Promising Advancements in Shear Wall Design: Updated Shear Values, Aspect Ratio Effects, and Drift Prediction By Jay Crandell, P.E.
NAHB Research Center, Inc. Have you ever wondered where certain numbers, limits, and design values come from in building codes? It is interesting to consider this question in the context of the unit shear wall design values found in today's building codes and engineering specifications [1][2][3][4][5][6]. Perhaps you have taken for granted that these critical values in the building code are accurate. Why wouldn't they be? Certainly they have provided serviceable designs for many years. Or have they? While some anecdotes about building code history and provisions are amusing, others deserve a much more thoughtful reaction, especially when new data challenges the old. This article focuses on the need to revise the basis of unit shear values that have existed in building codes without appreciable change since the time they were first introduced in the 1950s. The intent of this article is not to completely cover the topic of shear wall design and its history, but rather to bring some significant shear wall design issues to the attention of residential design professionals in light of recent research findings. It is assumed that the reader is familiar with existing codes and design practices for shear walls on light frame buildings. Much of the information presented is based on shear wall testing conducted at the NAHB Research Center, Inc. over the past several years and also at several universities and private laboratories in the United States and abroad. References are given in this article that provide technical resources and material for additional study. Background on Shear Wall Design Light-frame buildings typically use wood structural panel sheathing fastened to repetitive member framing to provide an adequate lateral force resisting system (LFRS) to withstand seismic and wind loads. Therefore, unit shear values used in the design of these systems are critical to the accuracy and efficiency of an engineering analysis and design for the LFRS of light-frame buildings. There are also many other design issues indirectly linked to the unit shear values. The key issues include the consideration of aspect ratio effects on shear wall performance (i.e. capacity and drift), connection forces (i.e. hold-down restraint), and the manner of distributing loads to various shear wall segments comprising the LFRS of a building. Traditional Shear Wall Design (The 'Segment' Method)
Unit shear values dictate the amount of shear wall bracing required based on the amount of lateral load (in-plane shear) to be resisted, the type of wood structural panel sheathing specified, and the specified fastening schedules. The unit shear values also affect the restraining forces to be resisted by connections that prevent the shear wall from rotating and not maintaining equilibrium under the applied lateral building loads. The basic principles are demonstrated in the simple shear wall segment model of Figure 1. This model is commonly used in current engineering practice to design wall segments throughout a wood frame building to resist lateral loads. In this simple approach, the effects of contributions from various connections and wall portions that are not part of the "designed" LFRS are neglected. Therefore, while the method provides a simple analysis, it requires greater amounts of connection hardware for each shear wall segment that impacts constructability and cost. This method of shear wall design is most appropriate for heavily loaded wood-frame walls and those with many large openings that effectively break a wall line into segments. An example would be the design of shear wall segments to either side of a garage opening that supports more than a roof load above. In other less demanding situations this process will tend to provide a conservative design with greater amounts of hold-down hardware than is necessary. This method is described in numerous technical resources on shear wall design[5][6][7][8][9].  Figure 1 Mechanics-based Shear Wall (Design Method)
This method is an extension or refinement of the traditional "segmented" shear wall design method. It allows a shear wall to be designed while accounting for the effects of dead load and structural sheathed portions of walls above and below openings. The method relies entirely on the assumption of rigid body behavior to allow an analysis based on engineering mechanics principles and the use of free-body diagrams. The method's primary benefit is its capacity to provide a means to calculate shear wall resistance and forces using familiar engineering principles while addressing the many shear wall design situations that depart significantly from the segmented model of Figure 1. Its disadvantages include the rigid body assumption, the resulting distribution of forces, and the degree of detailing that may be required to fit the construction to the model assumptions. The method requires a more rigorous analysis than required by the 'segmented' design approach. The method is published in at least one source [10]. Perforated Shear Wall Method (Empirically-based Design)
