Pallares and Hajjar

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L. Pallarés, J.F. Hajjar / Journal of Constructional Steel Research 66 (2010) 198–212 207 Fig. 5. Test-to-predicted values using only the steel formula (a, c, e, g) or the minimum of the steel and concrete formulas (b, d, f).
208 L. Pallarés, J.F. Hajjar / Journal of Constructional Steel Research 66 (2010) 198–212 Table 7 Evaluation of concrete formulas for headed stud anchors in shear from AISC 2005, EC-4, and proposed concrete formulas. Formula for Qnvc a µ σ C.O.V. φ β = 3 β = 4 AISC 2005 EC-4 � 0.5As f ′ c Ec Cv0.5 0.827 0.250 0.302 0.49 0.41 � f ′ c Ecm 0.965 0.249 0.258 0.61 0.52 Proposal 1 17.000As 17As � � ′ 0.452 f c (Ec) 0.041 � � ′ 0.45 f c (Ec) 0.04 � � ′ 0.209 Proposal 2 6.214As f c Ec � � ′ 0.2 6.2As f c Ec Proposal 3 18.197As 18As � � ′ 0.479 0.215 f c (h) � � ′ 0.5 0.2 f c (h) Proposal 4 8.915λ � f ′ �0.476 1.373 0.564 c (d) (h) 9λ � f ′ �0.5 1.4 0.6 c (d) (h) a Optimized formula/Simplified formula. Units: kips, inches. formulas of Proposals 1–3 (Fig. 6(a)–(c)) incorrectly control for hef /d > 4.5, even though steel failure often occurs in those tests. In Proposal 4 (Fig. 6(d)) (which is similar to the concrete formula of PCI 6th Edition) and in ACI 318-08 (Fig. 6(e)), prediction of the type of failure typically matches better with the actual failure mode. However, the results of using the minimum of the steel and concrete formulas tend to be unnecessarily conservative for hef /d > 4.5, and the prediction may be reasonable based upon 1.001 0.242 0.242 0.65 0.56 1.013 0.245 0.242 0.66 0.57 1.002 0.242 0.242 0.65 0.56 1.098 0.265 0.242 0.71 0.62 0.999 0.237 0.237 0.65 0.57 0.997 0.237 0.237 0.65 0.57 1.021 0.219 0.214 0.69 0.61 0.955 0.206 0.216 0.64 0.56 checking only the steel formula, as mentioned above, due to the limited cases with concrete or mixed failures and the reasonable predictions made for those specific cases using the steel formula. While Table 9 and Figs. 5 and 6 include tests with both normal-weight and lightweight concrete, to be conservative, all of the recommendations discussed so far in this section could be limited to the use of normal-weight concrete. This is because for lightweight concrete, 35% of the tests have hef /d > 4.5, whereas
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