Rectangular Angle

Written by Jerry Ratzlaff on . Posted in Structural

  • L beam rectangular 1A rectangular angle is a structural shape used in construction.

Structural Shapes

area of a Rectangular Angle formula

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

Where:

\(\large{ A }\) = area

\(\large{ d }\) = height

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Distance from Centroid of a Rectangular Angle formula

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

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

Where:

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

\(\large{ d }\) = height

\(\large{ l }\) = height

\(\large{ t }\) = thickness

\(\large{ c }\) = width

\(\large{ w }\) = width

Elastic Section Modulus of a Rectangular Angle 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

Perimeter of a Rectangular Angle formula

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

Where:

\(\large{ P }\) = perimeter

\(\large{ l }\) = height

\(\large{ w }\) = width

Polar Moment of Inertia of a Rectangular Angle 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 Rectangular Angle formula

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

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

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

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

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

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

Where:

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

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

\(\large{ l }\) = height

\(\large{ y }\) = height

\(\large{ t }\) = thickness

\(\large{ w }\) = width

\(\large{ z }\) = width

Second Moment of Area of a Rectangular Angle formula

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

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

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

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

Where:

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

\(\large{ A }\) = area

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

\(\large{ l }\) = height

\(\large{ y }\) = height

\(\large{ t }\) = thickness

\(\large{ w }\) = width

\(\large{ z }\) = width

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:

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

\(\large{ d }\) = height

\(\large{ t }\) = thickness

\(\large{ w }\) = width

 

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