Shear Flow and Moment of Inertia for deflections

[BR0]

Hi All,

I've read a lot of the threads about shear flow and designing bolts or welds and I haven't see this topic addressed so perhaps it isn't an issue.

I was wondering about the moment of inertia to be used for calculating deflections. In general, can you use the full cross section moment of inertia when using intermittent welds. I imagine I'm missing something easy here.

If you have a built-up I-beam and used full pen welds for the full length of the beam span, it does seem obvious that a full cross section moment of inertia could be used.

On the other-hand if you have a fairly long span beam and a moment controlled section, and you use VQ/I and have intermittent welds wouldn't the section deflect as if it has a changing cross section. As an example if you used 1" of full pen weld at 12" on center, would the beam need to modeled for deflection as if it were made of three independent plates in the gaps and only as a composite section in the weld areas?

A beam I'm designing right now has a 22" deep web and 8" wide flanges. When using VQ/I, the beam only requires a 1/4" weld at 12" O.C between the web and flanges. It somehow doesn't "seem" correct to use the full cross section for this

 

[KootK]

1) In my experience, for welded steel construction of the sort that you mentioned, engineers do not consider "fastener" slip to reduce the moment of inertia for deflection computations. This implicitly relies on the assumption that a particular kind of fastening does not cause much slip. I would say that assumption is true for stich welds but, at the same time, I can't claim to have actually investigated that in any meaningful way.

2) Wood is a good example of a material for which many common fasteners will produce slip that should often be accounted for in both strength and deflection estimates. Based on material that I've read on this forum, the European codes have methods for dealing with this explicitly.

It somehow doesn't "seem" correct to use the full cross section for this

3) You are not wrong. Any real world stress and strain pattern that is more convoluted than the simplified one that you assumed in design will produce additional movement. That, fundamentally, because a more convoluted path implies that more internal work is induced by the external loads. Even if the fastenings had no slip whatsoever, the changes that intermittent fastening makes in the beam stress patterns will increase movement. The key to this, I would say, is reconciling yourself with the relatively small magnitudes of these impacts in many cases.

 

[JoshPlumSE]

Take a look at AISC section E6 (which is related to built-up compression members.

This section talks about a "modified" L/r ratio for connection members. I think you could use the same concept to come up with a "modified" moment of inertia for the built-up member.

 

[JoshPlumSE]

Let me expand on my previous post a bit. I left a lot of stuff unsaid.
a) My assumption is that the modified L/r ratio is about reducing the buckling capacity of a member due to imperfect connection.

b) Euler Buckling stress for a regular member can be calculated as:

Fe = (Pi^2)E / (L/r)^2​

Written in terms of capacity and moment of inertia, where all I've done is substitute r = sqrt (I/a)

Pe = (Pi^2)E *I / L^2.​

c) Therefore, if (L/r)_modified = 1.2*(L/r) then I_modified = (I / sqrt(1.2))


This is not really the intent of the AISC code. But, it does give you a "ball park" idea of what the adjustment would be like if analogy between bending and buckling were to hold.

Once upon a time, I had a copy of the Euro codes at my desk. While I was not concerned at all with built-up members at the time, I kind of remember seeing a similar formulation. I just don't know if it was for bending or buckling.

 

[BR0]

Josh and KootK, thanks for the insight and recommendations. I will definitely look at what you suggest.

I wonder also if it just isn't a big deal as I've searched quite a bit for an example where they showed deflection calculations and have had no luck. Perhaps that is because the deflection would be the same as for a the full cross section moment of inertia.

 

[JoshPlumSE]

I imagine it's partly because deflection is a serviceability issue. And the material codes don't tend to focus on serviceability much.

 

[Settingsun]

the beam only requires a 1/4" weld at 12" O.C between the web and flanges

You've got a truss with chunky 'diagonals' and seemingly low shear force so the shear deformation is small. The effective bending modulus of a truss is approximated as the chord area multiplied by the depth squared. By the time you take your flanges plus part of the web as the chords of this notional truss, you've captured the vast majority of the composite beam stiffness.

 

[BR0]

Steve, I like this analogy. I'm unsure about using part of the web as part of the chord as it's unattached, but I will look at it and see how it calcs out.

 

[Settingsun]

I actually thought I was being conservative only taking part of the web. The change in length between welds is the same for the flange and the edge of the web if there's no weld elongation. So the average tension/compression would be the same over that length. That would imply the web is fully contributing to bending as its stress profile varies from the full tension value to full compression on the other edge.

It also makes me think that minimum weld might reduce stiffness as you may then get appreciable weld elongation.

 

[BR0]

Steve,
Yea, I guess I was tending to a more conservative view as it is hard to know how much the web would contribute to bending. I do see what you are saying and perhaps the web would contribute.

Thanks again.