Tapered Channel

Written by Jerry Ratzlaff on . Posted in Structural

  • C tapered 1AA 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 formula

\(\large{ C_x =  \frac{1}{3}  \;  \left[   w^2 \;s  +  \frac{h\;t^2}{2}   \;-\;  \frac{\frac{h \;-\; L}{2\;\left(w \;-\; t \right) } }{3}  \; \left( w + 2\;t  \right)  \left( w - t \right)^2 \right]   }\)

\(\large{ C_y =  \frac{l}{2}  }\)

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 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 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 formula

\(\large{ J_z =  I_x  +  I_y }\)

\(\large{ J_{z1} =  I_{x1}  +  I_{y1} }\)

Where:

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

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

Radius of Gyration of a Tapered Channel formula

\(\large{ k_x =   \sqrt{   \frac{  \frac{1}{12}   \; \left[ w\;l^3  \;+\;  \frac{1}{8\;\frac{h \;-\; L}{2\;\left(w \;-\; t \right)}}   \; \left( h^4 \;-\; L^4  \right)   \right]   }{ lt  \;+\;  a \;\left( s  \;+\;  n  \right) }   }   }\)

\(\large{ k_y =   \sqrt{   \frac{  \frac{1}{3} \; \left[ 2\;s\;w^3\; L\;t^3  \;+\;  \frac{\frac{h \;-\; L}{2\;\left(w \;-\; t \right)}}{2}   \; \left( w^4 \;-\; t^4  \right)   \right] \;-\; A \; \left( w \;-\; y  \right)^2  }{  l\;t  \;+\;  a\; \left( s  \;+\;  n  \right) }   }   }\)

\(\large{ k_z =   \sqrt{   k_{x}{^2}   +    k_{y}{^2}    } }\)

\(\large{ k_{x1} =   \sqrt{    \frac{ I_{x1} }{A}    } }\)

\(\large{ k_{y1} =   \sqrt{    \frac{ I_{y1} }{A}    } }\) 

\(\large{ k_{z1} =   \sqrt{   k_{x1}{^2}  +  k_{y1}{^2}     }  }\)

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 formula

\(\large{ I_x =  \frac{1}{12}   \;    \left[  w\;l^3  +  \frac{1}{8\;\frac{h \;-\; L}{2\;\left(w \;-\; t \right) }} \; \left( h^4 \;-\; L^4  \right)  \right]     }\)

\(\large{ I_y =  \frac{1}{3}  \;   \left[  2\;s\;w^3  +  L\;t^3  +  \frac{\frac{h \;-\; L}{2\;\left(w \;-\; t \right) }}{2} \; \left( w^4 \;-\; t^4  \right)  \right]    \;-\; A  \left( w \;-\; y  \right)^2          }\)

\(\large{ I_{x1} =   l_x  +  A\;C_y }\)

\(\large{ I_{y1} =  l_y  +  A\;C_x  }\)

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 Moment of Inertia Equations for Structural Steel Equations for Modulus