First moment of area of the reinforcement (Eurocode 2)


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)
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?

avscorreia shared a spreadsheet:

I need to find a correct equation to calculate S to use Clause 7.4.3 (6) Eurocode 2.


As shrinkage curvature occurs when there’s a difference between the top and bottom reinforcement, the area module that is calculated takes this effect into account by considering the effect of the top reinforcement with a negative sign.

Above is a snippet.

@avscorreia, please feel free to upload your spreadsheet to this topic so others can benefit by downloading it for further review.

Thank you.

Sorry, but no.

No worries. Your advice to others is always excellent.

Thank you.

@avscorreia Being a ChE, I was wondering what the practical use of a “first moment of area” is? And, is this the same or different from a “first moment of area of the reinforcement”, and what is the practical use of that?

I’m sorry @Latexman.
I know you and other mods have been doing an excellent job moderating this forum and ET. However, the presence of some MAGA cult followers spreading false information in a moment of pandemic makes me want to retreat from these forums in the present time as I want no further association with these folks. I’m sure I won’t be missed.
Please stay safe.

@avscorreia I understand your frustration with this subject. Really, I do! However, at SimpliEngineering (SE) you have at least two tools you don’t kave at ET. In your preferences, under Users, you can specify another user (or multiple users) to be Muted or Silenced. See: