Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
B-1 A P P E N D I X B ACIâAASHTO Resistance Factor Investigation
B-2 COMPARISON OF ACI AND AASHTO NOMINAL AND FACTORED RESISTANCES This document compares the nominal and factored resistances of various concrete structures and steel anchor bolts as determined by ACI and AASHTO. In this document the following abbreviations are used: ACI = ACI 318-11 (2011) Building Code Requirements for Structural Concrete. AASHTO = AASHTO (2010) LRFD Bridge Design Specifications, Fifth Edition. DESIGN APPROACH In all structural design calculations, the loads, Q, must be less than or equal to the resistance R (Eqn. 1). Due to varying levels of uncertainty, modification factors are applied to both sides of the equation (Eqn. 2). Both AASHTO and ACI follow this approach, but the values of the modification factors vary. (Eqn. 1) (Eqn. 2) The factored resistance, Rr, is comprised of resistance factors, , and the nominal resistance, Rn (Eqn. 3). (Eqn. 3) Note, ACI and AASHTO use different terminology for the LRFD design which is summarized in Table 1. This document adopts the AASHTO terminology. Table 1: ACI and AASHTO LFRD terminology. Term ACI AASHTO Design strength Factored resistance Strength reduction factor Resistance factor Nominal strength Nominal resistance As the factored resistance, Rr, is comprised of resistance factors, , and the nominal resistance, Rn, this document will evaluate both separately. First equations related to several
B-3 general concrete design situations will be compared followed by a comparison of the equations for bolt shear and tension. CONCRETE DESIGN COMPARISON Nominal Resistance The following compares the nominal resistances for concrete flexure, shear, compression, and bearing. Nominal Flexural Resistance Both AASHTO and ACI assume the Whitney stress block for flexural design and use the same definition for the factor, 1, which relates the depth of the equivalent rectangular compressive stress block to neutral axis depth. Nominal Shear Resistance Provided by the Concrete For non-prestressed sections and using the simplified procedures in ACI §11.2.1.1 and AASHTO §5.8.3.4.1 the equations for nominal shear resistance provided by the concrete are: ACI Eqn. 11-3 AASHTO Eqn. 5.8.3.3-3 If we assume normal weight concrete, then =1. In the ACI equation, f c is in terms of psi but is in terms of ksi in the AASHTO equation. If AASHTO Eqn. 5.8.3.3-3 is converted to terms of psi, the equation would need to be multiplied by . The factor is defined as 2.0 in AASHTO §5.8.3.4.1. With these assumptions and adjustments, the shear capacity provide by concrete for both standards reduces to: ACI Eqn. 11-3 AASHTO Eqn. 5.8.3.3-3 Nominal Uniaxial Compressive Resistance For non-prestressed sections, both ACI §10.3.6 and AASHTO §5.7.4.4 define the uniaxial compressive resistance for sections with spiral and tie reinforcement as:
B-4 Spiral reinforcement ACI Eqn. 10-1 AASHTO Eqn. 5.7.4.4-2 Tie reinforcement ACI Eqn. 10-1 AASHTO Eqn. 5.7.4.4-2 Nominal Bearing Resistance Both ACI §10.14 and AASHTO §5.7.5 define the bearing resistance as: ACI §10.14 AASHTO Eqn. 5.7.5-2 The modification factor, m, is allowed by both ACI and AASHTO. The factor m is illustrated in Figure 1 and expressed by both as: ACI §10.14 AASHTO Eqn. 5.7.5-3 Figure 1: Calculation of area A2 (courtesy ACI). Summary The above study shows that the nominal flexural, shear, axial compressive, and bearing resistances are identical as calculated by ACI and AASHTO. Resistance Factors The resistance factors as listed by ACI and AASHTO for several common conditions are presented in Table 2.
