Mohr

1
Mohr's Circle for Moment of Inertia
Mohrs circle can be used to graphically
determine a) the principle axes and principle
moments of inertia of the area about O b) the
moment and product of inertia of the area with
respect to any other pair of rectangular axes x
and y through O

• Graphical Solution Path
• On x-axis C(IxIy)/2
• R(Ix-Iy)/2)2Ixy2(1/2)
• ImaxACR IminBC-R
• Plot points (Ix, Ixy) (Iy, -Ixy), and draw a
  line to illustrate original moment of inertia.
• Proceed with analysis as in Mohrs circle for
  stress to find Ix, Iy and Ixy at different
  angles.

Algebraic Solution Equations IxMoment of inertia
about x axis IyMoment of inertia about y
axis IxyProduct of inertia Ix Ix cos2 ? Iy
sin2 ? 2 Ixy sin ? cos ? Ix Ix sin2 ? Iy
cos2 ? 2 Ixy sin ? cos ? Ixy Ixy cos2 ?
0.5 ( Ix Iy ) sin 2?
Poster by Rosanna Anderson, Jared McCombs, and
Mike Thompson