# ρ vs Ωo



## ZEZO4 (Mar 16, 2018)

In the seismic design, is there any general rule to know when We have to use  ρ or Ωo in the load combinations? 

Thanks.


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## Kamba (Mar 17, 2018)

in Steel Design is this determined by the "AISC Seismic Design Manual". Speaking of OMF  "Ordinary" moment frame design, Members are designed using 'roo' but connections are designed using 'Omega'. Generally, when it's a critical element (such as connections in OMF) overstrength is used.
I'm not sure about the concrete design.


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## ZEZO4 (Mar 19, 2018)

That what I think, but sometime use 'Omega' for column design, It is confusing.

Thanks Kamba.


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## Kamba (Mar 19, 2018)

Zaid:
for clarity: it depends on the type of moment resisting frame. what you have mentioned is correct for SMF "Special Moment Frame" that Overstrength factor is used for the design of columns. The case I discussed earlier about connections only applies to OMF "Ordinary Moment Frames".. I'm going to update my previous reply accordingly. sorry for any inconvenience this might may caused.
Again the Rule in steel design is the "Seismic Design Manual"


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## ZEZO4 (Mar 20, 2018)

That is making sense,

Thank you Kamba.


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## tenguy23 (Mar 21, 2018)

Zaid: This topic was always one of the trickiest for me.

With respect to ASCE, i would first observe sections 12.4.2.3 when speaking of rho; for these strength design load combinations, rho is ALWAYS included; the question is whether it is 1.0 or bigger. WHether it is 1.0 or greater is then explained in section 12.3.4. This section ends up quite "wordy", so ASCE, in its commentery Figer C12.3-6, gives a nice flowchart.

Now, there are certain items in a seismic lateral force resisting system that we ABSOLUTELY DO NOT WANT TO FAIL. ASCE has it's own provisions which results in "trigger" that forces the engineer to add Omega to the Load combinations per Section12.4.3, BUT OTHER CODES (aci, aisc) may add to that "trigger" for certain scenarios. With just my microscope on ASCE, sections 12.3.3.3 are a trigger for overstrength (discontinuous walls/frames) and section 12.10.2.1 as well (collectors) are designed for an even higher load level so that these critical locations do not fail in a seismic event.

To follow up on Kamba's example of code-specific instances that trigger Omega:

AISC (I'm looking at the 14th edition manual): Go to page 1-14 and 1-15: There is a nice summary of when Omega is to be applied (and where). HOWEVER, this omega sometimes points to ASCE (i.e. use ASCE"s omega values in ASCE table 12.2-1), and SOMETIMES omega is "buried" in the AISC seismic provision itself (i.e. Omega is defined by the AISC specification with a mathematical equation TOTALLY SEPARATE FROM ASCE).

ACI: I would argue this is similar to AISC; you need to read (verbatim) how ACI writes it's specification. If a particular element on the SLFRS is triggered by ASCE, use ASCE's Table 12.2-1. Otherwise, apply an Omega as per the ACI spec.


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## ZEZO4 (Mar 22, 2018)

Hi tenguy23,

Thank you for your explanation for me, yes it is very tricky subject and we have to pay attention for it, just one note of what you mentioned that the pages 1-14&amp;1-15 are in the seismic manual 2nd.ed. not in the AISC steel manual 14th. ed.

Regards.


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## EBAT75 (Sep 11, 2020)

New kid on the Forum. Saw this. Yes, this is a bit shaky ground, pardon the pun. I will give my understanding.

Applies only to SDC - D thru F. Rho is 1.3, 1.0 under exceptions. Omega is minimum 2.

Certain components of a structure such as collectors, connections, foundations, cantilever column connections can be subject to demands of *maximum forces deliverable *under higher seismic conditions. Why this higher Omega of 2 to 3 is applied only in SDC D thru F and not in B or C where the maximum forces under failure of redundant conditions will not be 2 to 3 times. Rho of 1.3 or 1.0 is acceptable risk for SDC B or C.

Please bear in mind that this topic has many exceptions to apply. What I have here is a general, conceptual thinking only.

Last but not least, I see references to AISC, Seismic Manual, Moment Frames etc. These code requirements are materials blind. It is only a load combination. It applies to Steel, Concrete, Masonry or Wood equally. The type of structure and strength of the material used will drive the design based on the loads calculated.


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## Reverse Polish (Sep 11, 2020)

Redundancy Factor, rho, pertains to the entire seismic force-resisting _system_, and has a value of either 1.0 or 1.3.  See 12.3.4.1 and 12.3.4.2 in ASCE 7 to determine which value is applicable to your system.

Overstrength Factor, omega, pertains to _elements_ along the seismic force-resisting load path that are not capable of resisting seismic forces through inelastic behavior.  Typically, this includes load transfer conditions--elements supporting discontinuous walls or frames, collectors, etc.  Be careful, though...sometimes omega is triggered in SDC C, as for collector design.

There are a whole host of exceptions for both factors, rho and omega.  I would make sure to understand all of these, and when they are applicable.


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## EBAT75 (Sep 12, 2020)

Reverse Polish said:


> Redundancy Factor, rho, pertains to the entire seismic force-resisting _system_, and has a value of either 1.0 or 1.3.  See 12.3.4.1 and 12.3.4.2 in ASCE 7 to determine which value is applicable to your system.
> 
> Overstrength Factor, omega, pertains to _elements_ along the seismic force-resisting load path that are not capable of resisting seismic forces through inelastic behavior.  Typically, this includes load transfer conditions--elements supporting discontinuous walls or frames, collectors, etc.  Be careful, though...sometimes omega is triggered in SDC C, as for collector design.
> 
> There are a whole host of exceptions for both factors, rho and omega.  I would make sure to understand all of these, and when they are applicable.


Omega is the ratio of base shear at initiation of failure mechanism to the design base shear in a structural system. It is a measure of the reserve capacity of an entire  structure to resist MCE acceleration. Values of Omega are tabulated by systems, not elements.

Rho is a 30% penalty for lack of redundancy in a structural system in order to delay the formation of a collapse mechanism under the design spectral response acceleration The penalty is not applied in some cases including when an element of the system is designed by choice using Omega in SDC A, B, and C. If it is only a Non-Parallel irregularity in SDC C, the penalty is not waived and 1.3 must be used, not 1.0.

Omega is the ratio of base shear at initiation of failure mechanism to the design base shear in a structural system. It is a measure of the reserve capacity of an entire  structure to resist MCE acceleration. Values of Omega are tabulated by systems, not elements. Omega encompasses the purpose of Rho, but not the other way around. Rho cannot be used in SDC D,E,F.

IMO, both Rho and Omega are systems based. They are not specified on the basis of structural elements. Once the loads effect to the members in the structural system is calculated using Rho or Omega as applicable, then the design of the elements such as foundations, collectors, connections etc follows from that.


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## EBAT75 (Sep 12, 2020)

Please delete the first para. I was rearranging and expanding the paragraphs. In so doing forgot to delete it.


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