485 Quarter circle C Rectangle Triangle Circle Semicircle Ellipse b y y' x' x 1 12 ⎯I x' = bh 3 1 12 ⎯I y' = b 3 h 1 8 I x = I y = r 4 1 4 J O = r 4 1 4 ⎯I x = ⎯I y = r 4 1 2 J O = r 4 1 36 ⎯I x' = bh 3 1 12 I x = bh 3 1 3 I y = b 3 h 1 12 J C = bh(b 2 + h 2 ) 1 3 I x = bh 3 h b x' x x r O y h C h 3 x O C y r x O C y r x b y a 1 16 I x = I y = r 4 1 8 J O = r 4 1 4 ⎯I x = ab 3 1 4 ⎯I y = a 3 b 1 4 J O = ab(a 2 + b 2 ) O Fig. 9.12 Moments of inertia of common geometric shapes. determination of moments of inertia is thus a prerequisite to the analysis and design of structural members. It should be noted that the radius of gyration of a composite area is not equal to the sum of the radii of gyration of the component areas. In order to determine the radius of gyration of a composite area, it is first necessary to compute the moment of inertia of the area. 9.7 Moments of Inertia of Composite Areas
Fig. 9.12 Moments of inertia of common geometric shapes.
determination of moments of inertia is thus a prerequisite to
the analysis and design of structural members. It should be noted
that the radius of gyration of a composite area is not equal to the
sum of the radii of gyration of the component areas. In order to
determine the radius of gyration of a composite area, it is first
necessary to compute the moment of inertia of the area.
