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How do you determine the weld size for a built-up column?

smitty9898 (Structural)
25 Mar 11 18:58
I'm trying to determine how to calculate the required weld size for a built-up column.  This is not a typical built-up column (i.e. lattice, etc.).  This built-up column consists of three plates to form an "I" section.  There are welds between the web and the flanges.

Obviously, the welds sizes could be determined if it was a beams by analyzing the shear flow.  However, I'm not sure how to determine the load on the welds as shown in the attached sketch.  Seems pretty straigtforward, but I could not find any info in textbooks or the internet.  Any help would be greatly appreciated.  Thanks,
ishvaaag (Structural)
25 Mar 11 19:17
The rate of change of longitudinal stress in the flanges will account for the neccesary connection to the web at the point. So you divide in segments, and examine for each segment and relevant hypothesis what is the maximum difference of force at the ends of the segments in the flange, then such is the capacity required to deliver within the segment length. Of course add a safety factor.

If,a ssditionally there are other meaningful stresses standing (say, pass a normal load) a interaction stress etc need be accounted to meet the interaction, as in any weld.
Lion06 (Structural)
25 Mar 11 19:57
Here are my thoughts.  If you have a properly sized cap plate then the weld only serves to keep the parts together, not to transfer any load.   What I would do, however, is provide enough weld top and bottom to develop each flange and then provide and intermittent fillet along the height.  I wouldn't provide a full height fillet weld on the four locations you show.  
hokie66 (Structural)
25 Mar 11 22:49
Agree with PA, unless the column is external or in an industrial environment subject to impact, in which cases I would weld it full length.
JAE (Structural)
25 Mar 11 23:00
For the column to function as a unit (3 plates = 1 shape) then the column must be able to resist buckling overall...and also each plate must be braced by the remaining shape to avoid local buckling.

For buckling overall, the deformed shape of a buckled column creates a moment curve along the length.  The critical buckling load P times e.  I believe this creates a shear along the length which, using VQ/I allows you to develop a weld pattern - like PAStruturalPE suggests - full length at the ends and stitch welds along the main length.

I'm away from my books right now but I believe you should NOT treat this as a pure axial loaded column (i.e. the welds only in longitudinal compression).  They will see shear if the column buckles and you must ensure that the parts work together in order to use the r value for the whole shape.

smitty9898 (Structural)
26 Mar 11 13:13

Thanks to all who posted.  The responses are of great help.  Here is my response.

I don't believe it is possible to determine numerical values for the curvature of a buckling column.  I can determine the theoretical buckling shapes for a buckling column (i.e. "k" values), but an actual maximum deflection of a buckling column cannot be determined.  The maximum deflection is required to determine the moment on the column (i.e. the M=Pe equation).

I understand that there are eccentricities due to lateral loads, initial curvature, connection eccentricities, etc.  I can determine the shear loads on the welds from these eccentricities.  However, I'm trying to determine the shear load on the welds from buckling only.   

I also understand that there can be localized buckling of the plates, if the weld spacing is too large.  This can be solved.

At first I thought this would be simple, but I'm finding out this problem may not be solvable.  See reference to Eurocode below.  It says nothing about accounting for shear from buckling.
Lion06 (Structural)
26 Mar 11 14:07
I think that ( I would appreciate others' insight on this thought) if you provide enough weld top and bottom to fully develop each flange, that you have,
by default, covered VQ/I hear flow for any load that won't overwhelm the total section as proportioned.  Once that is met, I believe as long as you meet AISC's requirements for welding of built-up compression members that you're covered (kl/r of any component < 0.75*kl/r of gross section).

As far as the buckling consideration, if buckling is a failure, is there a reason to design a weld to resist those forces if the gross section is unable to?  Additionally, and maybe I'm remembering my mechanics incorrectly, but I don't believe that buckling of a column is associated with a finite lateral displacement.  The column buckles because the lateral displacement is infinite (theoretically) because the section is unable to resist the moment (Pe) once an initial displacement occurs).

Am I mistaken with any of that?  
ishvaaag (Structural)
26 Mar 11 17:29
For a just axial load (assuming buckling) in just one plane, it comes a moment where the lateral deformation causes the load to be critical. You have then P·e moment at center, 0 moment at ends. Material nonlinearity is covered by the usual reductions of the applicable "modulus of elasticity". And initial imperfection is just one e0. Hence with some rational reduction you can venture what the moment is at center at the critical state, and so what "shear from buckling" you require, to proportion between end and center, whay you can do "elastically" (more where thre rate of change of moment is bigger a ends) of in a plastic disribution over half length.

ishvaaag (Structural)
26 Mar 11 17:43
In a further simplification (conservative to your purpose) the flange will attain at center its nominal capacity at Fy (it may need not go as high to bend-buckle). Then develop in shear the capacity of the flange between end and center.
ishvaaag (Structural)
26 Mar 11 17:52
Correction, the average nominal capacity in compression needs not to go as high as Fy (or nominal yielding value) to get bend-buckling. One side at least of the member needs to be yielding to be buckling critically in practice. For the doubly hinged case we may still not know what the axial force corresponding to such flange is at end; we may assume that if in single curvature, a value less than Fy, and conservatively, we can assume zero, of course a conservative approximation leading to the same practical rule stated in my previous post.

