First moment of area of the reinforcement (Eurocode 2) - Avscorreia
First moment of area of the reinforcement (Eurocode 2) - Avscorreia
(OP)
Dear everyone,
I would like to have your opinions on the following issue:
I've seen someone who calculated the first moment of area of the reinforcement about the centroid of the section, using the following formula:
S = -Asc (yc - d2) + Ast (d -yc)
where:
S = first moment of area of the reinforcement
Asc = area of steel in compression
Ast = area of steel in tension
d = effective section depth (from top fibre to tension steel)
d2 = concrete cover of compression steel
yc = distance from extreme compressive fibre to neutral axis
My question is: whether the minus sign ("-") in front of Asc was correct ?
Should it be + ? If it is correct, why would we need to subtract the compression steel component ?
the formula was used by @avscorreia in his spreadsheet
(http://files.engineering.com/getfile.aspx?folder=4...)
in another thread,
(http://www.eng-tips.com/viewthread.cfm?qid=402136)
which has been closed so I could not ask him there directly,
I need to find a correct equation to calculate S to use Clause 7.4.3 (6) Eurocode 2.
Thank you in advance.
Regards
NTCONLINE
I would like to have your opinions on the following issue:
I've seen someone who calculated the first moment of area of the reinforcement about the centroid of the section, using the following formula:
S = -Asc (yc - d2) + Ast (d -yc)
where:
S = first moment of area of the reinforcement
Asc = area of steel in compression
Ast = area of steel in tension
d = effective section depth (from top fibre to tension steel)
d2 = concrete cover of compression steel
yc = distance from extreme compressive fibre to neutral axis
My question is: whether the minus sign ("-") in front of Asc was correct ?
Should it be + ? If it is correct, why would we need to subtract the compression steel component ?
the formula was used by @avscorreia in his spreadsheet
(http://files.engineering.com/getfile.aspx?folder=4...)
in another thread,
(http://www.eng-tips.com/viewthread.cfm?qid=402136)
which has been closed so I could not ask him there directly,
I need to find a correct equation to calculate S to use Clause 7.4.3 (6) Eurocode 2.
Thank you in advance.
Regards
NTCONLINE






RE: First moment of area of the reinforcement (Eurocode 2) - Avscorreia
And thank you for taking the trouble to check it!
RE: First moment of area of the reinforcement (Eurocode 2) - Avscorreia
RE: First moment of area of the reinforcement (Eurocode 2) - Avscorreia
S = Asc (d2 - yc) + Ast (d -yc)
d2 should be the dimension to the centre of the bar, not the cover depth.
The Eurocode clause is for calculation of curvature due to shrinkage, and in an uncracked symmetrical section uniform shrinkage does not cause any curvature, so it makes sense that the effect of the top and bottom steel should have a different sign.
Note that in a cracked section, where the neutral axis is not at the centroid of the concrete section, symmetrical steel will generate significant curvature, even under uniform shrinkage.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: First moment of area of the reinforcement (Eurocode 2) - Avscorreia
I've also doubled checked : it is correct to have the negative sign.
My hand calculation for deflection makes sense now and I get the reasonable deflected shape.
Kind regards
NTCONLINE