Square I Beam

Written by Jerry Ratzlaff on . Posted in Plane Geometry

area of a Square I Beam formula

\(\large{ A =  w\;l \;-\; h \; \left( w \;-\; t  \right) }\)

Where:

\(\large{ A }\) = area

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Perimeter of a Square I Beam formula

\(\large{ P =  2 \; \left( 2\;w + l \;-\; t  \right) }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ l }\) = height

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Distance from Centroid of a Square I Beam formula

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

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

Where:

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

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ w }\) = width

Elastic Section Modulus of a Square 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

Polar Moment of Inertia of a Square 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 Square I Beam formula

\(\large{ k_{x} =   \sqrt {    \frac { w\;l^3 \;-\; h^3 \left( w \;-\; t  \right)  }  {  12 \; \left [   w\;l \;-\; h \; \left( w \;-\; t  \right) \right ] }    }   }\)

\(\large{ k_{y} =   \sqrt {    \frac { 2\; s\; w^3 + h\; t^3 }  {  12 \; \left [   w\;l \;-\; h \; \left( w \;-\; t  \right) \right ] }    }  }\)

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

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

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

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

Where:

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

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

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Second Moment of Area of a Square I Beam formula

\(\large{ I_{x} =  \frac { w\;l^3 \;-\; h^3 \left( w \;-\; t  \right)  }  {12} }\)

\(\large{ I_{y} =  \frac { 2 \;s\; w^3 + h\; t^3 }  {12} }\)

\(\large{ I_{x1} =   l_{x} + A\;C_y }\)

\(\large{ I_{y1} =  l_{y} + A\;C_x  }\)

Where:

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

\(\large{ A }\) = area

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

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

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ w }\) = width

Torsional Constant of a Square I Beam formula

\(\large{ J  =   \frac {  2\;w\;t^3 + \left( l \;-\; s  \right) \; t^3  }    {  3  }  }\)

Where:

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

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ w }\) = width

 

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