Unequal I Beam

Written by Jerry Ratzlaff on . Posted in Structural

area of a Unequal I Beam formula

\(\large{ A =  b\;s  +  h\;t  +  w\;s   }\)

Perimeter of a Unequal I Beam formula

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

Distance from Centroid of a Unequal I Beam formula

\(\large{ C_x =  0  }\)

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

Elastic Section Modulus of a Unequal I Beam formula

\(\large{ S_{x} =  \frac { I_x }  { C_y   } }\)

\(\large{ S_{y} =  \frac { I_y }  { C_x   } }\)

Radius of Gyration of a Unequal I Beam formula

\(\large{ k_{x} =    \frac{    \frac{1}{3}  \;   \left[    b \;  \left(l \;-\; C_y \right)^3  +  w\;C_{y}{^3}    \;-\; \left(b \;-\; t \right)   \;   \left(l \;-\; C_y  \;-\; s \right)^3      \;-\;  \left(w  \;-\;  t \right)     \;  \left(C_y  +  s \right)^3       \right]   }        {b\;s  + h\;t  + w\;s}    }\)

\(\large{ k_{y} =     \frac{  \sqrt {  s \; \left(s^2  +  3 \right) \;  \left(w \;-\;  t \right)^3  +  2\;h\;t^3 }  }        { 2\; \sqrt{6} \; \sqrt{w\;s  +  b\;s  +  h\;t }    }    }\)

Second Moment of Area of a Unequal I Beam formula

\(\large{ I_x =  \frac{1}{3}   \;  \left[    b \;  \left(l \;-\; C_y \right)^3  +  w\;C_{y}{^3}    \;-\; \left(b \;-\; t \right)      \left(l \;-\; C_y  \;-\; s \right)^3      \;-\;  \left(w  +  t \right)       \left(C_y \;-\;  s \right)^3       \right]    }\)

\(\large{ I_y =   2 \; \left[ 2 \; \left(   \frac{1}{96} \; s^3 \;  \left(w \;-\; t \right)^3  +  \frac{1}{32} \; s \; \left(w \;-\;  t \right)^3   \right)  \;+\;  \frac{h\;t^3}{24}      \right]    }\)

\(\large{ I_z =   l_x  +  I_y }\)

Torsional Constant of a Unequal I Beam formula

\(\large{ J  =   \frac { ws^3  +  b\;s^3  + \left( l \;-\; 5 \right) \; t^3  }    {  3  }  }\)

 

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