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Mechanics: Statics





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Second Moment of An Area of Geometric Shape
  Moment of Inertia of Areas
   Second Moment of Area of Rectangle
    Second Moment about x' by Double Integration
    Second Moment about y' by Single Integration
    Second Moment about x by Parallel-Axis Theorem
    Second Moment about y by Parallel-Axis Theorem
    Polar Moment about C from Rectangular Moments of Inertia
   Second Moment of Area of Circle
    Second Moment about x'  by Double Integration
    Second Moment about y'  by Double Integration
    Polar Moment about C from Rectangular Moments of Inertia
    Second Moment about A by Parallel-Axis Theorem
   Second Moment of Area of Triangle
    Second Moment about x' by Single Integration
    Second Moment about x by Parallel-Axis Theorem

Second Moment of An Area of Geometric Shape

The second moment of an area of a geometric shape can be determined by integration or the parallel-axis theorem. Imply

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Moment of Inertia of Areas

Second Moment of Area of Rectangle

Second Moment about x' by Double Integration

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The second moment of an area of a rectangle about the centroidal axis x' is

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Second Moment about y' by Single Integration

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The second moment of an area of a rectangle about the centroidal axis y' is

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Second Moment about x by Parallel-Axis Theorem

The second moment of an area of a rectangle about the axis x is

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Second Moment about y by Parallel-Axis Theorem

The second moment of an area of a rectangle about the axis y is

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Polar Moment about C from Rectangular Moments of Inertia

The polar moment of an area of a rectangle about the centroid C is

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Second Moment of Area of Circle

Second Moment about x'  by Double Integration

image

The second moment of an area of a circle about the centroidal axis x' is

image

Second Moment about y'  by Double Integration

image

The second moment of an area of a circle about the centroidal axis y' is

image

Polar Moment about C from Rectangular Moments of Inertia

The polar moment of an area of a circle about the centroid C is

image

Second Moment about A by Parallel-Axis Theorem

The second moment of an area of a rectangle about axis A is

image

Second Moment of Area of Triangle

Second Moment about x' by Single Integration

image

The second moment of an area of a triangle about the centroidal axis x' is

image

Second Moment about x by Parallel-Axis Theorem

The second moment of an area of a triangle about the axis x is

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References

  1. I.C. Jong; B.G. rogers, 1991, Engineering Mechanics: Statics and Dynamics, Saunders College Publishing, United States of America
  2. F.P. Beer; E.R. Johnston,Jr.; E.R. Eisenberg, 2004, Vector Mechanics for Engineers: Statics, McGraw-Hill Companies, Inc., New York
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ID: 121000007 Last Updated: 2012/10/16 Revision: 0 Ref:

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