Issue 29

L. Contrafatto et alii, Frattura ed Integrità Strutturale, 29 (2014) 196-208; DOI: 10.3221/IGF-ESIS.29.17 200 T HEORETICAL MODEL FOR THE PREDICTIONS OF THE PULL - OUT STRENGTH OF CHEMICAL ANCHORS number of studies exist in the literature concerning the calculation of the chemical anchor tensile load for different failure patterns. However, they are all referred to concrete. These models are based on the transfer of the applied load from the steel anchored element, through the adhesive layer, to the concrete along the entire bonded surface. They also account for the proximity of the anchor to the support edge and for the spacing in group anchors. The tensile failure load of individual chemical anchors is usually calculated as a function of the depth of the anchor. Cook, et al. [3] conducted a comprehensive investigation of more than 1000 tests with twenty types of adhesive products. According to this study, the parameters that affect the resistance of a chemical anchor are: adhesive strength; compressive strength of concrete; hole cleaning; humidity of the hole; high temperatures and creep; charging time. The possible failure mechanisms can be summarized as it follows: 1. if the embedment depth is very small, a concrete cone failure occurs. 2. if the depth of the anchor is greater we can have: a combined mechanism, given by a shallow concrete cone failure with sliding at the adhesive/concrete interface below the cone; a combined mechanism, given by a shallow concrete cone failure with sliding at the rod/adhesive interface below the cone; a combined mechanism, given by a concrete cone failure with sliding at the adhesive/concrete interface in the upper part of the anchor and sliding at the rod/adhesive interface in the lower part. 3. if the embedment depth is very high, the anchor is so resistant that the failure occurs for breakage of the steel bar. The minimum depth for obtaining the rupture of the bar represents the embedment length of the anchor, also depending on the properties of steel and resin. The theoretical models proposed in the literature and reported in Table 2 have been applied to the materials under investigation for testing the possibility of their applications also in the case of natural rocks. Model 1 is an elastic bond-stress model addressing the compatibility relationships between concrete, bonding agent and threaded rod. Model 2 is a uniform bond-stress model predicting the capacity of the anchor as a function of the uniform failure stress  0 . Model 3 is a uniform bond-stress model with real resistance of adhesive in which the bond area effect is represented by an additional modification factor  b . Model 4 is a bond models neglecting the shallow concrete cone , in which the effective embedment length is equal to the actual embedment length minus 3 times the diameter, to account for the shallow concrete cone. Models 5 and 6 are combined cone-bond models : model 5 is combined concrete cone/ bond model uniform ; model 6 is combined concrete cone / bond model elastic . Models 7 and 8 are interface bond model : model 7 is based on the sliding at the adhesive/concrete interface ; model 8 is based on the sliding at the steel/adhesive interface . Model 9 is a concrete cone model . Model Author Ultimate axial force 1 Doerr er al. [8] 0 max 0 0 ' tanh ' ef u h d N d d              2 McVay et al. (1996) [9] 0 0 u ef N d h    3 Nilson (1972) [1] 0 0 u b c N d      4 Cook et al. (1998) [10]   0 3 u ef N d h d     5 Cook et al. (1993) [11] 2 0 0 0.92 ' u ef ef N h f d h     6 Cook (1993) [2]   2 0 max 0 0 ' 0.92 ' tan ' ef cone u ef h h d N h f d d                7 Marti (1993) [12] 0 u ef N dh    8 Marti (1993) [12] 0 , c u ef c bw f N dh f    9 Eligehausen et al. (1984) [6] 2 0.92 ' u ef N h f  Table 2 : Theoretical concrete models for the prediction of the ultimate anchor strength. A