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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.

 

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area of a Thin Walled Circle formula

\(\large{ A = 2\; \pi \;r\; t }\) 

\(\large{ A = \pi \;D\; t }\) 

Area of a Thin Walled Circle - Solve for A

\(\large{ A = 2\; \pi \; r \; t }\) 

radius, r
thickness, t

Area of a Thin Walled Circle - Solve for r

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

area, A
thickness, t

Area of a Thin Walled Circle - Solve for t

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

area, A
radius, r

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

 

Perimeter of a Thin Walled Circle formula

\(\large{ P = 2\; \pi \;r }\)     (outside)  

\(\large{ P = 2\; \pi \; \left(  r - t  \right)  }\)     (inside) 
Symbol English Metric
\(\large{ P }\) = perimeter \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)

 

Radius of a Thin Walled Circle formula
\(\large{ r = \sqrt   {\frac {2\;A} {\pi} }   }\) 
Symbol English Metric
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ A }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)

  

Distance from Centroid of a Thin Walled Circle formulas

\(\large{ C_x =  r}\) 

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

 

Elastic Section Modulus of a Thin Walled Circle formula
\(\large{ S =  \frac { 2\; \pi \;r \;t }  { 3  }  }\) 
Symbol English Metric
\(\large{ S }\) = elastic section modulus \(\large{in^3}\) \(\large{mm^3}\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)

   

Plastic Section Modulus of a Thin Walled Circle formula
\(\large{ Z =  \pi \;r^2 \;t   }\) 
Symbol English Metric
\(\large{ Z }\) = plastic section modulus \(\large{ in^3 }\) \(\large{mm^3  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)

   

Polar Moment of Inertia of a Thin Walled Circle formulas

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

\(\large{ J_{z1} =  6\; \pi \;r^3 \;t  }\) 
Symbol English Metric
\(\large{ J }\) = torsional constant \(\large{ in^4 }\) \(\large{mm^4  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)

   

Radius of Gyration of a Thin Walled Circle formulas

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

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

\(\large{ k_{z} =     r  }\) 

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

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

\(\large{ k_{z1} =    \sqrt {3}  \; r   }\)
Symbol English Metric
\(\large{ k }\) = 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

\(\large{ I_{x} =  \pi \;r^3 \;t }\) 

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

\(\large{ I_{y1} =  3\; \pi \;r^3 \;t }\)
Symbol English Metric
\(\large{ I }\) = moment of inertia \(\large{ in^4 }\) \(\large{mm^4  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)

  

Torsional Constant of a Thin Walled Circle formula
\(\large{ J  =  2\;  \pi \;r^3 \; t    }\) 
Symbol English Metric
\(\large{ J }\) = torsional constant \(\large{ in^4 }\) \(\large{mm^4  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{mm  }\)
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{mm  }\)

 

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Tags: Perimeter Equations Inertia Equations Structural Steel Equations Modulus Equations