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2x4 splice

2x4 splice

(OP)
I have a client who cut the rotted end (about 24") of a 2x4 rafter out and spliced a 2x6 back in its place, but he only lapped them about 36". Inspector obviously doesn't like it. With old homes in our area, the Engineer can present information to the building dept that states that a structural modification has at least the same or greater strength of the original building, and avoid the often impractical cost of bringing the system up to current code load capacity.

Mechanics of Materials would suggest I need to take that moment (9420 in-lb) and divide it by the horizontal distance between the 2 nails (say 2" if each nail is 3/4" from the top/bottom edge). Then i get a tension/compression load of 4710 lb, which i need to divide by my 100 lb nail strength, deriving 47 nails I need along the top and bottom of the splice. If they are 2" apart, that is basically an 8 foot splice with nearly 100 nails. Or I have a 6 ft splice with nails 1.5" apart, staggered a little to avoid splitting.

Doesn't the moment arm between the outer nails count for something? i.e. what if i made an 8 ft splice, but just had (2) nails at each end, and (2) in the middle, (6) total. Having done that in practice, it seems like it would hold far more load than the other method would suggest. I'm obviously missing something.

RE: 2x4 splice

(OP)
If it were that simple I would have done it. Not easy to explain the limitations here.

RE: 2x4 splice

I would need to think about this but how about...

If you know the moment at the center of the splice, try the elastic vector distribution method. Basically rm=Mc/Ip, rp=P/n. R=sqrt((rmx=rpx)^0.5+(rmy=rpy)^0.5)

Where (assuming same size fasteners):
c = distance to fastener
Ip = sum(cy^2) + sum(cx^2) from center of fasteners
n = number of fasteners
P = load/shear over the length of the fasteners
M = Moment

This is used in steel connections (See AISC 13th edition page 7-9) but if your conservative and feel comfortable with it, it may work here as well. However I would imagine creep/nail slip could be an issue depending on loading.

EIT
www.HowToEngineer.com

RE: 2x4 splice

(OP)
Thank you, RFreund. I will look into that, but I may have a few questions when I do. Lets say I have 25 fasteners top and bottom, 2" apart both ways (48" total splice length). M=9420 in-lb. Does R = fastener reaction?

msquared48, I hope I didn't sound too curt. That was not my intention. I have greatly appreciated your comments in the past, and I always condone drawing back and thinking about the big picture. In this case it is just the splicing problem that needs solving so we know how to compare it to the other options.

RE: 2x4 splice

I'm a great believer in Bulldog PL Premium... so much better than nails... and the 36" lap seems to be adequate...

Dik

RE: 2x4 splice

I have only used actual load tests for repair of deeper members by sistering a splice and for composite action for reinforcing floor joists with steel straps glued to the bottom and have supplemented this with nail fasteners.

Dik

RE: 2x4 splice

(OP)
If 800 lb is conservative, how are you figuring V at the center of the bolt group?

RE: 2x4 splice

Basically I'm cutting the section at the center of the bolt group and designing the bolt group to resist the internal forces - Shear as the vertical force and moment as the moment if that makes sense.

EIT
www.HowToEngineer.com

RE: 2x4 splice

(OP)
I think that is where I am getting confused - by thinking in terms of the different beam shear diagram values at center of beam for uniform vs point load. I'm guessing the simplified way to look at it would be the 800 lb load comes down, the 12 nails "push it back up" into the wood (equally divided per nail for simplification) then it comes back down as 400 lb per reaction at each end of the beam? Since we are using n=12, that made me think using 800 would be "roughly" correct. My FBD skills are rusty for this type of application, which is what caused me to post to eng-tips in the first place. Your patience and time is much appreciated.

RE: 2x4 splice

Wow, this is a lot of analysis work for a single rotted out 2x4 rafter. Whatever load it was supporting (which can't be much being only a 2x4) probably transferred to the neighboring members a long time ago. Plus, cutting out the member finished off the load transfer if everything was not shored, then jacked up back to level before the repair was put in place.

Not that I am discounting the analysis discussed, just trying to keep things in perspective.

RE: 2x4 splice

(OP)
Yes it is! I have long since gotten past the issue at the project. We ended up getting around it without analysis - just sistering and adding to the inspectors satisfaction. I just wanted to finish the conversation so i had good information to apply the next time a splice question comes up. 99% of the time, we avoid the splice analysis by getting around it, but it is good to know what to do in that 1% situation.

RE: 2x4 splice

(OP)
Would anyone object to using the simplified method shown at the bottom of the attached sheet? The thought is to look at the outer nails for worst case, then add nails at a reasonable spacing throughout the splice to be conservative. I am fascinated at how many ways different people have come up with to look at this. Of course, eccentricity is being ignored considering top and bottom of rafter is braced by sheathing.