B-5 Table 2: Comparison of ACI strength reduction factors and AASHTO resistance factors. Factor ACI 318-11 AASHTO Tension controlled section 0.90 9.3.2.1 0.90 5.5.4.2.1 Compression-controlled sections (Spiral reinforcement) 0.75 9.3.2.2 0.75 5.5.4.2.1 Compression-controlled sections (Tie reinforcement) 0.65 9.3.2.2 0.75 5.5.4.2.1 Shear (normal weight) 0.75 9.3.2.3 0.90 5.5.4.2.1 Shear (lightweight) 0.601 9.3.2.3 0.70 5.5.4.2.1 Bearing 0.65 9.3.2.4 0.70 5.5.4.2.1 Note: 1. Assuming an average value of = 0.80 from ACI 8.6.1, and for comparison with AASHTO, the ACI phi factor reported in this table is â = = (0.75)(0.80) = 0.60. Factored Resistance Since the nominal resistances, Rn, for flexure, shear, axial compression, and bearing are identical as determined by ACI and AASHTO, the factored resistances, Rr, will only vary by their resistance factors. Therefore, the ratios of the factored resistance determined by ACI and AASHTO are presented in Table 3. Table 3: Ratio of factored resistance determined by ACI to AASHTO. Factor ACI/AASHTO Tension controlled section 1.00 Compression-controlled sections (Spiral reinforcement) 1.00 Compression-controlled sections (Tie reinforcement) 0.87 Shear (normal weight) 0.83 Shear (lightweight) 0.86 Bearing 0.93 Summary For all the cases evaluated, ACI is either identical to or more conservative than AASHTO in determining the nominal and factored resistances. STEEL TENSILE DESIGN COMPARISON Nominal Resistance The equations for the tensile strength of an anchor (or bolt) as computed by ACI 318-11 and AASHTO are shown below:
B-6 ACI (D-2) AASHTO (6.13.2.10.2-1) Both futa and Fub are the specified minimum tensile strength of the anchor. ACI limits this to 125,000 psi or 1.9fya. Ase,N is the effective cross-sectional area of the anchor while Ab is the gross area of the anchor corresponding to the nominal diameter. Ase,N is defined by ANSI/ASME B1.1 for threaded rods and headed bolts in Eqn. 4 where da is the anchor diameter and nt is the number of threads per inch. Values of Ase,N are readily tabulated as in AISC (2005) Steel Construction Manual. (Eqn. 4) Table 4 shows that the 0.76 multiplier in AASHTO to compute the effective cross- sectional area from the nominal area is a reasonable approximation. Table 4: Comparison of effective and gross cross-sectional areas. Bolt diameter (in.) Ase,N (in.2) Ab (in.2) Ase,N/Ab 0.226 0.307 0.74 0.334 0.442 0.76 0.462 0.601 0.77 1 0.606 0.785 0.77 1 0.763 0.994 0.77 1 0.969 1.23 0.79 1 1.16 1.49 0.78 1 1.41 1.77 0.80 1 1.90 2.41 0.79 2 2.50 3.14 0.80 Note: Values obtained from AISC (2005) Steel Construction Manual, 13th Edition Table 7-18. Resistance Factors For steel tensile failure, in ACI §D.4.3 the resistance factors are 0.75 for ductile steel elements and 0.65 for brittle steel elements. In AASHTO §6.5.4.2 the resistance factors are 0.80 for all bolt types.
