Square T Beam

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • T beam square 1A square T beam is a structural shape used in construction.

Structural Shapes

area of a Square T Beam formula

\(\large{ A =  w\;s + h\;t  }\)

Where:

\(\large{ A }\) = area

\(\large{ h }\) = height

\(\large{ t }\) = thickness

\(\large{ s }\) = width

\(\large{ w }\) = width  

Distance from Centroid of a Square T Beam formula

\(\large{ C_x =  0  }\)

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

Where:

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

\(\large{ A }\) = area

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ t }\) = thickness

\(\large{ s }\) = width

\(\large{ w }\) = width

Elastic section Modulus of a Square T Beam 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 T Beam formula

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

Where:

\(\large{ P }\) = perimeter

\(\large{ h }\) = height

\(\large{ s }\) = width

\(\large{ w }\) = width

Polar Moment of Inertia of a Square T Beam formula

\(\large{ J_{z} =  I_{x}  +  I_{y}{^2} }\)

\(\large{ J_{z1} =  I_{x1}  +  I_{y1}{^2} }\)

Where:

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

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

Radius of Gyration of a Square T Beam 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 T Beam formula

\(\large{ I_{x} =   \frac{  t\;C_{y}{^3} \;+\; w \; \left( l \;-\; C_y \right)^3  \;-\;  \left( w \;-\; t \right) \;  \left( l \;-\; C_y \;-\; s \right)^3 }{3}   }\)

\(\large{ I_{x} =   \frac{ h\;t^3  }{12}   +    \frac{ w^3 \;s  }{12}    }\)

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

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

Where:

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

\(\large{ A }\) = area

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

\(\large{ h }\) = height

\(\large{ t }\) = thickness

\(\large{ s }\) = width

\(\large{ w }\) = width

Torsional Constant of a Square T Beam formula

 \(\large{ J  =   \frac{  w\;s^3 \;+\; l \;-\;    \left(  \frac {s}{2}  \right) \;  t^3  }{3}     }\)

Where:

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

\(\large{ l }\) = height

\(\large{ t }\) = thickness

\(\large{ s }\) = width

\(\large{ w }\) = width

 

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