# Equal area axis

## Homework Statement

For this shape , it's clear that the centroid and the horizontal line of equal axis lies on the same horizontal line , am i right ????

## The Attempt at a Solution

I'm not sure . correct me if i am wrong . [/B]

#### Attachments

• 23.PNG
2.5 KB · Views: 605

Mark44
Mentor

## Homework Statement

For this shape , it's clear that the centroid and the horizontal line of equal axis lies on the same horizontal line , am i right ????

## The Attempt at a Solution

I'm not sure . correct me if i am wrong . [/B]
Do you mean "line of equal area"?
Anyway, yes, symmetry should convince you that you're right if there's no other information given.

fonseh
Do you mean "line of equal area"?
Anyway, yes, symmetry should convince you that you're right if there's no other information given.
Are you familiar with plastic analysis ? Zp here is the plastic modulus .

I use another method to do , but i get different answer , why ?

Here's my working : , Zp = Sum of area x ( difference between centroid of particluar area and the equal area axis )

Zp = [ (130)(20)(150-10) + (150)(20)(150/2) ] x 2 = 1178000 , but the ans provided is only 929040

Mark44
Mentor
Are you familiar with plastic analysis ?
No, I'm not, but I am familiar with the concept of centroids.
My answer is based on the fact that the shape in the drawing is symmetric about its horizontal midline.
fonseh said:
Zp here is the plastic modulus .

I use another method to do , but i get different answer , why ?

Here's my working : , Zp = Sum of area x ( difference between centroid of particluar area and the equal area axis )

Zp = [ (130)(20)(150-10) + (150)(20)(150/2) ] x 2 = 1178000 , but the ans provided is only 929040

If you had a rectangular piece of some uniform, rigid material 150 mm by 300 mm, its centroid would be at the center of the piece, at a point 75 mm to the right of the left edge, and 150 mm above the lower edge. If you cut out a rectangle 130 mm by 260 mm to form a "C" shape as in your drawing, the centroid of the piece you remove would be at its center, and the centroid of the remaining C-shaped piece would be along the horizontal midline, but a bit right of where it was for the original uncut piece of material.

PhanthomJay