Cracked vs Uncracked RC Sections - Modal Analysis/Response Spectrum

[fracture_point]

Couple of questions regarding model analysis and cracked/uncracked section properties:

1) Do we use cracked section properties for all of the modal analysis, i.e. to calculate periods, base shear, drifts, forces etc and would also give a worse p-delta effect..

or

2) Do we use uncracked sections to calculate structure periods (causing a lower period and higher base shear to develop) and cracked sections just for drift checks from base shear using periods of uncracked members?

I can't find any clear consensus and would appreciate some advice.

 

[JoshPlumSE]

My belief is that you should use the stiffness that is expected for the loading your are going to see. Therefore, in the case of seismic analysis, you will generally consider more cracking (i.e. less stiffness) than you would for serviceability limit states.

I generally use the stiffness that is appropriate for strength level limit states. However, you could argue that (due to the use of the "R" response modification factor) the cracking for seismic force levels is even more severe than for regular strength level limit states. I don't usually make that argument to reduce my stiffness further, but it is a valid concept.

 

[Agent666]

To throw something into the mix in NZS3101 the stiffness at serviceability is directly related to the ductility at the ultimate limit state, reasoning is if a design level event occurs the structure will crack, so remains cracked/softened for future SLS events.

1) Yes, though as Josh notes particularly for tall walls you need to assess whether or not the entire structure is cracked. This is often iterative in the sense that you assess with uncracked properties, find cracking moment is exceeded, revise stiffness in base of walls, rerun analysis, and reassess if other areas now exceed cracking moment, repeat until happy. The reality is structure starts out uncracked, but after a few cycles becomes progressively cracked/member capacities are reached with resulting inelastic action and formation of ductile mechanisms, period shifts to some steady state which you base your global analysis on, etc. A non-linear analysis for example might factor these effects into the analysis, evaluating the degradation of stiffness and progressive formation of plastic regions at each time step. Obviously for a response spectrum analysis you have to make some simplifications.

2) Only reason I have done this in the past is where structure is nominally elastic (ductility of 1.25), and our code requires you to consider different effective section properties at the ULS and SLS. For ultimate you should always consider the effective stiffness after consideration of cracking, the earthquake mobilises the full strength of your structure in forming a ductile mechanism, so it stands to reason the dynamic analysis should be based on the stiffness associated with reaching this capacity. In my code (NZS3101) this is defined as the effective stiffness at first yield, I believe this means evaluating the stiffness when the first bars reach yield. Usually codes have tables that are more or less meant to cover generically the stiffness for given scenario, for example see the following from NZS3101. In reality obviously these averages might be +/- some percentage but it generally doesn't affect the load distribution that much

 

[helfreco]

fracture point,
Agent 666 is correct that this process is usually iterative to find which elements have cracked at the seismic level you are analyzing.

As a quick start, I have seen that it is easier to make two models, a horizontal and vertical model. This is important when you are searching for your different mode shapes. Typically, in horizontal motion, walls will crack and floors won't: then vise versa in vertical motion.

If you are extracting building forces or ISRS from your model, extract the horizontal forces from the horizontal model, and the vertical forces from the vertical model. Then present them together in your reporting

 

[slickdeals]

Would also refer to the LA Tall Buildings Guide, refer to Section 2.5 and Table 3 (similar to what Agent666 posted)

http://www.tallbuildings.org/PDFFil..._Final_w_2018_ Supplements_FINAL_20180320.pdf