question on EC2 parabolic stress block being implemented as part of other code design procedures

[Agent666]

This hopefully a simple followup to my previous thread on this subject thread507-445334

I had a further question on the clarification of one point in working through implementing it in practice for those that participated, namely Rapt/Southard2/IDS, or anyone else that can contribute:-


In implementing a scenario whereby your own local code allow you to consider stress block relationships other than the standard typically defined rectangular stress block (i.e. see ACI318-14 clause 22.2.2.3 below), and specifically if designing a sections ultimate strength to one code (say ACI318 because most people are probably more familiar with it) but using another codes fundamental stress block relationship (say EC2 parabolic rectangular stress block) for the benifits/reasons noted in the previous thread. Would you approach this based on which of the following approaches or some alternative?

1. Use the fundamental equation for the parabolic stress block in its entirety, both the shape as a function of depth within the stress block plus any other factors related to determining the stress height at a particular location (like the alpha_cc factor in EC2 which is equal to 0.85 for the UK NA, and this factor replaces any stress height factors in the design code being used?). All strength reduction factors and other parameters as per the overarching design code, being ACI318.​

2. Just use the shape as a function of depth within the stress block, with any other factors scaling the stress height coming from ACI318 (or whatever other code is being used), i.e. the 0.85f'c from ACI318-14 clause 22.2.2.4.1 (while this factor is constant in ACI and the same as the alpha_cc factor in EC2, this is not the case in my own standard NZS3101 (NZ concrete standard), whereby this factor known as the alpha_1 factor varies depending on concrete strength (0.85 up to 55MPa, α1 = 0.85 – 0.004 (f´c - 55) over 55MPa but with a minimum of 0.75), so using this in place of the EC2 alpha_cc factor would potentially seem wrong as the nature of the refined parabolic shape overcomes/directly allows for this effect which NZS3101 is trying to account for due to the shortcomings of the rectangular stress block at higher concrete strengths? In a way penalising your strength by double counting this effect in this scenario). All strength reduction factors and other parameters as per the overarching design code, being ACI318.​

3. some other combination of factors?​

My reading of the statement referenced above from clause 22.2.2.3 is that its just talking about 'shape', but I guess this means both the change in stress with respect to the depth, and also the height of the stress block, so option 1 above would seem appropriate?

In terms of strength reduction factors I am assuming the shape of the EC2 stress block is just that, and the calibration of each standards approach in terms of differing strength reduction factors or partial factors of safety take care of the difference in acceptable strengths to comply with each design standard you might be working to.

In no way is the shape defined in EC2 dependent on the use of the EC2 strength reduction factors (except in EC2 of course). For example the 1/1.5 in EC2 for concrete is quite a bit different to the strength reduction factor I am required to use in NZS3101 being 0.85 for everything, but it's not tied to the fundamental shape of the stress block.

At what stage would you stop inheriting (stress block) parameters from EC2 is fundamentally what I am asking, if you were to use the parabolic rectangular EC2 relationship with another code.

Many thanks for any replies!

 

[IDS]

I would need to check the ACI code to see how I would handle it for that, but for the Australian codes (either AS 3600 or AS 5100) I would:

Use the parabolic-linear shape as defined in EC2, including the two strain limits.

Use everything else from the Australian codes, including a factor of 0.9 on the nominal concrete compressive strength, which is explicitly stated in both codes. The 0.9 factor is included in the variable stress reduction factor for rectangular stress blocks (alpha2). The strength reduction factor varies from 0.85 to 0.65 or 0.6 in the new AS 3600. The 0.65 factor for compression control is restricted to elements with higher live loads.

The new AS 3600 also requires a 5% capacity reduction for the rectangular stress block, Or 10% for other sections where the high strain region is narrower than the NA. That would obviously not be required if using a parabolic stress block.

I am a bit uncomfortable with the NZ 0.85 reduction factor everywhere, but that applies at least equally with the rectangular stress block.

Incidentally I'll be looking at using the EC2 triangular-linear stress block, compared with AS 3600 rectangular, with circular sections, on my blog in the next few days.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Agent666]

Thanks for the reply

I am a bit uncomfortable with the NZ 0.85 reduction factor everywhere, but that applies at least equally with the rectangular stress block.

We have much higher confinement requirements as I understand it to perhaps offset this, obviously backed up by a great deal of research and testing in the distant past by the likes of Park and Pauley, etc when modern capacity design procedures were beginning making their way into our NZ codes in the 1970's. Keep in mind as well as soon as we need to do a capacity design protected column the analysis axial loads due to seismic can be amplified in the order of 1.3-1.7 times so in general there is plenty of reserve capacity over and above for the gravity ULS case, its a whole different kettle of fish from a static gravity design dominated column (though we have these also). So we might look at your requirements as being too conservative! I guess you can't beat real world testing via recent larger than code earthquakes over here also.

