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aditya ...
Joined: 05 Apr 2008 Posts: 184

Posted: Tue Jul 21, 2020 6:03 am Post subject: Clarification on computation of modification factor for tension reinforcement in IS 456: 2000 


Dear Respected N. Subramanian Sir,
This refers to the provision of Span/Effective Depthrequirement for simplified check for deflection in RC beams & slabs as perclause 23.2.1 (c) of IS 456: 2000. In your book "Design ofReinforced Concrete Structures", it has been stated in page 160 & 137 that the modificationfactor k_{t} for tension reinforcement is given by k_{t}=1/[0.225+0.00322*f_{s}0.625*log_{10}(1/p_{t})] where f_{s}=(0.58*f_{y}*A_{st reqd}/A_{stprov}). IS 456: 2000 gives only the curves for this modification factor in Fig 4 page 38 while the equation has been given in SP24 only.
My query is regarding the interpretation of p_{t}=100*A_{st}/(b*d).When A_{st reqd}=A_{st prov}, there is no problem. But when A_{stprov} is not equal to A_{st reqd}, should we take p_{t} as p_{t} _{reqd} or p_{t prov}? This has not been explained in SP 24. By providing more A_{st} than required, service stress f_{s} is decreased by which we can reduce the thickness of RC Slab, especially when using HYSD bars and this provision has been really useful.
Referring to the solved examples Ex 5.17 page 197, Ex 9.1 page 351 & Ex 9.2 page 354 in your book, you have taken p_{t}=p_{tprovided} but from the figure given in IS 456: 2000, it appears that p_{t }is to be taken as p_{t required} (meaning that modification factor k_{t }is less if p_{t} _{reqd} is more) while p_{t} provided would alter f_{s}=0.58*f_{y}*(A_{streqd}/A_{stprovided}) only resulting in less service stress and thereby more value of modification factor.
Would you please clarify on this matter in reference to the original paper by Prof. A. K. Beeby on this check?
With best regards,
Aditya Shrestha


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Dr. N. Subramanian General Sponsor
Joined: 21 Feb 2008 Posts: 5468 Location: Gaithersburg, MD, U.S.A.

Posted: Wed Jul 22, 2020 2:00 am Post subject: 


Dear Er Aditya
You are right. The Equation is not given in the code but in SP 24:1983, based on a cement & Concrete Association publication by Prof. Beeby. As it is not possible to provide the exact calculated reinforcement, we usually multiply the fs value by the required area by provided area, which in any case will be small. Even Pillai and Menon book adopts this multiplication( see pp. 178 of that book).
As Prof. Beeby's paper is published in 1971, it may not be possible to get it now. If you are able to get it pass it on to me.
However, I am enclosing a fairly recent 2009 paper, which deals with this subject and may be of interest to you.
An interesting observation from this paper is given below:
"In the UK, it is common practice to minimize slabthicknesses by increasing the area of flexural reinforcement provided in the span A_{sprov} to as much as twice thatrequired for strength A_{sreq}. This practice frequently leadsto significant economies in whole building costs since itreduces the building height and hence the area of external cladding. Increasing A_{sprov}/A_{sreq} reduces the servicestress in the reinforcement and, hence, the deflection"
Regards
Subramanian
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aditya ...
Joined: 05 Apr 2008 Posts: 184

Posted: Sun Jul 26, 2020 5:59 am Post subject: 


Dear Respected N. Subramanian Sir,
Actually, my query was related to the interpretation of p_{t} in the SP 24 formula for modification factor for tension reinforcement. If we take pt=pt _{required}, the result would be different from what we get when we take pt=pt _{provided }though the error may be small. Would be please kindly clarify on this matter.
with best regards,
Aditya


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Dr. N. Subramanian General Sponsor
Joined: 21 Feb 2008 Posts: 5468 Location: Gaithersburg, MD, U.S.A.

Posted: Sun Jul 26, 2020 1:28 pm Post subject: 


Dear Er Aditya,
The formula is an empirical one. As I already informed, in a design situation, we can't provide Ast calculated and hence the Ast provided/Ast required is used by many authors, which unless a large Ast is provided deliberately will result in a value closer to 1.0 and hence, may not change the end result much.
Anyway the equation itself is only approximate.
In RCC we make so many assumptions. Hence it is not like rocket science where everything should be precise. We make several approximations. Many of the equations used are empirical, and derived based on limited number of test results.
Stay safe and healthy
Best wishes and regards
Subramanian
aditya wrote:  Dear Respected N. Subramanian Sir,
Actually, my query was related to the interpretation of p_{t} in the SP 24 formula for modification factor for tension reinforcement. If we take pt=pt _{required}, the result would be different from what we get when we take pt=pt _{provided }though the error may be small. Would be please kindly clarify on this matter.
with best regards,
Aditya 


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velrajkumar.g SEFI Regulars
Joined: 30 Mar 2013 Posts: 21 Location: coimbatore, india

Posted: Sat Sep 12, 2020 3:40 am Post subject: modification factor for reinforcemet  Reg 


Dear Sir,
As per IS 4562000, they have fs value from 120 MPa to 290 MPa. but my value for f_{s} =94.08 Mpa, P_{t }=0.17. Ast required =105 mm^{2 }and
Ast provided =262 mm^{2}
^{
}
Based on this equations
k_{t}=1/[0.225+0.00322*f_{s}0.625*log_{10}(1/p_{t})]
f_{s}= 0.58f_{y}( Ast required/Ast provided)
= 0.58x 415x (105/262)
= 96.46 MPa
kt = 1/[0.225+ (0.00322*96.46)(0.625*log_{10}(1/.17)]
= 1/[0.225+0.31 0.48]
= 18.18
Kindly do the needful sir.
Regards
g.Velrajkumar
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