What for a more exact determination of the required size of the welds even on rational simplification asks (if more precision is required) for a definition of how the load at the ends is being applied, and a rational evaluation of the change of the stresses whilst growing to the critical state.
smitty9898 (Structural)
26 Mar 11 17:54
Ishvaag – I'm not following you.  I've attached a sketch of a simple column with some numerical values.  Can you solve for "e"?  I'm assuming the column is perfectly plumb and straight, and the load is applied at the center of the section.
I still don't know how a moment can be computed from a buckling load?
smitty9898 (Structural)
26 Mar 11 18:12
PAStructuralPE – For your first part of your response, I would recommend checking out Jack McCormac, "Structural Steel Design" book on GoogleBooks.  Start around page 174.  It's a great resource for this topic.
I think your statement "I don't believe that buckling of a column is associated with a finite lateral displacement."  is correct.  Once the overall column begins to buckle, its going to fail.  The eccentricity is irrelevant at that point, which is why I don't believe there is a calculable moment from the buckling load.  Not sure?

I'm thinking the necessity for welds along the length is for the following:  prevent local buckling of each individual plate (so that the buckling load for the overall section can be reached), resist moments/shears from lateral loadings, and resist moments from physical eccentricities (i.e. load eccentricity, imperfections in plumbness, etc.)   I might be way off, I'm still looking into it.

I'm trying to analyze an existing column that was built prior to AISC requirements.
RFreund (Structural)
26 Mar 11 19:14
I haven't read all the posts above so I apologize if this has been recommended.  However look in AISC manual in built up columns and they will give the max distance between intermediate welds.  Also gives you an equation for a modified KL/r.  Also need to check individual member buckling.  They give some commentary I believe on shear flow between the members.  The problem is what strength of the weld is required.  I believe I actually asked this question here some time ago.


RFreund (Structural)
26 Mar 11 19:22
Sorry should have read the above comments.  Much better insight than my comment.


BAretired (Structural)
26 Mar 11 23:30
If we are talking about a slender column (elastic buckling) there is no specific eccentricity associated with buckling.  When load is increased to the point where an ininitesimal deflection is precisely held in equilibrium by the load, that is the critical load.  Any increase in load will cause deflection to increase without limit and the member will buckle.

Critical loads can be determined by numerical methods or, in simple cases, by closed form theoretical solutions as found in numerous text books.

I don't believe there is a shear requirement in the weld, but I agree with those who say that the spacing of the welds has to be such that individual plates have a kL/r less than the main member to prevent individual plate buckling.

For intermediate columns, the situation is a bit different because inelastic buckling is involved and short columns don't buckle.


SAIL3 (Structural)
27 Mar 11 15:45
Lets assume that all the local buckling of the col. elements have been adressed as mentioned in the previous posts.
This still leaves the question of the overall stability of the column as awhole.
To me, the concept of stability infers the ability to recover from or absorb a destabilizing event...lets say in this case an initial lateral deflection "e".
Addressing all of the local buckling concerns does not guarantee this.
To this end, the min shear requirement from VQ/I mentioned by JAE
still leaves the question of what value of "V" to use in designing the welds.
Here is how I would try to approach it, right or wrong.
To get a handle on the value of "V", I would look at the col. as a bm and assume a unifrm load on this beam that would represent, say, 25% of the capacity of the bm(without any axial load).
From this, I would get a value of "V" and then design the welds for the shear from VQ/I plus the axial load in the col.
To check if this assumption of 25% is reasonable, I would get the corresponding deflection of the above bm under this uniform load and evaluate it. If it turns to be equal to:
l/500....not good, try a loading of 40%
What I am looking for here is a certain level of robustness or margin of safety.
Ofcourse,in the real world,I would do as PAStructural suggested and move on.
JAE (Structural)
27 Mar 11 17:30
SAIL3 - that might be a rational approach.  I never meant to imply above that you knew what the "e" was and therefore could determine a buckling moment.  Once it buckles there's no static moment so I agree with the posts above.

I thought there was a way to determine a force difference between the flange and the web - assuming you engage in Af x Fy of the flange and ensure that the welds can transfer that force to the main body of the column.   
BAretired (Structural)
27 Mar 11 19:20
If the load is applied by a rigid block hinged in the middle and straddling the full column section, all plates are loaded simultaneously.  There is no shear flow and welding is required only to limit the kl/r of the individual plates.

If the load is applied to the web and not to the flanges, then welding is necessary in the end regions to transfer the load from the web to the flanges.  Those welds will carry shear, but there is no shear flow because V = 0 for the full length of the column.


