Thin Wall Circle

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.

Thin Wall Circle Index

 

area of a Thin Walled Circle formula

\( A = 2\; \pi \;r\; t \)
Symbol English Metric
\( A \) = area \( in^2 \) \( mm^2 \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = inside radius \( in \) \( mm \)
\( t \) = thickness \( in \) \( mm \)

  

Perimeter of a Thin Walled Circle formula

\( P = 2\; \pi \;r \)     (outside)  

\( P = 2\; \pi \; (  r - t )  \)     (inside) 

Symbol English Metric
\( P \) = perimeter \( in \) \( mm \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = inside radius \( in \) \( mm \)
\( t \) = thickness \( in \) \( mm \)

  

Radius of a Thin Walled Circle formula

\( r = \sqrt{  2 \; A \;/\; \pi   }  \)     (Radius of a Thin Walled Circle)

\( A =  r^2 \; \pi \;/\; 2   \)

Symbol English Metric
\( r \) = inside radius \( in \) \( mm \)
\( A \) = area \( in^2 \) \( mm^2 \)
\( \pi \) = Pi \(3.141 592 653 ...\)

 

Distance from Centroid of a Thin Walled Circle formulas

\( C_x =  r \) 

\( C_y =  r \)

Symbol English Metric
\( C_x, C_y \) = distance from centroid \( in \) \( mm \)
\( r \) = inside radius \( in \) \( mm \)

  

Elastic Section Modulus of a Thin Walled Circle formula

\( S =   2 \; \pi \; r \; t \;/\; 3 \)     (Elastic Section Modulus of a Thin Walled Circle)

\( r =  S \; 3 \;/\; 2 \; \pi \; t \) 

\( t =   S \; 3 \;/\; 2 \; \pi \; r \)

Symbol English Metric
\( S \) = elastic section modulus \( in^3 \) \(mm^3\)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = inside radius \( in \) \( mm \)
\( t \) = thickness \( in \) \( mm \)

    

Plastic Section Modulus of a Thin Walled Circle formula

\( Z =  \pi \; r^2 \; t   \)     (Plastic Section Modulus of a Thin Walled Circle)

\( r =  \sqrt{  Z \;/\; \pi \; t  }  \)

\( t =   Z \;/\; \pi \; r^2 \)

Symbol English Metric
\( Z \) = plastic section modulus \( in^3 \) \(mm^3  \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = inside radius \( in \) \( mm \)
\( t \) = thickness \( in \) \( mm \)

    

Polar Moment of Inertia of a Thin Walled Circle formulas

\( J_{z} =  2\; \pi \;r^3 \;t  \) 

\( J_{z1} =  6\; \pi \;r^3 \;t  \) 

Symbol English Metric
\( J \) = torsional constant \( in^4 \) \(mm^4  \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = inside radius \( in \) \( mm \)
\( t \) = thickness \( in \) \( mm \)

    

Radius of Gyration of a Thin Walled Circle formulas

\( k_{x} =   ( \sqrt {2}  \;/\;  2  ) \; r   \) 

\( k_{y} =   ( \sqrt {2}  \;/\;  2  ) \; r   \)

\( k_{z} =     r  \) 

\( k_{x1} =   ( \sqrt {6}  \;/\;  2  ) \; r   \)

\( k_{y1} =   ( \sqrt {6}  \;/\;  2  ) \; r   \)

\( k_{z1} =    \sqrt {3}  \; r   \)

Symbol English Metric
\( k \) = radius of gyration \( in \) \( mm \)
\( r \) = inside radius \( in \) \( mm \)

   

Second Moment of Area of a Thin Walled Circle formulas

\( I_{x} =  \pi \;r^3 \;t \) 

\( I_{x1} =  3\; \pi \;r^3 \;t  \) 

\( I_{y1} =  3\; \pi \;r^3 \;t \)

Symbol English Metric
\( I \) = moment of inertia \( in^4 \) \(mm^4  \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = inside radius \( in \) \( mm \)
\( t \) = thickness \( in \) \( mm \)

   

Torsional Constant of a Thin Walled Circle formula

\( J  =  2\;  \pi \;r^3 \; t    \)     (Torsional Constant of a Thin Walled Circle)

\( r  =  ( J \;/\; 2 \; \pi \; t )^{ \frac{1}{3} }    \)

\( t  =  J \;/\; 2 \; \pi \; r^3  \)

Symbol English Metric
\( J \) = torsional constant \( in^4 \) \(mm^4  \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = inside radius \( in \) \( mm \)
\( t \) = thickness \( in \) \( mm \)

 

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Tags: Structural Steel Circle