Concrete cracked stiffness

[Gile_]

Hi,

Code says depending on the N/fcAg the stiffness should be reduced accordingly. How do you interpret and apply this in your analysis and design?
Do you
1. Change the stiffness accordingly to the relationship between N and fcAg without checking if the section does crack or not. OR
2. Check the stress of every member and reduce its stiffness according to N/fcAg only when the member cracks, otherwise remain the stiffness unchanged. OR
3. Based on 2, after changing the stiffness of some members re-run the model and check if any more member cracks and reduce their stiffness and re run the model again and again until no more new members crack.

 

[STrctPono]

I'll assume that you are talking specifically about reducing column stiffness in regards to a response spectrum analysis. I am not aware of the need to reduce stiffness for any strength level model check.

ACI allows you to take a standard reduced stiffness (I believe 0.70Ig for columns and 0.35Ig for beams). Not sure about Australian code. In terms of applying the reduced stiffness... the simple way would be to apply this reduced stiffness to each of your columns and beams uniformly. A more accurate way, but quite a bit more involved, would be to develop non-linear models that can be used in a linear-elastic dynamic analysis and iterating the results. Run a moment-curvature analysis for each column section based on the calculated axial load. The tangent stiffness (EI) could then be calculated based on the moment demand at each column section from your moment-curvature curve. You would then have to manually change the stiffness for each section. The next run would slightly change the building's frequency and thus the load demands. Iterate stiffness and repeat until convergence.

This can be streamlined quite a bit with spreadsheets but is still very involved and monotonous work.

 

[Gile_]

Thank you. 0.4Ig for slab & beams in Australian Code while for columns and walls it ranges from 0 to 0.8 depending on the axial forces. The different stiffness reduction doesn't bother me much. What I am wondering is if you crack all members without checking if it does crack.

Does that mean you only crack the member for drift check? For strength if we don't reduce the stiffness even for those members that exceed their tensile strength, doesn't that mean we violate the Code?

When you say uniformly does that mean reducing ALL members without checking their actual tensile stresses to see if they do crack?

I was thinking about non-linear analysis but it seems overkill for a 8-storey building.

 

[rapt]

That section of AS3600 specifically says to use the uncracked stiffness if the section is not cracked for each individual member, based on the tensile strength of concrete defined in the code.

So you only reduce stiffness if the member is cracked.

And that clause applies to lateral Analysis, not gravity loads.

The code also says that where multiple possible scenarios exist, use the one that gives the most conservative answer.

 

[Gile_]

Thank you. Does that mean I should do iteration? ie. reduce the stiffness of those are cracked and re-run the model, and check if any more new members crack and on and on?

 

[STrctPono]

The codes are rather ambiguous on the specifics of the analysis refinement. This is an engineering judgement decision.

For low seismic zone designs I will not go through a rigorous analysis that involves multiple iterations to the structures stiffness. For a sway frame fixed at top and bottom, I'll provide the code prescribed cracked section EI for the upper and lower third of the column. (I design bridges and there is no effective cracked EI for prestressed girder elements.) I will not do any refinement beyond this.

For a structure in a higher seismic zone, I will run a moment curvature analysis on the column at top and bottom (if different) and then apply it to the upper and lower third of the column. I will then go through maybe 1 or 2 iterations to refine those stiffness values.

 

[Gile_]

Thank you. Understand that at column ends you have higher curvature but just wondering how you have different EI for one column. Do you model three line objects instead of one or do you just do edge release?

 

[STrctPono]

Understand that at column ends you have higher curvature but just wondering how you have different EI for one column

The relationship between moment and curvature is bound by the element's stiffness. EI = M/Ψ. As you mentioned, at the ends of the columns you have higher moment and thus higher curvature, however, the relationship is non-linear. The tangent stiffness (effective stiffness) is the slope of the lines on your Moment Curvature graph. Increasing moment demand equals a diminishing value on your stiffness.

Do you model three line objects instead of one or do you just do edge release?

I discretize my columns with a set amount of nodes along the height (might be 9 elements over the column height. I will model much more for very tall columns). I then manually modify the elastic modulus of the material and keep the geometric properties (I) of the column constant. This may require you to establish many different concrete material properties and assign them to different elements within the same column but this can be done easily so long as you label them clearly and stay well organized throughout your iterations. I deal with structures that have a manageable quantity of columns so it's not normally a problem for me. A building with hundreds of columns would be a big task, which is why I would think twice about how much level of effort you are willing to put in to this analysis based on your seismic zone.

 

[rapt]

Section 6.2.4.2 of AS3600-2018 seems pretty unambiguous to me.

 

[Gile_]

Thank you. Just have one more question. The extreme compressive stress for defining the boundary element is obtained by gross cross section properties from linear-elastic strength model according to AS standard (I believe that it is the same for the ACI). Does that mean I should use uncracked section properties for all my walls & columns in my MODEL for the purpose of finding the boundary elements OR do I get the design actions from the model with cracked section properties and then find the stress using gross section properties by N/A +- M/Z (where Z is elastic section modulus)?