Plastic collapse moment equations of throughwall axially cracked elbows subjected to in-plane bending moment

Plastic limit loads for pipe bends with circumferential through-wall crack under torsion moment

“…Based on the research of Christo et al [34][35][36] and Buckshumiyan et al [37,38] in-plane opening bending were taken into consideration and estimated equations based on FE analysis were proposed . Chattopadhyay and Tomar [7] and Chattopadhyay et al [39,40] evaluated plastic loads for combined loads and investigated the effect of internal pressure on the in-plane plastic moment of through-wall axially and circumferential cracked elbow. Kim et al [17] proposed plastic loads for pipe bends with circumferential through-wall and part-through surface cracks under in-plane bending and solutions with extending the allowable crack length in Chattopadhyay and Tomar [7] by means of FE limit load analyses.…”

Numerical Study of Defect Free Elbows Subjected to In-Plane Bending Moment

“…So it is very important to know the plastic carrying capacity of elbow and the plastic limit load calculation of uncracked elbow holds an important position in engineering practice. Much work on plastic limit analysis has been performed for straight pipes, but much less for elbows [1][2][3][4][5][6][7][8]. Though Griffiths [4], Yahiaoui [5,11], J.chattopadhyay [6,10], and etc.…”

“…Much work on plastic limit analysis has been performed for straight pipes, but much less for elbows [1][2][3][4][5][6][7][8]. Though Griffiths [4], Yahiaoui [5,11], J.chattopadhyay [6,10], and etc. have studied the plastic load carrying capacities of elbows subjected to in-plane bending moment, and proposed the closed form equations of plastic limit loads, these researches have limitations: (1) The present studies and the experimental and analytical research by Yahiaoui K et al [11] have indicated that those formulas are excessively conservative when elbows subjected to in-plane bending moment, and on occasions, no applicable to the cases for which they intended ; (2) Do not differentiate in-plane opening bending moment from closing mode bending moment, which the responses of elbows are markedly different under these two different modes of bending moment; (3) Even though differentiate the bending mode of bending moment in analyses, the limit loads are defined by twice-elastic-slope (TES) method based on load vs. end displacement curves, instead of the true limit load that causes overall structural instability.…”