by Trent Nagele, John Lawson, and Jeff Griffin

Tilt-up concrete construction has grown to be one of the most widely used methods (by square footage) of constructing low-rise buildings in the United States. The most common form is a single-story building with tall, slender concrete walls. Design of these slender walls is usually controlled by out-of-plane flexure and deflection with design typically following the alternative slender wall provisions in Section 11.8 of ACI CODE-318-19(22).¹ The historical basis for these provisions can be traced back to full-scale tests performed in the early 1980s by a joint venture of the Southern California Chapter of ACI (SCCACI) and the Structural Engineers Association of Southern California (SEAOSC).² These results were validated in recent tests conducted by the University of Nebraska in a 2022 report prepared for the Tilt-Up Concrete Association (TCA).³ This history is important because it validates the underlying assumptions of the design method. Wall designers who lack the appreciation of this history may implement different theoretical approaches with the belief that their efforts will increase accuracy and efficiency. But these usually run counter to the experimental behavior observed and can lead to significantly unconservative wall designs. Common errors include: 

• Using an effective moment of inertia instead of a cracked moment of inertia for strength design with second-order p-delta (P-Δ) effects; and 
• Using an incorrect modulus of rupture. 

In some instances, these errors may be facilitated by commercially available software packages—either by providing them as alternate methods or by embedding one or both within the source code. 

For additional information and more in-depth discussion of the topics in this article, refer to ACI’s TechNote, PRC-551.3-21, “Pitfalls of Deviating from ACI 318 Slender Wall Provisions.”⁴ 

Moment of Inertia

Designing slender walls for out-of-plane bending requires consideration of second-order effects. In some cases, the added moments from second-order effects can exceed the primary moments. Calculation of the second-order moments is a direct function of the out-of-plane deflection, which is dependent on the moment of inertia for the cross section. 

The response of slender wall panels was well established by testing in the 1980s and follows a clear bilinear curve when plotting lateral load or moments versus deflection (Fig. 1). The sudden change in slope at the inflection point in the curve is associated with cracking. At lower moments, the uncracked panel has an elastic response with very little deflection as shown by the nearly vertical portion of the curve. This portion of the curve uses a moment of inertia nearly equal to the gross moment of inertia, I_g. Once the panel cracks, however, the deflection increases dramatically with small increases in pressure or moment. At higher pressures, the deflections approach those associated with response found using the cracked moment of inertia, I_cr. 

Fig. 1: Comparison of wall deflection using different methods. Note that “Branson Eq.” is the equation used in ACI 318-99⁵ to 318-05,⁶ “Wall Response” is from the SEAOSC Slender Wall Task Group7 test data (from Bischoff and Scanlon⁸)

To use this observed wall response curve for design, the design equations in ACI CODE-318-19(22), Section 11.8, consider two distinct checks representing strength design (Section 11.8.3) and service deflection (Section 11.8.4). The intent of strength design is to ensure that minimum life-safety requirements are met. Because of this, Eq. (11.8.3.1c) prescribes the use of I_cr to calculate factored design moment, M_u. This approach recognizes that as the applied moment nears the nominal moment strength, the cross section’s moment of inertia approaches I_cr as Fig. 1 illustrates. This cracked section assumption also ensures a predictable and ductile failure mechanism, which is a fundamental philosophy of concrete design. 

In contrast, service deflection estimates the panel’s out-of-plane deformation at a lower force level and evaluates the panel’s serviceability using an iterative approach. Because of these differences, the service design equations have a two-part format (Table 11.8.4.1) to represent the bilinear curve of observed behavior assuming an uncracked or partially cracked section with an effective moment of inertia, I_cr or I_eff. 

The use of I_cr for strength design is intentional, and it would be a mistake to assume I_e can be casually substituted for greater accuracy and efficiency for the following reasons: 

• As evident in Fig. 1, wall stiffness drops precipitously at the onset of cracking. If the wall stiffness is based on a partially cracked section consistent with I_eff, slight inaccuracies in the calculated load or section properties can lead to significant inaccuracies in the calculated deflections and associated second-order moments;
  
• Most design engineers and commercial software programs use a stress-block model based on a fully cracked section for computation of the nominal moment capacity, M_n.  It’s important to be consistent and use a fully cracked philosophy on both the demand and capacity sides of the inequality φM_n ≥ M_u (Section 4.6.2).
  
• ASCE 7-16⁹ seismic forces for a design level earthquake are less than expected levels because of the anticipated benefits of the element’s ductility to resist overloads; however, this implies that the concrete section is more likely to fully crack than the design forces suggest, potentially leading to a sudden loss of out-of-plane stiffness; and
  
• Prior to a design-level event, a panel will be affected by lifting stresses, restraint of shrinkage or thermal contractions, or other previous loadings.  Consequently,there is no  way to ensure   it will not have already cracked beyond that predicted by design loads alone..
  

