Thin Wall Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• 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.

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