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

Table 7

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
8.03359176E-03	9.80846569E-03	9.78495657E-03	1.36815406E-02	1.78952610E-02	1.78530190E-02
6.23470796E-05	2.38312272E-05	2.37622611E-05	1.96249346E-04	7.87644610E-05	7.85560337E-05
8.84047353E-10	1.42486467E-10	1.41957335E-10	9.29161239E-09	1.76712267E-09	1.64043112E-09
3.12120416E-18	1.11022302E-16	1.11022302E-16	8.12816025E-17	4.44089210E-16	0.0