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

Table 2

Residual force and residual yield norms for typical load steps during the formation of first and third 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 106	Step 106	Step 106	Step 450	Step 450	Step 450
1.65303075E-03	1.20357837E-05	1.47408979E-05	3.87694523E-03	6.19251038E-04	4.56960163E-03
1.89552293E-06	1.23009056E-07	5.42558567E-07	1.60549380E-05	7.05089222E-07	5.25607314E-06
5.81448484E-13	1.04360964E-14	7.37188088E-14	4.57042787E-11	2.61368704E-12	7.06168457E-12