BUCKLING FEA - The case of a 'pinned' base plate 4

[human909]

One thing that I've often been curious about is the buckling behaviour of a nominally pinned column under compression with a typical 'pinned' base plate.

Examples:

For both of these I would consider these as 'pinned' connection and model them as such. Thus I'd would get zero moment transfer and effectively length of 1 if top of the column is braced but with no rotational restraint. As I understand it this is a pretty typical analysis approach under most codes and in most jurisdictions.

My question is:

Is this overly conservative? Would the compression and flat base plate not provide a degree of fixity and thus improve the critical buckling load? Here I define here a baseplate that is resting on a foundation but not restrained from uplift as a SEPPERABLE BASE PLATE.

It would surprise me if there isn't already plenty of literature on this matter. But I've never seen it. So I'd though I'd test it. And since I don't have a test laboratory at hand I figure I'd use FEA.

TEST APPROACH
-Non-linear plastic FEA analysis using NASTRAN
-Tri linear model of stress-strain curve used
-Iterative approach to converge on buckling solution (NASTRAN does have non-linear buckling analysis but not nonlinear PLASTIC buckling analysis)
-An additional lateral load of 1% of axial load was added to trigger the buckling. (This value is arbitrary but considered reasonable and conclusions not sensitive to this.)

TEST DETAILS
-Steel section: HEB160 S275 (EUROPEAN STEEL)
-Section length: 6600mm
-Minor axis translationally fixed, translationally fixed at the top, rotationally free.
-Base plate modelled in 3 ways; perfectly pinned; able separate but not slide AND; rigidly connected to foundation.
-Nominal mesh size - 50mm

CODE BUCKLING LIMIT:
Ncx = ~780kN (without any capacity reduction factor, both codes AS4100 and Eurocode within 2%)

FEA RESULTS
PINNED: Ncx = ~800kN
BASE PLATE (with sepparation): Ncx =~1150kN (equivalent le = 0.83)
BASE PLATE (RIGID): Ncx =~1150kN (equivalent le = 0.83)

As can be seen no discernible difference (<1% tolerance) between the rigidly connected base plate and a base plate with no uplift restraint.

CONCLUSION
In some/many circumstances it is not unreasonable to consider a typical column and base plate arrangement as 'fixed' for consideration of its buckling effective length. Without doing exhausting further testing I would suggest that this is reasonably representative for columns of 'intermediate slenderness' where inelastic buckling dominates.

ADDITIONAL TESTING
I was a little perturbed by the lack of discernible difference between a rigidly fixed base plate and one that is able to separate from its support. I hypothesised that this was due to inelastic buckling dominating before any appreciable rotation could occur at the base. This was tested by doubling the length of the HEB160 to 13200mm. To summarise this additional testing:
PINNED BASE = 275kN (Unreduced capacity in code 250kN)
BASE PLATE ON SURFACE = 460kN (equivalent le = 0.77)
FIXED BASE PLATE = 500kN (equivalent le = 0.74)

It was satisfying to see that for more slender columns the back calculated effective length approached the theoretical Euler elastic theoretical length. It was also satisfying to confirm that a fully fixed base base does exhibit better performance (as expected) compared to a separable base plate.


And here is a pretty FEA picture to keep everybody happy:

 

[KootK]

The soil and footing are common to the case of a conventional rigid connection. If we can't rely on them then the discussion is over AFAIC.

Fine, but not very "proofy". As I mentioned earlier, your conventional, rigid base connection is usually designed for load cases that are usually transient and short lived and, thus, not punishing from a creep perspective.

Creep will even out the stress in the grout. We get the good with the bad.

It will even out the stress but, in the process of doing so, you'll still wind up with more rotation than you would have if the stresses had been truly uniform to begin with.

It's not my intention to insinuate that I really think that creep is a big deal in this situation. What I am suggesting is:

a) That it's complicated.

b) That it's interesting.

Another interesting aspect of all this is that the efficacy of the base restraint will mostly be about the stiffness of that base restraint. A stocky column would require greater rotational restraint stiffness than would a slender column. So the real metric of interest, I think, would be the ratio of required base rotation stiffness to provided base rotation stiffness.

