# Centre of Area for a I-Section

Ok im completely stuck on this question, i have some idea on how to do it and know it is to do with moments but i cant figure out where to take the moments.

## Homework Statement

Calculate the value of Y-Bar for the I-section shown below, where Y-Bar is the vertical height of the centroid of the section above its base.

## Homework Equations

Y-Bar x Area of shape = XA * AA + XB * AB + XC * AC

## The Attempt at a Solution

Y-Bar x Area of shape = XA * AA + XB * AB + XC * AC

so

Y-Bar x 12,000 = XA * 3600 + XB * 3600 + XC * 4800

Y-Bar = (XA * 3600 + XB * 3600 + XC * 4800) / 12,000

I have gone through my notes and several text books but i cant work out where to take the moments to get the XA, XB and XC values. Its probably obvious but if someone can give me a nudge in the right direction it would be appreciated.

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As you need only Y so no need to worry about X(but it will be on the line through the center)

As you are not given anything about mass, i guess you can replace it with area (kind of predictable in most cases as more area means more mass)

Take Y axis passing through the center of body and take origin at center of lower rectangle!!

find center of mass Y coordinates of rest 2 rectangles (lower one has (0,0)

use YCM = (m1y1 + m2y2 + m3y3)/ (m1 + m2 + m3)

Im still kinda lost but i have a answer that looks plausible

YCM = (m1y1 + m2y2 + m3y3)/ (m1 + m2 + m3)

YCM = 3600 x 1 + 3600 x 100 + 4800 x 210) / (3600 + 3600 + 4800)

YCM = 114.3mm

Im not sure if i have the y values right though.

Im still kinda lost but i have a answer that looks plausible

YCM = (m1y1 + m2y2 + m3y3)/ (m1 + m2 + m3)

YCM = 3600 x 1 + 3600 x 100 + 4800 x 210) / (3600 + 3600 + 4800)

YCM = 114.3mm

Im not sure if i have the y values right though.
Its 0 not 1!!
how is Y of this block 210?

My train of thought might be wrong but here goes:

I meant 10 instead of 1 as that would be the centroid Y co-ordinates of the bottom shape

The centroid Y co-ordinates of the top shape is 10 but if you take into account the rest of the shape its 10 + 200 = 210

fixing my calculations i now get 97mm

Edit:

It seems i was taking it for the wrong shape.

Lets try again (I think this is right):

YCM = (10 * 4800 + 110 * 3600 + 210 * 3600) / (4800 + 3600 + 4800)
YCM = 100mm

Last edited:
PhanthomJay
Yes its correct!!! congratulation!!!! 