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Concrete In Australia : March 2013
Concrete in Australia Vol 39 No 1 31 larger than the tensile strength of the steel in headed anchors. In relation to plate edge-lift anchors, the minimum stress area of the anchors cross section can be matched to follow this design recommendation. Cannon et al 11 proposed to calculate anchors subjected to tension, shear and combined loads. e resulting recommendations included using a conical failure surface to calculate the tensile strength and were adopted in ACI 349-80 12. e design strength of concrete for anchorage was based on a uniform tensile stress of øt (4 √ fc ). e resistance factor, øt was 0.65. PCI (1978) adopted the conical failure surface to predict a brittle failure of the concrete and this method was retained in PCI 5th Edition (1999) 13, 14. However, PCI later adopted the provisions in ACI 318-02 Appendix D (2002), which are based on Concrete Capacity Design (CCD), to calculate the tensile strength of anchors assuming uncracked concrete 15, 3. In the CCD method the concrete strength of a single anchor is calculated assuming a four-sided pyramid failure surface, with a slope between the failure surface and the surface of the concrete member of 35°. e more recent versions of ACI 318 Appendix D, 2008 2 and 2005 8 use this approach. Figure 1. Conical failure surface of earlier editions of PCI Handbook 12. A comprehensive overview of state-of-the-art cast-in-place and post-installed anchors is included in ACI 355 Guide for design of anchorage to concrete: Examples using ACI 318 Appendix D(1997) & CEB (1994) 16,17. ese reports summarise the basis for current, general anchorage provisions of embedded anchors subjected to tension and tension plus shear interaction. In the PCI editions, there have been several formulations to compute the tensile strength of an anchor. A conical failure surface for an anchor in tension was adopted up to PCI (1999), as presented in Table 1, with a resistance factor of 0.85 13. As discussed earlier, PCI (2004) 3 changed the approach to a four sided pyramid cone, adopting a similar formulation to ACI (2008, 2005) 2, 8, though working with coefficients related to uncracked concrete. e results given by PCI (2004) then correspond with results given by the ACI 318-08M Appendix D (2008). Concrete failure occurs, when not influenced by edge conditions, when the minimum of either the pull-out strength or breakout strength is reached before the steel yield (or ultimate fracture) strength is reached. e expressions used to calculate the pull-out and breakout strengths are presented in Table 1, presenting the 5% fractile formula (which is used as the nominal strength formula) for PCI 5th Edition and distinguishing between the 5% fractile (nominal strength) formula and the average formula for the ACI 318-08M (CCD method), since the average formulae of CCD may be found elsewhere 6. PCI 6th Edition adopted the ACI 318 formulas in the particular case of uncracked concrete. e nominal strength (5% fractile) formula used in ACI 318 Appendix D for anchoring, such as Wollmershauser 18 reported, presents a 90% confidence that 95% of the anchor ultimate loads exceed the 5% fractile value. e formulas are summarised in the Table 1 for the various editions of codes and handbooks. Table 1. Predictive capacity formulae for steel failure, pull-out and breakout 2, 3, 14. Concrete Failure Pull-out Concrete Failure Breakout PCI 5th Edition No model included 12 6 .hhd f efefh c + () ACI 318-08M (Average) 8Af brg c 10 15 fh ce f . PCI 6th Edition (5% fractile) 11 2 . AfC brg c crp 333 92 . () fhh c ef ef Abrg -- bearing area of foot f'c -- 28 day concrete compressive strength hef -- effective embedment dh -- diameter of the anchor head λ -- light-weight concrete modification factor 3.0 EXPERIMENTAL PROGRAM 3.1 Test parameters Sixty footed anchors of Series 7 with a 50 mm effective embedment depth were cast in two reinforced concrete panels 2mx2mx150mmthickwith30anchorsineachpanel. e reinforcing was SL82 mesh and an N16 perimeter bar located 50 mm from the edge of the panel. ese anchors were tested in direct tension as the concrete matured in order to precipitate concrete cone failures; tests were conducted at compressive strengths ranging from 18 MPa to 26 MPa, with an average of 21 MPa. Concrete compressive data for all series is shown in Table 2. All anchors of Series 7 failed due to concrete cone failure. e footed anchors were arranged with sufficient edge distances such that concrete capacity was not reduced due to edge effects. irty footed anchors of Series 6 were cast in unreinforced concrete blocks of 2 m x 2 m x 0.6 m deep with two anchors per block. e anchors of Series 6 were tested in direct tension once the concrete had matured. e compressive strength was 42 MPa to 46 MPa, with an average compressive strength at time of testing (which was at 28 days) of 43 MPa (Table 2). is was to ensure the footed anchors failed due to steel tensile