AS3600 elastic analysis with secondary bending moments

No, moment magnification accounts for the slenderness of columns. Even after the P-delta analysis is performed, it doesn't allow that every column is then considered stocky, when the Le/r > 22 than moment magnification needs to be applied.

Clause 10.2.3 of the code (Design procedure using rigorous analysis) specifically states that where a "rigorous analysis" is carried out then "a column shall be designed in accordance with Clause 10.6 and 10.7 without further consideration of additional moments due to slenderness." It therefore does cover use of software that does a full p-delta analysis as long as other non-linear effects are included.

Clause 6.3.2 is specifically for "Elastic analysis of frames incorporating secondary bending moments", and design of columns for that case is covered by Cl 10.2.2 which requires the moment magnifier for braced columns to be used.

So the moment magnification to be applied depends on the degree to which p-delta effects are considered in the analysis, and it seems to me the code provisions cover the full range of possibilities.

Note that the current commentary is still referring to the 2009 version of the code. The new commentary should be published soon, but the relevant clauses seem to be unchanged in the new (2018) code, so presumably the commentary will be the same on these questions.


Doug Jenkins
Interactive Design Services

Thanks for the replies.

@Rscassar Commentary says that additional moment from magnification is equal to axial force times deflection so it's p delat.

@Ids I think rigorous analysis > linear elastic analysis with all p-deltas. Needs non-linear material and crookedness.

Coming from steel and trying to understand the differences. Steel has full p-delta analysis without magnification but concrete says to do hand magnification always, but that's maybe just outdated. Concrete doesn't have a Nc step like steel so is unconservative?

What is a "Nc step like steel"?


Doug Jenkins
Interactive Design Services

So with steel you do full p-delta analysis then the interaction check is based on member capacity Nc which is less than the section capacity. The Nc check is where crookedness of the column is handled. In concrete you do p-delta by moment magnification but the interaction check is based on section capacity. So crookedness isn't considered in the concrete check?

Rigorous analysis in concrete has to have the crookedness modelled in addition to p-delta analysis so it looks like the elastic analysis and code check misses it out.

I think the crookedness is handled by the minimum bending moment in Cl 10.1.2.

Doesn't seem right to me, a column with an Le/r ratio of 50 (for example) should be designed with minimum moments applied and moment magnifiers as a minimum requirement. Doesn't seem right that slender columns get passed as stocky on the basis that a p-delta analysis has been carried out.

A few points on the wording of the code:

The code doesn't actually define rigorous analysis, but I take it to mean that everything that has a significant effect on the behaviour of the structure is included. For reinforced concrete, the concrete is significantly non-linear at serviceability loads, so including material non-linearity seems a reasonable requirement.

The code does not use the word "crookedness" at all, but the commentary says:
"When non-linear analysis is undertaken for structures with thin columns, allowance should
be made for an initial eccentricity (crookedness) in the columns." (Cl. C6.5.1)

So it doesn't require it to be included in all cases, but I'm not sure how you would know if it is significant or not, unless you include it.

I don't do steel design, but I would guess that compared with concrete, the material non-linear effects are less significant, and the "crookedness" effects are more significant, so the differences in the code requirements seem reasonable.

rscassar - The moment magnifiers are provided to allow for geometric non-linearity effects, so if the analysis includes allowance for geometric non-linearity (plus material non-linearity and/or crookedness where appropriate), why would you still add on the moment magnifiers?



Doug Jenkins
Interactive Design Services

Thanks again everyone.

@rscassar I'm thinking about unbraced frames here. I should have said that. I think you're talking about braced? Same question but AS3600 limits km to 0.4 min which computer p-delta wouldn't. But N*/Nc > 0.6 needed for that to matter which looks high. I read some papers like Uniciv Report R-255 by BV Rangan which says 0.33 is the limit on page 30. Okay maybe diff situation but still double and looks too high.

@Retrograde that's a good point. For max Le/r=120 this would L/D about 25. Min eccentricity therefore L/500 which seems about right for crookedness and more than this for less slender columns. But it is minimum not added. If analysis give small moment but just more than min then nothing extra for crookedness.

The Uniciv report says moment magnifier can be grossly conservative for unbraced columns. I'm not trying to avoid that just make the calcs easier while still meeting code. It sounds like the conservatism is just due to the simplified method and not the intention but also full p-delta doesn't seem to be allowed instead. Would be good if the code clarified this since the commentary seems to say it's because software isn't capable when most now can do this.

SlowByrne said:

Would be good if the code clarified this since the commentary seems to say it's because software isn't capable when most now can do this.

Click to expand...

How can the commentary be saying the software isn't capable when it specifically talks about doing a rigorous analysis as an option?

What is the problem with including material non-linear effects?

Doug Jenkins
Interactive Design Services

@IDS I don't think reduced EI in elastic analysis is what they mean by rigorous. If using elastic material then would need to subdivide members and manually iterate the stiffness. I don't have software that does this automatically.

