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

Table 1

Residual force and residual yield norms for typical load steps during the formation of the second plastic hinge.

Single-vector return algorithm
Residual force; norm $r^{\mathrm{norm}\hspace{0.17em}}$	Residual yield; norm ${\mathrm{\Phi }}^{\mathrm{norm}\hspace{0.17em}}$	Residual force; norm $r^{\mathrm{norm}\hspace{0.17em}}$	Residual yield; norm ${\mathrm{\Phi }}^{\mathrm{norm}\hspace{0.17em}}$
Step 47	Step 47	Step 445	Step 445
1.47597039E-03	1.3055981E-03	8.56514641E-05	9.37779227E-05
1.48013748E-06	4.26512984E-07	5.9731394E-09	2.21160446E-09
3.72157338E-13	4.59632332E-14	9.21947265E-17	2.22044605E-16