Square Angle

on . Posted in Plane Geometry

L beam square 1Square angle is an angle iron with square legs, creating a right angle.  This type of angle iron has equal length sides forming a 90-degree corner.  It's commonly used as a structural component in various construction and engineering applications due to its rigidity and load-bearing capacity.  Square angles, like other angle iron profiles, come in various sizes, thicknesses, and materials to accommodate different load-bearing capacities and design requirements.  The cross-sectional properties of the angle, such as the moment of inertia and section modulus, determine its performance under different loading conditions.

Square Angle Index

 

area of a Square Channel formula

\(\large{ A =   t \; \left( 2\;w - t  \right)  }\)
Symbol English Metric
\(\large{ A }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{ mm }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

Distance from Centroid of a Square Angle formulas

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

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

Symbol English Metric
\(\large{ C }\) = distance from centroid \(\large{ in }\) \(\large{ mm }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{ mm }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

Elastic Section Modulus of a Square Angle formulas

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

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

Symbol English Metric
\(\large{ S }\) = elastic section modulus \(\large{ in^3 }\) \(\large{ mm^3 }\)
\(\large{ C }\) = distance from centroid \(\large{ in }\) \(\large{ mm }\)
\(\large{ I }\) = moment of inertia \(\large{ in^4 }\) \(\large{ mm^4 }\)

 

Perimeter of a Square Angle formula

\(\large{ P =  4\;w }\)
Symbol English Metric
\(\large{ P }\) = perimeter \(\large{ in }\) \(\large{ mm }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

Polar Moment of Inertia of a Square Angle formulas

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

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

Symbol English Metric
\(\large{ J }\) = torsional constant \(\large{ in^4 }\) \(\large{ mm^4 }\)
\(\large{ I }\) = moment of inertia \(\large{ in^4 }\) \(\large{ mm^4 }\)

 

Principal Axis of a Square Angle formula

\(\large{ d =  \frac{ w^2  \;+\;  w\;t  \;-\; t^2  }{ 2 \; \left( 2\;w \;-\; t  \right) \; cos\; 45^\circ   }  }\)
Symbol English Metric
\(\large{ d }\) = distance from principle axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{ mm }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

Radius of Gyration of a Square Angle formulas

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

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

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

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

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

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

Symbol English Metric
\(\large{ k }\) = radius of gyration \(\large{ in }\) \(\large{ mm }\)
\(\large{ A }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ I }\) = moment of inertia \(\large{ in^4 }\) \(\large{ mm^4 }\)

 

Second Moment of Area of a Square Angle formulas

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

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

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

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

Symbol English Metric
\(\large{ I }\) = moment of inertia \(\large{ in^4 }\) \(\large{ mm^4 }\)
\(\large{ A }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ C }\) = distance from centroid \(\large{ in }\) \(\large{ mm }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{ mm }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

Tortional Constant of a Square Angle formula

\(\large{ J  =   \frac{   \left[    w \;-\; \left(  \frac {t}{2}  \right)  \right]   \;+\;   \left[  w \;-\; \left(  \frac {t}{2}  \right)  \right] \; t^3    }{3}  }\) 
Symbol English Metric
\(\large{ J }\) = torsional constant \(\large{ in^4 }\) \(\large{ mm^4 }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{ mm }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

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Tags: Structural Steel