Column Design - concrete - Biaxial bending - Why the r/f area is not deducted from concrete area 3

[Pretty Girl]

I'm trying to understand the concept behind this. This is from "Reinforced concrete design to eurocodes" by prab bhat, page 370.
I'm bit confused of why the reinforcement area is not deducted from the compressed area of the concrete, when it calculates the "axial force in concrete (Nc)".

If we assume that it considers the r/f area as concrete (because r/f is more than sufficient to substitute concrete), still the calculation added compressive r/f area in the "axial force in steel (Ns)".

So it's like double adding the r/f area into the compressive steel area and also to the compressive concrete area (since the r/f area doesn't get deducted from concrete area).

Isn't it inaccurate to not to reduce r/f area from compressive steel if we already added that in compressive r/f area calculation?

Does that mean the calculation in the book not that accurate?

 

[Retrograde]

Because the area of reinforcement is probably only a few percent of the total area of the column, deducting the area of the reinforcement will make little difference to the answer.

 

[Pretty Girl]

Because the area of reinforcement is probably only a few percent of the total area of the column, deducting the area of the reinforcement will make little difference to the answer.

If it's insignificant, then why the calculation added compressive r/f area in the "axial force in steel (Ns)". They could have omitted in that as well. Why double standard?

 

[rapt]

It should be removed, or the reinforcement stress reduced by the stress in the concrete (gives the same result).

 

[Pretty Girl]

It should be removed, or the reinforcement stress reduced by the stress in the concrete (gives the same result).

Thank you. That means the book has a slight error.

 

[HTURKAK]

That means the book has a slight error.

The book ignores the effect of concrete stresses at correponding to the steel areas.


The corresponding compression stresses : 435, 102, and 293 MPa could be reduced by the stress in concrete at that level .

The following excerpt from Design of Conc. Structures ( by NARAYANAN ) for
DESIGN OF COLUMNS WITH AXIAL LOAD
AND BIAXIAL BENDING

 

[Pretty Girl]

The book ignores the effect of concrete stresses at correponding to the steel areas.


The corresponding compression stresses : 435, 102, and 293 MPa could be reduced by the stress in concrete at that level .

The following excerpt from Design of Conc. Structures ( by NARAYANAN ) for
DESIGN OF COLUMNS WITH AXIAL LOAD
AND BIAXIAL BENDING


View attachment 1467

Thanks a lot.

 

[bkal]

If it's insignificant, then why the calculation added compressive r/f area in the "axial force in steel (Ns)". They could have omitted in that as well. Why double standard?

Could it be that, becasue of a strain compatibility and a difference in elasitc mudulus between steel and concrete, the force in concrete is almost an order of magnitude smaller than the force in steel.

 

[rapt]

It is still nearly 10% of the steel force. It should not be ignored, especially in heavily reinforced columns.

 

[Pretty Girl]

It is still nearly 10% of the steel force. It should not be ignored, especially in heavily reinforced columns.

Thank you