ME 221 Statics

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ME 221 Statics Lecture 9Sections 9.1 9.6
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Homework 4

• Chapter 4 problems
• 52 54
• Chapter 9 problems
• 2, 11 32
• Due Monday, June 14
• MatLab Group Problems
• 4.13 plot as a function of R with 0º lt a lt 45º
• 4.51 plot as a function of length l
• 4.60 plot the equivalent force and point of
  action
• Due Monday, June 14

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Exam 1 Results

• Scores posted on Angel
• Solution posted on Angel
• See syllabus for regrade policy
• Last day to drop without a grade reported is
  Wednesday, June 9

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Second Moments of Area(Area Moments of Inertia)

• Second moments of area play a central role in
  mechanics of materials and dynamics

• Definition of second moment

• Basic areas (rectangle, circular, triangular)

• Definition of polar moment

• Basic areas (circular)

• Parallel axis theorem

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Moments of Area

• Characterize distribution of area about the
  centroid

• Normally, we want the moment with respect to
  centriod axes

• Moment about other axes derived from centroid case

• Moment of inertia

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Moments of Basic Shapes

• Rectangle

• Circular

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Polar Moment

• The polar moment is the second moment of area
  about the z-axis

Note that Ixx Iyy JOz
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Parallel Axis Theorem

• The centroid of the area MUST be one of the axes
  used in the parallel axis theorem.

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Radius of Gyration

• An alternate, equivalent way to represent the
  moment of an area

Distance from the point or axis to where the area
is concentrated
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Principal Second Moments

• Definition of product moment of inertia

• Product of inertia axis theorem

• Definition of principal axes

• Mohrs circle to find principal axes

• Example

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Product Moment of Inertia(Measures Antisymmetry)

• Basic section with two axes of symmetry

• Composite sections - product parallel axis theorem

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Mohrs Circle for Principal Inertia(Second
Moment of Area about any Axis)
ANGLES IN MOHRS CIRCLE ARE TWICE THOSE IN THE
CROSS SECTION!!!
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Example