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Chapter Summary
Area Moment of Inertia
  Represent second moment of area about an axis
  Frequently used in equations related to strength
  and stability of structural members or mechanical
  elements
  If the area shape is irregular, a differential
  element must be selected and integration over
  the entire area must be performed
  Tabular values of the moment of inertia of
  common shapes about their centroidal axis are
  available
Chapter Summary
Area Moment of Inertia
  To determine moment of inertia of these shapes
  about some other axis, parallel axis theorem
  must be used
  If an area is a composite of these shapes, its
  moment of inertia = sum of the moments of
  inertia of each of its parts

Product of Inertia
  Determine location of an axis about which the
  moment of inertia for the area is a maximum or
  minimum
Chapter Summary
Product of Inertia
  If the product of inertia for an area is known
  about its x’, y’ axes, then its value can be
  determined about any x, y axes using the parallel
  axis theorem for product of inertia

Principal Moments of Inertia
  Provided moments of inertia are known, formulas
  or Mohr’s circle can be used to determine the
  maximum or minimum or principal moments of
  inertia for the area, as well as orientation of the
  principal axes of inertia
Chapter Summary
Mass Moments of Inertia
 Measures resistance to change in its rotation
 Second moment of the mass elements of the
 body about an axis
 For bodies having axial symmetry, determine
 using wither disk or shell elements
 Mass moment of inertia of a composite body is
 determined using tabular values of its composite
 shapes along with the parallel axis theorem
Chapter Review
Chapter Review
Chapter Review
Chapter Review

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Calculating Moments of Inertia and Mass Moments

  • 1. Chapter Summary Area Moment of Inertia Represent second moment of area about an axis Frequently used in equations related to strength and stability of structural members or mechanical elements If the area shape is irregular, a differential element must be selected and integration over the entire area must be performed Tabular values of the moment of inertia of common shapes about their centroidal axis are available
  • 2. Chapter Summary Area Moment of Inertia To determine moment of inertia of these shapes about some other axis, parallel axis theorem must be used If an area is a composite of these shapes, its moment of inertia = sum of the moments of inertia of each of its parts Product of Inertia Determine location of an axis about which the moment of inertia for the area is a maximum or minimum
  • 3. Chapter Summary Product of Inertia If the product of inertia for an area is known about its x’, y’ axes, then its value can be determined about any x, y axes using the parallel axis theorem for product of inertia Principal Moments of Inertia Provided moments of inertia are known, formulas or Mohr’s circle can be used to determine the maximum or minimum or principal moments of inertia for the area, as well as orientation of the principal axes of inertia
  • 4. Chapter Summary Mass Moments of Inertia Measures resistance to change in its rotation Second moment of the mass elements of the body about an axis For bodies having axial symmetry, determine using wither disk or shell elements Mass moment of inertia of a composite body is determined using tabular values of its composite shapes along with the parallel axis theorem