Square T Beam

on . Posted in Plane Geometry

T beam square 1Square T-beam, also called T-shaped beam or Tee beam, is a type of structural beam with a T-shaped cross-sectional profile.  Unlike a standard I-beam that has a central vertical web and horizontal flanges at the top and bottom, a T-beam has a vertical stem and a horizontal flange extending from the stem at the top.  This configuration creates a cross-sectional shape that resembles the letter "T."  A Square T-beam is characterized by having equal-length stem and flange portions, resulting in a symmetrical T-shape.  The stem and flange can have varying dimensions and thicknesses, depending on the specific load bearing requirements and design considerations of the structure.

Square T Beam Index

 

area of a Square T Beam formula

\(\large{ A =  w\;s + h\;t  }\)
Symbol English Metric
\(\large{ A }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ h }\) = height  \(\large{ in }\)  \(\large{ mm }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{ mm }\)
\(\large{ s }\) = width  \(\large{ in }\) \(\large{ mm }\) 
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

Distance from Centroid of a Square T Beam formulas

\(\large{ C_x =  0  }\)

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

Symbol English Metric
\(\large{ C }\) = distance from centroid  \(\large{ in }\)  \(\large{ mm }\)
\(\large{ A }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ h }\) = height  \(\large{ in }\)  \(\large{ mm }\)
\(\large{ l }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{ mm }\)
\(\large{ s }\) = width  \(\large{ in }\) \(\large{ mm }\) 
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

Elastic section Modulus of a Square T Beam 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 T Beam formula

\(\large{ P =  2\;  \left( w + h + s  \right) }\) 
Symbol English Metric
\(\large{ P }\) = perimeter  \(\large{ in }\)  \(\large{ mm }\)
\(\large{ h }\) = height  \(\large{ in }\)  \(\large{ mm }\)
\(\large{ s }\) = width  \(\large{ in }\) \(\large{ mm }\) 
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

Polar Moment of Inertia of a Square T Beam formulas

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

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

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

 

Radius of Gyration of a Square T Beam 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 T Beam formulas

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

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

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

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

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 \(\large{ in }\) \(\large{ mm }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{ mm }\)
\(\large{ s }\) = width \(\large{ in }\) \(\large{ mm }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

Torsional Constant of a Square T Beam formula

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

 

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Tags: Structural Steel