Should we respect the ratio 1.4 second order over first order for columns carrying only axial loads ?

[structural87]

hello
In section 10.10.2.1 of aci 318-11, it is stated that the ratio of second order to first order moments should not exceed 1.4.
I have a special reinforced concrete shear wall system where i am hinging the columns at their top and bottom so they can take only axial forces and relying solely on the walls for seismic resistance.
In this case, should this limitation of 1.4 still be respected since I don't have end moments at the columns top and bottom except the minimal eccentricity ?
I am using the software Etabs and this latter calculates the delta-ns to cater for small P-delta and provides an error message once the delta-ns > 1.4 while still showing that the percentage is within the limits even by magnifying the minimal moments.
Thx in advance for your input

 

[271828]

Are you saying these columns with hinged ends have a P-little delta amplification exceeding 1.4? If so, then that would be very unusual unless the column is very long and slender.

What moment is being amplified -- the end moment due to a minimum eccentricity?

 

[structural87]

Yes this is correct. Not that slender I would say. i am talking about a column 800x250mm and delta-ns is coming large > 1.4.
The minimal moments are amplified but still within the P-M interaction curve.
The problem is that even if the moments are still within the interaction curve, from the moment that delta-ns exceeds 1.4, we need to enlarge the section and this is what i am asking about.

 

[Agbsh]

Always, there are 2 nonlinearity working together, the big P-Delta at story level and small P-delta for individual column buckling. For braced frame, the first could be ignored, however the later is indeed applied. Here the code gives you multiple options: either conservative method (the magnifier, delta_ns), or truly capture the effect by dividing the column to multiple segment. Either option you choose, 1.4 limit is to keep drift under 0.25, and that is not a small number at all and approaching it shouldn't be taken lightly. Actually the code goes little bit further to 1.4 instead of 1.33 corresponds to (1/(1-0.25)). Explore the options to increase (EI)_eff, hence higher Euler load and less delta_ns, in case you want the conservative method, this worked for me in many cases.

 

[desaut]

hello
In section 10.10.2.1 of aci 318-11, it is stated that the ratio of second order to first order moments should not exceed 1.4.
I have a special reinforced concrete shear wall system where i am hinging the columns at their top and bottom so they can take only axial forces and relying solely on the walls for seismic resistance.
In this case, should this limitation of 1.4 still be respected since I don't have end moments at the columns top and bottom except the minimal eccentricity ?
I am using the software Etabs and this latter calculates the delta-ns to cater for small P-delta and provides an error message once the delta-ns > 1.4 while still showing that the percentage is within the limits even by magnifying the minimal moments.
Thx in advance for your input

If ETABS doesn't show the moments doesn't mean that moments do not exist. As others pointed out there are always imperfections (out of plum and local) and eccentricities of load application causing moments. The ratio of second to the first order moments is just a measurement of stiffness. Building codes in other countries give slenderness or ratio of axial to buckling critical load as means of assessing stiffness.
You need to apply the minimum moments provided in the code.

 

[271828]

A P-little delta amplification of 1.4 is not believable for a column with regular proportions. If the column was very long and skinny, and loaded near buckling, then maybe.

Recommend you calculate the P-little delta amplification factor (B1 in AISC) and compare to what ETABS is reporting.

For a column with hinged ends, with single curvature bending and equal end moments:

B1 = 1 / (1 - P / Pe)

where:

P = column axial force for the load combination being checked

Pe = π^2 E I / L^2

 

[271828]

Are you getting 1.4 for all columns in this story? If so, then it sounds like the P-big delta amp.

A column with a hinge on both ends would not have any P-big delta amp.

 

[structural87]

Are you getting 1.4 for all columns in this story? If so, then it sounds like the P-big delta amp.

A column with a hinge on both ends would not have any P-big delta amp.

no only for one column. as i mentioned before, the columns are pinned for seismic resistance. the issue is the small delta.
after i run a few calculations, the column is loaded to its 25% of 0.75 Pc which is fair.
The factor affecting the calculations is the Cm considered as 1.0 once the delta-ns > 1 and 0.6 if the delta-ns is less than 1.0.
This is a conservative approach used by the software when there is no end moments in the column.

 

[271828]

Did you manually compute B1 and compare?

1.4 is not believable, even with Cm = 1.0, which is likely correct.

 

[271828]

I get the following. Unless my assumptions are way off, it's not believable that the P-little delta amplification is 1.4 for your column. You'd have to crush the column first -- with my assumed values anyway.

 

[structural87]

I get the following. Unless my assumptions are way off, it's not believable that the P-little delta amplification is 1.4 for your column. You'd have to crush the column first -- with my assumed values anyway.

Thanks for the effort but you forgot to multiply your flexural stiffness by 0.4 and then divide it by 1+beta to consider the effect of cracking & creep inside the concrete.
if you do the math, you will notice that you will reach quickly the 1.4.
f'c = 35Mpa -> Ec = 27805 Mpa
EI(eff) = 6330.8 kN.m2 considering of beta of 0.83
Pc = 6935 kN
Pu = 1500 kN (20% of critical Euler force)
delta-ns = 1.4

 

[271828]

Awesome. Thanks for clarifying that.

Just for my curiosity, how long is the column?

 

[structural87]

3 meters clear height so not that much. this is a residential building.

 

[271828]

I know you used hinges at each end as your design model. Does the column have some continuity with beams or slabs at the ends?

Edit, to close this out on my end:

If the column is hinged, then I would not feel comfortable with the design. At 250 mm (9.8 in.) wide and 9 m tall, it's fairly slender, and the 1500 kN (337 kip) load isn't small. A second-order amplification of 1.4 is pretty extreme IMO.

If the column has significant continuity, its buckling strength is much higher than computed so far, so the second-order amp would be much smaller. OTOH, the moments at the bottom and top of column would probably be larger than what's in your current calcs. To resolve this, I'd run it with continuous top and bottom to be sure.