Wood Beam Reinforcement through sistered members

[palves]

I have run into this case on numerous ocassions and want to make sure I'm looking at it correctly. I have an existing 4x12 beam that needs to be reinforced for a new loading. The new load produces a moment of 1763 ft-lb, and I will support this by sistering a 2x8 on either side of the beam. My question comes with the nailing required to make this beam act as a single unit and adequately resist the loads. I've gone through the horizontal shear calculation, but am not quite sure if this is the correct way to go about it. All examples I have seen assume that the beams stack on top of each other instead of side by side. I have attached my calculation so please take a look and let me know what you think. A few main questions.

1. Can I even use the horizontal shear equation when they're side by side?

2. Do I need to worry about the connection so much when they are side by side? I can see the merit when they stack vertically, but feel like they should act together with minimal nailing in this case. Maybe 2 rows of 10d at 6" o.c. staggered.

What is making me question myself is the 371 lb/in I am getting. I would need an excessive amount of nails to satisfy this shear when the extra load the beam will take appears to be rather small. Any thoughts?

 

[palves]

Awesome. I messed up the attachment, but this should do it.

 

[woodman88]

Typically I would consider this a deflection problem. Check the deflection of the 4x12. Find out what plf loading will deflect the 2x8's the same amount. If this 2x8's loading meets the addition loading requirements. Nail the 2x8's per the plf transfer required to the 2x8's. Extend the 2x8's to the bearing or 12” from the bearing and cluster nail for the reaction at each end of the 2x8's. Note to jack up 4x12 (per the deflection required by the 2x8's) to relieve the stresses before nailing together.

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.

 

[bookowski]

Are you extending the 2x8 all the way to the end and providing some kind of end connection to take out the shear? If so then I would say you don't need to look at shear flow between the two. Proportion the load carried by each based on the ratio of the EI of the member to the sum of the EI's, this ensures deformation compatibility for all three members. Then the nailing would only need to be enough to transfer the vertical load into the 2x8's through the 2x4.

 

[palves]

Bookowski, unfortunately I can't extend the 2x8's all the way to the end due to some messy end conditions. The 4x12 itself has adequate capacity for the excess shear so luckily I don't have to find a work around for that. Do you still think I need to calculate the shear flow as I have done it because I'm still a little unsure of that. I'm still checking into the deflection method and seeing how I feel with that. It seems promising.

 

[BAretired]

I don't think you have calculated the horizontal shear correctly. You want the total shear on a vertical plane between the 2x8 and the 4x12.

I found A* to be 1.5x7.25 = 10.875
y* = 4.92 - 7.25/2 = 1.295

Q = A*.y* = 14.08

On this basis, the horizontal shear is VQ/I = 3020 x 14.08/642.64 = 66#/"

That would be the total shear across the plane between each 2x8 and the 4x12, but it is not uniformly distributed. The fiber stress in each 2x8 varies from maximum tension at the bottom to a slight compression at the top of the 2x8, so the horizontal shear has a similar variation across the height of the 2x8.

You would need more nails near the bottom of the 2x8 than the top to handle this variation.

It would be better to laminate a 2x12 on each side of the 4x12 so that each lamination tends to have about the same deflection under its share of the load.

BA

 

[hokie66]

I don't see horizontal shear as having anything to do with this problem. You are not trying to create a composite member one over the other, but just two members side by side to share the load. It is purely a matter of consistent deflections and transfer of the vertical shear from one member to the other, then back into the member which bears at the support.

 

[BAretired]

Hokie, that is not correct. As I understand the first post, the OP is trying to create a composite member using nails to laminate the 2x8 members to the main beam. What other reason would there be for calculating the gross moment of inertia and other properties for the composite section?

BA

 

[BAretired]

If only consistent deflections are considered, I would expect the 2x8 members to carry a negligible portion of the load.


BA

 

[msquared48]

Hokie / BA:

I can see it both ways, and the answer depends on how the joists load the beam.

If the joists rest only on the top of the 4X12, then to get any load to the 2X8's, there must be horizontal nailing to estabish composite action to get any load to the 2X8's.

However, if the joists rest on top of the 4X12, and if there is solid blocking under the joists to the top of the 2X8's, then the load will be shared based on relative "I" values without the need for anything but nominal horizontal nailing.

The beam and 2X8's will deflect the same in either case here



Mike McCann
MMC Engineering

http://mmcengineering.tripod.com

 

[BAretired]

I_(2x8) = 95.3

I_(4x12)= 415.3

Portion carried by 2-2x8 = 95.3/(415.3 +95.3) = 0.186 or say 19% of the load (perhaps not negligible but not very much).

The OP will have to tell us what he means. I interpreted his attachment to mean that he was trying for the composite shape.



BA

 

[woodman88]

Wood being wood, I do not think that a good enough connection for a composite shape can be achieve in the field.

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.

 

[hokie66]

Maybe he will tell us more, BA, but 19% is substantial. Some folks worry about 3%.

Garth is right. Composite design in wood needs to be achieved by glue lamination, not by connectors.

