Cumulative overturning design for site-built and prefabricated shear walls

We all know that structures are subject to lateral forces. We’ve seen the awesome power of Mother Nature at work and learned valuable lessons from natural events, such as the Great San Francisco Earthquake of 1906; the Northridge, Calif., earthquake in 1994; and the destructive forces of wind during Hurricane Katrina in 2005. In wood-frame construction, building codes throughout the country either require structural engineers to calculate and design for wind or seismic forces or require contractors to build by a prescriptive method of resisting lateral forces.

Wood has become one of the most prolific building materials in the construction industry because of its versatility, availability, load capacity, and economic value. As such, a variety of design methods have been developed to resist lateral loads on wood structures. Within the past half-century, the use of site-built, wood-framed shear walls has grown in leaps and bounds as a means of resisting lateral forces. A relatively new design method also has arrived in the past decade: prefabricated shear walls, built out of wood or steel.

Wood structures today are one to six stories tall and include new design features such as higher floor-to-floor heights, taller doors, and larger window openings, typically along the front and rear exterior walls. Consequently, finding available wall space to meet the minimum load demands and wall lengths prescribed by the code is far more challenging when using site-built shear walls. The prefabricated shear wall was created out of the necessity to provide narrow shear wall solutions. These walls are designed to meet the high load and extreme aspect ratio demands. They also are being used in stacked configurations in multistory structures, introducing cumulative overturning into the designer’s calculations. Because of this, designers need to revisit the general mechanics of shear wall design as it applies to both site-built and prefabricated shear walls.

Fundamentals of shear wall design

When lateral (wind or seismic) forces engage the diaphragm of a structure, it’s easy to visualize the force pushing horizontally on the top of the shear wall. Sheathing then transfers the shear from the top of the wall to the bottom of the wall while holding the wall together to resist racking. If the bottom plate of the wall is anchored to the foundation to resist sliding, the far end of the wall will press down (compression force) and the near side of the wall will lift up (tension force)—this is overturning (see Figure 1).

The members at each end of a shear wall (typically wood studs or posts) are designed so that the capacity of these members will withstand the compression demand caused by overturning and gravity forces. The International Building Code (IBC), Section 2305.3.7 states, "Where the dead load stabilizing moment…is not sufficient to prevent uplift due to overturning moments on the wall, an anchoring device shall be provided. Anchoring devices shall maintain a continuous load path to the foundation." These components of the shear wall required to resist overturning are fundamental to the wall’s design, and proper calculation of the demand forces are important in single-story buildings and absolutely essential in multistory structures where forces are amplified and cumulative.

Errors to avoid

While the fundamental mechanics and code requirements for properly designing a shear wall are generally understood, a few unintentional errors may often spoil an otherwise good design. A common error is incorrectly calculating the overturning and resisting moments by using inaccurate moment-arm lengths. The use of the overall shear wall length as the resisting moment arm underestimates the actual overturning forces, as it uses a lengthened moment-arm dimension. To derive the correct tension and compression force, the resisting moment arm should be measured from the center of the compression-force resistance to the center of the tension-force resistance. This measurement can vary depending on the type of shear wall specified.

With a traditional site-built shear wall with a post/anchoring device (holdown), the resisting moment arm is measured from the center of the post or stud-pack to the center of the anchor bolt in the holdown device (see Figure 2).

The resisting moment arm for a prefabricated wood shear wall may be very similar to a site-built wall of the same dimension, but can vary depending on its construction. Similarly, prefabricated steel shear walls may not have an easily identifiable resisting moment arm. Instead, it is dependent upon how the wall is fabricated. Therefore, it’s important to seek information from the prefabricated shear wall manufacturer to find the correct moment arm for overturning resistance when specifying these products. Typically this information is provided in the manufacturer’s catalog and on its website (see Figure 3).

A different resisting moment arm exists for a hybrid rod/bearing-plate system. In this system, the compression members are typically symmetrical around the rod on each end of the shear wall, and therefore the resisting moment arm measures from the center of the rod to the center of the rod at each end (see Figure 4).

Factoring in cumulative overturning

When designing multistory structures, an extremely critical factor in shear wall calculation is cumulative overturning. In a multistory application, the overturning forces are magnified. If site-built shear walls are utilized, the resisting moment arm may shrink at each lower level as more compression studs are potentially required to resist the collective load demand. In addition, the overturning moment calculation must now incorporate the floor depth(s), increasing the moment arm length.

High aspect-ratio prefabricated shear walls are often installed in a stacked configuration. Simpson Strong-Tie recommends designers limit the stacking of prefabricated shear walls to two stories because of the high cumulative overturning forces inherent in this installation. Shear and the associated overturning forces, due to seismic/wind requirements, must be carried down to the foundation by the building’s lateral-force resisting system. These forces are cumulative over the height of the building, and shear forces applied at the second and higher levels of a structure will generate much larger base-overturning moments than the same shears applied at the first story.

Some reference texts have indicated that the overturning force is directly proportional to the unit shear and the plate height of the wall. Furthermore, when designing for cumulative overturning, these references imply that it’s acceptable simply to use the summation of this unit shear method in multistory applications to find the tension/compression forces at the lowest level. Although this method provides a fairly accurate preliminary estimate of the overturning force for a one-story building, it will significantly understate the actual forces on a multistory structure.

Calculating cumulative overturning

Correctly calculating cumulative-overturning forces at the bottom of a given floor requires the use of statics. To find the overturning moment, multiply the applied diaphragm shear force at each story above the current level you are designing by the overturning moment arm. The overturning moment arm extends from the base of the level you are designing to each diaphragm level above. Add these moments together and then divide this moment by the respective resisting-moment-arm length of the shear wall on the level in design. This provides the overturning tension and compressive forces. If cumulative overturning is not calculated properly using statics, the actual demand may be several times greater than the capacity of the lower shear wall, anchor bolts, and foundation. This can lead to premature failures within the lateral-force resisting system.

A matter of life safety

The main concern for a structural engineer is to design structures that provide life safety. Life safety is critical in multistory structures when designing the lateral-force resisting systems to withstand the maximum code-prescribed wind and seismic forces. With the recent surge of two-story, single-family production homes and the high demand for new mid- to high-rise buildings, there’s a greater need to ensure that the overturning forces in these structures are properly calculated. Using over-simplified shear wall design assumptions or a statically incorrect method to calculate cumulative-overturning forces may subject the public to life-safety concerns that can be avoided. It also potentially subjects designers to liabilities beyond their insurance limitations. By understanding the underlying elements of cumulative-overturning design and how it applies to the different lateral-resisting systems in wood-frame construction, we can provide safe and economical solutions for multistory structures in which we all can live, work, and play.

Bryan D. Wert, M.S., P.E., is a branch engineer for Simpson Strong-Tie. He works in McKinney, Texas, and services the Southeast region. He can be reached at bwert@strongtie.com.