Once I've finished the program I am working on the plan was to open source it, should be useful for comparing various codes and ultimate capacities. Hence the question, as I hit these sorts of fundamental questions that there doesn't seem to be a predefined way of doing things outlined anywhere I can find, as the expectation is you just use a rectangular stress block and carry on despite what is noted in the code regarding the ability to use alternatives. There seems like a lot of ways you can combine all these factors, but what is the right way consistent with still achieving the intent/safety indexes of the code!


I don't specifically have access to the latest version of AS3600 (apart from the screenshots provided in the referenced thread, which there was some talk if I remember correctly that they were possibly considering being amended, though not sure on this). So its a little hard to relate exactly what you are saying regarding some of the individual factors, as I don't have the background.

But essentially I take it you are saying you would be doing my option 2 as I read it? Just use the cross sectional shape of the stress block, but all the other reduction factors on the concrete stress and strength reduction factors from the design standard you are using (AS3600)?

a factor of 0.9 on the nominal concrete compressive strength, which is explicitly stated in both codes

I'm a little confused by this, I assumed you were referring to the Eurocode having the 0.9 (10% reduction) when the compression width is getting narrower towards the extreme compression fiber with a rectangular stress block, but then on re-reading it you specifically note this at the end as being something different? In EC2 there is no other 0.9 reduction? If following the UK NA, then the concrete strength is f_cd = f_ck * alpha_cc/ gamma_c, where alpha_cc = 0.85 & gamma_c = 1.5. Are you possibly confusing the 0.9 with this 0.85 reduction for my own clarification?

Note that the vanilla EC2 has alpha_cc=1.0, but UK National Annex notes 0.85 agrees better with testing, etc.

As I understand it this 10% reduction due to the narrowing is not required if you were using the EC2 parabolic curve as it inherently takes care of this aspect and is one of the benefits of using this formulation as you also note.

For AS3600 the final design concrete strength is f_c * 0.9 * 0.95 for the 5% reduction case, or f_c * 0.9 * 0.9 for the 10% reduction case I take it, so ranging from 0.855 to 0.81?

 

[rapt]

The .85 in NZS is the definition of the compressive strength in the rectangular stress block for concrete strengths below 55MPa. This then reduces gradually to .75 for higher strengths. Similar relationships are included in rectangular stress blocks in all codes.

It not suggesting it is the peak stress to use in a more accurate stress/strain relationship. It is an averaged value of the compression stress to use for the rectangular stress block over the defined depth of the rectangular stress.

The curve should be used as defined in code/document it comes from. Unfortunately NZS does not give good guidance on using other curves other than to say they can be used.

Eurocode itself actually sets the nominal strength factor to 1.0, while suggesting each country using it can set their own value. UK uses .85. Australia uses .9 in its latest versions, before 2009, Australia used .85.

 

[Agent666]

Thanks, that is nice and clear, if the code provides the nominal strength factor (0.85 UK, 0.9 AS) then use it. Otherwise adopting the alpha_cc=0.85 from Eurocode UK NA in lieu of NZS3101 not giving any specific guidance for this, is probably the best I can do.

Yeah I see the mismatch now if you were to apply the alpha_1 factor to the EC2 curve, not appropriate due this factor representing the 'equivalent' stress block and it not being a reflection of the actual stresses present in the concrete, which the EC 0.85 or AS 0.9 factor is trying to account for with a parabolic curve.

Yes, the alpha_1 factor on concrete strength varies from 0.75 to 0.85, our strength reduction factors though are 0.85 across the board, no reduction for compression controlled sections, etc like any other codes.

 

[Settingsun]

In the absence of clear code guidance eg AS3600 clause 3.1.4 (iirc - the 0.9 factor discussed above) and 0.85 UK annex, might the pure compression requirements provide guidance? I'm trying to recall distant lectures but I think I was told that the old 0.85f'c used for column capacity comes from old US tests where they found real columns had lower strength than cylinder tests because of lesser compaction, less curing and size effects. The tests were on very different concrete to current mixes (low strength, high water content instead of superplasticisers etc) but still retained in the code.

 

[Agent666]

Steveh49, I believe the origin of that factor was discussed in the thread I linked by Southard2, the k3 factor he discussed. He outlined some of the reasons for it in his thesis which he also linked to. In NZ and ACI318 this factor is 0.85. Thanks for the suggestion, it does make sense that these 0.9-0.85 factors have some similarities to this compression factor.

 

[Settingsun]

I hadn't clicked on the other thread but have now and remember it. I do wonder about still relying on Hognestad's 1951 work. The only structure of similar age that I can recall off hand used 17.6MPa concrete (specified in psi) which is less than the minimum 20MPa covered by AS3600 these days. Literally today I had a 0.29 water:binder mix cross my desk for comment. How much hydraulic lift will there be with no free water?