Issue 48

V. M. G. Gomes et alii, Frattura ed Integrità Strutturale, 48 (2019) 304-317; DOI: 10.3221/IGF-ESIS.48.30 314 of the plates hole surfaces with bolt threads, some little slippages on the grips and the deformation of plates. In other hand, in the numerical model the instant when the load increases again corresponds to a displacement of about 4 mm due only to the deformation of plates because the connection between grips and specimens is perfectly rigid and the bolt shank was modelled using the nominal diameter. Secondly, it is noted that there are two peak loads related to sliding of middle plates in relation to cover plates. This behaviour is due to inexistence of symmetry of specimen in both sides, inducing slippages in different testing time. These slippages in different testing time also occurred in slip tests. Inversely, the numerical model was only modelled ¼ of specimen and because for that simplification; it only appears one peak load in numerical load-displacement curve. Steel Grade (Surface Treatment) Type of Joint Snug Tight Bolts Preloaded Bolts 2mm thick 3mm thick 2mm thick 3mm thick 1+1 4+4 1+1 4+4 1+1 4+4 1+1 4+4 S355MC (Without coating) F max Exp . 36.69 100.57 59.18 153.45 39.03 105.10 63.05 161.66 CoV (%) 1.71 0.80 0.42 0.86 1.64 5.42 1.91 0.46 F max FEM 37.48 101.88 59.75 153.45 38.22 102.21 57.72 153.87 Error (%) -2.17 -1.32 -0.99 0.35 2.05 2.73 8.42 4.80 350GD (Zinc coating) F max Exp . 39.81 101.18 55.16 150.77 42.84 110.37 56.28 141.71 CoV (%) 1.38 1.55 1.15 0.24 3.83 5.08 5.46 2.11 F max FEM 37.65 100.11 56.36 150.77 39.18 100.77 57.39 152.16 Error (%) 5.40 1.03 -2.21 -5.58 8.53 8.68 -2.00 -7.40 350GD (Zinc plus paint coating) F max Exp . 37.96 100.18 52.09 139.17 39.85 99.91 55.45 140.35 CoV (%) 2.05 0.73 0.87 1.48 0.92 1.24 0.85 1.46 F max FEM 35.32 99.76 53.18 149.87 36.73 100.05 54.33 150.65 Error (%) 6.95 0.39 -2.14 -7.72 7.79 -0.16 1.99 -7.37 Table 6 : Summary of failure loads in kN: experimental values, F max Exp , (first row) vs. numerical predictions, F max FEM , (third row). Coefficient of variation from three tests performed for each surface treatment (second row), and errors between average experimental failure loads and failure loads by FEM (fourth row). As regards failure modes, Fig. 8 compares four distinct cases that were observed and modelled for 1+1 and 4+4 bolted joints. Fig. 8 shows that the numerical model can predict the failure location, as given by the equivalent plastic strain fields. Nevertheless, the numerical model does not use any damage approach (only plasticity), therefore it does not model the final cracking observed in experiments. The plasticity model predicts a plastic strain localization that results in strength reduction even before the final cracking. For the multiple bolted joints, this plastic strain localization is revealed with a more evident necking aspect. From Fig 8A and B (1+1 bolted joints) one verifies that the failure modes occurring on specimen of S355MC is by shear fracture; for specimen of S350GD steel the failure modes is a combination of shear and end splitting fracture. Regarding to 4+4 bolted joints, it is verified the same failure mode, where the crack begins between the first two holes. In addition, it was also verified that the bolts closer to end of the cover plate are more subjected to loading than the bolts near the symmetry plane. Fig. 8 also shows necking on net-section for the 4+4 bolted joints. From strain plots, one verifies that the numerical models can be appropriate to model the ultimate loads, reproducing local plastic strain fields similar to experimental results, being consistent with the critical points where the crack normally begins. Similar predictions of the failure models for bolted joints with thin plates were also obtained by He and Wang [15] using exclusively a plasticity model. This result was also validated by some of the authors of this paper in a previous publication [1]. In order to stablish a relationship between the geometry of single and multiple bolted connections and their fracture mode, the ratio between hole distances and hole diameter was calculated and compared with the definition of the bearing resistance proposed by Može and Beg [16]. Može and Beg refer that in case of single connections, if the member end distance is smaller than 2.5 times the D hole , the lower bound of the bearing resistance is usually represented by splitting