Ahsanullah University of Science and Technology

Pre-stressed Concrete Lab Course no. CE- 416 Course Teacher:

Mr. Galib Muktadir and Sabreena N. Mouri

Presented by:Tasnim Sharmin Preoti10.01.03.1164th year, 2nd semesterDepartment of civil engineering

CENTROIDS

Presentation on

Contents

• Definition.• Centroid of triangle and its location.• Centroid of rectangle.• Centroid of circle.• Centroid of semicircle.• Centroid of composite area.

Definition of centroid

• The centroid can be said as the center of mass of the object of uniform density.

• It is the point where the gravity force act.

• The object remains balanced at the point of center of gravity.

Centroid of a triangle

• At the point where three medians of the triangle intersects is known as centroid.

• Each median divides the triangle into 2 smaller triangles of equal area.

• The centroid is exactly two-thirds the way along each median.

Formula of centroid of triangle

Example

Centroid of rectangle

• Centroid of a rectangle is situated at intersection of its diagonals.

• Diagonals intersect at width (b/2) from reference x-axis and at height (h/2) from reference y-axis.

Centroid of circle

• Centroid is located at the center of the circle.

Centroid of semi-circle

• Centroid of semi-circle is located at a distance of 4R/3π from the base of semicircle.

Formula of centroid by integration

Centroid of a composite area

• Example:the dimension of the T-section of the cast iron beam is shown in the figure. Find the centroid above the base.

• Solution:

Application of centroid

• Support at centroid keeps any structure in balanced position.

• In the calculation of stress and deflection of beam, identification of centroid is very important.

• It is also important in designing a concrete wall.

Application of centroid

Location of centroid is important in the design of the concrete wall.

Thank you