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Moment of Inertia - 10.01.03.061

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Moment of Inertia - 10.01.03.061

  1. 1. Shafkat Islam ID: 10.01.03.061 Year: 4th Semester: 2nd Department of Civil Engineering Ahsanullah University of Science & Technology
  2. 2. Course No : CE 416 Course Title : Prestress Concrete Design Sessional Course Teacher: Munshi Galib Muktadir
  3. 3. Moment Of Inertia
  4. 4. What is Moment of Inertia? In physics, moment of inertia is a quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation. Equation : 𝐼 = 𝑚 ∗ 𝑟2 m = Sum of the products of the mass r = Distance from the axis of rotation
  5. 5. 𝑟1 α
  6. 6. What is Torque or Moment? Torque, moment or moment of force, is the tendency of a force to rotate an object about an axis. What is Angular acceleration? Angular acceleration is the rate of change of angular velocity and is usually denoted by the Greek letter alpha (α).
  7. 7. Moment of Inertia (Geometrical property of an area) The moment of inertia of plane area or second moment of inertia is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis.
  8. 8. Area Moment of Inertia The Area Moment Of Inertia of a beams cross-sectional area measures the beams ability to resist bending. The larger the Moment of Inertia the less the beam will bend. The moment of inertia is a geometrical property of a beam and depends on a reference axis. The smallest Moment of Inertia about any axis passes through the centroid.
  9. 9. 𝐼 𝑥= 𝑦 2 𝑑𝐴 𝐼 𝑦= 𝑥 2 𝑑𝐴 y is the distance from the x axis to an area dA x is the distance from the y axis to an area dA
  10. 10. Polar Moment Of Inertia Moment of Inertia about the z axis The Polar Area Moment Of Inertia of a beams cross-sectional area measures the beams ability to resist torsion. The larger the Polar Moment of Inertia the less the beam will twist.
  11. 11. 𝐼 𝑧 = (𝑥 2 +𝑦 2 ) dA y is the distance from the x axis to an area dA x is the distance from the y axis to an area dA
  12. 12. Thank You for Yours Patience

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