The resistance of shear walls with un-restrained openings can be determined with reasonable accuracy (i.e. ± 5%) by an empirical method known as the Perforated Shear Wall (PSW) method [11][12][13][14][15]. Many of the most efficient engineering design methods rely on empirical adjustments to classical engineering mechanics principles. A prime example is the design method for reinforced concrete beams in which actual internal stress distribution departs from a classical linear elastic model [16]. Another good example is found in the law of gravity where gravitational attraction is determined entirely on the basis of an empirical equation since the physical basis or constitution of gravitational forces is not known. Because of the non-linear behavior of wood materials and connections, wood shear walls exhibit non-linear behavior in both internal stress distribution and in global load-deformation characteristics. This explains the inability of strict mechanics-based methods to agree with empirical verification tests of long shear walls with various opening and restraint conditions [14][15]. The PSW method is very straightforward, and only requires that a fully-sheathed wall line with perforations for windows and doors be restrained at the ends with a hold-down bracket or adequate corner framing in lower capacity shear walls [17]. To determine the shear wall capacity, all that is needed is the unit shear value for the shear wall construction, the area of wall openings, the length of full-height wall segments, and the overall length of the wall. These values are inputs to a simple two-step equation that gives the overall wall capacity without the use of internal connection detailing or hold-downs. The wall capacity is less than what would be obtained with the segmented shear wall method, but fewer hold-down brackets are required. The capacity is similar to that determined using the mechanics-based methods, but the approach is simpler and more accurate. Base shear connection design and external vertical loads (i.e. wind uplift) are handled by conventional design analysis.
Wood Shear Wall Design Values: Out with the old, in with the new? When the current unit shear values for wood shear walls were first introduced into building codes in the 1950s, there were very few tests available to determine actual peak shear wall capacities. In an attempt to remedy this situation, a nail capacity theory was used to derive the unit shear values. However, the values do not represent the peak capacity of shear walls since the nail resistance theory did not take into account the non-linear, inelastic behavior of nailed connections. This condition occurred because the capacity of nails was based on a deformation limit state that occurs far ahead of peak capacity, particularly when used as a system of fasteners on a shear wall. In fact, most early nail shear tests were never even taken to a capacity failure mode. Since the 1950s many shear wall tests have added a tremendous amount of knowledge that has yet to be applied to revising the older unit shear values and design practices. As a whole, the test data from these sources consistently confirm two significant conclusions: Current wood frame shear wall design values have an actual safety factor commonly in the range of 3 to 5 though the current code-implied safety factor is 2.5. Reduction factors to account for density effects on "softer" species of wood are overly conservative.
From the available sources of shear wall test data and design values, particularly FEMA 273 [18] and APA 154 [19], shear wall design values based on average peak capacity have been assembled in Table 1. Some of the cells of Table 1 have more test replications by various sources than others. The ultimate unit shear values, when divided by a safety factor of 2.5, are significantly higher than those found in current building codes with the exception of the higher capacity sheathing and nailing schedules where some values decrease slightly. Revised species (density) adjustment factors are not included in the footnote (d) of Table 1 because the appropriate changes to these factors have not been completely resolved. At this point, the greatest reduction in unit shear values to adjust for lower density wood species (i.e. specific gravity less than 0.42) will likely be in the range of 0.7 to 0.9, not 0.65 as currently found in building code requirements. Also, the shear values for 2 inch edge nail spacing and sheathing have been deleted in Table 1 since the APA 154 data shows that the values are not greater than those for the three inch spacing (at least for the limited tests available at this condition). This behavior in the test data may be attributed to the possible