Column Design: Minimum moment and biaxial bending

[N.K.]

Hi Guys,

I am currently designing a rather slender column with a very heavy load on it, Upwards of 1MN. I just wanted to ask people's opinion on designing this column for minimum moment.
Due to the size of the column the minimum moment eccentricity exceeds the allowable tolerances stipulated in the code. Does the minimum moment still need to be applied fully? I do not think such a deviation in straightness should even be allowed for such a heavy column and therefore I think the minimum moment may be excessive.
Furthermore, would we check the column biaxially for minimum moment (when magnified). The way I understand it is that each axis needs to take a nominal moment but I did not think that also applies biaxially. If I was to resolve the biaxial minimum moment into eccentricity then it is very slanted.
Any advice would be helpful. Thank you!

 

[Strook]

1 MN, that's some load.

100mm from the face of the column, or at the centre of bearing, whichever is greatest, is what I'd take the eccentricity to be for your column axial design load(s). This is backed up by AS 4100, my local code. EDIT: There is provision for column caps/direct bearing situations to consider the eccentricity as acting at the face of the column. If you were to provide more information, it might be possible to recommend which approach is more suitable.

Generally this eccentricity is applied in the direction of the supported span, but suppose you have two supported spans perpendicular to one another, then yes you'd arrive at a bi-axial bending column case.

 

[N.K.]

Hi Strook,

This is actually a concrete column supporting a massive structure at the bottom levels. Its a 2m by 2m concrete column. It is a very slender column so moment magnification is is pretty big.
In my mind it makes sense to limit the minimum moment provisions after a certain size of column (0.05xDxn*). However, I am not 100% sure.

 

[dik]

If very slender, how tall is it for a 2000x2000 section? and what sort of restraints does it have? That load is only about 250K (1MN - I think in Imperial), and the concrete stress level is about 50 psi which is not high (sans moment). What strength of concrete? I've done a few columns of that size and you can feel the heat come off them for a week...

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

-Dik

 

[Strook]

Big column. I fail to see why the design eccentricity shouldn't be related to the scale of the column. Sounds like a case of trying to convince yourself the reverse or otherwise is true, simply because it suits your current situation. Dangerous game to play.

 

[N.K.]

Hi DIK,

Its 20m high 100 MPA. Its a pretty scary colun to deign to be honest.

Hi Strook,

I say that because there is a point when the eccentricity you design for seems unrealistic. I ask this because for the case of this column 100mm eccentricity for a 20m column taking 1MN is a bit large, dont you think.

 

[dik]

That's pretty tall... what sort of restraints top and bottom? and, how is the moment being applied?

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

-Dik

 

[Settingsun]

The axial stress is quite low, and it's not all that slender unless it's a cantilever (?).

Nonetheless, apply the minimum for each axis. The code doesn't provide a relaxation regardless of what the (old...) commentary says. Assuming AS3600 based on the location in your profile.

Edit: is it even relevant? The minimum moment only stops you using the very top of the interaction diagram. Your axial stress is low. The column itself weights 2MN so the applied load is nothing.

 

[Trenno]

Using the rule of thumb: Stocky columns 0.5*f'c at Le/r=20 then Slender columns 0.4*f'c at Le/r=35 ; 0.3*f'c at Le/r=45 ; 0.2*f'c at Le/r=60 and 0.05*fc at Le/r=100

ULS stress = 1000 kN / 2000*2000 = 0.25 MPa (very low at 0.025*f'c)
Assuming pin-pin, your Le/r = 20 000 / (0.3*2000) = 33.5 (not overly slender...)
So your rough capacity is 0.4*100*2000^2 = 160 MN

Obviously this is an edge case and second order effects and biaxial interaction may well bring the utilisation much higher.

 

[N.K.]

Ive gone and made a fool of my self 160MN (160000kN) is the actual load. Sorry guys I typed it wrong. No wonder noone was as worried about it as me.

I've assumed pin-pin for this column.

 

[Strook]

160MN, now that clears a few things up. It sounds from Trenno's buckling calculations you're close to the limit, not to mention the moment at play due to axial eccentricity, which will surely bring the column over capacity.

