Tapered T Beam

Written by Jerry Ratzlaff on . Posted in Structural

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

Structural Shapes

area of a Tapered T Beam formula

\(\large{ A =  w\;s  +  \frac{ h \; \left(T  \;+\;  t \right) }{2}   }\)

Where:

\(\large{ A }\) = area

\(\large{ h }\) = height

\(\large{ t }\) = thickness

\(\large{ T }\) = thickness

\(\large{ s }\) = width

\(\large{ w }\) = width

Distance from Centroid of a Tapered T Beam formula

\(\large{ C_x =  0  }\)

\(\large{ C_y =  l \;-\; \frac{1}{6\;A} \;  \left[    3\;w\;s^2  +  3\;h\;t  \; \left( l  +  s \right)  +  h \; \left( T - t \right) \; \left( h  +  3\;s \right)   \right]   }\)

Where:

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

\(\large{ A }\) = area

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ t }\) = thickness

\(\large{ T }\) = thickness

\(\large{ s }\) = width

\(\large{ w }\) = width

Elastic section Modulus of a Tapered T Beam formula

\(\large{ S_{x} =  \frac{ I_{x} }{ C_{y}   } }\)

Where:

\(\large{ S }\) = elastic section modulus

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

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

Perimeter of a Tapered T Beam formula

\(\large{ P =  2\;w  +  2\;s \;-\; T  +  t  +  2\;  \sqrt{   \left( \frac{1}{2} \right)^2  +  \left( \frac{T}{2} \right)^2       }   }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ t }\) = thickness

\(\large{ T }\) = thickness

\(\large{ s }\) = width

\(\large{ w }\) = width

Radius of Gyration of a Tapered T Beam formula

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

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

Where:

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

\(\large{ A }\) = area

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

Second Moment of Area of a Tapered T Beam formula

\(\large{ I_{x} =   \frac{  \left[  4\;w\;s^3  \;+\;  h^3 \;  \left( 3\;t \;+\; T \right)  \right]    \;-\; A \; \left( l \;-\; C_y \;-\; s \right)^2   }{12}   }\)

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

Where:

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

\(\large{ A }\) = area

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

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ t }\) = thickness

\(\large{ T }\) = thickness

\(\large{ s }\) = width

\(\large{ w }\) = width

 

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