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Table 2 Limit and shakedown load multipliers of cylindrical pipe subjected to internal pressure and bending

From: FEM-based shakedown analysis of hardening structures

Load combination Elastic factor Limit factor (perfectly plastic) Shakedown factor (perfectly plastic) Shakedown factor (bounded hardening) Shakedown factor (unbounded hardening)
0.0p_1.0 M 0.7338 1.0012 0.7338 0.7338 0.7338
0.2p_1.0 M 0.7228 0.9870 0.7297 0.7310 0.7304
0.4p_1.0 M 0.7011 0.9478 0.7228 0.7236 0.7231
0.6p_1.0 M 0.6570 0.8914 0.7131 0.7132 0.7134
0.8p_1.0 M 0.6023 0.8267 0.7011 0.7013 0.7014
1.0p_1.0 M 0.5509 0.7608 0.6667 0.6855 0.6853
1.0p_0.8 M 0.6168 0.8540 0.7696 0.8128 0.8127
1.0p_0.6 M 0.6921 0.9556 0.8906 0.9894 0.9894
1.0p_0.4 M 0.7727 1.0546 1.0179 1.2318 1.2346
1.0p_0.2 M 0.8486 1.1306 1.1204 1.3874 1.5506
1.0p_0.0 M 0.9019 1.1589 1.1586 1.4482 1.8091