 

[human909]

I disagree. Consider:

1) Creep in concrete occurs at even very low levels and;

I understand that however, like I said:

Quote (human909)
If creep was a factor we'd be seeing our buildings all the time.

I don't think that's true because:

3) The overwhelming majority of columns are designed K=1.0 and, so, do not depend on the presence of base rotational restraint.

I agree that the overwhelming columns are DESIGNED for k=1.0. However as demonstrated the base for a column that is largely axially load displays behaviour that close to a rigid connection than a pinned connection. The k value that the actual column is designed for is irrelevant what is relevant is whether the moment from eccentricity or other source is being transferred through the base plate.

My analysis as well as gusmurr's analysis shows that this moment is being transferred ALL the time and not just in peak loads or transient loads.

Though I'd welcome your comments on why you believe that moment isn't being transferred.

 

[KootK]

Though I'd welcome your comments on why you believe that moment isn't being transferred.

I never said that moment wasn't being transferred. What I said was that there need not be any first order moments, due to load eccentricity or anything else, for my arguments regarding creep to have validity. Initial imperfections and secondary effects will produce the base moments that I've been discussing.

However as demonstrated the base for a column that is largely axially load displays behaviour that close to a rigid connection than a pinned connection.

I agree and never said a word to the contrary. All that I said was that base rotational creep may be one of the factors, along with elastic flexibility, that keeps the base connection from being fully rigid.

The k value that the actual column is designed for is irrelevant what is relevant is whether the moment from eccentricity or other source is being transferred through the base plate.

My understanding of our prior discourse here is this:

1) I brought up creep as a potential, complicating factor that would reduce the effective, rotational stiffness of the base joint.

2) You said that, if creep were an issue, we would see real word evidence of it.

3) I pointed out that we would not reasonably expect to see real world column stability problems associated with base rotational creep because:

a) most columns are designed to K=1.0 and

b) the stability of K=1.0 columns would not be compromised by the absence of base rotational restraint.

In this context, the K-value associated with design is not just relevant, it's paramount.

 

[human909]

b) the stability of K=1.0 columns would not be compromised by the absence of base rotational restraint.

In this context, the K-value associated with design is not just relevant, it's paramount.

It is paramount if we are talking about structural failure. It isn't paramount if we are just talking about observation of rotational effects of long term moment loading. This isn't something that is often seen. And structural loading clearly IS something all our buildings see. And we both both ultimate loadings is likely something that our structures rarely if ever see.


EDIT... I've avoided using creep because I believe foundation movement and settlement would generally play a bigger role in revealing and (if large enough) partially relieving an applied moment. However I would expect than in most cases it simply isn't large enough (I haven't calculated it). If we got large rotations we've be seeing it more between our slabs and isolated footings in the for of cracks.

And yes I've seen slab cracking when the underlying footing has rotated when a "nominally" pinned column rotated under excess loads. The entire footing rotated and largely returned to original position. The evidence it left was a cracked slab and buckled roof membrane that failed lead to the column to rotation.

 

[Settingsun]

KootK, I think your base pressure sketch is too lumpy. It looks more like a force distribution with the peak under the flange on the side that's rotating upwards. I would expect less sudden variation, more like Gusmurr's from 3 November. The support in that analysis was described as stiff. Hopefully Gusmurr is reading and will clarify how stiff.

I waved away the soil stiffness because it's commonly taken into account using the K charts. The creep angle is interesting but I think I've put an order of magnitude on it. Multiply 1/1600 rotation by 3EI/L for the HEB160 example and you get 1.4 kNm relaxation, about half being from creep. Small compared with the 40+ kNm restrain that can develop and did in Human909's analysis.

I'm also not necessarily convinced that fixed bases usually have negligible sustained moment. They'll tend to attract it from dead loads.

 

[human909]

I'm in agreement with most of Steveh49s comments. Though I do welcome contrary opinions, so go nuts kootk.

I want to add more calcs and more modelling on this thread but I expect that will be weeks away. I am travelling at the moment.