a good article from 2017 on the subject. Sadly it's copyrighted and I can't share it here. I've run an analysis on the joist using EWP Studio, which runs off of the iStruct software platform for those who are familiar with it. I also ran it in ForteWeb with a roughly equivalent TJI (the actual joists are PJIs, which is an APA standardized, performance rated product).

Using ForteWeb, it gives me an allowable shear capacity at the hole in the joist of 562#, as opposed to the original joist which had a shear capacity of 2000#. When I use the regression formulas provided in the paper mentioned above, I get 1,885#. So if we went with a factor of safety of about 3.35, they'd be in agreement.

Using EWP studio, on the other hand, it says the allowable load at the hole is only 315# as opposed to the original joist which had a shear capacity of 1970#. So, again assuming they're using the same research, they are using a safety factor of roughly 6.

My actual shear at the hole is 430#. So I like what Forte is telling me. The EWP studio, on the other hand, would require reinforcement. Using the literature to predict the capacity of the joist with their reinforcement detail, I get up to 2093#. Using the factors of safety above, that would be 625# and 349#, respectively. I joists are governed by ASTM D5055, which requires a factor of safety of 2.1 compared to the 5% tolerance limit with a 75% confidence level.

In short, I'm lost at this point. While the paper mentions that their control group meets the ASTM requirement, they don't go into applying it to their data set. Perhaps that's because the existing data set for the repairs is too small to get a meaningful result? I'm not sure. Anyone have any good ideas? (By the way - I know I'm overthinking this, but I want to know...)

 

[SRCELL]

If the hole size voids the allowable dimensions I would give a repair. Depending on the actual hole size the plumber needs, you could look at TJI's TB-187 for a repair detail. If you reach out to Anthony they may have a recommendation.

 

[phamENG]

187 or 817? TB817 is one of the first things I found, and is similar to the repair proposed in the document I mentioned above. I've never seen a different kind of repair, and it's what I'll likely specify.

To be a little more clear, the point of my question is understanding the way in which these programs calculate the allowable shear loads, and what the acceptable practice. They are very "black box" about the whole thing and I've had trouble finding more information on it.

 

[phamENG]

Looks like not much traction on this one. Not surprising given the dearth of information out there. For anyone who may come later looking for information or others who may want to pick up the conversation, this is where my head is:

I-Joist reference design values for bending, shear, etc. are based on the statistical 5th percentile of strength from tested samples (adjusted for population size vs sample size etc., etc.). Then, they tack on a safety factor of 2.1. (This is from ASTM D5055.)

In the paper I linked above, the average failure load for each group of joists was slightly higher than the published capacity. In other words, if they were never loaded beyond the original design intent, none of those joists would have failed anyway. Granted, that's more like a 50th percentile with a safety factor of about 1.1, but it's an important data point.

The OSB collar provides only modest gains to actual shear strength in some of the applications, but it does something more important. It seems to preclude a sudden, brittle, and catastrophic failure of the joist. You end up with a slower diagonal shear failure in stead.

The paper presents control joists that, based on their test, have a safety factor of 4 when you compare their average capacity to design capacity for 20ft spans. Assuming that adequately captures the 5th percentile/SF=2.1 rule for this sample size, it seems a reasonable step to saying that a safety of factor of 4 could be applied to equations presented in the paper.

So for the joist I described above, the calculated capacity per that paper is 2026#. Apply a factor of safety of 4 to that, and I get 506# at the reinforced hole for my safe shear capacity.

If anyone has any other ideas or thinks I'm nuts, feel free to say so.

 

[JStructsteel]

why not just use dimensional lumber each side of hole to the bearing and use that capacity? Screw and glue it to the existing joist.

What am I missing about this?

Did anyone call the manufacture of the joist for their input?

