MOMENT OF INERTIA OF A TRIANGLE 235 



Consider an elementary strip of breadth By drawn parallel to 

 the base at a distance y from it. 

 If / is the length of this strip, 



I a 



and I = r (h y) 



Area of strip = I 8t/ = T (h y) &/ 

 n 



Moment of inertia of the strip about AB = j- (h y)y 2 8t/ 



a C h 



For the whole triangle I AB = r I (h y}y z dy 



" Jo 



_ 

 h 12 



12 



Let OX be an axis drawn parallel to the base and passing 

 through the centroid of the triangle. 



Then IAW = Imr + 



ah 3 ah 3 



To 1 Q 



L lo 



36 



Example. Find the principal moments of inertia of the section 

 of an angle iron S%" x 3" x \", and draw the momenta! ellipse 

 for the section. 



13 _ 7 1.3 



Now 



Then 



55 4 55 



The centroid O is evidently situated on the axis OX, and its 

 perpendicular distances from the sides AB and BC are each 

 1-058". 



