Tapered I Beam

Written by Jerry Ratzlaff on . Posted in Structural

Tapered I Beam - Geometric PropertiesI beam tapered 2

area of a Tapered I Beam formula

\(\large{ A =  lt  +  2a  \left( s  +  n  \right) }\)

Perimeter of a Tapered I Beam formula

\(\large{ P =  2w  +  4s  +  2L  +  4  \sqrt{ \left( \frac {w \; -\; a}{2} \right)^2  +  \left( s  +  n \right)^2 }   }\)

Distance from Centroid of a Tapered I Beam formula

\(\large{ C_x =  \frac { w }  { 2 }  }\)

\(\large{ C_y =  \frac { l }  { 2 }  }\)

Elastic Section Modulus of a Tapered I Beam formula

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

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

Polar Moment of Inertia of a Tapered I Beam formula

\(\large{ J_z =  I_x  +  I_y }\)

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

Radius of Gyration of a Tapered I Beam formula

\(\large{ k_x =   \sqrt{         \frac{  \frac{1}{12}  \left[ wl^3 \;-\;  \frac{1}{4g}  \; \left( h^4 \;-\; L^4  \right)   \right]   }        {  lt  \;+\;  2a \; \left( s  \;+\;  n  \right) }             }   }\)

\(\large{ k_y =   \sqrt{         \frac{  \frac{1}{3}  \left[ w^3 \;  \left( l \;-\; h  \right)  \;+\;  Lt^3  \;+\;  \frac{g}{4} \; \left( w^4 \;-\; t^4  \right)   \right]   }     {  lt  \;+\;  2a \; \left( s  \;+\;  n  \right) }            }   }\)

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

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

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

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

Second Moment of Area of a Tapered I Beam formula

\(\large{ I_x =  \frac{1}{12}  \left[  wl^3 \;-\; \frac{1}{4g}  \left( h^4 \;-\; L^4  \right)  \right]     }\)

\(\large{ I_y =  \frac{1}{3}   \left[  w^3  \left( l \;-\; h  \right)  +  Lt^3  +  \frac{g}{4}  \left( w^4 \;-\; t^4  \right)  \right]     }\)

\(\large{ I_{x1} =   l_{x}  +  AC_{y}{^2} }\)

\(\large{ I_{y1} =  l_{y}  +  AC_{x}{^2}  }\)

Slope of Flange of a Tapered I Beam formula

\(\large{ g =  \frac { h \;-\; L }  { w \;-\; t }  }\)

 

Where:

\(\large{ A }\) = area

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

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

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

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

\(\large{ P }\) = perimeter

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

 

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