Flitch beam design method 6

[hausfxr]

I'm an architect doing work in my basement and am attempting to design a flitch beam using our existing 4x6 wood beams. We are removing the center posts of four beams which are spaced at 5' o.c. and are perpendicular to the existing 2x6 joists. The plan is to sandwich the beams between two C-channels. The ceiling is low so head room counts, but I don't want to cut into the joists with a recessed beam - I like the idea of the exposed C-channels. I'm attempting to use a 5" tall channel which will allow drywall will extend over their tops to create a clean look.

All steel and wood members will be fully supported at both ends.

Only one beam has excessive loads on it. The others have only the floor load and seem adequate with having each C-channel on either side of the wood beam supporting half the load. However, the one beam with roof loads fails with half the load and it's the only beam I'll design as a flitched beam. I've included the BeamChek calcs for that beam with 47% of the load applied, and, it would appear that with 6% of the load taken by the existing wood, it may be adequate.

Here's my question: When I do the proportional calcs for the combined beam, it appears they are more than adequate and contradicts the marginal calculation from the BeamChek calc. I'm hoping someone can let me know if I'm on the right track. The only examples I could find as a guide used steel plates and those seemed straightforward - I'm not sure if you can use the same simple method with a C-section.

 

[Canuck65]

My opinion on this situation is ... design 2 steel channels, one on each side, to take the full load and attach them to the side of the existing beam. It is very often not worth the effort to optimize, especially with such a small beam, by using the combined resistance of the wood and steel together to safe a few pounds of steel.

 

[JLNJ]

I didn’t look at it too thoroughly, but shouldn’t it be more like 90% of the load goes to the channels when proportioned by EI?

 

[ProgrammingPE]

You can check the capacity of the flitch beam by determining the percentage of the load that goes to the wood beam and the percentage of the load that goes to the channels based on their EI values. If the wood beam check using its percentage of the load is OK and the channel check using its percentage of the load is OK, then the flitch beam is also OK.

I am getting that 13% of the load goes to the wood beam and 43.5% goes to each channel, so it looks like your FORTE (13% of 502% moment stress ratio = 65%) and BeamChek calculations show that the flitch beam will be OK.

Your BeamChek calc shows that the channels are only close to failing due to the deflection checks. The strength checks show that they have some additional capacity, which is why your calc at the end which was only doing the strength checks works easily.

I did notice several issues when I glanced through your calc at the end, though. A 4x6 is 3.5" x 5.5", but the calc used 3.75" x 5.75". Cf for a 4x6 should be 1.3, not 1.2. Iw was doubled for no reason. You also can't add S values for the wood and channels together to get a combined S value since they have different depths. (You can add the I values together and then divide that by each member's depth to get their different S values.) The check also needs to check the stress in the channels. (It currently just checks the stress in the wood.) Finally, the bolt calculations treat the load as uniformly distributed when in reality you have a very large point load that must get transferred from the wood to the channels at that location and another region with a higher uniform load so you need to locate the bolts based on your actual, non-uniform loading.

Canuck65, OP is using the simplified approach you suggest of only considering the 2 channels for most of the beams, but one of them is not working, which is why they're trying to include the strength of the wood beams.

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[dhengr]

Hausfxr:
The free engineering line is over there.

 

[hausfxr]

JLNJ:
I may not have been clear - the two steel channels support 94% of the load. The software calc was done using half the load on one C-channel.

Canuck65:
I completely agree with you. However, it's a tricky situation in that the bottom of the beams are just above 6'8 for most of the beams length, but, with a sloped slab, drop below right in front of the stair door. I can cut that door height down a bit and an inspector will likely not notice (6'-8" min. 3' in front of all doors), but if I instead use two C6 x 8.2 channels which will not require the wood to do any work, now I'm cutting the door down 2"... As I said in my original post, I trying to determine if my calculation method for the combined beam is correct - why the discrepancy?

I'm also replacing the stair, so the minimum height at the bottom of the stair, which is the door header, is 6'-8" per code (nothing's grandfathered in if it's replaced), so any lower height could mean applying for two code appeals if the inspector caught it... Just looking for the easiest solution short of replacing the beam altogether since the "optimal" solution has it's own challenges.

