Concentric Plastic Hinges

[kavir]

Hi
I Want to use rotational springs for plastic hinges with bilin material based on Ibarra-Krawinkler model.
for modifying stiffness of springs in the Ibarra& Krawinkler report (2005) bellow equation is provided.
1/Kmem=(1/Ks) + (1/Kbc) & Ks=n*Kbc ------> Ks=(n+1)*Kmem
so my question is:
is "Ks" stiffness of tow springs in a element ends or stiffness of each springs?

I think for a series of tow springs and a elastic beam column element for modeling a member, the resultant stiffness of assembly is:
1/Kmem= (1/Ks)+(1/Ks)+(1/Kbc)

[fmk]

element end .. and yes it a number of spring in series .. in theory Ks should be infinity, which is why a force formulation is better suited to the problem than the displ forumulation you are forced to use given how you have to model it.