Square Angle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • L beam square 1Two rectangles that intersect at a 90° angle at one end each.
  • A square angle is a structural shape used in construction.

Structural Shapes

area of a Square Angle formula

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

Where:

\(\large{ A }\) = area

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Distance from Centroid of a Square Angle formula

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

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

Where:

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

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Elastic Section Modulus of a Square 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 Square Angle formula

\(\large{ P =  4\;w }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ w }\) = width

Polar Moment of Inertia of a Square 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

Principal Axis of a Square Angle formula

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

Where:

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

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Radius of Gyration of a Square Angle formula

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

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

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

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

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

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

Where:

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

\(\large{ A }\) = area

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

Second Moment of Area of a Square Angle formula

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

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

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

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

Where:

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

\(\large{ A }\) = area

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

\(\large{ t }\) = thickness

\(\large{ w }\) = width

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:

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

\(\large{ t }\) = thickness

\(\large{ w }\) = width

 

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