# Seismic Design Coefficients: How they are determined for light-frame components

## Seismic Design Coefficients: How they are determined for light-frame components

are important to engineering innovation

As component manufacturers (CMs), our industry is usually not involved in the structural design of wall panels. However, with the recent changes in the energy codes, more and more customers of CMs are looking for ways to enhance the energy efficiency of their buildings without raising the cost. Often, customers try to do this by providing non-structural insulated foam sheathing over alternative shear resisting wall elements or alternative structural foam sheathing combination products in place of traditional plywood and OSB applications. The unfortunate reality is that innovation in the shear wall realm has been restrained because these traditional products have been very creative in getting the building code to assign design values that institutionalize a design value based competitive advantage. The same is true with respect to seismic design coefficients (SDC).

Figure 1 (at right): Cyclic test of alternative shear resisting wall element.

For CMs on the west coast and in other high seismic regions, this raises the question: What would happen to the seismic design if I used an alternative bracing method or a structural sheathing material other than OSB in my wall panels? To find the answer, one must examine the SDCs found in Table 12.2-1 of *ASCE 7* and, in particular, the Response Modification Factor or R factor.^{1}

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As seen in Table 1, there are two possible R factors for light-frame walls: 6.5 for wood structural panels (WSP) and 2 for all other materials. If a product competing with WSP does not have a code-defined research report^{*} establishing its R factor as 6.5, it must use the code-assigned value for all other materials.

A product with an R factor of 2 must be designed for 3.25 times the seismic load that a WSP shear wall is designed to resist. It is clearly important to CMs that, as new sheathing products come into the market, there is a rational engineering basis for evaluating their SDCs.

## The History

In 1959, the Structural Engineers Association of California (SEAOC) Seismology Committee published the first edition of the Blue Book “Recommended Lateral Force Requirements.” This seven-page document contained the four original R factors for seismic design (they were called “K” factors in those days). Fifty-five years and 81 R factors later, there is still not a definitive mathematical methodology to establish the R factor or, more broadly, any of the SDCs for a building system or the building components that make up that system. Instead, SDCs currently adopted by the building code are largely based on observations of past seismic performance and committee judgment.^{2,3,4,5,6}

In other words, they are purely engineering judgments that are not based on proven science or equal energy mathematics that were readily available in the literature and that would have provided a more rational basis for assigning SDCs based on the actual tested performance of a system.

## Purpose of the R Factor

The R factor, or response modification coefficient, results from simplifying the seismic design process so that linear elastic, static analysis can be used for most building designs.^{7} It is known from experience that structures can withstand greater forces, without collapsing, than they were designed for through inelastic strength behavior (see Figure 2).^{7} Designing for an expected seismic force using a fully linear elastic system would result in unnecessarily large lateral loads and a costly building design. Given this concern over the conservative nature of linear elastic design and its inherent high costs, the loads calculated for a fully linear elastic structure are reduced by the R factor to account for the fact the building is allowed to be damaged as long as it does not collapse (i.e., life-safety performance is provided, while allowing some building damage to occur). Thus, the larger the R factor, the smaller the design forces and the easier it is to find building components that can be used in the building design.

It is easy to see that the R factor serves as a basic measure of a system’s ability to resist seismic loads and that it is the single most important parameter in seismic design. The R factor is represented graphically in Figure 2 along with the remaining two seismic design factors: the system over-strength factor, Ω_{0}, which is a measure of the reserve strength (e.g., similar in concept to a factor of safety) of the building due to inelastic behavior; and the deflection amplification factor, *C** _{d},* which is used to estimate the drift of the structure by increasing the calculated elastic displacement of the structure to account for inelastic deformations.

Figure 2 shows that the elastic seismic base shear force, *V _{e},* is divided by the R factor to provide the design seismic shear force,

*V*

*The values of the R factor contained in the building code range from 1 to 8. Clearly, larger values of the R factor are better, given that they reduce the needed resistance to much lower seismic design forces.*

_{s}.## The Creation of Competitive Disadvantage: Equivalency Testing

Since the historical building code seismic design methods did not lend themselves to readily available numerical methods of establishing SDCs, equivalency testing is often used to assign the same seismic coefficients as a system already contained in the building code for newly developed building components.

It is important to note that a component itself cannot actually have a set of SDCs, since these factors only apply to the overall building structure. Thus, the goal of equivalency testing is to determine if a seismic force-resisting system, with SDCs assigned by the building code, can use the component in the overall structural design and not to determine the actual SDCs themselves.

ICC-ES AC130, *Acceptance Criteria for Prefabricated Wood Shear Panels, *presents one proprietary and non-consensus-standard-based means of comparing prefabricated wood shear walls to light-frame walls sheathed with WSPs to establish equivalency to WSPs. This is accomplished by using data from cyclic shear wall testing (e.g., *ASTM E2126*) to calculate three parameters which are indicative of the component’s ductility, deformation compatibility and overstrength.

Equivalency is established by comparing the parameters from the proposed component to maximum and minimum boundaries derived from a set of benchmark tests. If the parameters calculated for the tested product meet the prescribed limits, then it can use the same SDCs as light-frame (wood) walls sheathed with WSPs rated for shear resistance, which have an R factor of 6.5. If the system fails to meet these parameters, it is assigned an R factor of 2, which is used for light-frame walls with shear panels of all other materials. As described above, going from an R of 6.5 to an R of 2.0 has huge competitive product implications. If anyone wonders why WSPs have dominated the shear wall market, this is simply another area where the code provides WSPs with a key barrier to entry and competitive advantages that severely restrain any company’s ability to provide new innovative products into the market.

