Tapered Channel

Written by Jerry Ratzlaff on . Posted in Structural

Tapered Channel - Geometric PropertiesC tapered 1A

area of a Tapered Channel formula

\(\large{ A =  lt  +  lt  +  a  \left( s  +  n  \right) }\)

Perimeter of a Tapered Channel formula

\(\large{ P =  2a^2  +  2w  +  2h  \;-\;  2L^2  +  L  +  2s    }\)

Distance from Centroid of a Tapered Channel formula

\(\large{ C_x =  \frac { 1 }{ 3 }    \left[   w^2s  +  \frac{ht^2}{2}   \;-\;  \frac{g}{3}   \left( w  +   2t  \right)  \left( w \;-\; t \right)^2     \right]          }\)

\(\large{ C_y =  \frac { l }  { 2 }  }\)

Elastic Section Modulus of a Tapered Channel formula

\(\large{ S_x =  \frac { I_x }  { C_y   } }\)

\(\large{ S_y =  \frac { I_y }  { C_x   } }\)

Polar Moment of Inertia of a Tapered Channel formula

\(\large{ J_z =  I_x  +  I_y }\)

\(\large{ J_{z1} =  I_{x1}  +  I_{y1} }\)

Radius of Gyration of a Tapered Channel formula

\(\large{ k_x =   \sqrt{         \frac{  \frac{1}{12}         \left[ bl^3  +  \frac{1}{8g}   \left( h^4 \;-\; L^4  \right)   \right]   }      {  lt  +  a \left( s  +  n  \right) }             }   }\)

\(\large{ k_y =   \sqrt{         \frac{  \frac{1}{3}  \left[ 2sb^3 \; Lt^3  +  \frac{g}{2}    \left( b^4 \;-\; t^4  \right)   \right] \;-\; A   \left( b \;-\; y  \right)^2      }  {  lt  +  a \left( s  +  n  \right) }            }   }\)

\(\large{ k_z =   \sqrt {   k_{x}{^2}   +    k_{y}{^2}    } }\)

\(\large{ k_{x1} =   \sqrt {    \frac {  I_{x1}  }  { A  }    } }\)

\(\large{ k_{y1} =   \sqrt {    \frac {  I_{y1}  }  { A  }    } }\)

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

Second Moment of Area of a Tapered Channel formula

\(\large{ I_x =  \frac{1}{12}       \left[  wl^3  +  \frac{1}{8g}  \left( h^4 \;-\; L^4  \right)  \right]     }\)

\(\large{ I_y =  \frac{1}{3}     \left[  2sw^3  +  Lt^3  +  \frac{g}{2}  \left( w^4 \;-\; t^4  \right)  \right]    \;-\; A  \left( w \;-\; y  \right)^2          }\)

\(\large{ I_{x1} =   l_x  +  AC_y }\)

\(\large{ I_{y1} =  l_y  +  AC_x  }\)

Torsional Constant of a Tapered Channel formula

\(\large{ J  =   \frac {  2    \left( w \;-\;  \frac {t}{2}  \right)   n^3  \left( l \;-\; n  \right) \; t^3  }    {  3  }  }\)

 

Where:

\(\large{ A }\) = area

\(\large{ C }\) = distance from centroid

\(\large{ I }\) = moment of inertia

\(\large{ J }\) = torsional constant

\(\large{ k }\) = radius of gyration

\(\large{ P }\) = perimeter

\(\large{ S }\) = elastic section modulus

 

Tags: Equations for Moment of Inertia Equations for Structural Steel Equations for Modulus