Unequal I Beam
A 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