# Unequal I Beam

Written by Jerry Ratzlaff on . Posted in Structural

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

### 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