PSI - Issue 48

Nemanja Ilić et al. / Procedia Structural Integrity 48 (2023) 318 – 325 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

321

4

bottom and deck to other elements until the cross-section experiences ultimate strength, i.e., ultimate (maximum) bending mom ent or structure’s bending capacity. Afterwards, the structure is considered as collapsed. This collapse is called progressive collapse and such analysis – a progressive collapse analysis (PCA). PCA can be also evaluated using nonlinear finite element analysis (NFEM). Due to large computational time, NFEM is not taken into account here. PCA originated was done by Smith (1977). Currently, it is fully incorporated within the IACS (International Association of Classification Societies) rules, see IACS (2022). Moreover, authors developed a custom-made software to automate PCA procedure based on IACS procedure. PCA consists of the following steps:  Cross section of the hull (from Fig. 2) is divided into the three types of segments (stiffeners with attached plating, plating and hard corner), see also Fig. 3.  Stress-strain curve for each segment is defined with respect to tension and compression, see right part of Fig. 3. Tension part of the curve is defined as elastic – perfectly plastic, while the compression part is following the buckling and post-buckling behavior.  Cross section located between frames is subjected to incrementally increased curvature while keeping the cross-section plane. For each incremental curvature step the natural axis position changes. Therefore, it is calculated considering axial force equilibrium of the section, see Eq. (1) and Eq. (2). Only in Eq. (2), subscript “i” stands for segments in compression, while subscript “j” considers segments in tension. A, σ and z n are segments’ cross secti on area, axial stress and their vertical position of the neutral axis from the baseline, respectively. ∑ =0 (1) = (2)  For each incremental curvature step, a corresponding strain of each segment (both in compression and tension) is calculated according to Eq. (3). Curvature is l abelled here as χ. The segment’s strain is defined as ε i . = ( − ) (3) Plotted curve is representing bending moment – curvature of the cross section. When the slope of the curve becomes negative means that the bending moment has reached its maximum, such is considered as ultimate bending moment. Bending moment values are calculated bearing in mind contribution of all segments, see Eq. (4). = | − | (4)

Fig. 2. Progressive collapse analysis procedure.