A summary of the ICC-ES equivalency parameters per this non-consensus-standard-based document is given in Table 2.

Maximum and minimum boundaries for the parameters were determined by analyzing a benchmark WSP shear wall data set consisting of 48 WSP shear wall tests, which included a variety of aspect ratios, design capacities, WSP thicknesses, nail sizes and nail spacing. The lower limits on the ductility drift capacity, and overstrength for the AC130 equivalency process is based the average parameters of WSP tests in the benchmark data set minus 1 standard deviation.^{8} Table 3 provides a summary of the parameter values from the benchmark data set used to select the parameter boundaries given in AC 130.

Since the limits on the three parameters are not based on the minimum tested parameter, some of the WSP tests in the database will fail to be equivalent.

Of the 48 tests in the AC130 database, 14 tests, or almost a third, are not equivalent to the AC130 criteria as shown in Figure 3. These non-equivalent tests have ductility parameters that range from 6.4 to 43.4. Similarly, the overstrength parameters for the non-equivalent tests range from 2.5 to 5.2, and the drift capacities range from 2.3% to 4.1% of the height of the WSP shear wall tested.

This indicates that WSP tests with a wide range of behaviors could and do end up being non-equivalent under the AC130 criteria. The reason for this anomaly is that the AC130 task group considered each of the parameters separately and selected limits that more than 85% of the tests would exceed.^{9} However, in all cases, a test that failed one parameter meets the other two parameters. Thus, the 6%-12% of the data that failed each parameter must be summed to find the total number of tests passing the overall AC130 criteria, resulting in 29% of the tests failing to meet the equivalency requirements.

This means that an alternative component that has the exact same performance as one of the WSP walls in the AC130 database may be inappropriately rendered “not equivalent” by AC130.

As seen in Figure 3 and Table 3, the parameters for the WSP tests are highly variable. The fact that the test results for multiple component configurations is highly variable was recognized by the Task Group, as seen in the following statement:

*the Task Group judged that it was not appropriate for the proponent of a prefabricated shear panel to simply select test data from a single shear wall configuration to prove equivalency. Performance criteria established using this single data point may or may not be representative of the level of performance commonly associated with the population of walls that conform to the code-defined benchmark system.*

__Given the large variation in performance expected with all possible building code-permitted permutations of the benchmark system,__^{8}

Despite the known variability of WSP, little allowance was made for the variability of alternative products. The Task Group states:

*tested performance for*

__average__*It is not intended that each test replicate pass this criteria (too stringent), nor is it intended that some aggregate average of multiple prefabricated shear panel configurations be compared against the performance benchmark (too lenient).*

__each prefabricated shear____panel configuration.__^{8}

Therefore, as illustrated in Figure 4, the average performance of each configuration for an alternative product must be greater than the AC130 limits; while, in contrast, only a portion of the WSP shear wall configurations are actually greater than the AC130 limits.

In short, alternative products are not allowed to have the same range of performance as WSP shear walls. If WSP shear walls that fail to meet the equivalency parameters can use an R factor of 6.5, while alternative systems that fail to meet the equivalency parameters are required to use an R factor of 2, the ability of alternative products to compete in the marketplace is clearly constrained. All roads to a competitive market lead through equivalency to WSPs, a proprietary and non-consensus-standard-based method (AC130), and the private non-profit, ICC-ES.

Furthermore, in AC130, the checks on the overstrength and the ductility are performed independent of each other. However, as discussed by the 2003 edition of the *NEHRP Recommended Provisions and Commentary for Seismic Regulations for New Buildings and Other Structures,* the R factor results from a combination of the overstrength and the ductility of a system.

Checking the two factors separately neglects the interaction of the two components. This results in systems with less ductility and more overstrength being assigned an R factor of 2. As a consequence, OSB sheathed cold-formed steel stud walls, foam core panels, etc. can be inappropriately penalized.

Finally, the drift limit of 2.8% of the wall height can result in systems with good ductility and high initial stiffness being assigned an R factor of 2.

As shown in Figure 3, there are at least eight high-ductility systems that have an R factor of 2 due to the drift limit or overstrength checks. Figure 3 also clearly shows that there is no increase in the R factor as the AC130 ductility parameter increases, when you compare all the data points with an AC130 ductility parameter greater than 11.0. This is contrary to the understanding that highly ductile systems are more earthquake resistant.

## Conclusions

Newly developed alternative products, that have a sound engineering basis, may fail to meet the proprietary AC130 equivalency parameters and be considered not equivalent even when they have performance that is equivalent to or much better than that of WSP shear walls. It is therefore challenging, if not impossible, for new product development and innovation to efficiently take place because the AC130 process is simply an R factor equivalency approach where the R factor is hand-picked without any analytical basis. However, it is great for the “in” products, like WSP, because it creates a de facto competitive advantage in the marketplace. A better methodology for determining SDCs that can provide more accurate comparisons between different systems is critically needed and already exists in the literature. SBCA has used its extensive amount of industry test data to develop an energy based methodology that can provide more meaningful comparisons for testing and defining SDC equivalency.

This equal energy method uses basic calculus (you never thought you’d use that undergraduate class did you?) to measure the amount of energy dissipated by the lateral force-resisting system. The energy dissipated by the assumed linear elastic response is set as equal to the energy dissipated by the actual non-linear response. By equating the energy dissipated by the linear and non-linear responses, a formula for calculating the R factor can be derived.

**2014 May**