Despite these reasons, some designers (often aided by software) have chosen to use I_eff or I_e for strength design in place of I_cr, leading to potentially unsafe designs.

Modulus of Rupture

Following the full-scale slender wall tests, design equations were developed and eventually adopted by the Uniform Building Code (UBC) in the 1988 edition¹⁰. When the International Code Council created a single national model code in 2000,¹¹ the slender wall provisions from the 1997 UBC¹⁰ were incorporated in part into ACI 318-99, which was referenced by the 2000 IBC.¹¹ To make the slender wall design serviceability provisions fit better into ACI Code, two key parameters were changed to align with well-established formulations. The first was to replace I_crwith Branson’s effective moment of inertia, I_e, for serviceability design, which underestimated service-load deflections. The second was to increase the modulus of rupture, f_r, to 7.5√f_c‘ to align with the traditional equation provided in the ACI Code (refer to ACI CODE-318-19(22), Section 19.2.3.1). However, these changes created unconservative design results that did not accurately match the original SCCACI-SEAOSC Task Committee on Slender Walls test data.² The ACI 318-99 provisions were corrected in ACI 318-08¹² and future editions to maintain the fidelity of the original UBC design provisions after a SEAOSC Slender Wall Task Group⁷ validated the concerns (Ref. Lawson 2007)¹⁴.

The modulus of rupture predicts the transition point in the bilinear curve between the near vertical (uncracked) and near horizontal (cracked) portions of the curve. The SCCACI-SEAOSC Task Committee on Slender Walls test data² revealed the moment at first crack, M_cr = f_r × S, corresponded to a modulus of rupture of 5.0√f_ć   instead of the commonly used 7.5√f_ć in ACI 318 due to internal shrinkage restraint tensile forces (Ref. Gilbert 1999¹⁵). To correct for this difference, ACI 318 elected to place a two-thirds factor on M_cr and Δ_cr for slender walls instead of changing the 7.5 factor to 5.0. Nevertheless, some design engineers continue to face the option of using 5.0 versus 7.5 in some software programs without fully appreciating the consequences of their selection. 

Given this background, when prompted by a spreadsheet or program during the design process to specify the modulus of rupture, it is important to understand whether the design methodology being used internally is going to make the two-thirds adjustment or if it’s expected the designers will make adjustment on their own. When this confusion has occurred, significant inaccuracies in the analysis have resulted. 

Example Problems

The following text summarizes two examples provided in ACI PRC-551.3-21, demonstrating the effects of erroneously using I_e for strength design in slender walls and using 7.5√f_ć for calculation of I_e in strength checks. Code required serviceability checks are not addressed. Readers are encouraged to review ACI PRC-551.3-21 for details. 

Example 1

Example B.1 in ACI 551.2R, “Guide for the Design of Tilt-Up Concrete Panels,”¹³ is a panel 6-1/4 in. thick, 15 ft wide, 31 ft tall (29.5 ft unbraced length) supporting three roof joists, each with a load of 2.4 kips (dead load, D) and 2.5 kips (roof live load, L_r). Lateral load on the panel is 27.2 lb/ft² from wind (W). The panel is reinforced with No. 6 bars at about 12 in. spacing located in the center of the panel thickness. 

Following the slender wall provisions in ACI 318 and correctly using I_cr for the second-order effects, the total factored moment in the panel for load case (1.2D + 1.6L_r+ 0.5W) is 61.2 kip-ft and the deflection under factored loads, Δ_u, is 10.0 in. Several of the key parameters are summarized in the left column of Table 1. 

If the same panel is analyzed using I_e in place of I_cr, the results vary dramatically.

The results from this analysis are summarized in the right column of Table 1. Similar results would also be achieved if Branson’s effective moment of inertia equation was used. 

Table 1:

Summary of Example 1 results. Values for I_e (right two columns) illustrate incorrect results 

In comparing these design solutions notice that a negative value for I_e is calculated. This occurs because applied moment M_ua is less than M_cr and indicates that the panel is uncracked. Therefore, I_g is used in place of I_eor I_cr for the remainder of the analysis, even though I_g is over ten times the cracked moment of inertia prescribed by the ACI 318 equations. Using I_e = I_g, the resulting M_u in the uncracked section is then calculated to be 26 kip·ft, which is only 42% of the design moment required by ACI 318 using the assumption of a cracked section. The deflection of 0.4 in. is only 4% of the 10.0 in. calculated by ACI 318 deflection. While it may be tempting to argue that use of I_g is justified because M_ua is less than M_cr, and the panel is not cracked, this can lead to a panel design that is significantly deficient, particularly in light of the four concerns discussed previously. If the reduced moment and deflection values are used to size the reinforcing, the panel will be vulnerable to a sudden loss of out-of-plane stiffness if it cracks prior to, or during, a design event, which would then result in a dramatic increase in unexpected P-Δ moments that exceed the capacity of the reinforcing. 

