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Clarification on calculation of stability index of RC Frame
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aditya
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PostPosted: Sun Jul 12, 2015 9:59 am    Post subject: Clarification on calculation of stability index of RC Frame Reply with quote

Dear Sefians,
Clause 25.2 and Annex E Clause E2 of IS 456: 2000 gives the method to calculate the Stability Index Q to determine whether a storey is sway storey or not on the basis of which we have to determine the effective length of columns for column design of a particular storey. However, the clause does not elaborate on the following topics:
1. whether the lateral deflections, sum of axial forces and total lateral forces are to be computed for "EQ load case" only or for "load combinations involving EQ loads, e.g. 0.9DL+1.5EQ, etc. For example, provision for inter-storey drift is checked only for EQ LOAD CASE and not for EQ load combinations as per IS 1893-2002.
2. whether sway or non-sway cases will be different for different load combinations or not since if Q is to be calculated for LOAD COMBINATIONS, deflections, axial forces and lateral forces will be different for different load combinations and Q may be different for each combinations.
3. The example document "Design  Example of a Six Storey Building (EQ26) published by NICEE in section 1.9 page 17 seems to have calculated Q for EQ load case only and not for EQ load combinations.

I humbly request all Sefians to elaborate on this important topic.

with best regards,
Aditya
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N. Prabhakar
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PostPosted: Sun Jul 12, 2015 1:34 pm    Post subject: Reply with quote

Dear Er. Aditya,

The stability index Q determines only whether the column is a sway or no sway column.  If the Q value is more than 0.04, then the column has to be designed as a sway column which is the worst case for design.

Looking at the equation of Q given in ANNEX E of IS 456 : 2000, a higher value of Q is obtained when sum of the axial load of all column in the storey, Py is maximum.  For this reason, the load combination of 1.5 DL + 1.5 EQ or 1.5 WL (whichever is greater) should be considered in the calculation. Higher first order deflection due to EQ or WL also results a higher value of Q.  It is possible that the value of Q may be higher than 0.04 in one load combination only and not in the others.  In practice, the sway column as applicable to that load combination, always govern the design requiring larger size of column or higher grade of concrete or more reinforcement.

For further understanding on this subject, please also refer to APPENDIX D of SP : 24 -1963, Explanatory Handbook on IS : 456-1978 which has not changed in the 2000 version of the code.

With best wishes,

N. Prabhakar
Chartered Structural Engineer
Vasai (E)
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aditya
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PostPosted: Mon Jul 13, 2015 7:56 am    Post subject: Reply with quote

Dear Respected N. Prabhakar Sir,
Thanks a lot for your kind response. From your elaborations, I came to the conclusion that Q is to be calculated for LOAD COMBINATIONS, whichever is severest. The result for calculation will be definitely different for Load Case and Load Combination, since Pu and deflections will be different in the two cases.
I was little confused after going through the cited example (EQ26.pdf) and that's why I raised this question. Examples given in RCC Text Books by Dr. Subramanian and Dr Menon also talk about the given value of total load and given value of deflection for calculation of Q but details on derivation of loads and deflections are not given due to, may be, paucity of space in these books.
Thanks a lot again!
with regards,
Aditya
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Dr. N. Subramanian
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PostPosted: Mon Jul 13, 2015 6:40 pm    Post subject: Reply with quote

Dear Er Aditya & Er Prabhakar,

Thank you Er Prabhakar for clarifying this.

Er Aditya: This clause has been adopted in IS 456 from an earlier version of ACI 318 code. Now the stability index in ACI 318 is set as 0.05 instead of 0.04. Please read Commentary to Clause 10.10.5 of ACI 318-11: " In computing Q, ΣPu should correspond
to the lateral loading case for which ΣPu is greatest. A
frame may contain both non-sway and sway stories. This test
would not be suitable if Hu is zero.

