Square Angle

Written by Jerry Ratzlaff on . Posted in Structural

Square Angle - Geometric PropertiesL beam square 1

area of a Square Angle formula

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

Perimeter of a Square Angle formula

\(\large{ A =  4w  }\)

Distance from Centroid of a Square Angle 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 of a Square Angle formula

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

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

Principal Axis of a Square Angle formula

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

Polar Moment of Inertia of a Square Angle formula

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

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

Radius of Gyration of a Square Angle formula

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

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

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

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

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

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

Second Moment of Area of a Square Angle formula

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

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

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

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

Tortional Constant of a Square Angle 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 Moment of Inertia Equations for Structural Steel Equations for Modulus