Curious Question About Flitch Beam Design 7

[tc7]

I have an upcoming residential project that may require a stack of LVL's or perhaps a steel flitch beam configuration to replace a bearing wall spanning ~16 feet or so. To prepare, I've read as much of the available internet literature that I could find including the ubiquitous Destefano article in a 2007 Structure Magazine as well as a couple of good text books on structural wood design. I've also reviewed several dozen excellent Eng-Tips discussions on the subject of flitch beam design. With all this new found knowledge and my own familiarity with the NDS, I'm ready for the design work as soon as the owners are ready.

However, never in any of the discussions or references that I've seen has the effect of bolt holes been mentioned insofar as their reduction of beam section modulus and the consequent increase in the bending stress. A couple of 1/2" dia. bolt holes will take out a fair amount of cross section (~11% from a 1/2" steel plate). If those bolts are located ~2-inches from the top and bottom edges as depicted in the bolt pattern shown in the Destefano article, this could reduce the moment of inertia and section modulus of the steel plate by ~11% also.

This seems significant to me and perhaps should be accounted for in the design calculations, but I don't design flitch beams often (in fact, never). I would appreciate all thoughts on this matter and why the effect of bolt holes on bending stress and shear stress seem to be ignored.
Thank you.

 

[driftLimiter]

The section modulus effect should be easy enough to handle and give a good check. You can calculate the reduced section modulus and just check bending stress at the location where it coincides with peak moment. Staggering the bolts top and bottom would help alleviate this disturbance.

The MOI effect is interesting, but I suspect if you did a model with some 1-2" segments with reduced MOI spaced along the beam you could answer your question about how much of an effect it has. Its not a pretty model lol but could give some useful info.

You could also just design around the steel plate as the main member and the LVLs there to brace it only. This may reduce some of your concerns as well.

Finally both S and I get the most benefit from material near the extreme fiber which you will maintain I'd be looking at the numbers how much is the reduced S and I compared to unreduced. Maybe just use the smaller to be conservative?

 

[MotorCity]

It depends where the holes are located. If they near the middle of the cross section (i.e. the neutral axis) they will probably have little to no effect. Same goes for holes located near the compression face. Holes located near the tension face could be an issue. All of this of course assumes we are talking about small holes for bolts (which we are) as opposed to large holes cut out for pipes or the like to pass through.

 

[ProgrammingPE]

For a 3/8"x10" plate w/ (2) 1/2" diameter holes 2" from the top and bottom (6" from each other),

Ix,no holes = 1/12*(3/8 in)*(10 in)^3 = 31.3 in^4
Ix, holes = 1/12*(3/8 in)*(10 in)^3 - 2*1/12*(3/8 in)*(1/2 in)^3 - 2*(3/8 in)*(1/2 in)*((6 in)/2)^2 = 27.9 in^4​

So you're looking at a 11% reduction in Moment of Inertia as well as Section Modulus at the bolt holes. This is unlikely to affect the capacity of your flitch plate beam design, though, because of two reasons:[ol 1]
[li]The cross section only has bolt holes along a small percentage of the beam length (3% for bolts spaced 16" o.c.)[/li]
[li]The tensile stress of steel is much higher than its yield stress[/li]
[/ol]
If you design your beam ignoring the bolt holes, the yield stress will be exceeded at the bolt holes due to the reduced Section Modulus. This will result in some yielding at this point, but as long as the tensile stress is not exceeded, this will still be OK. This is because yielding is a failure that occurs over a long region. If too much of the beam yields, then you'll get excess deflections due to the reduced stiffness of the yielded steel. If there's some local yielding only at a few bolts near the beam midspan, it'll have a negligible effect on how the beam performs.

The reduced Moment of Inertia will also have an almost negligible effect on your beam deflection calculations since only 3% of the beam length has the 11% reduced Moment of Inertia.

Avg Moment of Inertia = 97%*(31.3 in^4) + 3% (27.9 in^4) = 31.2 in^4​

Structural Engineering Tools:

http://www.structuralcentral.com/tools/steel-connection

Structural Engineering Videos:

http://www.youtube.com/structuralcentral

 

[XR250]

I don't believe anyone considers this in their design.

 

[Goatenstein]

I second XR250. My supervisor and I have done many LVL + flitch plate designs, and we have never considered the strength reduction from bolt holes. The net effect is probably 1% or less.

 

[tc7]

ProgrammingPE-
This is a beautiful answer, you have validated my concern and at the same time, despite possible/probable yielding near a bolt hole or two at mid-span, nearly convinced me it won't make too much difference.

However, I think I favor the idea of avoiding any theoretical yielding and rerunning my beam sizing calculations as a final check using a bolt hole reduced section modulus.