 

[BAretired]

I agree with Garth as well, but there are two issues in this thread. First, is the calculation correct assuming the members can be made to act compositely? Answer: no. Second, are nails or other fasteners adequate to develop composite action? Answer: probably not.

I do recall beefing up a 5" wide glulam beam some years back with a 5 x 3/8 plate pre-drilled with holes to receive glulam rivets and fastened to the underside of the beam. It did work with that type of fastener but it took a lot of elbow grease to install the fasteners.

If 19% is adequate, then the 2-2x8 fix may be sufficient but the OP has said that they cannot extend to the supports so special provisions would still be required to make the attachment.


BA

 

[hokie66]

With two members side-by-side, what is the advantage of making them actually composite? When we talk about composite action, it means the materials are one over the other. When they just share the load relative to their stiffness, they don't need to be composite. I suppose if the intention is to offset them vertically to create a sort of flange top or bottom, that might be achievable, but I doubt the OP wants that.

 

[dicksewerrat]

Why not use 2 x 12's on both sides bolted through. Again, take the load off the 4 x 12 before any work is started.

Richard A. Cornelius, P.E.

http://WWW.amlinereast.com

 

[dhengr]

We always called this type of beam a flitch beam, and usually had 2x’s with added steel pls., all bolted together. The OP’er. still leaves plenty for us to guess at, but I’ll assume the existing joists rest atop the 4x12 beam. Thus, the new, added, load will be distributed through the 4x12 to the two side members. He will have to make some determination on the allowable stresses for the old and new lumber and check the stresses however he arranges the side members. And, he will have to jack the 4x12 a little above level before attaching the 2x’s so they are really brought into play when the jacks are released. For the cost difference I would sooner see 2x10's or 2x12's, and I would center them on the depth of the 4x12, not flush to the bottom. I agree with BA’s ratios of the I’s as a means of distributing the load to the three members. This leads to a bolt/structural screw size and spacing to transfer about 9.5% of the load to each side member, along the length of the beam. But, the thing that’s a bit of a head-scratcher for me is, that since the side members don’t run all the way out to the beam bearings, the side member loading must be transferred back into the 4x12, a foot or so inboard of the beam bearings, almost as if the 2x side member had a reaction point at its end termination. The design and layout of this termination connection could get kinda messy. I’d take a good look at BA’s steel bottom reinforcing plate, 3.5" x .375" or .5", or some such. And, not do too much connecting to the 4x12 in the middle third, high fiber stress region of the beam. The existing beam might also be prestressed with a couple harped side rods and turnbuckles.

 

[palves]

Wow, nice work everybody. I'm liking it, but it looks like I need to provide a few clarifications. I'll try and get to all of the questions you raised.

1. The original roof joists (2x4's) do not sit up on top of the 4x12 beam, but rather are attached on the side with hangers. This is the main reason that I am using 2x8's. I just don't have room to add in a full 12" deep section to match the beam. This being said, I can just tell the contractor to scoot the 2x8's up so that they create a bearing condition with the roof joists. This way we can be sure that the load will bear on both the 4x12 and 2x8's simultaneously, and then can just add in minimal nailing as long as deflections are considered. The bottoms of the 4x12 and 2x8's won't be flush like my sketch shows, but that really doesn't matter.

2. Just out of curiosity, how do you all think the connection would change if I weren't able to jam the 2x8's under the 2x4's so that they actually had bearing? Would this change the nailing requirements? The load path would go directly into the 4x12, and then have to be distributed out into the 2x8's so that is where I feel like a tighter nailing pattern would be required. Msquared seems to say that this case would require the horizontal nailing that I was initially trying to calculate and I agree.

Hope that helps. Let me know if I can provide any more info.

 

[hokie66]

You have to provide nails, screws, or bolts to transfer the 2x8's portion of the load from the 4x12, but those are just shear connectors, not connectors for composite action. Then you have to get the end reaction of the 2x8's back into the 4x12. This would require a concentrated connection, several bolts, a lot of nails, maybe even shear connectors like split rings or shear plates.

 

[Teguci]

For bottom flush condition your numbers are wrong:
2x8 to 4x12, Qxx = -14.0 in3
Ixx total = 566.6 in4
Qxx/Ixx = -0.025 in-1
Integrate V over L = desired anchor spacing x Qxx/Ixx = Required Z for lag connector
This will give you composite action for bending. Verify that 4x12 can take the shear at the ends.

The 4x12 is already taking the existing load. Recommend relieving that load prior to sistering. Otherwise the 4x12 will carry the full existing load and then share with the 2x8 the added load (potential overstress on the 4x12).

In response to your questions:
1. Can I even use the horizontal shear equation when they're side by side? - Yes, if you want composite action with beams that do not have a common neutral axis. As noted above, you can always treat them separately, but your load distribution will be relative to their stiffnesses.

2. Do I need to worry about the connection so much when they are side by side? Yes, if you want composite action. In bending the 2x8s will take more tension which will be balaqnced by more compression in the 4x12.