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Clarification on computation of modification factor for tension reinforcement in IS 456: 2000

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

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 kt for tension reinforcement is given by kt=1/[0.225+0.00322*fs-0.625*log10(1/pt)] where fs=(0.58*fy*Ast reqd/Astprov). 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 pt=100*Ast/(b*d).When Ast reqd=Ast prov, there is no problem. But when Astprov is not equal to Ast reqd, should we take pt as pt reqd or pt prov? This has not been explained in SP 24. By providing more Ast than required, service stress fs 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 pt=ptprovided but from the figure given in IS 456: 2000, it appears that pt is to be taken as pt required (meaning that modification factor kt is less if pt reqd is more) while pt provided would alter fs=0.58*fy*(Astreqd/Astprovided) 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
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PostPosted: Wed Jul 22, 2020 2:00 am    Post subject: Reply with quote

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 Asprov to as much as twice thatrequired for strength Asreq. This practice frequently leadsto significant economies in whole building costs since itreduces the building height and hence the area of external cladding. Increasing Asprov/Asreq reduces the servicestress in the reinforcement and, hence, the deflection"

Regards
Subramanian



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aditya
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PostPosted: Sun Jul 26, 2020 5:59 am    Post subject: Reply with quote

Dear Respected N. Subramanian Sir,
Actually, my query was related to the interpretation of pt 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
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PostPosted: Sun Jul 26, 2020 1:28 pm    Post subject: Reply with quote

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 pt 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
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PostPosted: Sat Sep 12, 2020 3:40 am    Post subject: modification factor for reinforcemet - Reg Reply with quote

Dear Sir,

As per IS 456-2000, they have fs value from 120 MPa to 290 MPa. but my value for fs =94.08 Mpa, Pt =0.17.  Ast required =105 mm2 and
Ast provided =262 mm2



Based on this equations


kt=1/[0.225+0.00322*fs-0.625*log10(1/pt)]


fs= 0.58fy( Ast required/Ast provided)
   = 0.58x 415x (105/262)
   = 96.46 MPa

kt = 1/[0.225+ (0.00322*96.46)-(0.625*log10(1/.17)]
    = 1/[0.225+0.31 -0.48]
    = 18.18
Kindly do the needful sir.

Regards
g.Velrajkumar



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