 

[Enable]

JStructSteel: phamEng does not appear to be curious about the repair so much as he is the software he is using to design/check TJIs. As noted in his response above, the software is not transparent in its calculations and he is trying to calibrate the model output with a rational analysis of the capacity. The actual repair methodology is provided by the manufacturer in this case.

phamEng: what is the #? I have never seen that used as a symbol. Is that a stress or a total load? And does it indicate particular units or is it just generic and units are inferred by context?

 

[phamENG]

Before the advent of twitter and hashtags, # was referred to as "pound" in the era of touch tone phones. Some consider it a bad habit to use it in engineering, and I never use it in formal writing, but it's a convenient shorthand for informal stuff - or so I thought, at least.

JStructSteel - Enable is correct, I'm less interested in the repair itself than I am in understanding the methods being used to calculate reduced allowable capacity by the major software available for the purpose and, within the same context, interpret some of the testing that has been done on typical repair methods. But since you bring it up, dimensional lumber to bearing won't work for two reasons - 2x16s are tough to come by on the one hand, and the electrical wiring running through the joist would have to be taken back to the panel on the opposite end of the house, necessitating removal of several hundred square feet of drywall, etc. They don't making the plumber move some pipes, since he caused the mess, but the rest of it is a bitter pill to swallow if they don't have to. And as for calling the manufacturer, that was the original plan. When I first dinged them on it, I referred them to the supplier to have them get a detail. The one that came back was not workable for the reasons stated above as it was just a generic detail. So they asked me if I could do better.

 

[XR250]

In these situations, sometimes the path of least resistance is a 4x4 post on a small footing.

 

[phamENG]

XR- True enough. Sadly I don't think the buyers of this brand new house would appreciate hitting their refrigerator door on a post every time they try to open it.

 

[Enable]

phamENG: I tried to do something with hand calcs but failed miserably. Why are you looking so hard into wood joists again? It's wood for goodness sake! LOL. But now I am a tad curious so here's a new thought: the literature on new joist capacity & allowable opening sizes should furnish a decent amount of data for me to run a simple multiple linear regression model in R. I'll try and code that up tomorrow and see if there are section properties that seem to stand out / can be used to rationalize the capacities in that you are seeing in the software.

If you could give me your joist dimensions that would be swell (said it was 16" but which series). Also, if you have any data on joist capacity let me know and I'll code it into the model (reduced capacity at holes and the like would be great if you have).

If you really want to go down the rabbit hole you know what you need to do....load testing!

EDIT - Actually I had a way of calculating the shear capacity at the unreinforced hole of 1859lbs, which I think is pretty close to what the model from the paper said? Okay now I am very confused. I'll still do the regression though. Maybe it'll help. Meh.

 

[Enable]

Found some good stuff in this paper:

http://support.sbcindustry.com/Archive/2006/aug/Paper_263.pdf?PHPSESSID=ju29kfh90oviu5o371pv47cgf3

I will code these up and see what I get. But my lord do these TJIs seem to have excess capacity. Look at specimen 14, which has openings top to bottom in the web, no reinforcement, and still has a safety factor of 3.1 when compared to the published design literature.

 

[XR250]

@Pham,

Got it - thought it might be on the first story over a crawlspace. One repair strategy I have used in the past when the hole is close to the bearing (as your is) is to header off the joist to the adjacent joists. They may have sufficient capacity to support the additional load.

 

[phamENG]

Enable: The specific joist I was looking at is a 16" deep with 2.5"x1.5" flanges, 3/8" web. (It's a PJI 60). And I discovered the journal article I linked was actually a small piece of a larger doctoral dissertation: [URL unfurl="true"]https://open.library.ubc.ca/cIRcle/collections/ubctheses/24/items/1.0343438[/url]. There's some good information in there and yes the 1859 comes pretty close to what they got (your 8% lower than their regression analysis). I'd certainly love to do some load testing. Breaking stuff is always fun. Yet another candidate for the master's thesis I may never get around to actually finishing. (If I don't don it this year I think my credits start to expire...). You are right about the large safety factor, though. But then, most wood does have a large one. The natural variability makes it hard to get a more accurate estimate, so in theory 95% of all I-joists will have a safety factor for bending exceeding 2.1 (and 2.37 for shear). So most probably fall in the 3.5-4.5 range.