on-set of a different failure mode (i.e. failure is limited by sheathing strength rather than nail capacity). What about the new light-gage steel shear wall values? The values in Table 1 are consistent with the shear wall values now recognized for light-gage steel shear walls using wood structural shear panels [2]. The proposed resistance factor of 0.55 and safety factor of 2.5 are also consistent. The new values for light-frame steel shear walls are based on a comprehensive shear wall testing program conducted at the University of Santa Clara [20][21]. The values are also consistent with perforated shear wall tests of light-gage steel framing conducted at the NAHB Research Center, Inc. [22]. Additional perforated shear wall tests are currently being conducted on light-gage steel-framed shear walls at Virginia Tech. While the unit shear wall values for wood- and steel-framed shear walls are actually comparable, there are certain advantages and disadvantages to consider for each material choice that are beyond the scope of this article. Aspect Ratio Effects on Unit Shear Values The values in Table 1 are relevant to a shear wall aspect ratio of 1/1 (i.e., 8 feet tall and 8 feet long). Therefore, a method to account for aspect ratio effects on unit shear capacity of shear walls with an aspect ratio greater than 1:1 (i.e. the shear wall segment height greater than the length) was developed and included in footnote (b) of Table 1. The aspect ratio adjustment equation is empirically derived from various sources of test data currently under review by the wood technical subcommittee of the NEHRP seismic provisions update for the year 2000. This equation fits the data over the range of conditions represented in Table 1 with an accuracy generally within 5% and exhibits a slight conservative bias. The fit is very good for practical design purposes. In terms of performance-based design, the concept is rather simple. The greater the aspect ratio the less the capacity and stiffness. With the correct design principles to account for these effects, the problem becomes self-limiting and arbitrary limits on aspect ratios become somewhat moot. For example, if more demand is needed from a shear wall, longer wall segments or a greater number of narrow wall segments will be needed to resist the load with adequate overall capacity and stiffness. The design is then based on meeting the necessary performance objective. Thus, current code limitations on shear wall segment aspect ratios should be viewed as necessary place holders until better, performance-based solutions are developed, such as given in footnote (b) of Table 1. Prediction of Shear Wall Drift Current design practice for wood shear walls commonly ignores explicit drift and stiffness calculations because it is believed that the unit shear values inherently provide adequate stiffness and meet the required drift limitations. This assumption is generally correct for the current code-approved shear wall design values and also for those proposed in Table 1 with factoring in accordance with footnote (a), but only for aspect ratios not exceeding about 2:1 or 1:1, respectively. If aspect ratio limitations are to be removed in favor of a performance-based approach, the effects of shear wall segment aspect ratio on stiffness and drift must also be explicitly defined in the design process. For this reason, the recent shear wall test data was also studied to develop a methodology to determine the load-drift relationship for shear walls. The following empirical drift equation was developed to predict shear wall segment drift for loads from zero up to the peak capacity: 
The above drift equation can also be solved to give an approximation of the shear wall segment load at a given amount of drift as follows: 
where the symbols are defined as before and h has units of feet. The design ramifications of these two equations are significant. They essentially provide a complete prediction of the non-linear load-drift behavior of a wood frame shear wall segment. The drift equation accuracy is generally within 10% and exhibits a tendency to over-predict drift. The data used to develop the drift equation encompasses a variety of tests and connection hardware installed in laboratory conditions. From a design application standpoint, Equation 1 can be used to determine the drift of any independent shear wall segment based on any amount of demand not exceeding the peak capacity of the shear wall segment. Of course, the drift prediction may vary depending on the load-deformation characteristics of restraint connections, on the amount of wood shrinkage that may cause eventual "free-play" in the connection, and installation quality. The tendency of Equation 1 to overestimate drift will tend to offset these concerns, particularly when a shear wall segment receives additional restraint from dead loads, from wall framing above and below adjacent wall openings, and from non-structural wall