Advertisement Remove all ads

Find the Centroid of the Shaded Portion of the Plate Shown in the Figure. - Engineering Mechanics

Answer in Brief

Find the centroid of the shaded portion of the plate shown in the figure.

Advertisement Remove all ads

Solution

Y = X is the axis of symmetry
The centroid would lie on this line 

Sr.no. PART AREA(in mm2) X co-ordinate(mm) Ax(mm3)
1. RECTANGLE =1000 X 1000
=1000000
`1000/2` = 500 500000000
2. TRIANGLE (to be removed) `1/2` X 750 X 750
= -281250
1000 –`750/2`= 750 -210937500
3. QUARTER CIRCLE (To be removed) `(pir^2)/4`
= 441786.4669
`(4 x 7509)/(3pi)`= 3141.5926 -140625000
  TOTAL 276963.4669   148437500

`overlineX =(Σ Ax)/(Σ A)=(148437500)/(276963.5331)=535.946 mm`
𝑦̅ = 𝑋̅ = 535.946 mm
CENTROID IS AT (535.946,535.946)mm

Concept: Centroid for Plane Laminas
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×