Slenderness bound

[ZoranB]

I'm from Europe (not using ACI Codes) and working on a paper dealing with slender columns design.
I need a help concerning some ACI regulations.
I guess that ACI prescribes a bound when second order effects need not to be taken into account when designing RC columns.
EuroCode says:
second order effects may be neglected when:
lambda < 25 or lambda * SQR(ni) < 15,
where
lambda is slenderness of a column,
ni is relative axial force.
Can someone tell me how is it defined in ACI?

thanks in advance

 

[Qshake]

ACI Section 10.11.4 explains that slenderness can be neglected for compression members braced against sidesway when the slenderness ratio, k(lu)/r is less than
34-12(M1b/M2b). And for compression members not braced against sidesway, k(lu)/r is less than 22. So for slenderness ratios larger than those prescribed above for the given bracing slenderness must be considered.

k is the effective length factor
lu is the unbraced length
r is the radius of gyration

M1b is the smaller factored end moment and
M2b is the larger factored end moment

Also note that approximate methods are allowed by ACI for slenderness ratios up to 100. When the ratio is greater than 100 a rigorous analysis must be performed. This would be Pdelta analysis. Nowadays, it is more common to use the PDelta analysis for all situations just because it is more commonplace in our structural software. Though for smaller structures where the computer is not used in analysis moment magnification is still favored.

 

[ZoranB]

Thanks Qshake for a quick answer. It was really useful.

I've got one more question.
Are there any suggestions in ACI how to determine effective length of a column.
I've understood that for columns in braced structures one should use conservative value of k=1.
But, how do you usually determine column's k-factor value in unbraced frames in order to compare it to value of 22?
We (in Europe) use (in absence of more accurate methods) nomograms or approximate equations.

And one more question.
When using P-delta method, how do you apply effective stiffness (taking into account cracks, duration of load...).
Section 10.10.1 (I'm reading ACI 318-75 ) says that accurate (rigorous) analysis should take those effects into account.
Which software do you use?

Sorry for bothering you.

 

[HochwaltPE]

In the US we also use nomographs for the determination of k's. The nomograph appears in the ACI commentary which for the 77 code was in a separate document from the code itself. In the 1999 ACI the code and commentary are in a single document.

ACI also has specific recommendations for cracked section properties. Historically, guidance on cracked properties appeared in the commentary, but in 1995 it was brought into the body of the code itself. The code also includes an additional requirement to reduce these stiffnesses further when sustained loads act.

If you really want to compare slender column design in the US with that of Europe, it's essential that you work with the 1995 or 1999 versions of the ACI code. Slender column design is one of the areas that have seen the greatest change since 1977.

 

[ZoranB]

Thanks.

OK. I see - I'll buy newer ACI code.

But, meanwhile, please answer the following question:
What criteria ACI prescribes to determine whether the structure is braced or not against sidesway?

In SAP2000 manual, I noticed that it uses PDelta analysis to classify structure as braced or non-braced. Are there any simpler criteria?
I'm dealing with necessity of taking into account second order effects, so Pdelta analysis is the one that I'm trying to avoid (if it could be avoided). I guess there must be something like &quot;structure is assumed braced against sidesway when...&quot;.


Thanks again

 

[JAE]

There is!!

Look in ACI 318-99 or 318-95, section 10.11.4.2

Or, for ACI 318-89 (rev 92), see the commentary on secton 10.11.2.

Both of these provide a limit on when PDelta moments are significant, i.e. whether you have a sway or non-sway frame.

 

[ZoranB]

Well, wasn't that obvious from previous message that I still don't have newer ACI code?

I will buy them, I promise, but could you tell me the answer now. If I would have code i wouldn't ask it at all.
It takes some time to get those codes (few weeks).

thanks

 

[HochwaltPE]

The portion of ACI 318-99 that JAE referred to tells the designer to calculate an index &quot;Q.&quot; If Q is less than 0.05 for any given story, then that story can be considered braced. Q is calculated by (Sigma Pu x Delta0) / (Vu x lc ) where:
Sigma Pu = the total vertical load at the story (ultimate)
Delta0 = the first order story displacement due to Vu
Vu = the story shear (ultimate)
lc = the center to center column length

 

[ZoranB]

Thanks again.