The commentary says the rigorous analysis section is for future situation when this type of software is available.

SlowByrne said:

The commentary says the rigorous analysis section is for future situation when this type of software is available

Click to expand...

Well actually it says (published in 2014 for the 2009 code):
"Commercial computer programs, featuring a variety
of concrete constitutive models, are commonly available and implementation of guidelines
into Standards, such as AS 3600, reflects progress in the field."

It also says:
"In everyday engineering practice, the use of non-linear stress analysis in the design of concrete structures remains an
emerging field and a great degree of care and experience is needed for its correct application."

but that does not say it should not be used, it says it should be used carefully, which remains true.

Your problem seems to be that a simplification available in the steel code is not available in the concrete code, but reinforced concrete is not steel, and in particular (to quote the commentary again):
"The challenge in numerical modelling of reinforced concrete arises from its composite
nature. Important aspects such as cracking, crushing, tension stiffening, compression
softening, aggregate interlock, creep, shrinkage and bond-slip give rise to non-linear
behaviour of reinforced concrete members."

Edit:

SlowByrne said:

I don't think reduced EI in elastic analysis is what they mean by rigorous.

Click to expand...

I didn't suggest that it was. If you want to avoid applying moment magnification factors you have to include material non-linearity in the analysis. If you don't want to do that you can follow the requirements of Cl. 10.2.2.

Doug Jenkins
Interactive Design Services

@Retrograde You are right. The minimum eccentricity is for imperfection in straightness. I didn't read the commentary for that before. It was additional eccentricity in AS1480 like I thought it should be but AS3600 just copied minimum from US/BS codes.

@IDS
"Your problem seems to be that a simplification available in the steel code is not available in the concrete code"

Yes that's exactly my question from the start. Is this on purpose or just copied from 1983 US code and never updated? AS3600 gives rigorous for exceptional structures and grossly simplified for everything else but not so convenient anymore (was good for hand calc). Is there really a problem with something in between? AS4100 says they are valid alternatives.

SlowByrne said:

es that's exactly my question from the start. Is this on purpose or just copied from 1983 US code and never updated? AS3600 gives rigorous for exceptional structures and grossly simplified for everything else but not so convenient anymore (was good for hand calc). Is there really a problem with something in between? AS4100 says they are valid alternatives.

Click to expand...

But that's not what it gives. It provides a linear elastic method, a large P-Delta method with linear elastic material properties, and a method incorporating both material and geometric non-linearity.

As I have said before, reinforced concrete is highly non-linear under working loads, so it seems quite reasonable to require moment magnifiers unless that is taken account of,

Doug Jenkins
Interactive Design Services

@IDS
"t provides a linear elastic method, a large P-Delta method with linear elastic material properties, and a method incorporating both material and geometric non-linearity."

Commentary says rigorous is only expected for exceptional structures so the writers expect the elastic methods for most cases. Four professors who worked on the code make a lot of comments about how rough the magnifier is in their textbook and also not guaranteed conservative. The magnifier is based on elastic analysis not concrete non linearity.

What I've found from reading up on this is AS3600 still the same as 1994 and prob 1988. It was based on 1983 US code. The 1995 US code is online and requires moment magnifier. The 2008 US code changed to allowing subdivided P-delta like I want to use or moment magnification. Really seems like AS3600 just abandoned this section not magnification covering something P-delta misses out. Stuck with it I guess.

OK, I give up. Stick with treating a single statement in the commentary as overriding everything else in the commentary and everything in the code if you want.

Doug Jenkins
Interactive Design Services

@IDS I've reread your posts. I think you're saying moment magnifier is required with elastic analysis. Full p-delta without magnifier isn't compliant with either the elastic or rigorous code sections. That's how I read it but wanted opinions. But is something in the magnifier calc critical to concrete design? Like I said the Americans who we copied have moved on and the professors pointed out a lot of approximations. And it's based on elastic maths anyway. If magnifier is special I want to understand, or confirm it isn't but the code still requires it.

Moment magnification is how consideration of buckling effects is stitched into AS3600. I am not an expert on non-linear material models but I would say that it's important to consider buckling effects when designing slender columns.

Otherwise you end up just doing concrete section design (as for a short column) where axial capacity is not at all related to column height. In my experience consideration of p-delta effects just accounts for geometrical non-linearities and has nothing to do with member buckling.

Moment magnifier is just p-dekta by hand and short columns are just columns with <10% p-delta. That's why even long braced columns are called short for low load and opposite moments in clause 10.3.1 because p-delta will still be small. Moment magnifier covers euler buckling but so does second order elastic analysis as it won't converge. Sway buckling is covered by 1.5 max sway magnifier or L/250 ULS deflection limit in analysis.  So 2nd order analysis does cover buckling.

Now not sure about 6.3.2(c) combined with sway magnifier instead of doing both p-deltas in the analysis. Can it be unconservative for vertical load cases? Magnification is meant to apply to 1st order end moment but 2nd order end moment might actually be smaller if sway moment is small like in vertical load cases.