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Column Design - concrete - Biaxial bending 1

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Pretty Girl

Structural
Joined
Nov 22, 2022
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AU
I'm trying to understand the concept behind the axial force calculation from steel stress. This is from "Reinforced concrete design to eurocodes" by prab bhat, page 368.
I'm bit confused of why in the "0.002 bh/4", 0.002 bh is divided by 4.

The steel percentage is 4%, and there are 4 bars.

So, the steel for each bar should be 'Ast/bh = 0.04/4 = 0.01'

Ast = 0.01 bh
So, there's no need to divide it by 4 again, as we already got the Ast value for one bar already.

Nst = (Ast/bh) * fst, so the answer should be -530 * 0.01 bh = -5.3 bh

But the book states, the following. Why?
Ns = (317 – 435 – 435 + 23) × (0.02 bh/4) = –2.652 bh (tensile)

If it's only for the tensile, but we can't ever know which steel bars are in tension because it's biaxially bending. So we can't be sure that exactly two bars are in tension.

If it's so clear that only two bars are in tension, then, why the book has added the stresses of all the 4 bars together (317 – 435 – 435 + 23).

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Further, why there's inconsistency as the Mxs is all positive, and Mys is negative at some numbers. I can't understand the logic.
1731322971808.png


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Here's the screenshot of the question in the book

Screenshot 2024-11-11 at 5.31.56 pm.png
I
 
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So, there's no need to divide it by 4 again, as we already got the Ast value for one bar already.

You are right. There is an error . Steel percentage shall be 2% . As =0.02* b*h
 
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