Example 2

Example 2 is a panel 6-1/2 in. thick, 8 ft. wide, 30 ft. tall (28.0 ft unbraced length) supporting a single girder load of 18.6 kips (D) and 31.8 kips (L_r). Lateral load on the panel is 23.0 lb/ft² from wind (W). It is reinforced with No. 5 bars at 16 in. spacing in the center of thickness. 

In this example, I_e will first be used to analyze the proposed design and then checked using the prescribed ACI 318 equations I_cr. 

Table 2 summarizes the results from this panel analysis and shows the results of calculations based (incorrectly) on I_eversus I_cr. Note again that I_e was computed as negative, indicating an initially uncracked panel, so I_e is assumed to be equal to I_g.

Table 2:

Summary of Example 2 results. Values for I_e(left two columns) illustrate incorrect results 

The left two columns in Table 2 summarize results from using I_e (M_u of 17.8 kip·ft and deflection of 0.42 in.). This analysis incorrectly justifies the assumed reinforcing (No. 5 bars at 16 in. spacing in the center of the panel). An experienced designer would be wary of this because it’s common for panels supporting heavy girder loads to be reinforced with a “cage” that incorporates bars at each face. 

The right two columns of Table 2 show the parameters computed using the ACI 318 provisions, and these results raise additional concerns. M_u appears to be −15.7 kip·ft, with a deflection of −4.28 in. The minus signs in these values are red flags since this is a simply supported panel and there shouldn’t be any negative moments. 

To illustrate what is happening here, consider Fig. 2 which shows a plot of M_u versus the effective area of steel, A_se. At low levels of reinforcing, M_u erroneously appears with a negative value and increases toward an asymptote indicating potential instability. ACI 551.2R-15 notes that the minimum area of steel that should be selected is the point where the nominal flexural strength, φM_n, intersects a positive M_u (refer to the red arrow in Fig. 2). For this panel, however, φM_n is 47.3 kip·ft, which mathematically is greater than either M_u of 17.8 kip·ft calculated using I_e, or M_u of −15.7 kip·ft calculated using ACI 318. φM_n is also greater than M_cr, which is a provision required by ACI CODE-318-19(22), Section 11.8.1.1c. However, the design is still not acceptable. 

Fig. 2: Variation of factored moment and nominal moment capacity as area of effective tension reinforcement increases (Fig. Ba in ACI 551.2R-15¹³)

To get a meaningful positive M_u, the panel stiffness, K_b, needs to be increased. This is most easily accomplished by increasing the reinforcing depth either by placing bars at each face of the panel or simply by thickening the panel. By using reinforcement at each face here, the appropriate M_u based on ACI 318 methodology is approximately 61 kip·ft and avoids an over-reinforced condition (ρ < 0.6ρ_bal) that would result if center bars were spaced more closely. This is a significantly different design than the design that was falsely shown to be adequate when checked using I_cr. The example therefore highlights the dangers of blindly following equations and ignoring implausible results. If a negative M_u is accepted at face value, adjusting the amount of reinforcing alone is not likely to substantially change the erroneous result. 

Conclusions

The provisions for slender wall design provided in ACI CODE-318-19(22), Section 11.8 have been empirically validated using data from full-scale tests. If designers or their design software employ substitute equations or methodologies—either inadvertently by using outdated ACI 318 provisions or intentionally by using alternative theories in search of more accuracy or efficiency—the result could be panels that do not have adequate strength and stiffness. This can lead to wall panels that are very sensitive to cracking and are capable of dramatic, unexpected increases in P-Δ moments. Designers are encouraged to review their calculations and design methodology considering the intent of the current ACI 318 provisions and their underlying empirical basis. If substitute equations or alternate methodologies are used, designers must ensure they are employed rationally and are consistent with observed behavior from a full-scale testing program. If this is not possible, the resulting panel may be vulnerable to a sudden loss of stiffness when cracking occurs.

