Review parallel axis theorem
Class Today
x’-axis = centroidal horizontal axis.
(BE careful, different books use
different notations!! Some may
use x[no prime] here)
• Print notes and examples
• Moments of Inertia for Composite
shapes
Ix = moment of inertia about an axis
– Review terms in equation
– Setting up problems
_
of interest parallel to the
centroidal axis
Ix’ = moment of inertia about the
centroidal axis
• Products of Inertia
• Example Problems
• Group Work Time
A = area of shape or element
dy = distance between centroidal
axis and axis of interest
1
Setting Up Problems
2
Product of Inertia
Calculate Just like moment of inertia except you
take the moment about each axis once.
Integration:
• Separate composite into simple shapes.
• Assemble solution in table format for organizational
purposes.
Shape
Ix’
Ad2y
Ix’ + Ad2 y
triangle
Composites:
circle
square
Σ: Sum column
3
4
Product of Inertia
• If a shape has at least ONE axis of symmetry then
product of inertia is ZERO
• Whether the product of inertia has a positive or
negative sign depends on the location of the
shape in the coordinate plane.
5
26_Moments of Inertia_composites
1