Thin Walled Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Thin Walled Circle - Geometric Propertiescircle thin wall 4

area of a Thin Walled Circle  formula

\(\large{ A = 2 \pi r t }\)

\(\large{ A = \pi D t }\)

Center of a Thin Walled Circle

All points on the line circumference are at equal distance from the center point.

Perimeter of a Thin Walled Circle formula

\(\large{ P = 2 \pi r }\)   (Outside)

\(\large{ P = 2 \pi \left(  r - t  \right)  }\)   (Inside)

Radius of a Thin Walled Circle formula

\(\large{ r = \sqrt   {\frac {2A} {\pi} }   }\)

Distance from Centroid of a Thin Walled Circle formula

\(\large{ C_x =  r   }\)

\(\large{ C_y =  r   }\)

Elastic Section Modulus of a Thin Walled Circle formula

\(\large{ S =  \frac { 2 \pi r t }  { 3  }  }\)

Plastic Section Modulus of a Thin Walled Circle formula

\(\large{ Z =  \pi r^2 t   }\)

Polar Moment of Inertia of a Thin Walled Circle formula

\(\large{ J_{z} =  2 \pi r^3 t  }\)

\(\large{ J_{z1} =  6 \pi r^3 t  }\)

Radius of Gyration of a Thin Walled Circle formula

\(\large{ k_{x} =    \frac { \sqrt {2}  }  {  2  }  r   }\)

\(\large{ k_{y} =   \frac { \sqrt {2}  }  {  2  }  r    }\)

\(\large{ k_{z} =     r  }\)

\(\large{ k_{x1} =   \frac { \sqrt {6}  }  {  2  }  r   }\)

\(\large{ k_{y1} =   \frac { \sqrt {6}  }  {  2  }  r   }\)

\(\large{ k_{z1} =    \sqrt {3}   r   }\)

Second Moment of Area of a Thin Walled Circle formula

\(\large{ I_{x} =  \pi r^3 t }\)

\(\large{ I_{y} = \pi r^3 t }\)

\(\large{ I_{x1} =  3 \pi r^3 t  }\)

\(\large{ I_{y1} =  3 \pi r^3 t }\)

Torsional Constant of a Thin Walled Circle formula

\(\large{ J  =  2  \pi r^3  t    }\)
 

Where:

\(\large{ A }\) = area

\(\large{ C_x, C_y }\) = distance from centroid

\(\large{ d }\) = diameter

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

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

\(\large{ k }\) = radius of gyration

\(\large{ P }\) = perimeter

\(\large{ r }\) = radius

\(\large{ S }\) = elastic section modulus

\(\large{ Z }\) = plastic section modulus

\(\large{ \pi }\) = Pi

 

Tags: Equations for Moment of Inertia Equations for Structural Steel Equations for Modulus