RE: 2x4 splice

Yes, Off the top of my head and neglecting any eccentricity or prying, I think it should be as follows:

Span = 10'
Center of nail group at 4.25' from support
Moment at center of nail group: M= [(80plf)(4.25')(5.75')/2] [12"/'] = 11730 # in
Shear at center of nail group: V = (80 plf)(0.75') = 60#

Ix = (4 nails)(6")2 + (2 nails)(0")2 = 144
Iy = (6 nails)(1")2 = 6
Ixy = 144 + 6 = 150
cxy = sqrt(62 +12)= 6.08"

Lateral Force on Nail
z = Mc/I + P/n = (11730)(6.08)/150 + 60/6 = 485#
If you want to shave off a pound, you could calculate the vector sum of Mc/I and P/n rather than simply adding them together.

RE: 2x4 splice

I think we are looping on ourselves. But in regards to your question (KIS) I would agree. Essentially we are just decoupling the moment and into a force couple and account for direct shear.

EIT
www.HowToEngineer.com

RE: 2x4 splice

In reviewing keyp's PDF, I'm wondering if the analysis started out with a nailed solution, then changed to a bolted solution at the bottom: 12 fastners vs 4. The spliced length for the top drawing is 2.5', not 3' as shown near the bottom (unless you increased the length of the wood splice and moved the bolts out accordingly, but such wasn't noted in the analysis). With a welded steel splice, the length would be 3', but not for wood. The ends of the wood outside of the fasteners don't count.

Even with 12d nails, I'd bet on the splicing wood splitting with only 1.5" to the ends of the wood. At 260lbf/nail, that's a big nail...bigger than 40d (which is the largest nail shown in tables in my NDS). If bolts are used in the lower drawing, the minimum diameter in my old NDS is 1/2" for a double shear connection, indicating a minimum 4" clearance to the end of the splicing member.

There is also the issue of having 2x nails on either side of the rafter. Correctly, nails were specified as to being staggered to prevent wood splitting. However, in real world, paper calcs need a safety factor added because contractors won't take the care to install as the engineers design says to. (one of the very two best truss repairs I ever saw was by a musician who made a cardboard template from my specs---beautiful job. the other was by a contractor.)

Based on the very few basic bits of info on the existing install, it appears the house is very old; 100 years or so. Why? 10' spans were common back then, when roofing was wood shingles with spaced sheathing and usually only one layer of roofing. This means the wood is very old, very hard, and prone to splitting unless one predrills.

The above 3 paras are why the inspector wanted a longer splice (which apparently was done, after all). I've found that good, experienced inspectors may not know the math, but they have good sense.

I suspect the question here is only for the analysis of the fasteners. However, at 80plf, the rafters are over loaded even at 12" o.c. and using old dimensional lumber at 2"x4" and a high Mod of Elasticity (both of which cannot be assumed for old houses--the wood usually was 2" x 3.5"-3.75" or so). The overloading is because of excess deflection at center span. Fb and Fv are adequate at 12" o.c., but not 24"oc, and maybe or maybe not at 16"oc, depending on the grade of wood. Our analysis should also consider this. I know there was no mention of cracking, but I'd recommend accounting for the load across the entire member. Part of this is risk management since once you touch it, you then own the liability.

Since the rafter end was removed, this tells me the splice is near the rafter tail. As such, I think the calculations shouldn't use maximum moment since max moment occurs in the center of the span. At the ends of the rafter, shear forces govern your repair.

There's a comment that the rafters have lateral resistance at tops and bottoms with sheathing. Now, this is an odd installation. There's sheathing on the underside of the rafters? That might explain some of the limitations for using a full length sister, but if they cut out 3=4' of lower sheathing, I probably would've had them cut the rest of the way and install 2 2x4s so that the bottom sheathing could be reinstalled, thus replacing the diaphragm it served as. Having personally inspected hundreds of old homes, I'd really like to see a photo of rafters with upper and lower sheathing.

I'd recommend consulting the National Design Specification for Wood Construction. There are a number of other factors that need to be considered beyond just the math around moments (for example, accounting for periods of higher live loads). The NDS was a great help to me when I was getting started in these kinds of repair scenarios. The theory is a great start, but we engineers are supposed to migrate it to the real world. Don't mean to lecture, just to remind us of our strength and role.

Wow, I am way longer than intended. Sorry.

b/r

A John Gironda III, P.E.
"As long as you are in the seat...make a difference"---Capt James T. Kirk

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