Square L Beam

Written by Jerry Ratzlaff on . Posted in Structural

Square L Beam - Geometric PropertiesL beam square 1

area formula

\(\large{ A =   t  \left( 2w - t  \right)  }\)

Perimeter formula

\(\large{ A =  4w  }\)

Distance from Centroid Axis formula

\(\large{ C_x =  \frac { w^2 + wt  -t^2  }  { 2  \left( 2w - t  \right)  }  }\)

\(\large{ C_y =  \frac { w^2 + wt  -t^2  }  { 2  \left( 2w - t  \right)  }  }\)

Elastic Section Modulus formula

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

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

Principal Axis formula

\(\large{ d =  \frac { w^2 + wt  -t^2  }  { 2  \left( 2w - t  \right) \; cos\; 45^\circ   }  }\)

Moment of Inertia about Axis formula

\(\large{ I_{x} =   \frac  {  t  \left( w - C_y  \right)^3  +   w  \left[  w - \left( w - C_y \right)  \right]^3      -   \left( w - t \right)     \left[  w - \left( w - C_y \right) -t  \right]^3   }  {3}   }\)

\(\large{ I_{x} =   \frac  {  t  \left( w - C_y  \right)^3  +   w  \left[  w - \left( w - C_y \right)  \right]^3      -   \left( w - t \right)     \left[  w - \left( w - C_y \right) -t  \right]^3   }  {3}   }\)

\(\large{ I_{x1} =  I_{x}  +  A C_{y} }\)

\(\large{ I_{y1} =  I_{y1}  +  A C_{x} }\)

PolarMoment of Inertia about Axis formula

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

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

Radius of Gyration about Axis formula

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

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

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

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

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

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

Tortional Constant formula

\(\large{ J  =   \frac {   \left[    w - \left(  \frac {t}{2}  \right)  \right]   +   \left[  w - \left(  \frac {t}{2}  \right)  \right]  t^3    }              {  3  }  }\) 

 

Where:

\(\large{ A }\) = area

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

\(\large{ d }\) = distance from principle axis

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

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

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

\(\large{ P }\) = perimeter

\(\large{ p }\) = principal axis

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

 

Tags: Equations for Structural Steel