B-7 Factored Resistance For ductile anchors the ratio of the factored resistances calculated by ACI to AASHTO are presented in Table 5 for various bolt diameters. Table 5: Ratio of factored resistance for steel strength in tension as computed by ACI and AASHTO for ductile steel elements. Bolt diameter (in.) Nsa(ACI)/ Tn(AASHTO) 0.91 0.93 0.95 1 0.95 1 0.95 1 0.97 1 0.96 1 0.98 1 0.97 2 0.98 Note: The resistance factors used are =0.75 for ACI design equation and =0.80 for AASHTO design equation. Fub = futa. Summary The above ratio of factored resistances calculated by ACI to AASHTO varies between 0.91 and 0.98 over the selected range of anchor diameters. STEEL SHEAR DESIGN COMPARISON Nominal Resistance The equations for the shear strength of an anchor as computed by ACI are shown below: Cast-in headed stud ACI (D-28)
B-8 Cast-in headed bolt and hooked bolt anchors and for post- installed anchors where sleeves do not extend through the shear plane ACI (D-29) For post-installed anchors where sleeves extend through the shear plane or ACI §D.6.1.2(c) ACI §D.6.1.3 also reduces the shear strengths determined above with a 0.80 multiplier when anchors are used with built-up grout pads. The value of futa is as defined earlier. Ase,V is calculated per Eqn. 4 and is identical to Ase,N. The 0.60 multiplier in ACI (D-29) is based on the understanding that the shear strength is 60% of the tensile strength. Cast-in headed studs do not have the 0.60 multiplier as they have higher shear strengths attributed to the fixity of the weld between the bolt and the baseplate as discussed in ACI §RD.6.1.2. ACI §D.6.1.2(c) provides for the shear strength to be determined from tests in accordance with ACI 355.2-07 due to special shaft geometries, configurations, and the presence or absence of sleeves found in anchor bolt applications apart from the regular threaded rods and bolts addressed in AISC (2005) Table 7-18. The equations for the shear strength of an anchor as computed by AASHTO are shown below: Where threads are excluded from the shear plane AASHTO (6.13.2.7-1) AASHTO (6.13.2.12-1) Where threads are included in the shear plane AASHTO (6.13.2.7-2) Resistance Factors In ACI §D.4.3 the resistance factors are 0.65 for ductile steel elements and 0.60 for brittle steel elements. Based on the definition for ductile steel element in ACI §D.1, A307 and F1554 (within the range of bolt diameters listed) are considered ductile steel elements. In AASHTO §6.5.4.2 the resistance factors are 0.75 for A307 and F1554 bolts. These resistance factors are summarized in Table 6.
B-9 Table 6: ACI 318-11 and AASHTO resistance factors for steel shear strength by bolt type. Bolt ACI AASHTO A307 0.65 0.75 F1554 0.65 0.75 Factored Resistance For ductile anchors ratio of the factored resistances determined by ACI (D-29) to AASHTO (6.13.2.7-2) with threads included in the shear plane are presented in Table 7. Table 7: Ratio of factored resistance for steel strength in shear as computed by ACI and AASHTO for A307 & F1554 bolts. Bolt diameter (in.) Vsa(ACI)/ Rn(AASHTO) 1.01 1.03 1.05 1 1.06 1 1.05 1 1.08 1 1.07 1 1.09 1 1.08 2 1.09 Note: The resistance factors used are: o =0.65 for ACI 318-11 design equation. o =0.75 for AASHTO design equation. Fub = futa.. Assumes one shear plane. Summary The above ratio of factored resistances calculated by ACI to AASHTO over a range of anchor diameters varies between 1.01 and 1.09 for A307 and F1554 bolts. COMBINED SHEAR AND TENSION ACI provides a tri-linear expression in §D.7.1 for the interaction between shear and tension. AASHTO §6.13.2.11 provides an elliptical curve but allows for no reduction of the tensile load when Vu/Vn 0.33 (or when Vu/ Vn 0.44 assuming = 0.75). ACIâs approach is equal to or more conservative than AASHTOâs up until Vu/ Vn = 0.98 as illustrated in Figure 2.
B-10 Figure 2: Comparison of ACI and AASHTO tensile-shear interaction equations. ACI §RD.7 allows for any interaction expression which has been verified by test data, so either expression should be acceptable. However, it must be pointed out that the values used in the interaction expression are the limiting tension and shear limit states for the overall anchor design. While it is preferable that the limit states are steel failure, it is possible that the other limit states discussed in ACI Appendix D might control and should be used in the shear-tension interaction. CONCLUSION In conclusion, based on the comparison of the design approaches in ACI and AASHTO for concrete design and steel tension and shear design it would be acceptable to determine both the nominal and factored resistances of anchorage to concrete based on the design provisions from ACI Appendix D for use in designs in which the loads and other limit states were determined by the AASHTO.
