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Seismic Response Modification Factor - R


This structural technote addresses the "R" value we show in our General Notes sheet in our drawing set - what it signifies, what the ramifications are and how we determine which value to use. But first, a little history...

In it's very simplest sense, our seismic design procedure (design lateral force) is based on several factors - the general seismicity (relative strength of seismic activity) of a given area (Ss and S1), the amplification of the motion due to the soil properties at a given site (Site Classification), the type of the building structure (R factor) and the use of the building (Importance Factor). The equation we use most frequently in the Carolinas looks like this:

design lateral load = ( Sds * Ie / R ) * weight of building

In order to create such a simple looking equation, the engineers and seismologists charged with developing the seismic design procedures looked at data from many different earthquakes (worldwide), the effects of site soils in proximity to the epicenters and responses of many different types of buildings then plugged all that data into a black box to come up with this normalized equation. We briefly touched on the Sds value in our Seismic Design Category 101 article which accounts for the seismicity and soil properties at the site. Those values are specific to a site and are not affected by any other properties of the building or occupancy. 

The Importance Factor, Ie, basically provides for an additional factor of safety of the design loads on the building with values of 1.00 to 1.50 used for seismic design (more on this in a later article). 

Finally, the "R" factor (formally referred to as the Response Modification Coefficient) accounts for the ductility of the building and adjusts the design lateral loads accordingly. Studies of existing buildings during earthquakes (some based on actual accelerations from instruments located in the buildings) have demonstrated that ductile buildings (like flexible moment frames) perform much better in seismic events than rigid buildings (like masonry shearwall buildings) because of the inherent ability of flexible systems to dissipate the energy of the ground motion.

R value:
With the "R" value located in the denominator of the calculation for the lateral load on the building, you can see a higher "R" value reduces the total load on the building. ASCE7-10 (referenced in the 2012 IBC) has 84 different types of structures listed from concrete to masonry to steel to wood to metal stud and shearwalls to moment frames. As a point of reference, back in 1997 when NEHRP issued their recommendations for seismic design, there were 69 building types. Constant research and newly tested concepts increase the design options regularly.

"R" values range from 1-1/2 for unreinforced concrete and masonry shearwalls (very brittle/stiff systems) to 8 for properly detailed shearwalls, braced frames and moment frames (all very ductile/flexible systems). Notice I mentioned "properly detailed" for the higher "R" values. To ensure ductile behavior of the building, the Code has very specific detailing requirements (based on lab testing) for the structural members involved in the lateral force resisting system. This ensures the members don't fail prior to reaching the required ductility. This additional detailing, of course, translates into more construction $$$s. Hence the trade-off:

high "R" value -> lower design lateral loads -> more detailing expense
low "R" value -> higher design lateral loads -> less detailing expense.

What "R" value to use?:
There isn't a whole lot of rocket science to figure this out but it does take careful consideration with regards to the project budget and comparison shopping of the design lateral loads.

If you're designing a steel building (a relatively light structure) at the beach with 120 mph wind, you might find that lateral loads due to wind are relatively high. This would allow you to use a relatively low "R" value and still not have seismic lateral loads controlling the design thereby minimizing the extra detailing. It would be wasteful to use a high "R" value in this case when seismic doesn't control the design but you have to pay for the additional detailing expense.

Conversely, if we are designing a concrete building (a relatively heavy building) in a relatively high seismic area with low wind loads, we might find the seismic design forces are controlling over wind. In this case, we would increase the "R" value to bring the seismic lateral loads down to the wind load levels but not use the maximum "R" so we only incur the additional amount of detailing expense necessary.

For most of the (non-essential building) work we do here in the Carolinas, we find that using an "R" factor = 3 is the most cost effective. The "R" = 3 is a special lateral system for steel buildings that does not require any specific detailing for seismic. There are still plenty of other traditional checks we need to make, but no extra ones related to seismic issues.

There are some other considerations for selecting an "R" value for a building design, but we'll cover those in another article.