PSI - Issue 62

Alberto Gennari Santori et al. / Procedia Structural Integrity 62 (2024) 339–346 Gennari Santori A. et al. / Structural Integrity Procedia 00 (2019) 000–000

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frequencies and the corresponding inflection lengths, it is possible to estimate the acting stress. In this case study, the contribution of the bending stiffness EI can be considered negligible, the Equation 1 can be simplified as the following:            (2) To measure the natural vibration frequencies and respective modal shapes of each Dywidag bar, MM technique was used. Since the first decade of the 2000s it was already widely employed in the industrial field, however, it can be considered innovative for this type of application (Fioriti et al., 2018; Wu et al., 2012; Zhang et al., 2005; Ciarallo et al., 2023). MM technique using the recording of a digital video can extrapolate the displacements over time allowing the analysis in the frequency domain of the phases and amplitudes for each point (or pixel) of the video. In detail, the method uses an Eulerian approach which is based on the definition of a "field" consisting of a set of points in space, and on the consequent representation of the motion as a function of their position (position x) and time t. For the application described on the paper, the "field" consists of a camera's frame and the points within it are represented by the pixels of the frames and their luminous intensity variation ( I ). Essentially, in a first phase the method records the variations of “ I” over time converting them into displacement variations. Finally, in a second phase the displacement variation is amplified by a factor α to make them visible through a magnified video. Each bar has been considered pinned at both ends, therefore the effective length was equal to the geometrical length.

Average axial stress (MPa)

481

518

446

388

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404

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445

525

552

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Axial stress [MPa]

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Axial Stress (MPa)

Bar alignment Bar alignment

Fig. 5. Vibrating wire method - Diagram of the estimated pulls in the bars grouped by transversal positioning (alignment), with indication on top of average axial load for each Dywidag bar alignment.

The tensile stress ( σ ) was performed on 137 bars distributed over the different mid-span special joints. The results in terms of tensile load acting on the bars have been plotted on Fig. 5 grouped by their location with indication of average axial stress for each Dywidag bar alignment. In detail, number 1 indicates the three bars (ABC) on the left hand side, whereas number 10 the three on the right-hand side. The obtained results highlighted the bars located on both side of the joints are characterized by a higher value of the tensile force.

4.2. XRD Method

XRD method is a non-destructive technique used in many scientific and industrial fields to measure different properties of materials. The technique consists in measuring the angle of maximum diffraction of an X-rays beam incident on the surface of a mono or polycrystalline material (James et al., 1980; Lu et al., 1998; Pineault, J.A.,2002). In the field of engineering and mechanical constructions, diffractometry is used to measure the stresses acting on metallic materials and whose reference standard is EN15305:2008. According to Bragg’s law, the X-rays interacting with the material surface are absorbed and reflected at the same frequency along a certain direction and with a certain diffraction angle. By measuring the variation of the diffraction angle, it is possible to evaluate the variation of the distance between the crystalline planes and to relate it with the strain in the crystal lattice. Measurements were performed on a total of six Dywidag bars. The analyzed bars have been on span 7 bars 1B, 2A and 9A and on span 9 bars 1A, 4A and 10A. After the installation of the XRD frame and tools, the measurement points on each bar were treated with solvent to eliminate the layer of paint protecting the bars (Fig. 6). An electrolytic removal of the steel surface layer was also carried out in order to reduce measurement uncertainties.