If the lateral load deflections of the frame have been
computed using service loads and the service load moments
of inertia given in 10.10.4, it is permissible to compute Q in
Eq. (10-10) using 1.2 times the sum of the service gravity
loads, the service load story shear, and 1.43 times the firstorder
service load story deflections."
This has been mentioned in pp. 513 of my RC Design book

Best wishes
NS

aditya wrote:
Dear Respected N. Prabhakar Sir,
Thanks a lot for your kind response. From your elaborations, I came to the conclusion that Q is to be calculated for LOAD COMBINATIONS, whichever is severest. The result for calculation will be definitely different for Load Case and Load Combination, since Pu and deflections will be different in the two cases.
I was little confused after going through the cited example (EQ26.pdf) and that's why I raised this question. Examples given in RCC Text Books by Dr. Subramanian and Dr Menon also talk about the given value of total load and given value of deflection for calculation of Q but details on derivation of loads and deflections are not given due to, may be, paucity of space in these books.
Thanks a lot again!
with regards,
Aditya
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suresh_sharma
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PostPosted: Tue Jul 14, 2015 4:41 am    Post subject: Reply with quote

Dear Dr. N S and Mr. Prabhakar,

Shall I be correct in assuming that stability index is required to be checked only when the column is structurally long?
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N. Prabhakar
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PostPosted: Tue Jul 14, 2015 5:51 am    Post subject: Reply with quote

Dear Er. Suresh Sharma,

Generally speaking, columns in a frame with strong shear walls or with diagonal bracings  in the vertical plane (rare in RC frames) by which lateral deflections do not take place, may be considered as 'No Sway' columns.  Otherwise, columns in the bare frame only are to be considered as 'Sway' columns only.   In the doubtful latter case where the lateral deflections do take place, if one wants to determine whether it is classified as 'Sway' or 'No sway' columns  by a more precise method, it is necessary to  do the calculation of Stability Index Q.

Sway columns have effective length factor of more than 1.0 resulting larger size of column or higher grade of concrete or more reinforcement.

N. Prabhakar
Chartered Structural Engineer
Vasai (E)
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suresh_sharma
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PostPosted: Tue Jul 14, 2015 6:33 am    Post subject: Reply with quote

Mr. Prabhakar,
What I could understand from your posting that in lieu of checking Q value, one may directly go in for determining Beta1 and Beta2 and determine the effective length of the column. In exceptionally doubtful cases, one may be required to determine Q value. Is it what you mean to say?
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N. Prabhakar
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PostPosted: Tue Jul 14, 2015 12:33 pm    Post subject: Reply with quote

Dear Er. Suresh Sharma,

The answer to your query is 'Yes'.  In practice, it is not that easy to calculate the value of Q, and may be still doubtful.  It is safer and easier to calculate Beta1 and Beta2 , and find out the effective length of column for the case of  a sway frame.  You can calculate the effective length of column from the Excel Spreadsheet contained in RCDesign Ver 2.0 which you have bought from me.

In the book on RC Design by Dr NS, reference to Clause 10.10.1 of ACI 318 is made which considers the frame as braced against sway (i.e. no sway frame) when shear walls have a total stiffness of at least 12 times the gross stiffness of all the columns in the storey.  This is a useful guide and easier to calculate also.

With best wishes,

N. Prabhakar
Chartered Structural Engineer
Vasai (E)
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aditya
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PostPosted: Wed Jul 15, 2015 9:26 am    Post subject: Reply with quote

Dear respected N. Prabhakar Sir,
I beg your pardon for further clarification on this topic. Should we calculate Hu (sum of lateral shear of a particular storey) as well as first order interstorey deflection delta also for 1.5 DL+1.5 EQ (or 1.5DL+1.5Wind)?i.e combined effect of Dead Load and EQ load (or Wind as the case may be).
I am confused since Hu and delta for EQ load case only will be different from the result for complete load combination.
with regards,
Aditya
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N. Prabhakar
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PostPosted: Thu Jul 16, 2015 6:17 am    Post subject: Reply with quote

Dear Er. Aditya,

In the calculation of Q, the values of Py, Delta and Hy considered are to be for the same combination of loads, and not inter-mixing from one combination with the other.  Whichever combination of loads that leads to a higher value of Q of more than 0.04 will result in critical condition for the design as a sway column.   In practice, no one considers the case of EQ load case only for design.  I believe, I have answered your doubt.

With best wishes,

N. Prabhakar
Chartered Structural Engineer
Vasai (E)
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