Hi,How can calculated inelastic period of SDOF structure when subjected to ground motion?

- bakhtiyar offline
**Posts:**46**Joined:**03 Sep 2012, 04:16

It depends on which "inelastic period" you wish to calculate, bakhtiyar.

Let K be the initial (un-yielded) stiffness of the SDOF oscillator.

Let a be the ratio of the post-yield stiffness to the elastic stiffness, K.

Let u be the displacement ductility demand, Dmax/Dy.

Prior to yielding, the SDOF operates at its initial period:

Ti = 2(pi)sqrt[m/K]

Once a bi-linear oscillator has yielded it is operating at a period calculated using the post-yield stiffness.

Ty = 2(pi)sqrt[m/(aK)]

A frequently used measure of inelastic period is the so called "effective period". The effective period is calculated using the effective, or secant stiffness, to maximum displacement, Keff = Fmax/Dmax. The effective period is given by:

Teff = (Ti)[sqrt(u/(1+au-a))]

Note that Ty is independent of the loading. But Teff depends upon the particular loading since the secant stiffness at Dmax is used, and Dmax depends on the loading.

Best of luck bakhtiyar.

Let K be the initial (un-yielded) stiffness of the SDOF oscillator.

Let a be the ratio of the post-yield stiffness to the elastic stiffness, K.

Let u be the displacement ductility demand, Dmax/Dy.

Prior to yielding, the SDOF operates at its initial period:

Ti = 2(pi)sqrt[m/K]

Once a bi-linear oscillator has yielded it is operating at a period calculated using the post-yield stiffness.

Ty = 2(pi)sqrt[m/(aK)]

A frequently used measure of inelastic period is the so called "effective period". The effective period is calculated using the effective, or secant stiffness, to maximum displacement, Keff = Fmax/Dmax. The effective period is given by:

Teff = (Ti)[sqrt(u/(1+au-a))]

Note that Ty is independent of the loading. But Teff depends upon the particular loading since the secant stiffness at Dmax is used, and Dmax depends on the loading.

Best of luck bakhtiyar.

Tim Huff

- huffte offline
**Posts:**750**Joined:**22 Jul 2011, 10:19**Location:**Cookeville, Tennessee, USA

Hi,Dear huffte

I want to Calculation of Increased period during the earthquake excitation.

I want to Calculation of Increased period during the earthquake excitation.

- bakhtiyar offline
**Posts:**46**Joined:**03 Sep 2012, 04:16

Hi bakhtiyar. I reiterate my previous answer. In SeismoSignal, you specify the post-yield stiffness, a, in the Program Settings --> Response Spectra tab. You specify the displacement ductility, u, in the Elastic/Inelastic Response Spectra tab.

So, for any given initial period, Ti, you can compute the yielded period, Ty, or the effective period, Teff.

Ty = 2(pi)sqrt[m/(aK)] = (Ti)/sqrt(a)

Teff = (Ti)[sqrt(u/(1+au-a))]

Note, that for elastic-perfectly-plastic behavior with a = 0, the yielded period becomes infinite.

So, for any given initial period, Ti, you can compute the yielded period, Ty, or the effective period, Teff.

Ty = 2(pi)sqrt[m/(aK)] = (Ti)/sqrt(a)

Teff = (Ti)[sqrt(u/(1+au-a))]

Note, that for elastic-perfectly-plastic behavior with a = 0, the yielded period becomes infinite.

Tim Huff

- huffte offline
**Posts:**750**Joined:**22 Jul 2011, 10:19**Location:**Cookeville, Tennessee, USA

dear huffte.Thanks for your explanation. i want time history variation period During ground motion excitation.

- bakhtiyar offline
**Posts:**46**Joined:**03 Sep 2012, 04:16

Unless my previous responses satisfy your question, I am not clear as to what you are asking, bakhtiyar. I do not understand the term "time history variation period"?

