Second Moment of Area Formula |
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\( I_x \;=\; \int \; y^2 \cdot d \cdot A \) \( I_y \;=\; \int \; x^2 \cdot d \cdot A \) |
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| Symbol | English | Metric |
| \( I_x \) = moment of inertia | \(in^4\) | \(mm^4\) |
| \( I_y \) = moment of inertia | \(in^4\) | \(mm^4\) |
| \( x \) = x axes | \(in\) | \(mm\) |
| \( y \) = y axes | \(in\) | \(mm\) |
| \( d \) = distance between the two axes | \(in\) | \(mm\) |
| \( A \) = area cross-section | \(in^2\) | \(mm^2\) |
Second moment of area, also called area moment of inertia, (English area unit \(in^4\), Metric area unit \(mm^4\)), is a geometric property of a area cross-section that quantifies its resistance to bending and deflection. It is not a physical property like mass or density but rather a mathematical measure of how the area of a shape is distributed around a particular axis. The further the area is from the axis, the greater its contribution to the second moment of area, because the distance from the axis is squared in the calculation. This is why beams with a large portion of their material far from the neutral axis, such as I-beams, are highly resistant to bending.
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