Tapered I Beam

Written by Jerry Ratzlaff on . Posted in Structural

  • I beam tapered 2A tapered I beam is a structural shape used in construction.

Structural Steel

area of a Tapered I Beam formula

\(\large{ A =  l\;t  +  2\;a  \;\left( s  +  n  \right)  }\)

Where:

\(\large{ A }\) = area

\(\large{ l }\) = height

\(\large{ n }\) = thickness

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ a }\) = width

Distance from Centroid of a Tapered I Beam formula

\(\large{ C_x =  \frac{ w }{ 2 }  }\)

\(\large{ C_y =  \frac{ l }{ 2 }  }\)

Where:

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

\(\large{ l }\) = height

\(\large{ w }\) = width

Elastic Section Modulus of a Tapered I Beam formula

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

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

Where:

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

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

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

Perimeter of a Tapered I Beam formula

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

Where:

\(\large{ P }\) = perimeter

\(\large{ L }\) = height

\(\large{ n }\) = thickness

\(\large{ s }\) = thickness

\(\large{ a }\) = width

\(\large{ w }\) = width

Polar Moment of Inertia of a Tapered I 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 Tapered I Beam formula

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

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

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

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

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

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

Where:

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

\(\large{ A }\) = area

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

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ L }\) = height

\(\large{ n }\) = thickness

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ a }\) = width

\(\large{ w }\) = width

Second Moment of Area of a Tapered I Beam formula

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

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

\(\large{ I_{x1} =   l_{x}  +  A\;C_{y}{^2} }\)

\(\large{ I_{y1} =  l_{y}  +  A\;C_{x}{^2}  }\)

Where:

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

\(\large{ A }\) = area

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

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ L }\) = height

\(\large{ g }\) = slope of taper

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Slope of Flange of a Tapered I Beam formula

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

Where:

\(\large{ g }\) = slope of taper

\(\large{ h }\) = height

\(\large{ L }\) = height

\(\large{ t }\) = thickness

\(\large{ w }\) = width

 

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