Question: What is the Cd factor in seismic design in the new ASCE-7?

Answer: The Cd factor recognizes that as a structure deforms, the actual response of the structure deviates from the deformation model due to the non linearity (plastic response) of the system.  Structural materials like masonry systems are rigid and have very low Cd factors because they have little plastic behavior.  Ductile systems like wood shear walls and steel moment resistant frames have very high Cd factors because they are expected to have a large “plastic region” in their deformation curves.

In seismic design, the assumption is made that damage will occur in a structure.  That means the structure will spend some time in the inelastic region of the deformation curve.  The Cd factor addresses the likelihood that the deformations in an earthquake will be greater than those indicated by the linear deformation equations.

At first glance the large Cd factor would appear to greatly penalize the use of redundant/plastic materials and systems.  Not so, because the Cd factors are not used alone.  They are used in conjunction with R factors that reduce the design load.  On redundant systems like wood shear walls, there is a R value of 6 -1/2.  So we reduce the design value by 6.5, calculate the deformations, and then increase them by a factor of 4 (the Cd factor for the system).  As a comparison, look at ordinary plain masonry shear walls (#A.12) in Table 12.2-1 of ASCE 7-05.  These systems have a reduction (R value) of 1.5 but are recognized as being non ductile with a Cd of 1.75.  Notice no unreinforced masonry in the table – zero ductility!

The idea is to pick a correct balance between the building’s response to lateral forces (R value) and the building's ability to absorb the energy of the event (Cd).  Now we would like to think that the Table 12.2-1 values were developed by hyper-intelligent, super mutant engineers!  Not so, they are just regular smart engineers trying to do the right thing by looking at existing earthquake damage and relating it to design forces.  The tabular values are best-guess committee-developed numbers and subject to change as we gain more knowledge on real system performance.  The fact is, they have been in place pretty much as they are now for over a decade and have been working pretty well.  There is now a push to determining a rational way of developing such numbers.

A good (and free) reference that is a must for your library if you are asking such questions is “NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures – FEMA 450-2/2003 Edition Parts 1 and 2.  The question above is addressed in Part 2, on pages 35-36.  Their example is for structural steel frame with plastic hinges forming.  A wood shear wall building doesn’t have plastic hinges but does have nail deformation at edges of shear wall panels and the real deformation curve for shear wall structures looks similar to the one in the figure shown for a steel structure.

Copies of this publication can be obtained from FEMA at 1-800-480-2520 or can be downloaded from www.bssconline.org.  (It is about 700 pages.)

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