Plastic loads of pipe bends under combined pressure and out-of-plane bending

Abstract

This paper provides plastic limit and TES (twice-elastic-slope) plastic load solutions for 90 • pipe bends under combined pressure and out-of-plane bending, via threedimensional non-linear FE analyses using elastic-perfectly plastic materials. Without internal pressure, a closed-form approximation is given. For combined pressure and out-of-plane bending, tabulated data are given, from which TES plastic loads can be interpolated. It is found that TES plastic loads for pipe bends under out-of-plane bending are lower than those under in-plane opening bending, but are higher than those under in-plane closing bending. It suggests that the in-plane closing bending mode is the most critical loading mode for 90 • pipe bends, which is fully consistent to existing findings.Keywords Combined pressure and out-of-plane bending · Finite element limit analysis · Pipe Bend · Twice-elastic-slope plastic load Nomenclature E Young's modulus M Out-of-plane bending moment M o TES plastic out-of-plane moments of pipe bends P Internal pressure P o Limit pressure of a pipe bend P s o Limit pressure of a straight pipe = 2 √ 3 σ o t r R Bend radius r Mean pipe radius t Thickness of pipe

Plastic loads for 90° thick-walled elbows under combined pressure and bending

“…Comparison of this particular test with others under different loading indicates that the plastic load for opening bending is lower than that for out-of-plane bending. As the plastic load for opening bending is generally larger than that for out-of-plane bending [15,16,23,24], reliability of these test data is somewhat questionable. For austenitic stainless steel data, ratios range from 1.0 to 1.36, except for two of the test data; for one datum, the ratio is 0.91.…”

“…Accordingly, closed-form solutions for plastic loads of elbows have been proposed, for instance, under internal pressure [3], under in-plane bending [1-3, 14, 18-23], under out-of-plane bending [24], and under combined pressure and bending [13,14,18]. Several points are worth noting for existing plastic load solutions.…”

“…Owing to its significance in structural integrity analysis of piping components, numerous papers on plastic loads for elbows can be found in the literature, including analytical studies [1][2][3], experimental studies [4][5][6][7][8], and numerical studies [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Accordingly, closed-form solutions for plastic loads of elbows have been proposed, for instance, under internal pressure [3], under in-plane bending [1-3, 14, 18-23], under out-of-plane bending [24], and under combined pressure and bending [13,14,18]. Several points are worth noting for existing plastic load solutions.…”

Investigation on structural integrity of shape distorted 90° back-to-back pipe bends under in-plane closing bending moment

“…The appropriate reaction moment was obtained from moment versus angular rotation curve at the multipoint constrain node for each model. The collapse load was deduced by the specialised technique called TES method (Balakrishnan et al, 2021;Lee et al, 2008) and illustrated in Figure 4. 2014) was adopted to achieve a relatively close approximation.…”

Determination of collapse loads in pipe bends with ovality and variable wall thickness under internal pressure and in-plane opening moment

“…(9) with the difference of 25.76% for no ovality and with the maximum difference of 49.2% for the ovality of 20%. It is expected that the experiment value to be higher due to the strain hardening effect present during experiment [31] while the finite element analysis assumes the material to be elastic-perfectly plastic. The second comparison in Table 2 reveals that there is less difference of 0.18% between experiment collapse load and Eq.…”