 

[dik]

I think you nailed it Canuk... I would have ignored the effect of the wood beam, the steel is so much stiffer. Careful, a C6 is 1/2" deeper than a 6x6...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[hausfxr]

ProgrammingPE:
Thanks so much for you feedback.
What EI are you using for wood? From NDS, DF-L No. 2 is 1600 ksi, and I'm using 2900 ksi for the steel.

The beam is a 100 year-old 4" x 6" - it's actually just over the dimension I used, so I thought why not take advantage of the additional area.

I'll revise the section addition and thanks for the point load bolt shear correction.

 

[dik]

100 years... Is there any historical significance of the structure?

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[Agent666]

I think in taking account of any load sharing in these situations you need to be aware that the existing members already potentially have some considerable load locked in.

If you're not changing the support conditions for the beam, and just strengthening it to carry a larger load, then it won't see the full load until the existing wood member fails in a way to shed that load to the steel strengthening members. Unless of course you jack all of the load out of the system, which can be done, but how do you practically gauge the point at which the original member is in a neutral "no-load" position.

If truly after a composite load sharing scenario, then your new members will only see the incremental load added after the strengthening is applied in most cases (and consideration of achieving some load sharing). If changing support conditions, like removing a post this is a different matter of course, but to some degree you'll still potentially be locking in some loads depending on how you construct and connect the members.

But I'd advise in general to forget about sharing the load to the wood, if it was maxed out before adding the strengthening, then all you're proving is you potentially failed the wood, not loading it to 6% or whatever you've assumed, it could be like 106% with your channels at 6%. Design the extra steel for the full load and move on is my advice. Otherwise consider getting an actual structural engineer to look at it and take the risk, at which point the moral of the story would be 95% would probably just use the channels on their own.

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[hausfxr]

Thanks for your feedback Agent666. Started strategizing as to how to lower the total load on the beam, and it occurred to me that I'm putting up 2x4 partition walls for insulation around the basement exterior and I can put a post against the outside wall and add a footing below (no existing spread footings - 1920s house!) and just shortening the bearing point 4" allows the C5 x 9 channel to do all (half) the work. So, I can use the wood to transfer the load to the steel, and, as you suggest, disregard the wood.

 

[SlideRuleEra]

I may not have been clear - the two steel channels support 94% of the load.

False. The two steel channels support 84.5% of the load (completely in line with JLNJ's engineering judgement approximation).

Reasons for the discrepancy are because the attached calcs produce "garbage" answers. Then the software does exactly what it should, mindlessly take input "garbage" and precisely calculate output "garbage".

I don't mean to be rude, but I don't "Make This Stuff Up" either.

1) To start, without using software or even pencil/paper, an "Old-School" engineer can see from your original post that the proposed 5" channels spell "Trouble" for a 164" span... Span to Depth Ratio >> 24:1. It's actually 32.8:1. Even if you can meet shear, bending stress, and deflection requirements, floor movement (springy like a trampoline) will probably be objectionable.

2) Unless the two materials (one transformed, the other not) have the same Moment of Inertia, the following is not true:

The load distribution ratio is based on "E" and "I" of the two materials (one transformed, the other not). For these calcs, the math works out to 84.5% of load on the two channels.

3) Also, the calcs have an error for "I" of the 4x6. The 4x6 is erroneously accounted for twice:

For the one 4x6, "I" is 59.4 in⁴ not 118.8 in⁴.

4) There is another discrepancy that may be minor for this application, but should be noted. Unless both channels and the 4x6 share a common X-axis (unlikely based on your comment about drywall)

The parallel-axis theorem needs to be used to adjust (increase) the composite "I".

In your latest post you seem to be considering installing the channels without attaching them to the 4x6. Do this and the laterally unbraced channel length goes from inches to 13.67 feet ( >> Lu of 5.6')... perhaps collapsing under load.

Hire a structural engineer, I don't want you to "trash" your house.