![FORMULA OF CENTROID
• The formula for the centroid of a triangle is used to find
the coordinates of the centroid of a triangle, for which
the coordinates of vertices of the triangle are
known. Centroid = [ x 1 + x 2 + x 3 3 , y 1 + y 2 + y 3 3 ] .
Observe the below figure which shows the vertices of
the triangle in the form of coordinates.
• x1, x2, x3 are the x-coordinates of the vertices of a triangle.
• y1, y2, y3 are the y-coordinates of the vertices of a triangle.](https://image.slidesharecdn.com/micanicsforenginnerra-230526084652-62f1e2d1/85/CENCEPT-OF-CENTROID-4-320.jpg)
![EXAMPLE
• Determine the centroid of a triangle whose vertices are (5,3), (6,1) and
(7,8).
• Solution
• Given parameters are,
• (x1, y1) = (5,3)
• (x2, y2) = (6,1)
• (x3, y3) = (7,8)
• The centroid formula is given by
• C = [(x1 + x2 + x3)/ 3, (y1 + y2 + y3)/ 3)
• C = [(5 + 6 + 7) / 3, (3 + 1 + 8) / 3]
• C = (18 / 3, 12 / 3)
• C = (6, 4)](https://image.slidesharecdn.com/micanicsforenginnerra-230526084652-62f1e2d1/85/CENCEPT-OF-CENTROID-5-320.jpg)
CENCEPT OF CENTROID
- 2. CONTENT ❖DEFINITION OF CENTROID ❖FORMULA OF CENTROID ❖PROPERTIES OF CENTROID ❖EXAMPLE ❖CENTER OF MASS ❖CENTER OF GRAVITY ❖APPLICATION OF CENTROID
- 3. DEFINITION OF CENTROID •The centroid is the centre point of the object. The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle.
- 4. FORMULA OF CENTROID • The formula for the centroid of a triangle is used to find the coordinates of the centroid of a triangle, for which the coordinates of vertices of the triangle are known. Centroid = [ x 1 + x 2 + x 3 3 , y 1 + y 2 + y 3 3 ] . Observe the below figure which shows the vertices of the triangle in the form of coordinates. • x1, x2, x3 are the x-coordinates of the vertices of a triangle. • y1, y2, y3 are the y-coordinates of the vertices of a triangle.
- 5. EXAMPLE • Determine the centroid of a triangle whose vertices are (5,3), (6,1) and (7,8). • Solution • Given parameters are, • (x1, y1) = (5,3) • (x2, y2) = (6,1) • (x3, y3) = (7,8) • The centroid formula is given by • C = [(x1 + x2 + x3)/ 3, (y1 + y2 + y3)/ 3) • C = [(5 + 6 + 7) / 3, (3 + 1 + 8) / 3] • C = (18 / 3, 12 / 3) • C = (6, 4)
- 6. PROPERTIES OF CENTROID •The properties of the centroid are as follows: •The centroid is the center of the object. •It is the center of gravity. •It should always lie inside the object. •It is the point of concurrency of the medians.
- 7. CENTER OF MASS • The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses. • For simple rigid objects with uniform density, the center of mass is located at the centroid
- 8. CENTER OF GRAVITY • The center of gravity is the point through which the force of of gravity is then in exactly the same position as the center gravity acts on an object or system. In most mechanics problems the gravitational field is assumed to be uniform. The center f mass. The terms center of gravity and center of mass tend to often be used interchangeably since they are often at the same location.
- 9. APPLICATION OF CENTROID • Support at centroid keeps any structure in balanced position • In the calculation of stress and deflectional of beam ,identification of centroid is very important • It is also importation designing a concrete wall