CENTROID

hello this is Bulbul Ahmed.

1. CENTROID

2. Presented by: Md.Bulbul ahmed Id:10.01.03.003 4 th year 2 nd semester Department of civil engineering Ahsanullah university of science and technology ( Aust )

3. what is centroid ? The Centroid of any object refers to the point within which the downward force of gravity appears to act. On any point along a vertical line that passes through the centroid , the object remains balanced.

4. Estimating Location Of CENTROID Eye estimation: By drawing at least two lines, each of which seems to divide the area into two parts, each of which appears to have the same moment about the line. The intersection of these lines should locate the CENTROID approximately.

5. CONTINUE PRINCIPLE OF SYMMETRY: If a plane figure has a line or lines of symmetry, its centroid lies on that line or lines.

6. Formulas to Find Out CENTRIOD Plane Triangle: The point through which all the three medians of a triangle pass is called Centroid of the triangle and it divides each median in the ratio at 2:1. Centroid = where ,               (x 1 , y 1 )   (x 2 , y 2 )   (x 3 , y 3 )be the coordinates of the vertices of the triangle.

7. Formulas to Find Out CENTRIOD Rectangle: Centroid of rectangle lies at intersection of two diagonals. Diagonals intersect at width (b/2) from reference x-axis and at height (h/2) from reference y-axis. Centroid of rectangular area

8. Continue Examples: Find the centroid of rectangular wall whose height is 12 ft. and base length of wall is 24 ft SOLUTION : Centroid of rectangular section lies where two diagonals intersect each other.

9. Continue Hence, centroid from reference Y-axis (X)= b/2 = 24/2 = 12 ft. Centroid from reference X-axis; (y)= h/2 = 12/2 = 6 ft.

10. Formulas to Find Out CENTRIOD Circle: Centroid of circular section lies at its center i.e., D/2 R= D/2 = 20/2 = 10cm= Answer

11. Formulas to Find Out CENTRIOD Semicircle: Half circle is known as semi-circle. Centroid of semi-circle is at a distance of 4R/3π from the base of semi-circle. As shown in the figure below:

12. Formulas to Find Out CENTRIOD Right Circular Cone: Centroid of right circular cone lies at a height h/4 from reference x-axis. As shown in figure below;

13. Formulas to Find Out CENTRIOD

14. COMPOSITE FIGURES Illustrated example: Centroid of a composite figure:

15. Real life application of Centroid Centroids indicate the center of mass of a uniform solid. stick a pivot at the centroid and the object will be in perfect balance. Lots of construction applications and engineering applications to design things so that minimal stress and energy is used to stabilize a component. In stress and deflection analysis of a beam , the location of centroid is very important.