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Radius of Gyration of an Isosceles Trapezoid

 

Radius of Gyration of an Isosceles Trapezoid formulas

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

\(  k_{y} \;=\;     \dfrac{ 1 }{ 12 }   \cdot  \sqrt{  6  \left( c^2 + a^2 \right)  }    \) 

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

\(  k_{y1} \;=\;      \sqrt{  \dfrac{ 3 \cdot a + 5 \cdot c }{ 12 \cdot \left( a + c \right) } \cdot a   }    \)

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

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

isosceles trapezoid 6

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