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.

 

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area of a Thin Walled Circle formulas

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

Where:

 Units English SI
\(\large{ A }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\) 
\(\large{ D }\) = outside diameter \(\large{ in }\) \(\large{mm  }\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)

 

Perimeter of a Thin Walled Circle formulas

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

Where:

 Units English SI
\(\large{ P }\) = perimeter \(\large{ in }\) \(\large{ mm }\) 
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)

 

Radius of a Thin Walled Circle formula

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

Where:

 Units English SI
\(\large{ A }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\) 
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)

 

Distance from Centroid of a Thin Walled Circle formulas

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

Where:

 Units English SI
\(\large{ C_x, C_y }\) = distance from centroid \(\large{ in }\) \(\large{ mm }\) 
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)

 

Elastic Section Modulus of a Thin Walled Circle formula

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

Where:

 Units English SI
\(\large{ S }\) = elastic section modulus \(\large{\frac{lbf}{in^2}}\) \(\large{Pa}\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)

 

Plastic Section Modulus of a Thin Walled Circle formula

\(\large{ Z =  \pi \;r^2 \;t   }\)   

Where:

 Units English SI
\(\large{ Z }\) = plastic section modulus \(\large{ in^4 }\) \(\large{mm^4  }\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)

 

Polar Moment of Inertia of a Thin Walled Circle formulas

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

Where:

 Units English SI
\(\large{ J }\) = torsional constant \(\large{ in^4 }\) \(\large{mm^4  }\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)

 

Radius of Gyration of a Thin Walled Circle formulas

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

Where:

 Units English SI
\(\large{ k }\) = radius of gyration \(\large{ in }\) \(\large{mm  }\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)

 

Second Moment of Area of a Thin Walled Circle formulas

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

Where:

 Units English SI
\(\large{ I }\) = moment of inertia \(\large{ in^4 }\) \(\large{mm^4  }\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)

 

Torsional Constant of a Thin Walled Circle formula

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

Where:

 Units English SI
\(\large{ J }\) = torsional constant \(\large{ in^4 }\) \(\large{mm^4  }\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)

 

 

Tags: Equations for Perimeter Equations for Inertia Equations for Structural Steel Equations for Modulus