Sounds like some serious review of end restraint/ column sizing is due, but I don't see a valid reason for lowering the eccentricity.

Keen to hear from others if they've worked on columns of this size with experience reducing the design eccentricity and reasoning & in-service evidence of the design down the track.

 

[N.K.]

Yeah sorry about, i was quite confused when everyone thought it was nothing. The axial load alone pushes moment magnifiers too high. Otherwise it could work.

 

[Trenno]

Assuming pin-pin, min moments and near 4% rebar (say 120no 40mm bars in 2 layers) the column appears to work very hard with an amplified moment of around 30MNm. It appears to be valid design though.

 

[Settingsun]

I quadruple checked before replying before, was sure I must have been off by a factor of 10/100/1000.

I don't see a way around the minimum moment if you must comply with AS3600 or AS5100. Neither seems to state the requirement in negotiable terms. Sharpening the magnified bending moment with rigorous analysis would be the path IMO if the column can't be made larger. And a proper design review, of course.

 

[HTURKAK]

Still i am not sure for the figure 160MN is correct.. Let me explain, this could be the service load of 30 storey bldg with 500 m2 storey areas..

If the figure is correct, you need to increase the size of the column. Assume the concrete class C 35 , for stocky columns, the column area (Ac) for 3% steel ;

Ac = N/22 =160000000/22=2800 mm X2800 mm

Will you pls explain the origin of this load and the use of column 2m X 2m dimensions?..

 

[dik]

that's why we need to know how the load is applied and what the restriant conditions are to maybe provide a little guidance.

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

-Dik

 

[dik]

What concrete strength can you reliably use? and what strength of reinforcing is available? >400MPa? With heavily loaded columns concrete and steel strength plays a big part... can you get 40 or 50 MPa concrete? Can you use steel? Make for a much smaller footprint...

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

-Dik

 

[KootK]

I do not think such a deviation in straightness should even be allowed for such a heavy column and therefore I think the minimum moment may be excessive.

Obviously your governing code says what it says but, logically, I'm inclined to agree with your intuition. Unfortunately, the appropriateness of a relaxation is a function of what the intent of the code provisions were intended to address to begin with. And I've not seen a great explanation of that in my travels. Some food for thought:

1) If the name of the game is primarily about addressing the eccentricity of the applied load, then I absolutely can envision situations in which the code requirements would be excessive for a column of the proportions that you're considering. I suspect that those requirements were developed with more conventional proportions and framing situations in mind. As dik intimated, we'd need to know more about the source of the load and the nature of the framing conditions at the top and bottom of the column in order to render an informed judgment.

2) To the extent that the code requirements are intended to cover eccentricity arising from imperfections and misalignment in the column itself, I don't feel that a relaxation should apply.

3) To the extent that the code requirements are intended to cap the applied load, as a ratio of the squash load, to a reasonable maximum to prevent slenderness effects from going nutso, I don't feel that a relaxation should apply.

ACI 318 allows one to analyze slender columns using a true second order analysis rather than moment magnification. The handful of times that I've taken that approach, I've been astounded by how much it improves the results. This is probably the approach that I'd be taking for your situation. Even if it's not officially sanctioned by your governing code, it might give you some valuable piece of mind on the design of a member coming out marginally acceptable per your codes requirements.

 

[dik]

Did you sort that out? Do you have an actual moment at the top/bot? In Canadian codes, you can run with a minimum eccentricity of 5% if memory serves with conditons... will have to check that out.

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

-Dik

 

[dik]

Does anyone know if there's a maximum concrete strength that CSA A23.3 uses for columns? I couldn't find one. Found it 8.6.1.1... can use 50 MPa to as high as 80 MPa with qualifications... also can use up to Grade 500 for rebar... will try with 50MPa and 500 to see where it lands...

Based on CSA there is a real problem with the load, let alone any moments and I need to see if I can increase the concrete strength to maximum... for 'kicks', I'm writing an SMath program for this...

Without reductions, it squeeks by with 4% reinf @ 500 Grade and conc @ 60 MPa... Haven't checked the calcs and now looking at slenderness issues... Can you stagger rebar splices to go greater than 4%?

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

-Dik