References

1. ACI Committee 318, “Building Code Requirements for Structural Concrete and Commentary (ACI CODE-318-19) (Reapproved 2022),” American Concrete Institute, Farmington Hills, MI, 2019, 624 pp.
2. ACI-SEAOSC Task Committee on Slender Walls, “Test Report on Slender Walls,” J.W. Athey, ed., ACI Southern California Chapter and Structural Engineers Association of Southern California (SEAOSC), Los Angeles, CA, 1982, 134 pp.
3. Maguire, M., and Al-Rubaye, S., “Tilt-Up Partially Composite Insulated Wall Panels,” Tilt-Up Concrete Association, Mount Vernon, IA, 2022, 399 pp.
4. ACI Committee 551, “Pitfalls of Deviating from ACI 318 Slender Wall Provisions—TechNote (ACI PRC-551.3-21),” American Concrete Institute, Farmington Hills, MI, 2021, 12 pp.
5. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-99) and Commentary (ACI 318R-99),” American Concrete Institute, Farmington Hills, MI, 1999, 391 pp.
6. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05),” American Concrete Institute, Farmington Hills, MI, 2005, 430 pp.
7. Ekwueme, C.; Lawson, J.; Pourzanjani, M.; Lai, J.S.; and Lyons, B., “UBC 97 and ACI 318-02 Code Comparison – Summary Report,” SEAOSC Slender Wall Task Group, Jan. 2006, 47 pp.
8. Bischoff, P., and Scanlon, A., “Effective Moment of Inertia for Calculating Deflections of Concrete Members Containing Steel Reinforcement and Fiber-Reinforced Polymer Reinforcement,” ACI Structural Journal, V. 104, No. 1, Jan.-Feb. 2007, pp. 68-75.
9. ASCE 7-16, “Minimum Design Loads and Associated Criteria for Buildings and Other Structures,” American Society of Civil Engineers, Reston, VA, 2017, 800 pp.
10. “1988 Uniform Building Code,” International Conference of Building Officials, Whittier CA, 1989, 926 pp.
11. “1997 Uniform Building Code,” Volume 2: Structural Engineering Design, International Conference of Building Officials, Whittier, CA, , Apr. 1997, 492 pp.
12. “2000 International Building Code (IBC),” International Code Council, Falls Church, VA, 2000, 796 pp.
13. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2008, 465 pp.
14. Lawson, J.,”Deflection Limits for Tilt-up Wall Serviceability,” Concrete International, V. 29, No. 9, Sept. 2007, pp. 33-38.
15. Gilbert, R.I., “Deflection Calculations for Reinforced Concrete Structures – Why We Sometimes Get It Wrong,” ACI Structural Journal, V.96, No. 6,  Nov.-Dec. 1999, pp. 1027 – 1032.
16. ACI Committee 551, “Design Guide for Tilt-Up Concrete Panels (ACI 551.2R-15),” American Concrete Institute, Farmington Hills, MI, 2015, 72 pp.

Selected for reader interest by the editors.

Bischoff, P., and Darabi, M., 2012, “Unified Approach for Computing Deflection of Steel and FRP Reinforced Concrete,” Andy Scanlon Symposium on Serviceability and Safety of Concrete Structures, ACI SP-284, American Concrete Institute, Farmington Hills, MI. (CD-ROM) 

Gilbert, R. I., 1999, “Deflection Calculations for Reinforced Concrete Structures – Why We Sometimes Get It Wrong,” ACI Structural Journal, V. 96, No. 6, Nov.-Dec., pp. 1027-1032. 

Lawson, J., 2007, “Deflection Limits for Tilt-up Wall Serviceability,” Concrete International, V. 29, No. 9, Sept., pp. 33-38. 

ABOUT THE AUTHORS

Trent Nagele, P.E., S.E., MACI

Trent Nagele is a Structural Engineer and Senior Principal with VLMK Engineering + Design. He is one of the primary authors, along with John Lawson and Jeff Griffin, of ACI 551 Committee’s recently published PRC-551.3-21 Tech Note.  Trent has an MS degree in structural engineering and over 27 years of design practice experience with a broad range of project and construction types. He has been part of the review committee for several tilt-up documents, including FEMA P1026, the Tilt-up Concrete Association’s Engineering Tilt-Up, and Limit Design of Tilt-Up publications. 

John Lawson, P.E., S.E., MACI

John Lawson is Professor in Architectural Engineering at Cal Poly, San Luis Obispo, and a licensed Structural Engineer (CA, AZ). With over 25 years of design experience, Lawson oversaw the engineering of over 100 million square feet of tilt-up building construction. He has a BS in Architectural Engineering from Cal Poly, San Luis Obispo, and a MS in Structural Engineering from Stanford University, and is a member of ACI Committee 551.

Jeff Griffin, PhD, P.E., P.M.P., MACI

Jeff Griffin is a senior project manager with LJB Inc. (Miamisburg, OH). He designs and manages the construction of single and multi-story office, warehouse, military, and retail buildings. In his 26-year career, Mr. Griffin has designed facilities with a variety of building materials but has particular expertise in the design of structures built with site cast tilt-up concrete wall panels. He is a past chair of the ACI 551 Tilt-Up Committee and co-chaired the publication of a tilt-up industry design guide through the American Concrete Institute. Mr. Griffin holds professional registration in 14 states and has certification as a Project Management Professional.