Unequal I Beam
Unequal I Beam - Geometric Properties
area of a Unequal I Beam formula
\(\large{ A = bs + ht + ws }\)
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
\(\large{ C_x = 0 }\)
\(\large{ C_y = l \;-\; \frac{ 1 }{2A} \left[ tl^2 + s^2 \left(b \;-\; t \right) + s \left(w \;-\; t \right) \left(2l \;-\; s \right) \right] }\)
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
\(\large{ k_{x} = \frac{ \frac{1}{3} \; \left[ b \; \left(l \;-\; C_y \right)^3 \;+\; wC_{y}{^3} \;-\; \left(b \;-\; t \right) \; \left(l \;-\; C_y \;-\; s \right)^3 \;-\; \left(w \;-\; t \right) \; \left(C_y \;+\; s \right)^3 \right] } {bs \;+\; ht \;+\; ws} }\)
\(\large{ k_{y} = \frac{ \sqrt { s \; \left(s^2 \;+\; 3 \right) \; \left(w \;-\; t \right)^3 \;+\; 2ht^3 } } { 2 \sqrt{6} \; \sqrt{ws \;+\; bs \;+\; ht } } }\)
Second Moment of Area of a Unequal I Beam formula
\(\large{ I_x = \frac{1}{3} \left[ b \left(l \;-\; C_y \right)^3 + wC_{y}{^3} \;-\; \left(b \;-\; t \right) \left(l \;-\; C_y \;-\; s \right)^3 \;-\; \left(w + t \right) \left(C_y \;-\; s \right)^3 \right] }\)
\(\large{ I_y = 2 \; \left[ 2 \; \left( \frac{1}{96} \; s^3 \; \left(w \;-\; t \right)^3 \;+\; \frac{1}{32} \; s \; \left(w \;-\; t \right)^3 \right) \;+\; \frac{ht^3}{24} \right] }\)
\(\large{ I_z = l_x + I_y }\)
Torsional Constant of a Unequal I Beam formula
\(\large{ J = \frac { ws^3 \;+\; bs^3 \;+\; \left( l \;-\; 5 \right) \; t^3 } { 3 } }\)
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