A Radial Return Algorithm Application in Elastoplastic Frame Analysis Using Plastic Hinge Approach

Table 6

Four-legged jacket type-1. Residual force and residual yield norms for typical load steps during the formation of the first and second plastic hinges.

Two-vector return algorithm
Residual force norm $r^{\mathrm{norm}\hspace{0.17em}}$	Residual yield norm ${\mathrm{\Phi }}_1^{\mathrm{norm}\hspace{0.17em}}$	Residual yield norm ${\mathrm{\Phi }}_2^{\mathrm{norm}\hspace{0.17em}}$	Residual force norm $r^{\mathrm{norm}\hspace{0.17em}}$	Residual yield norm ${\mathrm{\Phi }}_1^{\mathrm{norm}\hspace{0.17em}}$	Residual yield norm ${\mathrm{\Phi }}_2^{\mathrm{norm}\hspace{0.17em}}$
Step 12	Step 12	Step 12	Step 41	Step 41	Step 41
8.03978006E-03	9.81043834E-03	9.79441075E-03	1.36989462E-02	1.79089005E-02	1.78810582E-02
6.24153357E-05	2.38396940E-05	2.37928885E-05	1.96679153E-04	7.88306625E-05	7.86893201E-05
8.85460742E-10	1.48586699E-10	1.44924517E-10	9.31316656E-09	1.60199565E-09	1.58390967E-09
8.20520831E-17	0.0	3.33066907E-16	2.40162583E-17	0.0	0.0