Centroids & Moment of Inertia

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Centroids Moment of Inertia

• EGCE201 Strength of Materials I
• Instructor ??.???????? ????????? (?.??)
• ????????? 6391 ???????????????????
• E-mail egwpr_at_mahidol.ac.th
• ???????? 66(02) 889-2138 ??? 6391

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Centroid

• Centroid or center of gravity is the point within
  an object from which the force of gravity appears
  to act.
• Centroid of 3D objects often (but not always)
  lies somewhere along the lines of symmetry.
• The centroid of any area can be found by taking
  moments of identifiable areas (such as rectangles
  or triangles) about any axis.
• The moment of an area about any axis is equal to
  the algebraic sum of the moments of its component
  areas.
• The moment of any area is defined as the product
  of the area and the perpendicular distance from
  the centroid of the area to the moment axis.

Hollowed pipes, L shaped section have centroid
located outside of the material of the section
Centroidal axis or Neutral
Sum MAtotal MA1 MA2 MA3 ...
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centroid example simple rectangular shape
Sum MAtotal MA1 MA2 MA3 ...
Take ZZ as the reference axis and take moment
w.r.t ZZ axis
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Moment of Inertia (I)

• also known as the Second Moment of the Area is a
  term used to describe the capacity of a
  cross-section to resist bending.
• It is a mathematical property of a section
  concerned with a surface area and how that area
  is distributed about the reference axis. The
  reference axis is usually a centroidal axis.

where
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Moment of Inertia example simple rectangular
shape
Centroid or Neutral axis
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I is an important value!

• It is used to determine the state of stress in a
  section.
• It is used to calculate the resistance to
  bending.
• It can be used to determine the amount of
  deflection in a beam.

gt Stronger section
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Built-up sections

• It is often advantageous to combine a number of
  smaller members in order to create a beam or
  column of greater strength.
• The moment of inertia of such a built-up section
  is found by adding the moments of inertia of the
  component parts

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Transfer formula

• There are many built-up sections in which the
  component parts are not symmetrically distributed
  about the centroidal axis.
• To determine the moment of inertia of such a
  section is to find the moment of inertia of the
  component parts about their own centroidal axis
  and then apply the transfer formula.
• The transfer formula transfers the moment of
  inertia of a section or area from its own
  centroidal axis to another parallel axis. It is
  known from calculus to be