Pallares and Hajjar

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Table 2 Headed steel anchor test configurations. Reference hef /d # Tests Viest (1956) [7] Shoup and Singleton (1963) [40] Chapman and Balakrishnan (1964) [41] Buttry (1965) [22] Chinn (1965) [9] Mainstone and Menzies (1967) [12] L. Pallarés, J.F. Hajjar / Journal of Constructional Steel Research 66 (2010) 198–212 201 2.47, 2.55, 3.23, 3.22, 4.53, 4.67, 4.77, 5.50, 7.00 8.00, 6.30, 5.20, 6.67, 9.33, 9.65 12 1 Type Type of test Type of concrete Range of f ′ c ksi (MPa) 4 studs (2 per side) Normal: 12 tests 3.19–4.39 8 studs (4 per side) Lightweight: 0 tests (22.0–30.2) 9 2 8 studs (4 per side) 2, 3.29, 4.67, 7.29 9 1 4 studs (2 per side) 2.00, 3.33, 3.50, 4.67, 5.38, 5.90, 7.38 3.33, 3.38, 3.41, 4.00, 4.67, 5.38, 4.67 22 1 4 studs (2 per side) 10 1 4 studs (2 per side) 4.67 11 1 4 studs (2 per side) Davies (1967) [11] 4.67 19 Steele (1967) [10] 3.50 18 1 4 studs (2 per side) Dallam (1968) [24] 4.00, 4.67, 5.90, 7.38 17 1 4 studs (2 per side) Baldwin (1970) [25] 3.50, 4.00, 4.67, 5.90, 7.38 26 1 4 studs (2 per side) Menzies (1971) [42] 4.67 6 1 4 studs (2 per side) Hawkins (1971) [44] 2.00, 2.33, 2.86, 3.00, 3.51, 4.00, 4.67 22 2 1, 2, 3 Ollgaard et al. (1971) [15] 3.50, 4.21 48 1, 2 Klingner and Mendonca (1982) [45] Hawkins and Mitchell (1984) [34] 11 8 5 ‘‘In the field’’ 3.33 2 5 ‘‘In the field’’ Jayas and Hosain (1989) [26] 4.30 1 3 12 studs (6 per side) Zhao (1993) [46] 2.27, 2.96, 4.09 18 5 ‘‘In the field’’ An and Cederwall (1996) [47] 3.51 8 2 8 studs (2 per side) Gattesco et al. (1996) [35] 6.58 1 5 ‘‘In the field’’ Saari et al. (2004) [39] 6.67 2 4 4 studs (2 per side) Shim et al. (2004) [43] 5.68, 5.22, 4.70 17 2 8 studs (4 per side) Anderson and Meinheit (2005) [4] 3.62, 4.21, 4.81, 5.32, 5.93, 9.84 unsafe for 60% of the tests. The results for EC-4 (2004) are more conservative, since 309 of the 391 tests resulted in ratios less than 1, indicating that the formula is unsafe for 21% of the tests. 105 5 ‘‘In the field’’ Normal: 9 tests 3.43–4.89 Lightweight: 0 tests (23.6–33.7) Normal:9 tests 3.64–6.10 Lightweight: 0 tests (25.1–42.0) Normal:9 tests 3.02–6.22 Lightweight: 13 tests (20.8–42.9) Normal:8 tests 3.99–5.48 Lightweight: 2 tests (27.5–37.8) Normal:11 tests 3.74–5.02 Lightweight: 0 tests (25.8–34.6) 4, 6, or 8 studs Normal:19 tests 3.76–5.52 (2, 3, or 4 per side) Lightweight: 0 tests (25.9–38.0) Normal:3 tests 2.98–4.37 Lightweight: 15 tests (20.5–30.1) Normal:2 tests 3.89–6.11 Lightweight: 15 tests (26.8–42.1) Normal:2 tests 2.99–8.07 Lightweight: 24 tests (20.6–55.6) Normal:6 tests 2.47–7.33 Lightweight: 0 tests (17.0–50.5) 4 studs (2 per side) Normal:22 tests 2.89–5.04 8 studs (4 per side) Lightweight: 0 tests (19.9–34.7) 4 studs (2 per side) Normal:18 tests 2.67–5.08 8 studs (4 per side) Lightweight: 30 tests (18.4–35.0) Normal:8 tests 4.28 Lightweight: 0 tests (29.5) Normal:2tests 1.97–8.98 Lightweight: 0 tests (13.6–61.8) Normal:1tests 4.37 Lightweight: 0 tests (30.1) Normal:18 tests 3.13–3.36 Lightweight: 0 tests (21.6–23.1) Normal:8 tests 4.46–13.2 Lightweight: 0 tests (30.7–90.9) Normal:1 tests 3.77 Lightweight: 0 tests (25.9) Normal:2 tests 4.44–5.04 Lightweight: 0 tests (30.6–34.7) Normal:17 tests 5.13–9.35 Lightweight: 0 tests (35.3–64.4) Normal:105 tests 5.15–7.15 Lightweight: 0 tests (35.5–49.3) Additional insight can be gained by separating the tests based on the failure mode before computing the average testto-predicted ratio. For steel failures, the AISC 2005 prediction is
202 L. Pallarés, J.F. Hajjar / Journal of Constructional Steel Research 66 (2010) 198–212 Table 3 Steel and concrete strength by AISC, PCI 6th Edition, and ACI 318-08. Steel failure φQnvs = φvCvAsFun Concrete failure (pryout, or ‘‘in the field’’) φQnvc = φvCvRvn φv Cv φvCv φv Cv φvCv Rv b Average formula 5% fractile � AISC 1.00 1.00 1.00 1.00 1.00 1.00 0.5As f ′ c Ec � EC-4 0.66 0.48 0.5As f ′ 0.80 0.80 0.64 0.80 c Ecm PCI 6th 1.00 0.75 0.75 0.70 1.00 0.70 317.9λ � f ′ c (d)1.5 � �0.5 hef ACI 318-08 a Ductile steel element 0.65 1.00 0.65 0.70 1.00 0.70 kcp40λ � f ′ Brittle steel element 0.60 1.00 0.60 � �1.5 c hef a The formulas for a ductile headed steel anchor have been used in this work. b Units: pounds, inches for ACI 318-08 and PCI 6th Edition; Units: kips, inches for AISC. N, mm for EC-4. c The Cv factor depends on the height of the stud. Table 4 Test-to-predicted ratios for steel failure in tests using the minimum strength provided by the standards. Shear forces 202 tests Without resistance factor With resistance factor 0.74 c 0.60 215λ � f ′ c (d)1.5 � �0.5 hef kcp24λ � f ′ � �1.5 c hef AISC EC-4 ACI 318-08 PCI 6th AISC EC-4 ACI 318-08 PCI 6th Average 0.986 1.215 1.150/1.344 a Stand. dev. 0.158 0.195 0.560/0.815 a a γ 1/γ 2 : γ 1: uses the average value; γ 2: uses the 5% fractile formula. 