Tall, Slender Masonry Walls

Two Strength Design Approaches.

The strength design procedure for tall, slender walls is found in Section 9.3.4.4 of TMS 402-22 and in Section 9.3.5.4 of TMS 402-16 and TMS 402-13. This procedure requires that the engineer accounts for P-delta effects. This can be done in one of three ways. The first is a step-function analysis, which is iterative. The second allows the use of a second-order analysis, such as that used in some software. The third is a moment magnifier method that is less cumbersome than the step-function method but can also be more conservative. This article reviews the step-function method and the moment magnification method.

The step-function method dates back to the 1985 Uniform Building Code (UBC) and limits the axial capacity of a tall, slender wall to 20% of f‘_m, unless the effective height to nominal thickness, (h/t) exceeds 30. If h/t exceeds 30, then the maximum axial capacity drops to 5% of f‘_m. Such a large step function is unusual and may puzzle some engineers.

Using a nominal 8-inch-thick masonry wall and an h/t ratio of 30 limits the wall height to 20 feet. Many masonry structures, such as big box stores, supermarkets, auditoriums, and gymnasiums, have 8-inch masonry wall heights greater than 20 feet, triggering the 5% of f‘_m limitation.

The origin of this large step-function method dates back to 1979. At that time, the maximum effective height to nominal thickness of a masonry wall was limited to 25. The only masonry design provisions in the code at that time were based on allowable stress design. There was a new procedure for the design of tilt-up concrete walls, but the City of Los Angeles wanted the theory behind this procedure validated. For these reasons, in 1979, the Structural Engineers Association of Southern California (SEAOSC) and the American Concrete Institute, Southern California Chapter (ACI-SC) formed the “Task Committee on Slender Walls.” The task committee tested 32 full-scale slender walls constructed of concrete masonry, clay masonry, and concrete. All of the test specimens were 4 feet wide and 24 feet, 8 inches tall. Thicknesses ranged from 4.75 inches to 9.63 inches. The h/t ratios of these walls ranged from 30 to 60.6, so all of them exceeded the then-current limiting h/t ratio of 25. The tests subjected all of the walls to small eccentric vertical loads of either 320 plf or 860 plf, to simulate lightweight panelized wood roof loads at a purlin or girder. An airbag was used to simulate static wind loads. Applied lateral loads ranged from 40 psf to 162 psf, and deflections under those loads ranged from 7 to 19.6 inches. Figure 1 presents a graphical representation of the test frame. Figure 2 shows a masonry wall being tested.

The original report was published by ACI-SC and SEAOSC. The results of this work were also reported as “Design of Reinforced Masonry Tall Slender Walls,” published by the Western States Clay Products Association in 1984. Finally, the Masonry Institute of America published the results in 1984 and updated them after the 1994 UBC was published. 

These test reports resulted in the adoption of tall, slender wall strength design provisions, which first appeared in the 1985 UBC. Based on the “Task Committee on Slender Walls” testing program, the maximum h/t ratio was increased from 25 to 30 in the 1985 UBC, and the maximum axial capacity was limited to 4% of f‘_m. In subsequent editions of the UBC, the 4% limit was raised to 5%. The 5% limit is in effect because the wall tests used very light axial loads. This procedure was introduced into the 2002 masonry standard and modified in the 2005 masonry standard. It has remained relatively unchanged between 2005 and 2022.

The step-function design procedure first presented in the 1985 UBC is itself a second-order analysis. When the design moment is applied, the wall deflects. The axial load, acting on the deflected wall produces secondary moments, which increase the deflection. The secondary moment is added to the design moment and the wall is reanalyzed. Since the sum of the design moment and the secondary is larger, it produces a larger deflection. The analysis is repeated again with this larger deflection and increased secondary moment. The procedure is iterative. The secondary moments and deflections are typically smaller and smaller in each iteration. After several iterations, the increase in secondary moments and deflections typically are reduced to the point where the system can be considered stable. The commentary of TMS 402 states that “The designer should examine all moment and deflection conditions to locate the critical section…” This includes roof and, if appropriate, floor diaphragm deflections.

Structural engineers use second-order analysis to account for P-Δ effects in frames with lateral loads. There is, however, a way of avoiding the use of the step-function procedure, or any other second-order analysis. This is the third method mentioned at the beginning of this article. It uses a magnified first-order analysis. 

One way of magnifying the moments derived from a first-order analysis is to apply increased column buckling effective lengths. This methodology can be cumbersome. For masonry and concrete structures, the more common approach is the application of a moment magnifier. This method is used in the strength design of both concrete and masonry elements. TMS 402 has used a moment magnifier approach for P-Δ strength design of unreinforced walls since the 2008 edition of TMS 402. When the committee started looking for an alternate approach for the design of tall, slender reinforced masonry walls, the use of a moment magnifier was an obvious choice. In TMS 402/602-13, a new moment-magnifier analysis method was added at Section 9.3.5.4.3. It is in Section 9.3.4.4.3 in TMS 402/602-22. 

Because the moment magnifier analysis is not iterative, it reduces design time substantially. The moment magnifier methodology eliminates the step function, the 20% of f‘_m limitation on the maximum strength design axial stress of the wall, the h/t limitation of the tall, slender wall design and tends to be conservative.

While providing an actual design example is beyond the space limitations of STRUCTURE Magazine, a design example from a 2018 seminar presented by the Northwest Concrete Masonry Association demonstrates the difference in the amount of effort required by these two methods. The out-of-plane wall design example was for a 22-foot tall, 8-inch nominal, concrete masonry wall. The wall was lightly loaded and did not exceed the 5% f‘_m limitation. Seismic loads controlled the out-of-plane design. The tall, slender design procedure resulted in vertical reinforcement of #5 at 24 inches on center. The design procedure included two iterations for service load deflections and four iterations for flexural capacity and strength level deflections. No iteration was required for the moment magnifier method

The strength level moment for the tall, slender wall procedure was 2.22 kip-ft per foot. The moment magnifier method was more conservative and had a strength level moment of 3.08 kip-ft per foot. However, both methods resulted in #5 at 24 inches on center for the vertical reinforcement. The service load deflection for the tall, slender wall procedure was 0.16 inches, which was less than the 0.20 inch service load deflection using the moment magnifier method. Both service load deflections were far less than the allowable deflection of 1.85 inches for this 22-foot tall wall.

Conclusion

This example highlights that moment magnifier method is conservative. In this case, conservatism did not result in additional reinforcement. There may well be cases where the moment magnifier method may require additional reinforcement, or an increase in masonry unit strength. Nonetheless, its savings in design time; and the elimination of the 0.5 f‘_m step function, the 20% of f‘_m limitation on the maximum strength design axial stress of the wall, and the h/t limitation of the tall, slender wall design should make it attractive to structural engineers designing tall, slender walls.■