 

[dauwerda]

I agree with everything that ProgrammingPE stated. This is exactly how it is handled in the structural codes for steel design and is precisely why we check "yield on gross area" and "rupture on net area"

 

[BridgeSmith]

The AASHTO bridge design spec includes calculations for effective area for yielding of splice plates with holes. With 2 hole of 1/2" diameter in a 10" wide plate, The effective area would equal the gross area.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[StrucPatholgst]

Just a heads up, designing a flitch beam takes about three minutes with ClearCalcs.

 

[tc7]

Hi StrucPatholgst-
I wonder if ClearCalcs adjusts the MOI & section modulus to account for bolt holes as we're discussing? I'll bet it doesn't (I know that a similar low cost software package, BeamChek does not).
Anyway, I can now run through a more thorough set of hand calcs, selecting appropriate adjustment factors and size the beams + steel in about 15 minutes. I enjoy/prefer the thought process that goes into them.

Tom C

 

[StrucPatholgst]

Actually ClearCalcs allows you to calculate a custom moment of inertia and use that for a custom profile, and then run the calculation.

 

[jerseyshore]

Great post ProgrammingPE.

Usually not checked though as others have mentioned. I think as long as you have a good edge distance of the bolts that's really the key to prevent issues.

A critical element that is often overlooked is the bolts at the end to transfer the shear (if the plates aren't bearing).

 

[tc7]

dauwerda-
If you're still viewing - I'm fascinated by your reply; I gather the steel Codes that you mentioned allow a member to exceed yield when analyzing a member based on "net area" i.e., cross section minus area of holes, but what is the allowance criteria? how far past yield does the steel Code permit ?

 

[phamENG]

tc7 - the American Institute of Steel Construction code (AISC 360) allows, for laterally stable beams, the use of the plastic section modulus in capacity calculations. That's because it is now widely accepted that partial yielding of a section is not a failure. If you form a plastic hinge in a simply supported beam, yes, that's bad. But for LRFD design the moment at ultimate load is limited to 90% of lower bound plastic hinge formation and in ASD service loads are limited to 60% of lower bound plastic hinge formation (roughly).

(Note: this is very general. There are a lot of hoops to jump through to ensure your capacity analysis is correct for steel of various shapes, but this is the gist for most of it.)

 

[tc7]

Very good phamENG, thank you for that.
You structural steel Code folks are awesome. But it amazes me that absolutely all of the prior Eng-Tips flitch beam discussions, all readily available published literature and the National Design Specifications and residential building codes (where steel flitch beams are most likely to be employed) are absolutely mute when it comes to addressing net cross sectional area and the comparable level of capacity analysis that you and dauwerda have mentioned. Perhaps this is because the typical deflection criteria (L/360 or L/240) is so restrictive that any beam design will never approach yield even when perforated with bolt holes ?? I don't know. How would you know unless it were analyzed?
Someday I'll submit an official inquiry to the NDS spec writers about this and maybe I'll get a rational reply. Perhaps I'll reach out to folks in the Jim Destefano organization and ask for their point of view on this.
Thanks again to all who have participated in this, it's been eye opening for sure.
Tom C

 

[XR250]

@tc7:
It is likely due to the fact that the difference gets lost in the noise of the design. Same issue with residential I-beams - no one takes nailer holes in the top flange into account. If you don't want to go broke being an SE, you have to pick your battles.

 

[tc7]

XR250-
" . . . lost in the noise of the design . . ." could be a subtitle to what this thread is about. There should be no noise in design work especially where public safety is concerned, just ask the structural steel folks - they've got their act together.
Nails driven into wood beams and joists are not in the same realm as drilled bolt thru-holes; nails are more likely to cleave between wood fiber rather than cut through them and this preserves the bulk of their inherent beam strength. Besides the NDS specifies nail size and spacing and these specs are backed up by testing by American Wood Council, as well as manufacturers (Weyerhaeser, Boise-Cascade, etc.). Meaningful test data on wood/steel flitch beams, if it exists, is well hidden.

 

[Enable]

XR250 not sure about your code but up here we can safely ignore fastener holes in the flange if it amounts to less than 15% of the cross-section. So nails, etc would certainly fall into that category. So no battle to be picked on that one even if one wanted to I think?

 

[phamENG]

There should be no noise in design work especially where public safety is concerned

An idealism that many of us wish we could follow, but we all (or at least most) know we can ill afford. Most examples out there are set up for practical application. If an issue like localized plastification around a very small percentage of bolt holes is irrelevant to the outcome of the design, it doesn't get included because we unfortunately have to crank out as many as we can to turn a profit.

I'm not aware of any large scale testing or academic approaches to the problem that explore all possible failure modes. Might be nice, for teaching new engineers, but for the most part we just show them the minimum of what needs to be checked to ensure a safe and reliable design.