PSI - Issue 60

Thondamon V et al. / Procedia Structural Integrity 60 (2024) 484–493 Author name / StructuralIntegrity Procedia 00 (2019) 000 – 000

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Fig. 2. Experimental test set-up [4].

Fig. 3. TES method [6].

3. Limit load evaluation TES method as per ASME has been used for evaluation of limit loads of elbows. Figure 3 shows a sample load deflection curve with elastic line and limit line indicating the limit load as per TES method. Load-displacement curves from the experimental data has been used for this study. Figures 4 to 6 show load displacement curves of the elbow specimens used for this study. The expressions proposed by Chattopadhyay and Tomar (2006), Chang-Sik and Kim (2006) and Hong et al. (2010) as a result of finite element analysis have been used for estimating the limit loads for elbows of same geometry as the experimental study. 3.1. TES Method According to ASME [6], limit load or collapse load is calculated using twice elastic slope method. A load deflection curve is plotted with load on the y-axis and deflection on the x-axis. The angle that the elastic part of the load-deflection curve makes with the y- axis is called θ. A second straight l ine, termed as collapse limit line, is drawn through the origin so that it makes an angle φ = tan - 1 (2 tan θ) with the y -axis. The limit load is the load at the

intersection of the load-deflection curve and the collapse limit line. 3.2. Expressions proposed by Chattopadhyay and Tomar (2006) [1]

Elbows with different sizes of circumferential cracks, healthy elbows, various wall thicknesses for each case, various internal pressure values and cases in both opening and closing bending modes were considered in the analysis. Table 2 presents the details of limit load evaluation expressions proposed based on the numerical studies for various conditions considered.