Thin Wall Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • circle thin wall 4Two circles each having all points on each circle at a fixed equal distance from a center point.
  • Center of a circle having all points on the line circumference are at equal distance from the center point.
  • A thin wall circle is a structural shape used in construction.

 

Structural Shapes

 

Formulas that use area of a Thin Walled Circle

\(\large{ A_{area} = 2\; \pi \;r\; t }\)   
\(\large{ A_{area} = \pi \;D\; t }\)   

Where:

\(\large{ A_{area} }\) = area

\(\large{ D }\) = outside diameter

\(\large{ r }\) = inside radius

\(\large{ t }\) = thickness

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

 

Formulas that use Perimeter of a Thin Walled Circle

\(\large{ P = 2\; \pi \;r }\)   (outside) 
\(\large{ P = 2\; \pi \; \left(  r - t  \right)  }\)  (inside) 

Where:

\(\large{ P }\) = perimeter

\(\large{ r }\) = inside radius

\(\large{ t }\) = thickness

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

 

Formulas that use Radius of a Thin Walled Circle

\(\large{ r = \sqrt   {\frac {2\;A_{area}} {\pi} }   }\)   

Where:

\(\large{ r }\) = inside radius

\(\large{ A_{area} }\) = area

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

 

Formulas that use Distance from Centroid of a Thin Walled Circle

\(\large{ C_x =  r}\)   
\(\large{ C_y =  r}\)   

Where:

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

\(\large{ r }\) = inside radius

 

Formulas that use Elastic Section Modulus of a Thin Walled Circle

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

Where:

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

\(\large{ r }\) = inside radius

\(\large{ t }\) = thickness

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

 

Formulas that use Plastic Section Modulus of a Thin Walled Circle

\(\large{ Z =  \pi \;r^2 \;t   }\)   

Where:

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

\(\large{ r }\) = inside radius

\(\large{ t }\) = thickness

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

 

Formulas that use Polar Moment of Inertia of a Thin Walled Circle

\(\large{ J_{z} =  2\; \pi \;r^3 \;t  }\)   
\(\large{ J_{z1} =  6\; \pi \;r^3 \;t  }\)   

Where:

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

\(\large{ r }\) = inside radius

\(\large{ t }\) = thickness

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

 

Formulas that use Radius of Gyration of a Thin Walled Circle

\(\large{ k_{x} =    \frac { \sqrt {2}  }  {  2  } \; r   }\)   
\(\large{ k_{y} =   \frac { \sqrt {2}  }  {  2  } \; r    }\)   
\(\large{ k_{z} =     r  }\)   
\(\large{ k_{x1} =   \frac { \sqrt {6}  }  {  2  } \; r   }\)  
\(\large{ k_{y1} =   \frac { \sqrt {6}  }  {  2  } \; r   }\)  
\(\large{ k_{z1} =    \sqrt {3}  \; r   }\)  

Where:

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

\(\large{ r }\) = inside radius

 

Formulas that use Second Moment of Area of a Thin Walled Circle

\(\large{ I_{x} =  \pi \;r^3 \;t }\)   
\(\large{ I_{x1} =  3\; \pi \;r^3 \;t  }\)   
\(\large{ I_{y1} =  3\; \pi \;r^3 \;t }\)  

Where:

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

\(\large{ r }\) = inside radius

\(\large{ t }\) = thickness

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

 

Formulas that use Torsional Constant of a Thin Walled Circle

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

Where:

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

\(\large{ r }\) = radius

\(\large{ t }\) = thickness

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

 

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