Unequal I Beam

Written by Jerry Ratzlaff on . Posted in Structural

  • I beam unequal 1A unequal I beam is a structural shape used in construction.

Structural Shapes

area of a Unequal I Beam formula

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

Where:

\(\large{ A }\) = area

\(\large{ h }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ b }\) = width

\(\large{ w }\) = width

Distance from Centroid of a Unequal I Beam formula

\(\large{ C_x =  0  }\)

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

Where:

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

\(\large{ A }\) = area

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ b }\) = width

\(\large{ w }\) = width

Elastic Section Modulus of a Unequal I Beam formula

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

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

Where:

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

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

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

Perimeter of a Unequal I Beam formula

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

Where:

\(\large{ P }\) = perimeter

\(\large{ l }\) = height

\(\large{ t }\) = thickness

\(\large{ b }\) = width

\(\large{ w }\) = width

Radius of Gyration of a Unequal I Beam formula

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

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

Where:

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

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

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ b }\) = width

\(\large{ w }\) = width

Second Moment of Area of a Unequal I Beam formula

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

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

\(\large{ I_z =   l_x  +  I_y }\)

Where:

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

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

\(\large{ h }\) = height

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ b }\) = width

\(\large{ w }\) = width

Torsional Constant of a Unequal I Beam formula

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

Where:

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

\(\large{ l }\) = height

\(\large{ s }\) = thickness

\(\large{ t }\) = thickness

\(\large{ b }\) = width

\(\large{ w }\) = width

 

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