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Dr. N. Subramanian General Sponsor
Joined: 21 Feb 2008 Posts: 5538 Location: Gaithersburg, MD, U.S.A.
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Posted: Fri Nov 19, 2021 4:44 pm Post subject: In Doubly Reinforced beams using WSM, why we get Pc greater than Pt? |
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Someone asked this question. In tables 72 to 75 of SP 16, Pt is greater than Pc, where sigmast is 140 (fy is 250 MPa) and sigma cbc is 5 to 10.0. Whereas, In tables 76 to 79, when sigmast is 230 (fy is 415 MPa), Pc is greater than Pt. Why?
I asked Prof. H.J. Shah as I forgot WSM, as it is not used for design for a long time (may be eliminated in the next version of IS 456- WSM may
still be used for serviceability checks like deflection, vibration, etc.). I also found the reason independently, by the time Prof. Shah answered.
In the working stress method, permissible stress in compression reinforcement is taken as (1.5m-1) times stress in adjoining concrete.
This value is very small resulting in a large required compression area.
I think that the same doubly reinforced beam will become economical if we design it by LSM, anyone may check it out by taking a specific example. |
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vikram.jeet General Sponsor
Joined: 26 Jan 2003 Posts: 3839
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Posted: Sat Nov 20, 2021 8:59 am Post subject: |
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Doubly Reinforced Beam
WSM vs LSM
For same BM , WSM requires higher depth for a section to be singly reinforced vis a vis LSM.
For same section size (B,D) WSM requires higher Compression steel vis a vis LSM in doubly Reinforced beam
The main reason lies in an overall safety factor :
In WSM , safety factor for stresses are :
Concrete Bending compressive stress - 3
Steel bending stress (tensile)- about 1.80
Load factor = 1.0
In LSM the safety factors are :
Load Factor = 1.5. (Under Normal conditions on gravity loadings)
Partial safety for bending comp stress in concrete = 1.5
Hence overall computed safety factor for cbc = 1.5*1.5 = 2.25
For steel partial safety factor bending stress tension = 1.15
Hence overall computed FOS for tensile steel = 1.5*1.15= 1.725
Overall
From above it is seen that computed overall safety factors are :
WSM = 3.0 Whereas LSM = 2.25 (for concrete bending stress cbc)
WSM = 1.80 whereas LSM = 1.725 (for steel tensile stress Sigma st)
Thus computed overall safety factors in LSM are 25% lesser than WSM in concrete and AND marginally lesser (about 5℅) for tensile steel stresses .
Compression steel :
Compressive steel stress in WSM is 1.5*m* c at compression steel location.
WSM M20 value ( 1.5*m*c) = 1.5*14*7.0 =147 Mpa*
M25 = 1.5* 11* 8.5 = 140 Mpa*
M30. = 1.5*9*10 = 135 Mpa*
* Stress will be slightly less depending on c at compression steel.
Referring to SP-16 , based on d'/d comp stress in steel is given in table F.
In LSM compressive stress in steel is based on a stress of 0.87 fy.
The net compressive stress for comparison with WSM is 0.87/1.5=0.58 fy. (Slightly less as per d'/d )
It is seen that the steel compressive stress in WSM is about 60% the steel compressive stress in LSM. (Slightly vary as per d'/d).
Designs are therefore economical in LSM. |
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vikram.jeet General Sponsor
Joined: 26 Jan 2003 Posts: 3839
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Posted: Sat Nov 20, 2021 2:06 pm Post subject: |
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Further : Stress in compression reinforcement
Since the permitted bending comp stress in conc under WSM is Fck /3 and same in LSM is Fck/2.25 (on computed overall FOS basis), hence a higher stress in compression reinforcement in LSM to the extent = (3/2.25 ) is expected . |
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pvgraju ...
Joined: 07 Jun 2020 Posts: 66
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Posted: Mon Nov 22, 2021 10:29 am Post subject: In Doubly Reinforced beams using WSM, why we get Pc greater than Pt? |
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Dear Sir,
Permissible working stress in compression steel is 1.5xmxstress in concrete around steel.
stress in concrete around steel is mx2/3 fc = 280/3fc x 2/3 fc = 280/9 fc
so permissible stress in compression steel will be
= 1.5xmxmx280/9 fc.
so as long as fc is not changing permissible working stress in compression shall not change.
Regards,
P.V.Gavarraju. |
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vikram.jeet General Sponsor
Joined: 26 Jan 2003 Posts: 3839
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Posted: Mon Nov 22, 2021 10:51 am Post subject: |
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In WSM , stress in compression steel depend on stress in concrete around it. But permissible stress in concrete in bending is Fck/3.
Same seems true in LSM , but overall FOS (computed) for conc bending stress = 2.25
Hence stress in compression steel depend upon Fck/2.25.
This could be the reason that compression steel computed in WSM will be higher on two counts :
(I) Lesser Moment capacity as singly reinforced
(ii) Lesser stress available around compression steel |
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