The role of Cracked Stiffness in Analysis and Design 2

[kellez]

Hello everyone,

My question is in regards of the cracked stiffness of elements in the analysis and design stages of Reinforced Concrete structures.

1. EC8 as other standards suggest reducing the stiffness of elements (cracked elements) to 0.5 of the
uncracked elements in order to cary out the seismic analysis.

2. Once the analysis is carried out (w/reduced stiffness), the resultant moments and shear forces are
available for the design of the elements.

Question:
Therefore my question is...for the design of the elements do i have to use the reduced stiffness (smaller section) that was also used in the analysis or
do I the use stiffness of the uncracked elements (original section)?

 

[JAE]

kellez - not familiar with EC8 at all but the ACI code in the US has similar provisions.

What it is attempting to do is more correctly model the concrete frame at its ultimate state, which is typically a cracked condition.
This has the effect on your analysis of increasing frame lateral drifting such that second order effects can be included in the analysis.

By including a less stiff structure, the drifting is higher and therefore the moments will be higher.

In the ACI code they use different reductions (0.35 for beams and 0.7 for columns) since columns tend to be axially loaded and thus the cracking moment must be higher.

Now all this is in your analysis. Not your design.
The analysis gets you your design forces.

With those design forces you would then simply apply those to the original shapes and determine reinforcement.

So if you have a 600mm wide x 900mm high concrete beam - the reduced stiffness would be on the order of a 300 x 900 beam (based on your 0.5 factor)
Once you get your loads - use the 600x900 to design the beam.


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[kellez]

Great that is exactly how I carried out my design, thanks a lot for your reply, this is crystal clear now, you couldnt have explained this any better.

You mention that

By including a less stiff structure, the drifting is higher and therefore the moments will be higher.

However the acceleration of the structure due to the seismic load will decrease due to a less stiff structure right? With higher stiffness you get higher acceleration isnt it?

 

[JAE]

For seismic, you are dealing with the response of the structure in an extreme "ultimate" event such that cracked sections already have occurred.
We use ASCE 7 here in the US and it requires the following:
1. Stiffness properties of concrete and masonry elements shall consider the effects of cracked sections.
2. For steel moment frame systems, the contribution of panel zone deformation to overall story drift shall be included.

So the way a static seismic analysis is set up in the US, the type of system you have (concrete frame, steel frame, X-brace, etc.) determines a response coefficient which provides you with a seismic demand.
The seismic demand is thus correlated with the system you are using...and the cracked or deformed response of that system to extreme seismic events is already included in determining that demand.

Now if you are doing a full modal response analysis (vs. a static analysis) then I think you'd have to include a cracked condition in your model when analyzing it under seismic accelerations.



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[dcStrucEng]

I think we should make a further distinction between a service level analysis and a strength level analysis. In the Commentary of Section 10.10.4.1 of ACI 318-11, it states the following:

So a service level analysis which is used to determine deflections, drift, periods, etc. can utilize 1.43 times the cracked moment of inertia.

For a building analysis, this may mean that if you are using a software program like RAM SS or Etabs, you should make two models: one for serviceability using 1.43 times cracked factors and one for design without the 1.43 factor.

 

[Celt83]

dcStrucEng: keep in mind that the program generated lateral cases for both wind and seismic will be based on ultimate loads, assuming designing to the latest ASCE 7 and IBC, so applying section 10.10 under those applied loads will likely be inaccurate.

 

[JAE]

Well you can always set up service load combinations in your analysis as well - in fact for wind serviceability checks you should be doing that anyway.

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[dcStrucEng]

It's very possible that I'm misinterpreting something (please let me know if I am) but,

Celt83: If you are performing a strength design of a concrete structure using a program, you'd create load cases using the ultimate wind and seismic loads and modify the various structural members using the crack factors from 10.10.4. But if you are analyzing the serviceability of a concrete structure (drift, period, etc.) you'd create serviceability load cases using the lower wind speeds in the ASCE 7-10 commentary along with including the 1.43 multiplier to the crack factors. With this methodology, do you think the applied loads would be inaccurate?

JAE: Even setting up service load combinations (to check serviceability) you'd still need to use the 1.43 multiplier to the crack factors.

If the above is accurate, then I don't see how it's possible to create a single analysis model to design for strength and serviceability of a concrete structure if serviceability design per 10.10.4 enables one to increase the crack factors by 1.43 and strength design does not, since these would be modifiers to each structural member.

(Sorry, if this is slightly off the OP's topic)

 

[JAE]

I believe the 1.43 factor is only used to "up-facctor" the reduced moments of inertia "given here".

If you start with service loads (unfactored) and then check for cracking and derive Ie values accordingly, you don't have to go through the steps of downgrading, then upgrading (1.43) the moments of inertia.



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[Celt83]

dcStrucEng: that sounds correct to me at least for the wind case, was more just pointing out to be mindful of the default settings particularly in RAM. For seismic my memory isn't what it used to be, but believe the story drift limits in ASCE 7 are based on the ultimate level loads.

under that line of thinking think you would need to run your model several times to capture serviceability and strength design, or as you noted have multiple models covering the various parameters.

 

[JAE]

dcStrucEng,

I think you can do what you (and 10.10) suggest:
1. Set up a model and adjust the moments of inertia down per 10.10.4.1 (ACI 318-11) and analyze using factored load combinations. Design for strength.
2. Take your same model, but then adjust your moments of inertia back up by 1.43. Then use unfactored combinations to check for serviceability criteria.
3. So in essence you do have two different models - one with reduced stiffnesses for strength design and one with less reduced or non-reduced stiffnesses for serviceability design.

Alternatively:
1. Set up a model and adjust the moments of inertia down per 10.10.4.1 (ACI 318-11) and analyze using factored load combinations. Design for strength.
2. Take your same model and remove the stiffness reductions.
3. Run the model with full uncracked stiffnesses using unfactored load combinations.
4. Investigate members (columns and beams) and if cracked, modify the stiffnesses per 10.10.3 (ACI 318-11) which is essentially similar to deriving Ie values including axial effects per 9.5.2.3.
5. The investigation of each member would require possibly cracking only portions of the member along its length as some portions crack and other don't.
6. Step 4 above is iterated as the members sequentially crack further until the model analysis converges.

Granted, the second option is much more work and...why would you? Unless there is some unique features in the model where the global reductions per 10.10.4.1 might not be accurate.

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[kellez]

My question has already been answered therefore keep going, additional information is always good.