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

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

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

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

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

\(\large{ I_{x} =   \frac  { h\;t^3  }  {24}   +    \frac  { w^3\; s  }  {24}    }\)

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

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

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