XR- thanks. That was my first attempt, since it's nice and clear and predictable. But the area was just too congested. The hole was created because a plumbing wye splits off from the main line through the joist. To fit it up, the plumber cut a nearly foot long hole in the joist. With the main drain line running parallel to the damaged joist, there was no where to put a header that wouldn't have to have a giant hole in it, too.

The cat's out of the bag as far as the repair goes - I delivered my sketch to the contractor and expect a call Monday to inspect the finished product. But I'm still curious about the way the software is doing their calculations. My working hypothesis is that the iStruct software just spits out the ultra conservative estimate their prescriptive tables are based on, while Forte uses some more "advanced" method of combing various factors to give a more realistic number. If I have time this week I'm going to pursue that further - no luck getting good answers yet from either.

 

[Enable]

So, I’ve gone down the rabbit hole as much as I am willing to go. I’ve come to the conclusion that these joists are not well understood, and that the software you are using is probably intentionally vague because there are no good ways to put numbers to such things.

I’ve attempted to create a “rational” (read: highly crude but at least somewhat logically based) model for what should be the value at unacceptable openings. See end of this post. Do take a look as it comes CLOSE to the 562lbs from your one software (I calculate 540lbs)

For anyone interested here is what I found as my background (calculations are in next post):

Background on TJIs
I found a literature review that summarized the design philosophy for TJIs in a general sense. It is a bit dated, but as noted in the thesis phamEng links to above, not much has changed so I believe this survey to be a decent primer.

As you would expect, design is based on standard beam considerations. Flanges assumed to provide full moment capacity, and webs take full shear. Capacity is variable depending on quite a bit, but the modulus of elasticity (MOE) of flange material plays a crucial role. Despite shear capacity assumed to be fully provided by the web, the MOE of the flanges can interact and affect overall shear capacity.

For long moment governed TJIs the moment capacity seems to be in accordance with theoretical values based on simple beam theory and flange capacity. For short shear governed TJIs, this is not the case. Shear values have thus been based primarily on experimental data.

Web Openings

The literature is scantly consistent. Fergus (1979) found that moment governed TJIs were not compromised even with circular openings removing up to 70% of web depth. In much of the research, there appears to be a vast difference between circular and rectangular openings. With the latter causing severe stress concentrations that the webs have a hard time redistributing. But even that is contentious because research in 2006 from Afxal et al found that the difference between circular/rectangular is irrelevant.

Wang and Cheng (1995) found that for 2.8m and 3.6m long TJIs, with rectangular web openings from 33% to 100% of cross section at distances 0.5m to 1.0m away from the supports, resulted in shear strength reduction of up to 79% from original capacity. The same research did NOT find any issue with openings at the same location equal to less than 33% of the web.

Note for phamEng: The last bit is very close to your situation with your rectangular opening compromising about 31% of the web.

Research by Dinehart and Morrisey (2006) found that circular holes up to full depth of the web placed near the support reduced moment capacity from original up to 41%.

Capacity Prediction

There appears to be a disconnect between the academic literature and published design aids from manufacturers. The manufacturers typically provide Max Moment Capacity and Max Shear Capacity. The literature all seems to predict a “capacity” in terms of a kN force. I don’t exactly know why this disconnect exists, but I surmise it’s due to the ASTM standard the academics are testing the beams to. From what I gather the standard requires them to load the joists equally at two points at the 1/3rd points from the end. So the Pu value reported is actually the equivalent of two point loads at half that value centered at the 1/3rd span. From this you can back-calculate actual shear and moment capacity from standard beam tables for such a loading condition.

Some prediction ranges from the simple:

Pu= 36.4kN – 25.9 (diameter of circular opening / height of web)

To regression equations. All the way to some very complex analytical formulas based on nonlinear fracture mechanics.