Tim Huff

- huffte offline
**Posts:**750**Joined:**22 Jul 2011, 10:19**Location:**Cookeville, Tennessee, USA

bakhtiyar,

Is your query related to SeismoSignal or to SeismoStruct?

As huffte tried to explain, obtaining in SeismoSignal the period elongation of a SDOF system is a somewhat peculiar concept, given that in SeismoSignal the period of vibration of the SDOF systems (that are subjected to dynamic analyses in order to derive the response spectra) does not really change.

On the contrary, if you are using SeismoStruct, and your SDOF consists e.g. of a reinforced concrete column with a mass on top, then, if you subject such SDOF structure to an accelerogram that will first crack the concrete and then also yield its reinforcement, then you may certainly observe an elongation of the period as the analysis progresses.

Best,

Rui

Is your query related to SeismoSignal or to SeismoStruct?

As huffte tried to explain, obtaining in SeismoSignal the period elongation of a SDOF system is a somewhat peculiar concept, given that in SeismoSignal the period of vibration of the SDOF systems (that are subjected to dynamic analyses in order to derive the response spectra) does not really change.

On the contrary, if you are using SeismoStruct, and your SDOF consists e.g. of a reinforced concrete column with a mass on top, then, if you subject such SDOF structure to an accelerogram that will first crack the concrete and then also yield its reinforcement, then you may certainly observe an elongation of the period as the analysis progresses.

Best,

Rui

- ruipinho offline

**Posts:**156**Joined:**07 Dec 2013, 14:37

Hi,I want to estimate the dominating inelastic period of SDOF system with elastic period= 0.7s and constant-ductility = 5, subjected to seismic action by computing the Fourier spectrum of its acceleration response time-history, residual displacement occurs in end of displecement time history but maximum fourier amplitude occurs in period=0.7s. please help me. I probably need to yield displacement for calculated inelastic period

- ghanbari offline
**Posts:**4**Joined:**23 Mar 2016, 09:15

hi

Dear timothy

How can I calculate the softening damage index by maximum period and final period of SDOF system subjected to ground motion by using SeismoSignal ?

DiPasquale and Cakmak [1990] developed softening damage model based on the evolution of the natural period of a time-varying linear system equivalent.in this method necessary to have the input ground acceleration and the acceleration at the top of the structure!!!!????

Dear timothy

How can I calculate the softening damage index by maximum period and final period of SDOF system subjected to ground motion by using SeismoSignal ?

DiPasquale and Cakmak [1990] developed softening damage model based on the evolution of the natural period of a time-varying linear system equivalent.in this method necessary to have the input ground acceleration and the acceleration at the top of the structure!!!!????

- ghanbari offline
**Posts:**4**Joined:**23 Mar 2016, 09:15

Hi ghanbari. SeismoSignal models a single-degree-of-freedom bilinear oscillator. So, there are really only 3 periods which have meaning.

1. The initial period of the structure, Ti = 2(pi)sqrt(m/k1)

2. The yielded period of the structure, Ti = 2(pi)sqrt(m/k2)

3. The effective period of the structure, Teff = 2(pi)sqrt(m*dmax/Fmax)

So I am not sure your question applies to SeismoSignal. I suppose you could take the yielded period as the final period and perform calculations in line with the subject paper. But being unfamiliar with the referenced work, I cannot say whether this would be proper.

1. The initial period of the structure, Ti = 2(pi)sqrt(m/k1)

2. The yielded period of the structure, Ti = 2(pi)sqrt(m/k2)

3. The effective period of the structure, Teff = 2(pi)sqrt(m*dmax/Fmax)

So I am not sure your question applies to SeismoSignal. I suppose you could take the yielded period as the final period and perform calculations in line with the subject paper. But being unfamiliar with the referenced work, I cannot say whether this would be proper.

Tim Huff

- huffte offline
**Posts:**750**Joined:**22 Jul 2011, 10:19**Location:**Cookeville, Tennessee, USA

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