1.051/1.498 a 0.183/0.311 a Table 5 Test-to-predicted ratios for concrete failure in tests using the minimum strength provided by the standards. Shear forces 114 tests Without resistance factor With resistance factor 0.986 1.518 1.974 2.142 0.158 0.244 1.141 0.441 AISC EC-4 ACI 318-08 PCI 6th AISC EC-4 ACI 318-08 PCI 6th Average 0.849 0.996 1.576/2.097 a St. dev. 0.244 0.245 0.766/1.026 a a γ 1/γ 2: γ 1: uses the average value; γ 2: uses the 5% fractile formula. accurate and safe (Fig. 1(b)), with EC-4 showing more conservative results due to the 0.8 reduction factor (Fig. 1(f)). For tests in which the concrete failed, the scatter is much larger and many test-topredicted ratios are less than 1 (Fig. 1(c)) for AISC 2005; EC-4 again presents a more conservative range of results (Fig. 1(g)). The comparison between the different provisions for concrete failure modes has been carried out using the average formula, the 5% fractile formula provided by ACI 318-08 and PCI 6th Edition, and taking into account the resistance factors specified in Table 3, in order to assess the accuracy of the different approaches. The testto-predicted ratios for ACI 318-08 Appendix D and PCI 6th Edition are shown in Fig. 2. The headed stud strength plotted in Fig. 2 is the minimum of the strength of the steel (AsFu) and the strength computed for pryout (‘‘in the field’’) failure mode. Based on using the average formula for predicting stud strength in shear, it can be seen that PCI 6th Edition (Fig. 2(b)) is more accurate than ACI 318-08 Appendix D (Fig. 2(a)) in predicting the local failure of the concrete surrounding stud, and its standard deviation shows less scattered results. ACI 318-08 is more conservative than PCI 6th Edition due primarily to the auxiliary coefficient kcp equaling 1 in ACI 318-08 when the headed stud is less than 2.5 in (63 mm), as pointed out by Anderson and Meinheit [4]. AISC has lower average ratios than ACI 318-08 and PCI 6th Edition, and the scatter is larger, with a considerable number of tests (approximately 60%) having a test-to-predicted ratio less than 1.0 (Fig. 1(a)). The results derived from applying 5% fractile formulas for pryout strength given by ACI 318-08 and PCI 6th Edition are shown in Fig. 2(c) and (d). The scatter of the results applying the 5% fractile formulas, both with and without resistance factors (Fig. 2(e) and (f)) is larger than results given by average values (Fig. 2(a) and (b)), and ACI 318-08 provides more conservative results in comparison to PCI 6th Edition. The differences between [30], ACI 318-08 and 1.011/1.495 a 0.168/0.249 a 0.849 1.245 2.997 2.127 0.244 0.307 1.465 0.363 PCI 6th Edition also typically become larger when the respective resistance factors are applied. The formulas used for stud strength in shear in AISC and EC- 4 were derived by looking at all tests in aggregate, regardless of the mode of failure. It is informative to compare the accuracy of the various formulas for predicting the steel or concrete failure modes by comparing each formula only to tests failing in the steel or concrete, respectively. If only tests that failed in the steel are examined (202 tests), EC-4 provides the most conservative results (Table 4). PCI 6th Edition provides the most conservative results when using the 5% fractile equation or when resistance factors are applied. Similarly, for headed stud anchors failing in the concrete (114 tests), ACI 318-08 is shown to be the most conservative, while PCI 6th Edition is accurate with small scatter (Table 5). AISC is seen to be unsafe for both groups of tests. The strength prediction (AsFu) for steel failure (202 tests) may be seen in Fig. 3. This formula becomes more conservative when the specified (nominal) values of the steel strength are used rather than measured values. Fig. 4 shows the results of using concrete failures to assess tests that failed in the concrete. It can be seen that PCI 6th Edition is more accurate than ACI 318-08 Appendix D, although PCI 6th Edition restricted its proposed formula for ‘‘in the field’’ cases, or pryout, for headed studs with the ratio hef /d < 4.5. ACI 318- 08 Appendix D again provides very conservative results when the effective height of the stud is less than 2.5 in (63 mm), due to the kcp coefficient, as discussed earlier. If the AISC formula for concrete failure is used similarly, the results are less conservative, especially without resistance factors (Fig. 1(c)). For EC-4, the average result is conservative (Fig. 1(g)).
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