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Percentage of reinforcement as per Concrete grade and steel grade(SP-16)

 
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ramu_se
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Joined: 30 Oct 2017
Posts: 60

PostPosted: Tue May 03, 2022 10:09 am    Post subject: Percentage of reinforcement as per Concrete grade and steel grade(SP-16) Reply with quote

Dear All,

Reinforcement % for singly reinforced sections and doubly reinforced sections are given in SP-16 for the grade of concrete up to M30(fck) and grade of steel up to 500(fy).

How do we get the reinforcement % for M40 and above-grade concrete and 550-grade steel??

Thanks & Regards,
Ramu.
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vikram.jeet
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Joined: 26 Jan 2003
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PostPosted: Thu May 05, 2022 8:10 am    Post subject: Reply with quote

Dear Er Ramu ji,

Going by limit stage design  , I  think following basic relations can be used :

Depth of NA Xu  limiting value for any grade of steel :

As per IS 456
Strain in conc at extreme fiber Sc= 0.0035
Strain in steel at its centroid  Ss = {Fy/(1.15 *Es)} + 0.002

Considering Strain diagram ( linear variation of Strain in section)

Xu =  [Sc / (Sc +Ss)  ] d

For Fe500 the value work to Xu = o.456 and rounded by IS 456 to Xu =0.46

Accordingly for Fe 550 Xu = 0.4435

You can also verify for Fe 250 as well as Fe 415

VALUE OF Es taken = 2 x 100000 mpa

To be cont'd _ _ _
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vikram.jeet
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PostPosted: Thu May 05, 2022 8:36 am    Post subject: Reply with quote

Max % of reinf in singly reifd sections

This can be calculated by equating compressive force to tensile force at  a balanced section

Compressive force in conc = 0.36Fck Xu B

Tensile force in steel = 0.87 Fy Ast

Xu = k*d  and it's limiting value for Fe 550 as calculated in prev post = 0.4435 *d

Doing calcs for Fe 500 to verify  k= 0.456 d

Hence using Fe 500  % reinf  max for singh reifd section can be calculated for any conc grade be it M40

Equating

0.36Fck * k*d*B = 0.87Fy*Ast

Ast/Bd = 0.36 Fck*k / (0.87Fy)

For Fe 500 and M20 , the value works to 0.7548  and Sp16 charts
rounds to 0.755

Similarly u can check for others
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ramu_se
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PostPosted: Sun May 15, 2022 4:40 pm    Post subject: Reply with quote

Thank you sir.
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