Square Channel

Written by Jerry Ratzlaff on . Posted in Plane Geometry

area of a Square Channel formula

\(\large{ A =  w\;l \;-\; h \; \left( w \;-\; t  \right) }\)

Where:

\(\large{ A }\) = area

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Perimeter of a Square Channel formula

\(\large{ P =  2 \; \left( 2\;w + l \; \right)  \;-\; 2\;t  }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Distance from Centroid of a Square Channel formula

\(\large{ C_x =  \frac { 2\;w^2 \;s \;+\; ht^2  }  { 2 w\;l \;-\; 2\;h \; \left( w \;-\; t  \right)  }  }\)

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

Where:

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

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Elastic Section Modulus of a Square Channel formula

\(\large{ S_{x} =  \frac { I_{x} }  { C_{y}   } }\)

\(\large{ S_{y} =  \frac { I_{y} }  { C_{x}   } }\)

Where:

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

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

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

Polar Moment of Inertia of a Square Channel formula

\(\large{ J_{z} =  I_{x}  +  I_{y} }\)

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

Where:

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

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

Radius of Gyration of a Square Channel formula

\(\large{ k_{x} =  \sqrt {     \frac { w\;l^2 \;-\; h^3 \; \left( w - t  \right) }      { 12 \; \left[   w\;l^2 \;-\; h^3 \; \left( w \;-\; t  \right)    \right]  }          }   }\)

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

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

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

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

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

Where:

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

\(\large{ A }\) = area

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

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Second Moment of Area of a Square Channel formula

\(\large{ I_{x} =  \frac { w\;l^2 \;-\; h^3 \; \left( w \;-\; t  \right) }  { 12 }  }\)

\(\large{ I_{y} =  \frac { 2 \;s\;w^3 \;+\; h\;t^3 }  { 3 } \;-\; A \;C_{x}{^2} }\)  

\(\large{ I_{x1} =  I_{x}  +  A\; C_y }\)

\(\large{ I_{y1} =  I_{y}  +  A\; C_x }\)

Where:

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

\(\large{ A }\) = area

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

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Torsional Constant of a Square Channel formula

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

Where:

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

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ w }\) = width

 

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