components. In monotonic (non-cyclic) tests, the contribution of interior gypsum wallboard causes Equation 1 to further overestimate drift. All things considered, these uncertainties and complications pose no new challenges to the prediction of shear wall drift, and Equation 1 is a reasonable, empirical-based design tool with suitable accuracy for general applications. Equation 2 offers a simple solution to some of the more difficult aspects of shear wall design when considered at the level of the LFRS of a building. Equation 2 allows a shear wall segment's response to be determined with non-linear stiffness characteristics up to the point of peak capacity. Thus, Equation 2 can be used to distribute loads to various shear wall segments in a given shear wall line based on their relative stiffness and the assumption that the deflection for each segment is equivalent. Indeed, this assumption must be close to accurate if the individual shear wall segments are properly connected with wall framing members. Also, the forces in wall framing members between the shear wall segments of different load-drift characteristics may also be determined with reasonable accuracy. These design functions have been traditionally addressed by comparing relative strength of shear walls which is closely related to stiffness. By using Equation 2, the load-drift characteristic for each segment in a shear wall line can be determined and then superimposed using simple hand calculations or a computer spreadsheet to determine the load deflection characteristic for the entire shear wall line comprised of multiple segments. This process can easily be repeated for all designated shear wall lines in a structure's LFRS and used to distribute forces on a given story level based on stiffness so that story drift due to translation and torsion may be rationally determined. The distribution of forces and the translational and torsional story drift can then be predicted for any load up to the peak capacity of the lateral force resisting system. The non-linearity of global shear wall behavior is accounted for in Equations 1 and 2. Appendix A presents a spreadsheet example of using Equation 2 to determine the shear wall capacity for a wall line that has three shear wall segments with different aspect ratios is shown in Figure 2. The top curve is the 'sum' of the independent shear wall segments' load-drift curve as represented by Equation 2 (multiplied by each segments width, w, to work in units of load instead of unit load). By using the new unit shear values from Table 1 (in this case 905 lbs/ft) and adjusting for each segment according to its aspect ratio, the non-linear response given by Equation 2 can be easily accommodated in the design process to determine an entire wall line's behavior up to peak capacity. This approach also eliminates the need to have arbitrary limits on aspect ratios. Some Final Thoughts The applications described above have been primarily focused on the traditional segmented shear wall design method described previously. Therefore, the contributions that come from portions of walls that are not specified shear wall segments are neglected in this approach. As such, the approach will tend to underestimate actual capacity and overestimate actual drift for a real LFRS in typical design situations that depart significantly from the simple shear wall segment model of Figure 1. The perforated shear wall method, the focus of many recent studies, has greater promise in resolving this issue since it captures the total wall in determining the behavior of a shear wall line. The unit shear wall values in Table 1 are applicable for use in the perforated shear wall method. In the near future, it is expected that a drift equation following the principles of the perforated shear wall method will be developed for application in design. It will likely address drift behavior of these types of shear walls in a very accurate manner. Design Recommendations - Try the unit shear values in Table 1 on a design project and compare the results to your current design practice. This is a simple substitution of unit shear values.
- Bring the subject matter of this article to the attention of your local building department and plan reviewers. Seek approval for use, if required, and obtain any additional references that may be required for substantiation.
- Use the load-drift equations (Equations 1 and 2) to determine load-drift characteristics of wood shear walls and to determine force distribution in the LFRS on a given story level. Compare the results to current practice.
- Become familiar with the use and application of the perforated shear wall method. If it is not already approved for use in your area, seek assistance from the American Forest & Paper Association (202-463-2700), American Wood Council (202-463-2700), the American Iron and Steel Institute (1-800-898-2842), or the NAHB Research Center, Inc. (1-800-898-2842 ToolBase hotline).
