Engineer Boards

# Seismic Response Coefficient

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Please help if you can; I have searched for this question and not found an answer. I have two references, Hiner and Mansour, that tell me that if Ts<T<TL, ASCE 7-05 equation 12.8-3 should be used, since this is supposed to provide a lower Cs than eq'n 12.8-2, which is what the designer will like (lower base shear). However, in at least two examples, the approximate period, Ta, is less than 1.0 sec, which means that eq'n 12.8-3 provides a higher Cs than eq'n 12.8-2 (since T is in the denominator). The code language is that 12.8-2 shall be used, but Ta need not be greater than eq'n 12.8-3 and 12.8-4 (and of course the minimums must be checked).

Neither reference seems to account for the possibility that 12.8-3 can provide a higher Cs than 12.8-2, even with example problems. So if I am eligible to use 12.8-2 and it is a lower Cs than from 12.8-3, shouldn't I do so?

Thank you so much for your time.

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I think you need to take a step back and focus on ASCE 7-05 Figure 11.4-1. If you built an infinitely stiff structure (and a fundamental period of zero) ASCE 12.8-3 would have a seismic response coefficient of infinite. Then again ASCE 12.8-3 is just an equation (1 of 3) to better represent the true acceleration response spectrum as represented in Figure 2.5 of Hiner's book.

Keep in mind that from pg 352 of ASCE 7-05 paragraph 2 that "the design forces are intended only as approximations to produce the same deformations...as would occur in the same structure should an earthquake ground motion at the design level occur." Wouldn't make a lot of sense to use 12.8.3 when you have a structure with a very small fundamental period. 12.8.2 is a better approximation of reality as seen from Figure 2.5 of Hiner's.

Checking 12.8-3 as the maximum just ensures you're sliding down the slope towards longer periods.

And if you're wondering what forces could deform an infinitely stiff structure...then my head will explode.

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I think you need to take a step back and focus on ASCE 7-05 Figure 11.4-1. If you built an infinitely stiff structure (and a fundamental period of zero) ASCE 12.8-3 would have a seismic response coefficient of infinite. Then again ASCE 12.8-3 is just an equation (1 of 3) to better represent the true acceleration response spectrum as represented in Figure 2.5 of Hiner's book.

Keep in mind that from pg 352 of ASCE 7-05 paragraph 2 that "the design forces are intended only as approximations to produce the same deformations...as would occur in the same structure should an earthquake ground motion at the design level occur." Wouldn't make a lot of sense to use 12.8.3 when you have a structure with a very small fundamental period. 12.8.2 is a better approximation of reality as seen from Figure 2.5 of Hiner's.

Checking 12.8-3 as the maximum just ensures you're sliding down the slope towards longer periods.

And if you're wondering what forces could deform an infinitely stiff structure...then my head will explode.

Thanks, that's what I thought. My confusion seems to have come from not noticing the difference in the design accelerations used for 12.8-2 (SDS ) and 12.8-3 (SD1)... doh! However, just to spell it out, I will need to calculate 12.8-2 regardless of period, and then check the mins and maxes, as applicable, correct?

BTW, the only infinitely stiff structures I know of are people's political ideologies, and no force known to exist has been shown to deform (alter) them. (Thank God that's not an engineering problem).

Thanks again.

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Yeah that's correct. It puts that equation out there first to ensure that the most critical case regardless of the building period is checked.

lol at political ideologies, now that's a joke only engineers would understand.

Edited by txpaul01

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Please help if you can; I have searched for this question and not found an answer. I have two references, Hiner and Mansour, that tell me that if Ts<T<TL, ASCE 7-05 equation 12.8-3 should be used, since this is supposed to provide a lower Cs than eq'n 12.8-2, which is what the designer will like (lower base shear). However, in at least two examples, the approximate period, Ta, is less than 1.0 sec, which means that eq'n 12.8-3 provides a higher Cs than eq'n 12.8-2 (since T is in the denominator). The code language is that 12.8-2 shall be used, but Ta need not be greater than eq'n 12.8-3 and 12.8-4 (and of course the minimums must be checked).

Neither reference seems to account for the possibility that 12.8-3 can provide a higher Cs than 12.8-2, even with example problems. So if I am eligible to use 12.8-2 and it is a lower Cs than from 12.8-3, shouldn't I do so?

Thank you so much for your time.

It means that you made mistakes in your calculation. The Cs value from Eq. 12.8-3 will never be greater than that from Eq. 12.8-2

If you take a look at the design spectral curve in Chapter 11, you will understand why that

Cs = Sds/(R/I) (12.8-2), when T <= Ts = Sd1/Sds governs

Cs = Sd1/T(R/I) (12.8-2), when Ts< T <=TL governs, which means that when Ts< T, Cs = Sd1/T(R/I) <Sd1/Ts(R/I)=Sds/(R/I)

Edited by K=1.0