Thin Wall Circle

• Two 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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• Geometric Properties of Structural Shapes

 

area of a Thin Walled Circle formulas

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

Where:

Units	English	Metric
\(\large{ A }\) = 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	Metric
\(\large{ P }\) = 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

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

Where:

Units	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

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

Where:

Units	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

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

Where:

Units	English	Metric
\(\large{ S }\) = 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	Metric
\(\large{ Z }\) = 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	Metric
\(\large{ J }\) = 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	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

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

Where:

Units	English	Metric
\(\large{ I }\) = 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	Metric
\(\large{ J }\) = 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	\(\large{3.141 592 653 ...}\)