TABLE 1: Average Ultimate Shear Resistance (lb/ft) for Wind or Seismic Forces on Structural Use Panel Shear Walls with Framing of Douglas-fir, Larch, or Southern Pinea,b,c,d,e,f Panel Grade | Nominal Panel Thickness (in) | Minimum Nail Penetration in Framing (in) | Panels Applied Direct to Framing |
|---|
Nail Size (common or Galv. Box) | Nail Spacing at Panel Edges (in) |
|---|
6 | 4 | 3 | 2(e) |
|---|
Structural 1 | 5/16 | 1 1/4 | 6d | 821 | 1122 | 1256 | 1333 |
|---|
3/8(h) | 1 1/2 | 8d | 833 | 1200 | 1362 | 1711 | 7/16(h) | 1 1/2 | 8d | 905 | 1356 | 1497 | 1767 | 15/32 | 1 1/2 | 8d | 977 | 1539 | 1722 | 1800 | 15/32 | 1 5/8 | 10d(g) | 1256 | 1701 | 1963 | 2222 | Sheathing(i) | 1/4 or 5/16 | 1 1/4 | 6d | 695 | 781 | 1034 | -- |
|---|
3/8 | 1 1/4 | 6d | 737 | 888 | 1143 | -- | 3/8(h) | 1 1/2 | 8d | 777 | 978 | 1362 | -- | 7/16(h) | 1 1/2 | 8d | 800 | 1000 | 1497 | -- | 15/32 | 1 1/2 | 8d | 913 | 1155 | 1578 | -- | 15/32 | 1 5/8 | 10d(g) | 929 | 1526 | 1651 | -- | 19/32 | 1 5/8 | 10d(g) | 1111 | 1667 | 1858 | -- |
Table Notes:
(a) Values are average ultimate shear capacity and shall be multiplied by a resistance factor of f = 0.55 with a time effect factor of l = 1.0 for Load and Resistance Factor Design load combinations. The table values shall be divided by a safety factor of 2.5 for use with Allowable Stress Design load combinations. For single-family dwellings, the values shall be multiplied by a resistance factor of 0.7 for use with LRFD load combinations. The table values shall be divided by a safety factor of 2.0 for use with ASD load combinations.
(b) Values apply to aspect ratios, h/w, no greater than 1/1. For h/w ratios greater than 1/1, the tabulated values shall be determined by the following equation:
where:
v = the factored ultimate shear resistance - Table 1 value adjusted in accordance with footnote (a)
v'= the factored ultimate shear resistance adjusted for aspect ratio
a = h/w, shear wall segment (panel) aspect ratio.
(c) All panel edges backed with 2-inch nominal or wider framing. Panels installed either horizontally or vertically. Space nails at 6 inches on center along intermediate framing members for 3/8-inch panels installed with strong axis parallel to studs spaced 24 inches on center and 12 inches on center for other conditions and panel thicknesses.
(d) For framing of other species, multiply the table values as follows: 0.82 for 0.42 <= G < 0.49 or 0.65 for species with G < 0.42 where G is the specific gravity.
(e) Values are for panels on one side of the wall. Values shall be permitted to be doubled for panels on both sides. Where panels are applied on both faces of a wall and nail spacing is less than 6 inches on center on either side, panel joints shall be offset to fall on different framing members or framing shall be 3-inch nominal or wider and nails on each side of joint shall be staggered.
(f) Framing at adjoining panel edges shall be 3-inch nominal or wider and nails shall be staggered where nails are spaced 2 inches on center.
(g) Framing at adjoining panel edges shall be 3-inch nominal or wider and nails shall be staggered where 10d nails having a penetration into framing of more than 1-5/8 inches are spaced 3 inches or less on center.
(h) The values for 3/8-inch and 7/16-inch panels applied directly to framing are permitted to be increased to the values shown for 15/32-inch panels provided studs are spaced a maximum of 16 inches on center or panel is applied with strong axis across studs.
(i) 'Sheathing' includes sheathing and panel siding. References [1] BOCA National Building Code, Building Officials and Code Administrators International, Inc.(BOCA), Country Club Hills, Illinois, 1999.
[2] Uniform Building Code, International Conference of Building Officials (ICBO), Whittier, California, 1997.
[3] Standard Building Code, Southern Building Code Congress International, Inc. (SBCCI), Birmingham, Alabama, 1997.
