PSI - Issue 60

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

488

5

Table 2. Expressions proposed by Chattopadhyay and Tomar (2006). Bending Mode Proposed Equations

Applicability

Healthy elbows with internal pressure M 0 4 R 2 t σ y =X X= [−0.0617+1.04885h 1 3 + 1.2 h 182p 1 3 +7.8509p 9.6431 ][1−p] X= [1.075h 2 3 + 2.071p 1.418 h 0.223 +8.41p 12.129 ][1−p] Elbows with circumferential through-wall crack without internal pressure M X =X M 0 X = {1.1194 − 0.7236 ( θ π )−2.0806( θ π ) 2 1 X = {1.1185 − 0.342 ( θ π )−2.52( θ π ) 2 1 X = {0.9655 + 1.0152 ( θ π )−4.68( θ π ) 2 1 X = {1.14 + 0.3 ( θ π )−3.6( θ π ) 2 1 X = {0.64 + 0.342 ( θ π )−7.92( θ π ) 2 1 θ π ) 1.3053 − 4.2133 ( θ π )+3.8386( θ π ) 2 Elbows with circumferential through-wall crack with internal pressure M X =X M 0 X={ 1−1.2776( X = 1.1194 − 0.7236 ( θ π )−2.0806( θ π ) 2 −3.4164p 0.8408 ( θ π ) 2.1758 X = 1.4423 − 1.495 ( θ π ) 0.6687 −2.9803p 0.7136 ( θ π ) 1.7345 X = 1.6039 − 1.0847 ( θ π ) 0.4082 −3.1773p 0.4807 ( θ π ) 1.4381 X = 1.4298 − 0.0789 ( θ π ) 0.5435 −3.3789p 0.2336 ( θ π ) 0.9644 X = 7.7803 − 6.8959 ( θ π ) 0.0231 −4.1061p 0.5464 ( θ π ) 1.2776 X={ 1−0.8( θ π ) 1.127 − 1.8108 ( θ π )

0.1≤h≤0.6 0≤p≤1.0 5≤R⁄t ≤20 0.1≤h≤0.6 0≤p≤1.0 5≤R⁄t ≤20

Opening Moment

Closing Moment

R/t = 5 – 20 for 2θ < 45 0 for R/t = 5 for R/t = 7.5 for R/t = 10 for R/t = 15 for R/t = 15 for R/t = 5 – 20 0 < p < 1 for 2θ < 45 0 for R/t = 5 0 < p < 1 0≤X ≤1 2θ≤150 0 R/t = 7.5 0 < p < 1 0≤X ≤1 2θ≤150 0 R/t = 10 0 < p < 1 0≤X ≤1 2θ≤150 0 R/t = 15 0 < p < 1 0≤X ≤1 2θ≤150 0 R/t = 20 0 < p < 1 0≤X ≤1 2θ≤150 0

45 0 ≤2θ≤150 0 45 0 ≤2θ≤150 0 for 2θ < 45 0 60 0 ≤2θ≤150 0 for 2θ < 60 0 60 0 ≤2θ≤150 0 for 2θ < 60 0 90 0 ≤2θ≤150 0 for 2θ < 90 0 90 0 ≤2θ≤150 0 for 2θ < 90 0 45 0 ≤2θ≤150 0

Opening Moment

Closing Moment

Opening Moment

Closing Moment