Properties of the centroid of an area

1. Jun 6, 2013

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.

2. Jun 6, 2013

SteamKing

Staff Emeritus
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.

3. Jun 7, 2013

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.