[4] Load and Resistance Factor Design Manual for Engineered Wood Construction, Structural Use Panel Supplement, APA - The Engineered Wood Association, Tacoma, Washington, 1996.
[5] Wood Frame Construction Manual for One- and Two-Family Dwellings - 1995 SBC High Wind Edition, American Forest & Paper Association, American Wood Council, Washington, DC, 1996.
[6] Standard for Hurricane Resistant Residential Construction - SSTD 10-97, Southern Building Code Congress International, Inc., Birmingham, Alabama, 1997.
[7] Beyer, Donald E. Design of Wood Structures, Third Edition, McGraw-Hill, Inc. New York, NY, 1993.
[8] Hoyle, Robert J., Jr., and Woeste, Frank E. Wood Technology in the Design of Structures, Fifth Edition, Iowa State University Press, Ames, Iowa, 1986.
[9] Ambrose, James and Dimitry Vergun. Design for Lateral Forces, John Wiley & Sons, Inc., New York, NY, 1987.
[10] Wood Construction and Engineering Handbook, Chapter 8: Diaphragms and Shearwalls, by E. D. Diekmann.
[11] Dolan, J.D., and A.C. Johnson, Monotonic Tests of Long Shear Walls with Openings, Report TE-1996-001,Virginia Polytechnic Institute and State University, Brooks Forest Products Research Center, Blacksburg, VA, 1997.
[12] Dolan, J.D., and A.C. Johnson, Cyclic Tests of Long Shear Walls with Openings, Report TE-1996-002, Virginia Polytechnic Institute and State University, Brooks Forest Products Research Center, Blacksburg, VA, 1997.
[13] The Performance of Perforated Shear Walls with Narrow Wall Segments, Reduced Base Restraint, and Alternative Framing Methods, Prepared for the U.S. Department of Housing and Urban Development by the NAHB Research Center, Inc., Upper Marlboro, MD, 1998.
[14] Dolan, J.D., and C.P. Heine, Monotonic Tests of Wood-frame Shear Walls with Various Opening and Base Restraint Conditions, Report TE-1997-001, Virginia Polytechnic Institute and State University, Brooks Forest Products Research Center, Blacksburg, VA, 1997.
[15] Dolan, J.D., and C.P. Heine, Sequential Phased Displacement Cyclic Tests of Wood-frame Shear Walls with Various Opening and Base Restraint Conditions, Report TE-1997-002, Virginia Polytechnic Institute and State University, Brooks Forest Products Research Center, Blacksburg, VA, 1997.
[16] Building Code Requirements for Structural Concrete (ACI 318-95) and Commentary, American Concrete Institute, Farmington Hills, MI, 1996.
[17] Dolan, J.D., and C.P. Heine, Sequential Phased Displacement Tests of Wood-framed Shear Walls with Corners, Report TE-1997-003, Virginia Polytechnic Institute and State University, Brooks Forest Products Research Center, Blacksburg, VA, 1997.
[18] Guidelines for Seismic Rehabilitation of Buildings, FEMA Report 273, Federal Emergency Management Agency, Washington, DC, 1997.
[19] Structural Panel Shear Walls, Research Report 154, American Plywood Association, Tacoma, WA, 1993.
[20] Serrette, Reynaud, Georgi Hall, and Joang Ngyen. Shear Wall Values for Light Weight Steel Framing. Santa Clara University, Santa Clara, CA, 1996.
[21] Serrette, Reynaud, et al. Additional Shear Wall Values for Light Weight Steel Framing. Santa Clara University, Santa Clara, CA, 1997.
[22] Monotonic Tests of Cold-Formed Steel Shear Walls with Openings, prepared for the U.S. Department of Housing and Urban Development and the American Iron, Steel Institute, and the National Association of Home Builders by the NAHB Research Center, Inc., Upper Marlboro, MD, 1997.
Appendix A |
