Tapered Channel
A tapered channel is a structural shape used in construction.
Structural Shapes
area of a Tapered Channel formula
| \(\large{ A = l\;t + a \; \left( s + n \right) }\) |
Where:
\(\large{ A }\) = area
\(\large{ l }\) = height
\(\large{ n }\) = thickness
\(\large{ s }\) = thickness
\(\large{ t }\) = thickness
\(\large{ a }\) = width
Distance from Centroid of a Tapered Channel formulas
| \(\large{ C_x = \frac{1}{3} \; \left[ w^2 \;s + \frac{h\;t^2}{2} \;-\; \frac{\frac{h \;-\; L}{2\;\left(w \;-\; t \right) } }{3} \; \left( w + 2\;t \right) \left( w - t \right)^2 \right] }\) | |
| \(\large{ C_y = \frac{l}{2} }\) |
Where:
\(\large{ C }\) = distance from centroid
\(\large{ h }\) = height
\(\large{ l }\) = thickness
\(\large{ L }\) = thickness
\(\large{ s }\) = thickness
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Elastic Section Modulus of a Tapered Channel formulas
| \(\large{ S_x = \frac{ I_x }{ C_y } }\) | |
| \(\large{ S_y = \frac{ I_y }{ C_x } }\) |
Where:
\(\large{ S }\) = elastic section modulus
\(\large{ C }\) = distance from centroid
\(\large{ I }\) = moment of inertia
Perimeter of a Tapered Channel formula
| \(\large{ P = 2\;a^2 + 2\;w + 2\;h - 2\;L^2 + L + 2\;s }\) |
Where:
\(\large{ P }\) = perimeter
\(\large{ h }\) = height
\(\large{ L }\) = height
\(\large{ s }\) = thickness
\(\large{ a }\) = width
\(\large{ w }\) = width
Polar Moment of Inertia of a Tapered Channel formulas
| \(\large{ J_z = I_x + I_y }\) | |
| \(\large{ J_{z1} = I_{x1} + I_{y1} }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ I }\) = moment of inertia
Radius of Gyration of a Tapered Channel formulas
| \(\large{ k_x = \sqrt{ \frac{ \frac{1}{12} \; \left[ w\;l^3 \;+\; \frac{1}{8\;\frac{h \;-\; L}{2\;\left(w \;-\; t \right)}} \; \left( h^4 \;-\; L^4 \right) \right] }{ lt \;+\; a \;\left( s \;+\; n \right) } } }\) | |
| \(\large{ k_y = \sqrt{ \frac{ \frac{1}{3} \; \left[ 2\;s\;w^3\; L\;t^3 \;+\; \frac{\frac{h \;-\; L}{2\;\left(w \;-\; t \right)}}{2} \; \left( w^4 \;-\; t^4 \right) \right] \;-\; A \; \left( w \;-\; y \right)^2 }{ l\;t \;+\; a\; \left( s \;+\; n \right) } } }\) | |
| \(\large{ k_z = \sqrt{ k_{x}{^2} + k_{y}{^2} } }\) | |
| \(\large{ k_{x1} = \sqrt{ \frac{ I_{x1} }{A} } }\) | |
| \(\large{ k_{y1} = \sqrt{ \frac{ I_{y1} }{A} } }\) | |
| \(\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }\) |
Where:
\(\large{ k }\) = radius of gyration
\(\large{ h }\) = height
\(\large{ l }\) = height
\(\large{ L }\) = height
\(\large{ s }\) = thickness
\(\large{ t }\) = thickness
\(\large{ a }\) = width
\(\large{ w }\) = width
Second Moment of Area of a Tapered Channel formulas
| \(\large{ I_x = \frac{1}{12} \; \left[ w\;l^3 + \frac{1}{8\;\frac{h \;-\; L}{2\;\left(w \;-\; t \right) }} \; \left( h^4 \;-\; L^4 \right) \right] }\) | |
| \(\large{ I_y = \frac{1}{3} \; \left[ 2\;s\;w^3 + L\;t^3 + \frac{\frac{h \;-\; L}{2\;\left(w \;-\; t \right) }}{2} \; \left( w^4 \;-\; t^4 \right) \right] \;-\; A \left( w \;-\; y \right)^2 }\) | |
| \(\large{ I_{x1} = l_x + A\;C_y }\) | |
| \(\large{ I_{y1} = l_y + A\;C_x }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ A }\) = area
\(\large{ C }\) = distance from centroid
\(\large{ h }\) = height
\(\large{ l }\) = height
\(\large{ L }\) = height
\(\large{ s }\) = thickness
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Torsional Constant of a Tapered Channel formula
| \(\large{ J = \frac{ 2 \; \left( w \;-\; \frac {t}{2} \right) \; n^3 \; \left( l \;-\; n \right) \; t^3 }{3} }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ l }\) = height
\(\large{ n }\) = thickness
\(\large{ s }\) = thickness
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Tags: Equations for Inertia Equations for Structural Steel Equations for Modulus