Question on Takeda

Hi everybody,

sorry for my questions. If I use Modified Takeda hysteresis (number 4 in Ruaumoko manual) I can put alfa, beta, the reloading stiffness power factor and KKK. But...how can I put the value of the yielding point and so the initial stiffness K0?

Thanks to everybody

Phi=M/EI, therefore changing the intertia I you can control the yielding curvature if it is a member (K0 = EI).

Ok, but EI are for the elastic part of the member. At both ends I have plastic hinges and I don't want that stiffness but the stiffness I have in the moment-curvature diagram. If I understand I put in the elastic properties M/phi as stiffness?

thanks

I guess you will have to accept that the whole member has cracked stiffness (secant stiffness at first yield). If this approximation is not good enough for you, you'll have to split up your members and give different effective stiffness values I am afraid.
This is exactly the drawback of lumped plasticity versus fiber analysis..

Some new questions on the modified Takeda rule as implemented in Ruaumoko.

1) Say yield has occurred in both directions and I am now on a reloading curve (towards a +ve displacement). What happens if my reloading curve does not reach yield again, but instead begins to unload (towards a -ve displacement). What will my unloading stiffness be? Ku=Ko(Dy/Dm)^a?

2) After this unloading I begin to reload again (still in the -ve direction). What is the reloading stiffness? Do I aim towards Dm or do I aim towards Dm-Bdp?

I note that this seems to fall into the category of "inner loop rules," which a number of authors say exist but do not discuss much. Hope someone can help me out!

Matt Fox.