Pallares and Hajjar

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