It is worth noting that the predictions from all the above due not seem to be reflective of actual capacity but rather capacity already considering the 2.1 safety factor for bending and 2.37 for shear that phamEng discusses in his post.

Note for phamEng: what that means is that the capacity calculated by the equations you identified should already have the safety factors inherent to them. You would NOT need to apply it again to the calculated value. This means the software is grossly over-conservative.

 

[Enable]

My Attempt at a "Rational Approach"

Given what appears to be the wide variability in all things here the regression approach I suggested earlier on is absolute folly. What we can do, however, is back-calculate some standard deviations of section strengths from empirically derived safety factors and apply that to the case of an "unacceptable" opening.

The ASTM standard to which these TJIs are manufactured results in, 95% of the time, the following minimum safety factors (don’t judge me that I am using PHI to indicate a FOS…remember when phamEng used a hashtag to indicate lbs-force??):

Phi(bending) >= 2.1
Phi(shear) >= 2.37

Lets focus on bending for a moment.

If we take the expected (average) safety factor to be 4, which seems to be in agreement with the UBC thesis (average safety factor of 3.3 or 4 for original depending on beam size) and on the research by Dinehart and Morrisey (safety factor of 4.6). We can then back-calculate the standard deviation of section strength assuming a normal distribution (recall that a 95% confidence belt is constructed with +/- 2*Sigma):

Sigma(bending) = (Mean FOS – FOS at lower 95% bound) / 2
= (4-2.1)/2 ~ 1

For curiosity we see that Sigma / Mean ~ 25%, which is pretty high I thought.

But we need a way to apply this to beams with unacceptable holes in them AND account for the type of hole. Well, that’s too hard given the data that we have to work with. But we can do something crude here.

Lets lump all the “Acceptable” configurations into one bucket and all the “Unacceptable” configurations into another bucket, and find the distribution of Phi(bending). The data in Dinehart and Morrisey is quite nicely laid out for this exercise so I’ll rely on that, but if desired, you could combine all the sources we have here to form a more granular matrix of holes vs capacity.

I did want to bust out R, and since I didn’t get to do that regression I wanted to, I will use it for simulation. But since we are combining normal distributions analytical methods are both simple and tractable here. This is mostly for fun for me.

So, if we lump all “unacceptable” configurations into one bucket (that is, any beam with unacceptable holes made into the web) we get the following:
Mean Capacity of Original = 0.70
Sigma = 0.10

If we compare Sigma / Mean for these cut beams to Sigma / Mean for the original beams, we find that we are seeing a bit of difference in the variability: 14% for the cut beams and 25% for the original beams. May be a result of our crude analysis or simply that the biggest determinant of capacity in a cut beam is the fact that it is cut beyond spec, not the exact dimensions/location.

In either case, I think the sigma for the cut case is a bit low. We will handle that in the simulation by assuming sigma_cut beam is itself half-normally distributed. Here’s what we do.

First,
Simulate 1,000,000 beams being drawn for a Normal distribution with U=4.0, Sigma=1.0 in units of FOS.

Second,
For each simulated beam we draw a capacity of an “unacceptably cut beam” from a Normal distribution with U=0.70 and Sigma = (0.1 + half-normal(theta=0.025). Here I am assuming sigma is not static but itself is distributed half-normally with a base value of 0.1 and sigma 0.025. This is to take into account the fact that the sigma for cut beams implied straight from the research is a bit low relative to the sigma for uncut beams. We use half-normal because we do not think it is any lower than this.

Third,
Find distribution of capacity for cut beams by combining the draws from the reduced capacity for cut sections with the simulated original FOS.

