PSI - Issue 84

Andrea Nino Consiglio et al. / Procedia Structural Integrity 84 (2026) 914–921

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point static bending test was implemented. This choice allowed to consider an area along the PC beam specimens having a constant bending moment. The laboratory setup was represented in Fig. 1 (it remained unchanged during all the three phases of testing). The “cracking” method determines the decompression load requiring that the PC beam is loaded to induce flexural cracking, and that the locations of such cracks are marked. In this way, they can be located and instrumented after loading is removed. The PC beam is loaded with steps to allow the operator depicting the cracks through a visual inspection. All cracks are identified and marked, as shown in Fig. 1. After completion of the loading steps, the PC beam is unloaded and then prepared for the decompression loading test. The load is increased until that vertical flexural cracks develop in the bottom flange and extend along the bottom part of the PC beam’s web. The load is then removed, resulting in closure of the developed cracks. Some cracks are selected for instrument installation to detect the crack opening during reloading. Specifically, cracks located near the PC beam’s midspan are instrumented. The equipment is installed on the surface of the PC beam above the indicated cracks. Moreover, the decompression load is found by examining the “load-strain” curve for each instrument. Such curves typically exhibit a bilinear response. In the first stage of this bilinear response, an increase in loading is accompanied by a proportional increment in tensile strain which corresponds to a reduction in prestressing. Instead, during the second stage, an increase in the applied load is no longer accompanied by a proportional increase in strain, as the load is no longer transferred across the crack at the PC beam’s surface. The load that corresponds to this change in strain (or displacement) rate is taken as the decompression loading. Thus, to approximate the load causing the crack opening, the two linear branches of each curve are continued, while the intersection of the two lines is selected as the point at which the crack opens, as depicted in Fig. 2a (the symbol F PR represents the effective pre–tensioning). (a) (b) Fig. 2. (a) “Load-strain” graph; (b) “Static deflected shape method: The 2D FE model of the PC beam specimen (B2) including shear deformation. The equivalent beam–tendon system according to Jaiswal (2008). The load corresponding to this point is determined as the “decompression loading”. The moment at the location of the crack (corresponding to this load) is calculated. At this moment, the effective pre–tensioning force can be evaluated using the following equilibrium equation: (1) Here M is the bending moment in correspondence of the crack location from the applied load, whilst F PR is the effective pre–tensioning in the strands. A is the gross cross-sectional area of the PC beam, while e is the eccentricity of the pre– tensioning with respect to the centroid of the PC beam’s cross-section. Additionally, the section modulus of the PC beam is S , whilst the bending moment resulting from the dead load is M D . In this experimental campaign, a cracking experiment was conducted on a pre–tensioned concrete beam specimen to determine the available compressive stress at its bottom flange and the effective residual pre–tensioning in its strands. These values were compared with the results obtained from the “static deflected shape” method described in the following section.

2.2. Non-destructive method proposed by Bonopera and De Matteis (2026)

The reference solution of the “static deflected shape” method according to the Euler–Bernoulli theory, which focuses on a simply supported PC beam of length L , is illustrated in Fig. 1(a–c) in Bonopera et al. (2018). The member is subjected to an eccentric prestressing force ( N ) with respect to the centroid of its cross-section ( e : eccentricity) and