28 



RESISTANCE OF MATERIALS 



22. I for triangle. Consider a triangle of base b and altitude h 

 and compute first its /with respect to an axis AA through its vertex 

 and parallel to the base (Fig. 24). The moment solid in this case 

 is a pyramid of base bh and altitude A, the volume of which is 



1 hJ) 2 



V=- base x altitude = 



O > 



Since the centroid of this pyramid is at a distance y Q = f h from 

 the vertex, we have 8 



FIG. 24 



To find /for the triangle with respect to an axis 00 through its 

 centroid and parallel to A A, apply the theorem 



I A = I +d*A. 



Since in the present case I A , A = -, and d = - h, we have 



therefore 



W 



IO ~ IA "86" 



Similarly, for the axis BB we have 



23. I for circle. In computing the / for a circle, it is convenient 

 to determine it first with respect to an axis through the center of 

 the circle and perpendicular to its plane (the so-called polar 

 moment of inertia of the circle). 





