PSI - Issue 48

Nikola Momčilović et al. / Procedia Structural Integrity 48 (2023) 12 – 18 N. Mom č ilovi ć et al / Structural Integrity Procedia 00 (2023) 000 – 000

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2.1. PCA method

In this paper incremental-iterative PCA is used. The origin of the procedure lays in a method published by Smith (1977) and it is codified in IACS Common Structural Rules for Bulk Carriers and Oil Tankers, see IACS (2022), where the complete procedure description can be found. Thus, the following steps are employed according to IACS (2022):  cross section is partitioned into the segments: stiffener with attached plating, plates, hard corners),  a stress-strain curve is designated to the each of the segment (elastic-perfectly plastic curve for tension, various modes of buckling for compression),  the incremental-iterative curvature is subjected to cross section,  in each step of the curvature increment, the sum of the axial forces has to be zero; and the change of neutral axis, the strain of each segment and corresponding bending moment ( M u ) has to be calculated according to formulations given in Eq. (1). A i , σ i , ε i and z i stand for cross section area, stress, strain and vertical position of segments, respectively; while χ is the imposed curvature and z p is the instantaneous position of the neutral axis. ∫ =0 =0 = ( − ) =∑ =1 | − | (1) The length of the elements is their length between the main frames or floors. The detailed formulation of the buckling modes for plate buckling and stiffener with attached plating buckling can be found in IACS (2022). Hard corner elements are assumed to experience elastic perfectly plastic behavior in both tension and compression. 2.2. PCA method updated with corrosion effects Pitting and uniform corrosion effects are updated within the PCA procedure. Pitting is incorporated according to the proposal given by Piscopo and Scamardella (2021). The procedure starts with the pitted element defined by its level of DOP and DOC. DOP stands for pitting intensity degree, i.e., the percentage representing the ratio between the pit affected and element area. DOC stands for corrosion intensity degree of pit affected area. Using DOP and DOC, the total loss of volume of the element due to pitting can be calculated (ΔV), see Eq. (2). In the next step, as shown in Eq. (3), an equivalent thickness (t eq ) of the pitted element is derived based on DOP and DOC. Consequently, non corroded element slenderness (β) is replaced by pitting corroded slenderness of the structural element (β eq ), which includes the new equivalent thickness (t eq ), see Eq. (4). Furthermore, PCA beam-buckling model is modified to consider the diminution of attached plating of the stiffeners due to pitting. It is accomplished by replacing the standard ultimate strength formula ( ϕ u ) for structural elements from Eq. (5) by the modified formula for ultimate strength of pitted element ( ϕ u,pit ), given in Eq. (6). The same procedure is carried out for buckling of pitted plates and stiffeners with attached plates. On the other hand, torsional and web local buckling of longitudinal stiffeners are defined by modifying their thickness, see Eq. (3). Uniform corrosion is updated in PCA in simplistic procedure, by the reduction of thickness. Consequently, this reduction affects the slenderness of diminished plate and furthermore, an ultimate strength of the structural element. = ⋅ (2) = (1 − ⋅ ) (3) = √ (4)