Moment of Inertia

Example | Radius of Gyration | Parallel Axis Theorem |
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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. |
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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 throught the centroid. | |||
The following are the mathematical equations to calculate the Moment of Inertia: | |||
Ix |
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equ. (1) | |
Iy |
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equ. (2) | |
y is the distance from the x axis to an infinetsimal area dA. | |||
x is the distance from the y axis to an infinetsimal area dA. | |||
Example |
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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. |
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The following are the mathematical equations to calculate the Polar Moment of Inertia: | |||||||
Jz |
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equ. (3) | |||||
x is the distance from the y axis to an infinetsimal area dA. | |||||||
y is the distance from the x axis to an infinetsimal area dA. | |||||||
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Using the PERPENDICULAR AXIS THEOREM yeilds the following equations for the Polar Moment of Inertia: |
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Jz = Ix+Iy | equ. (4) | ||||||
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