To me, the concept of stability infers the ability to recover from or absorb a destabilizing event...lets say in this case an initial lateral deflection "e".
Addressing all of the local buckling concerns does not guarantee this.

Why does it not guarantee this?  If the load is below critical load, then I believe it does guarantee this because every fiber of the built up member has the same strain energy as the equivalent fiber of a solid beam section.  The bult up member cannot buckle.


smitty9898 (Structural)
27 Mar 11 22:09
RFruend – Excellent reference with your prior post.  I would recommend everyone check out the following link. I'd also recommend downloading the article, if you have access to it.

JAE (Structural)
27 Mar 11 22:20
Here is the Modern Steel Construction Magazine Q & A on the question that the original poster presented:

Modern Steel Construction Q & A link

They refer you to an AISC Engineering Journal article from 1992:

"Analytical Criteria for Stitch Strength of Built-Up Compression Members" (Engineering Journal, 3rd quarter, 1992)

This can be downloaded from AISC's website

AISC Engr Journal 3rd Q 1992 link

smitty9898 (Structural)
27 Mar 11 22:21
If you notice on the Aslani + Goel equation, the force on the intermediate connecter is independent of the applied load.  

Therefore, I think it can be assumed that there is no load on the weld until the buckling load is reached?  Not sure.
ToadJones (Structural)
28 Mar 11 8:46
Size end continuous weld for MQ/I
Size intermittent weld for VQ/I

M=SxFy * allowable factor (say 0.66) with Sx being for the entire section.

To get V:

M=PL/4 (simple beam point load analogy)

P= 4M/L

V= P/2

Use Blodgett's percentage charts to size your intermittent weld based on the size of the continuous weld.

If your application is very light, this is probably a conservative approach.

I tried it for 20'-0" long column with 1/2" x 8" flanges and 1/2" x 7" web of A36 steel and got continuous 1/4" fillets at the ends for 12" and shear flow of 1.5 k/in along the length...pretty low numbers
ToadJones (Structural)
28 Mar 11 8:55
You cannot load a column without any eccentricity. It is virtually impossible. Even simple shear connections will induce a small moment in the column.
SAIL3 (Structural)
28 Mar 11 9:58
BA--you bring up some interesting points, all good.
To my simple mind, the concept of stability is as follows:
Stability is not a load is more a capacity condition which is measured by Kl/r.
In using Kl/r of the entire X-section, it assumes that all elements of the X-section act together as one unit or has the capacity(reserve) to resist the particular mode of buckling under consideration.
If the potential buckling mode of the WF is in the strong direction, it implies potentail curvature in that direction and hence the development of this shear flow "V".
Wheather the col. will ever have to use this capacity is not the issue.
If, for some reason, one does not choose to use the full deveopment of the flanges in calculating this "V" as an upper bound, the question still remains...what value of this "V" would one use so you can sleep at nite?.
ToadJones (Structural)
28 Mar 11 10:41
this column will have shear flow as it will be impossible to load without inducing bending.  
BAretired (Structural)
28 Mar 11 11:27
I agree with Toad that it is impossible to load the column without bending, but bending does not produce shear flow.  Shear produces shear flow.  

A column with hinged ends, loaded axially will develop a small bending moment if the member is curved, but it will not develop horizontal reactions at the hinges.  The only shear it will have is P*α where P is the axial load and α is the angle in radians from a plumb line.

However, I was not aware of the Aslani Goel equation and will have to think about that a bit more.


ToadJones (Structural)
28 Mar 11 11:29
BA is correct.
However, if there is an eccentric load, there will be shear.  
ishvaaag (Structural)
29 Mar 11 5:18
This time and a rare one I have to partially diverge with BAretired. You might (theoretically) load the column without eccentricity, but what those dealing with buckling came to understand is that there must be "some" initial eccentricity causing what is then called "buckling". Giotto in the Quattrocento draw the column breaking that way, and in the 1700's Euler gave the basic numbers to it. Upon the bending of the column, it would be rare that a constant moment develop, in fact it is stated as P·e with e varying (and zero if and where hinges), and as soon as there is moment variation there is shear transfer between the web and flanges. This is just to remember the drawing with the stresses in the most stressed part of the buckling member of the early XXth century.

The determination is precisely by the numerical methods referred by BAretired. I purchased the book by Godden someone recommended  me and made some Mathcad 2000 worksheets on it. I post a pair of them for constant section members, one gives the elastic critical load Pcr and the other an in-plane Bend Buckling Strength "Pn" that still lacks the influence of local and torsional buckling.

In them it is clear that an e can be determined and is key precisely to the evaluation of the critical or limit loads on buckling.  
csd72 (Structural)
29 Mar 11 6:34
I think what the OP meant was that the question referred to the component from a purely concentric load as he understood the shear flow component.

I dont think they actually meant that there was no eccentricity.

I understand the reason for the qustion as it is not very intuitive but I think BA hit the nail on the head with his first post.

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