Results,
From this we get capacity of our simulated cut members, with Mean = 2.8, and Sigma = 0.86. The 95% confidence procedure gives us a Reduction Factor of = Mean – 2*Sigma = 1.08

So still way above design load, but assuming we want to maintain original FOS our capacity would then be:
Reduced capacity = Original * 1.08/4 = 27% original
For our application this would result in:
Reduced capacity = 2000lbs * 0.27 = 540lbs

That is the BEST I can come up with. Decently close to the one software…

 

[phamENG]

Enable - that is impressive to say the least. Thanks for going through that. I'll have to re-read some of the literature regarding safety factors and the equations they provided - I tested the one I was using against their experimental results and it was agreeing to within a few percent. That lead me to believe it didn't include the safety factors and other allowable capacity considerations. I may be wrong though, so I'll read into it some more.

The lack of understanding is a little troubling, considering their ubiquity and the propensity for trades to mercilessly destroy structural members in light frame construction (and those OSB webs are so fragile and tempting for them!).

I'm curious - what's your background, Enable? I see you're new to the forum, but you seem to have been around the block a few times (probably more times than I have).

don’t judge me that I am using PHI to indicate a FOS…remember when phamEng used a hashtag to indicate lbs-force??

And by the way - I may technically be a millennial, but tweeting is for birds, the only book of faces I have are old yearbooks collecting dust in the attic, and hash is another term for potatoes. # is, and always will be, pound.

 

[Enable]

The lack of understanding is a little troubling, considering their ubiquity and the propensity for trades to mercilessly destroy structural members in light frame construction (and those OSB webs are so fragile and tempting for them!).

I think the reason for such lack of understanding comes from the very fact you mentioned. With other materials, say steel, research into connections and design can have economically beneficial impacts in practice. For example, if it is shown a new, cheaper connection can be just as safe as older less economical designs, great, lets do it!

For TJIs, even if we understood them perfectly would anyone ever be comfortable lessoning the design criteria (taking them down to, say phi=0.90, like in steel)? I mean, the designs may be more economical, but the plumbers/electricians/trades are still going to do their thing. The only difference is now we have joists in the field that are actually going to fail on-mass. That sounds bad! Who wants to be on the wood standards committee that is going to basically approve a bunch of failures to happen LOL?

Hard to get funding for research when there is little industry benefit, I suspect.

I'm curious - what's your background, Enable? I see you're new to the forum, but you seem to have been around the block a few times (probably more times than I have).

I’m a millennial myself but I don’t have twitter. So perhaps technically not?

My academics are in structural engineering and applied mathematics. I grew up in the restoration industry due to my dad being in the business as a consulting engineer (mostly commercial infrastructure). Been a contractor my entire working life. Started in the field as a laborer for about a year, went on to do some project management, and then started my own contracting firm and went back to being a laborer lol.

I specialize in highly complicated restoration projects. Basically the GCs bid jobs they have no idea how to do, but throw enough money in the bid that they’ll figure it out if they get it, and if they win they call me. It has been a fun little niche. Nothing is ever the same. But because of the nature of the projects, and the absolute lack of proper engineering from the consultants in my field, I have been wearing 3 hats for a good number of years now (laborer, contractor, and engineer). So, my years are numbered but my mileage is pretty high. You learn a lot when you have to think about complicated projects from every single perspective. I have also been aided a great deal by my family connection, which gave me exposure to engineering properly done early on - unfortunately not an exposure everyone gets.

We also have a CofA and perform shoring designs for outside contractors. That is fairly recent though!

How about you? I’ve noticed you seem to focus on more nuanced structural concerns. I mean, this thread is case in-point!

 

[phamENG]

Enable - without a doubt you are correct. Sadly it leaves those of us with problems to solve little to fall back on but what feels like a roll of the dice. Loaded dice in this case, but a lack of surety that can be uncomfortable.

My background - started as a laborer when I graduated high school while awaiting my trip to boot camp. I spent 6 years splitting uranium and boiling water. Then I went to school and knocked out my CE degree (focus in structures) and went to work.

I worked at a small to medium firm doing a wide range: commercial, industrial, residential, and historical restoration design. I also became the guy that was willing and able to figure our the weird stuff that came in and required it if the box thinking (or just practical application of first principals). I think I'm an academic at heart, but my statistics needs some serious work to get there.