Properties of the centroid of an area

[Jacobim]

Hello,

I am calculating the centroid of an area using this equation for composite bodies:

sum(indivudual area times individual centroid)/sum(individual area) = distance from axis to centroid

this is just y bar for a cross section that is symmetrical about the y axis

I was under the impression that when you find y bar, then the areas of the cross section on either side of y bar would be equal, but this is not the case. Is this correct and if so why?

I thought surely the centroid would mean there would be equal mass (or area in this case) on either side of it.

 

[SteamKing]

No, the centroid establishes the line about which the first moments of area are equal. That comes from the formula for finding the centroid of a composite figure.

 

[pongo38]

You may be interested to know that although the centroidal axis often is used for all sorts of things, the equal are axis has a use in the plastic design of steel cross-sections, when the sections are bent beyond their elastic limit.