Seismic Response Modification Factor Interpretation

[designrider]

Question: What is the proper use of Seismic Response Modification Factors:

Option 1:
Response Modification Factor values greater than 1.0 , which are applied to select member effects in recognition of ductility and energy dissipation ability, should only be applied to member moments. R value use for column seismic axial effects is not appropriate as it would be contrary to the design specifications intent.

OR

Option 2:
Response Modification Factor considers inelastic deformation (i.e. ductility) of the system that allows the seismic response to be justifiably reduced. Seismic forces develop from ground shaking while the level of ductility of the system reduces the energy transmitted into the structure which engineers model as a lateral force. Thus, ALL seismic force effects (moment, axial, shear) are reduced because the system itself is dissipating the energy before it can develop as a resulting lateral force.

ASCE7/IBC uses R to reduce the Base Shear. AASHTO LRFD uses the R factor to reduce the “force effects”.

Which interpretation above more accurately defines the loading occurring in a member?

 

[JAE]

Are you designing a bridge or a building?

 

[designrider]

A bridge, however I don't think seismic theory should differ dramatically between the two. I am readily familiar with building codes also.

 

[JoshPlumSE]

A couple of years ago, I read an article in structure magazine that gave a really good explanation about this. I like to think that I understood it all already. However, I was never able to easily explain it to others. Now, I just reproduce Figure 1 from this article and then everyone understands why we use R, Omega and Cd and what they are intended to represent.

http://www.structuremag.org/article.aspx?articleID=756

The figures aren't as clear in the web version of the article, unfortunately. However, I think you should get the basic point.

 

[designrider]

Great resource JoshPlum! After review, I don't think either option I described above was accurate. The first is too conservative, the second is not conservative enough. ASCE7 lets you apply the R factor reduction right from the start be reducing the Base Shear respectively, which I think is a false sense of security for designers because (per the article you reference) "force controlled members that are designed to remain elastic would experience a significantly higher seismic force level than that predicted based on actual design forces". Thus, ASCE7 makes you scale up the effects using the overstrength factor, but overstrength is always less than the R factor. In my opinion this factor down then factor up method seems tedious, but just skipping these two steps and applying elastic response forces to axial loads would be overly conservative. AASHTO LRFD Bridge Code takes a different approach, using a less obvious method (at least to me) as it does not include system overstrength but only material overstrength (1.25 for steel, 1.3 for concrete). Then it applies different "force effect" requirements depending on the seismic zone you are designing for. I am still chewing on this, but I welcome any comments from others.

 

[designrider]

New thoughts. Any feedback is appreciated.

Only one component of the structure must pass through elastic and transfer to the inelastic range. This is known as the “first significant yield”, and this will occur in the most highly stressed member, but not in all members simultaneously. As seismic load develops, this will occur before the entire system can respond to its full elastic potential. This member will form a mechanism, a plastic hinge, which will become a part of the resultant resisting system. Now that the system has been modified by an internal hinge, the system will no longer be able to develop the original elastic level forces. In turn, the seismic axial forces of the columns in question that develop due to overturning are a system response, and are subsequently based on the modified system. If the system is designed to have a mechanism form before the system reaches full elastic response, then it is only sensible to reduce all force effects including moment, axial, and shear respectively.

For additional commentary regarding the Response Modification Factor, FEMA gives the following clarification:

“The ratio R, is always larger then 1.0; thus, all structures are designed for forces smaller than those the design ground motion would produce in a structure with completely linear-elastic response. This reduction is possible for a number of reasons. As the structure begins to yield and deform inelastically, the effective period of response of the structure tends to lengthen, which for many structures, results in a reduction in strength demand. Furthermore, the inelastic action results in a significant amount of energy dissipation, also known as hysteretic damping, in addition to the viscous damping. The combined effect, which is also known as the ductility reduction, explains why a properly designed structure with a fully yielded strength that is significantly lower than the elastic seismic force demand can be capable of providing satisfactory performance under the design ground motion excitations.” (FEMA p.37)

That said, other references comment that the components that are not to yield are then “proportioned by the capacity design procedure to ensure that these components remain in the elastic range.” Why?

I am still struggling with an accurate conclusion here.

References:
AASHTO, AASHTO LRFD Bridge Design Specifications 2010, 5th ed., American Association of State Highway and Transportation Officials, pp.3-51 thru 3-99
FEMA 450, Recommended Provisions for Seismic Regulations for New Buildings and Other Structures- Part 2: Commentary, 2003 ed., The Building Seismic Safety Council (BSSC), pp.35-45
Chen, Wai-Fah, Bridge Engineering Handbook, 2nd ed., CRC Press, pp.39-2 thru 39-4
SEAIC Seismology Committee, “A Brief Guide to Seismic Design Factors.” Structure Magazine, Vol. 6, No. 5, September 2008, pp. 30-32
AISC 341-05, Seismic Provisions for Structural Steel Buildings, 2006 3rd printing., American Institute of Steel Construction, pp.35-45

 

[VoyageofDiscovery]

It looks like you're getting a good grasp of things, however I think you are looking at it from the wrong end.

As a designer I utilize the factor to trigger yielding based on the component, so for example my foundation pile cap will not be designed to yield.

HTH

VoD