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Radius of Gyration of a Trapezoid

 

Radius of Gyration of a Trapezoid formulas

\(  k_{x} \;=\; \dfrac {h}{6} \cdot \sqrt{ 2 + \dfrac{ 4\cdot c\cdot a}{ \left( c + a \right)^2 }  }   \) 

\(  k_{y} \;=\;   \sqrt {  \dfrac {I_y}{A_{area}}    }    \) 

\(  k_{z} \;=\;   \sqrt  { k_{x}{^2}  + k_{y}{^2}  }   \) 

\(  k_{x1} \;=\;   \dfrac{1}{6} \cdot  \sqrt{  \dfrac{ 6\cdot h^2 \cdot \left( 3\cdot c + a \right)  }{c + a}  }    \)

\(  k_{y1} \;=\;    \sqrt {  \dfrac {I_{y1}} {A_{area}}    }    \)

\(  k_{z1} \;=\; \sqrt  { k_{x1}{^2}  + k_{y1}{^2}  }    \)

Symbol English Metric
\( k \) = radius of gyration \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)
\( h \) = height \( in \) \( mm \)

trapezoid 12

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