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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3.3. Expressions proposed by Chang-Sik and Kim (2006) [7] Plastic collapse loads were determined for healthy elbows with and without internal pressure using finite element analysis for the large geometry change option. Twice-elastic-slope (TES) method was used for estimating the collapse load. The material was considered to be elastic – perfectly plastic for the analysis of the elbows. Table 3 presents the details of limit load evaluation expressions proposed based on the numerical studies for various conditions considered.

Table 3. Expressions proposed by Chang-Sik and Kim (2006). Bending Mode

Proposed Equations

Applicability

Healthy elbows without internal pressure M 0S =4 R 2 t σ y M 0 ( M P=0) 0S =1.048h 1⁄3 −0.0617 M 0 M 0S =A C (h+k C ) n C With A c = 0.800 (Rt ) −0.017 k c = 1.460 (Rt ) −0.911 n C = 0.423 (Rt) 0.127 Healthy elbows with internal pressure Weakening factor m= M 0 M 0 (P=0) ; p= P 0 σ y R t m = 1 + 0.05p − 0.85p m = 1 − 0.35p − 0.88p 2 +0.08p 3 m=1+αp+βp 2 +γp 3 α = −0.18 + 0.07 (Rt) β = 0.0005 (Rt ) 3 − 0.0075 (Rt ) 2 + 0.0375 (Rt ) − 0.05 γ = −0.011 (Rt) 2 + 0.110 (Rt ) − 0.880 2 +0.31p 3

Opening Moment

Closing Moment

R⁄t=5 R⁄t =10

Opening Moment

5≤R⁄t ≤10

Closing Moment

3.4. Expressions proposed by Hong et al. (2010) [8] Finite element analysis was performed considering both material and geometric non-linearity. The elbow was considered to be elastic – perfectly plastic material. For faster computation, only a quarter of the elbow was modeled and geometrical symmetry was considered. Table 4 presents the details of limit load evaluation expressions proposed based on the numerical studies for various conditions considered.

Table 4. Expressions proposed by Hong et al. (2010). Bending Mode

Proposed Equations

Applicability

Healthy elbows without internal pressure M 0S =4 R 2 t σ y M 0 ( M P=0) 0S =1.048h 1⁄3 −0.0617

Opening Moment

M 0 ( M P=0) 0S = 0.800 (Rt )

−0.017 (h + 1.460 (Rt ) −0.911 ) n C

Closing Moment

With n C =0.423( R t ) 0.127