Radius of Gyration of a Tapered I Beam formulas |
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\( k_x \;=\; \sqrt{ \dfrac{ \dfrac{1}{12} \cdot \left[ w\cdot l^3 - \dfrac{1}{4\cdot g} \cdot \left( h^4 - L^4 \right) \right] }{ l \cdot t + 2\cdot a \cdot \left( s + n \right) } } \) \( k_y \;=\; \sqrt{ \dfrac{ \dfrac{1}{3} \cdot \left[ w^3 \cdot \left( l - h \right) + L\cdot t^3 + \dfrac{g}{4} \cdot \left( w^4 - t^4 \right) \right] }{ l \cdot t + 2\cdot a \cdot \left( s + n \right) } } \) \( k_z \;=\; \sqrt{ k_{x}{^2} + k_{y}{^2} } \) \( k_{x1} \;=\; \sqrt{ \dfrac{ I_{x1} }{ A } } \) \( k_{y1} \;=\; \sqrt{ \dfrac{ I_{y1} }{ A } } \) \( k_{z1} \;=\; \sqrt{ k_{x1}{^2} + k_{y1}{^2} } \) |
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| Symbol | English | Metric |
| \( k \) = radius of gyration | \( in \) | \( mm \) |
| \( A \) = area | \( in^2 \) | \( mm^2 \) |
| \( h \) = height | \( in \) | \( mm \) |
| \( l \) = height | \( in \) | \( mm \) |
| \( L \) = height | \( in \) | \( mm \) |
| \( I \) = moment of inertia | \( in^4 \) | \( mm^4 \) |
| \( n \) = thickness | \( in \) | \( mm \) |
| \( s \) = thickness | \( in \) | \( mm \) |
| \( t \) = thickness | \( in \) | \( mm \) |
| \( a \) = width | \( in \) | \( mm \) |
| \( w \) = width | \( in \) | \( mm \) |
Radius of gyration is a measure of how the area, mass, or particles of an object are distributed relative to an axis. It represents the distance from the axis (perpendicular to its plane) at which the entire area or mass of the object could be concentrated without changing its moment of inertia. Mathematically, the radius of gyration is calculated as the square root of the ratio of the moment of inertia to the area cross-section (for area distribution) or mass (for mass distribution). A larger radius of gyration generally indicates that the object’s material is distributed farther from the axis, which increases its ability to resist bending or buckling.
