10.01.03.116 (presentation on centroid)
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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