Rectangular Angle

Written by Jerry Ratzlaff on . Posted in Structural

Rectangular Angle - Geometric PropertiesL beam rectangular 1

area of a Rectangular Angle formula

\(\large{ A =   t  \left( w  +  d \right)  }\)

Perimeter of a Rectangular Angle formula

\(\large{ A =   2  \left( w  +  l \right)  }\)  

Distance from Centroid of a Rectangular Angle formula

\(\large{ C_x =  \frac { t \; \left( 2c  \;+\;  l \right)  \;+\;  c^2  }  { 2 \;\; \left( c  \;+\;  l  \right)  }  }\)

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

Elastic Section Modulus of a Rectangular Angle formula

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

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

Polar Moment of Inertia of a Rectangular Angle formula

\(\large{ J_z =  I_x  +  I_y }\)

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

Radius of Gyration of a Rectangular Angle formula

\(\large{ k_x =   \frac {   ty^3  \;+\;  a \; \left( l \;-\; y  \right)^3   \;-\;  \left( w \;-\; t  \right)  \; \left( w \;-\; y \;-\; t  \right)^3   }  { 3t \;\; \left( w  \;+\;  l \;-\; t  \right)  }     }\)

\(\large{ k_y =    \frac {   tz^3  \;+\;  l \; \left( w \;-\; z  \right)^3   \;-\;  \left( l \;-\; t  \right) \;  \left( l \;-\; z \;-\; t  \right)^3   }  { 3t \;\; \left( w  \;+\;  l \;-\; t  \right)  }     }\)

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

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

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

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

Second Moment of Area of a Rectangular Angle formula

\(\large{ I_x =   \frac  {  ty^3  \;+\;  w \;\; \left( l \;-\; y \right)^3  \;-\;  \left[  w \;-\; t \right)  \;  \left( l \;-\; y  \;-\; t \right)   }  {3}   }\)

\(\large{ I_y =   \frac  {  tz^3  \;+\;  l \;\; \left( w \;-\; z \right)^3  \;-\;  \left[  l \;-\; t \right)  \;  \left( w \;-\; z  \;-\; t \right)   }  {3}   }\)

\(\large{ I_{x1} =  I_x  +  A C_{y}{^2} }\)

\(\large{ I_{y1} =  I_y  +  A C_{x}{^2} }\)

Tortional Constant of a Rectangular Angle formula

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

 

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