Thin Walled Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Thin Walled Circle - Geometric Properties

area of a Thin Walled Circle  formula

$$\large{ A = 2 \pi r t }$$

$$\large{ A = \pi D t }$$

Center of a Thin Walled Circle

All points on the line circumference are at equal distance from the center point.

Perimeter of a Thin Walled Circle formula

$$\large{ P = 2 \pi r }$$   (Outside)

$$\large{ P = 2 \pi \left( r - t \right) }$$   (Inside)

Radius of a Thin Walled Circle formula

$$\large{ r = \sqrt {\frac {2A} {\pi} } }$$

Distance from Centroid of a Thin Walled Circle formula

$$\large{ C_x = r }$$

$$\large{ C_y = r }$$

Elastic Section Modulus of a Thin Walled Circle formula

$$\large{ S = \frac { 2 \pi r t } { 3 } }$$

Plastic Section Modulus of a Thin Walled Circle formula

$$\large{ Z = \pi r^2 t }$$

Polar Moment of Inertia of a Thin Walled Circle formula

$$\large{ J_{z} = 2 \pi r^3 t }$$

$$\large{ J_{z1} = 6 \pi r^3 t }$$

Radius of Gyration of a Thin Walled Circle formula

$$\large{ k_{x} = \frac { \sqrt {2} } { 2 } r }$$

$$\large{ k_{y} = \frac { \sqrt {2} } { 2 } r }$$

$$\large{ k_{z} = r }$$

$$\large{ k_{x1} = \frac { \sqrt {6} } { 2 } r }$$

$$\large{ k_{y1} = \frac { \sqrt {6} } { 2 } r }$$

$$\large{ k_{z1} = \sqrt {3} r }$$

Second Moment of Area of a Thin Walled Circle formula

$$\large{ I_{x} = \pi r^3 t }$$

$$\large{ I_{y} = \pi r^3 t }$$

$$\large{ I_{x1} = 3 \pi r^3 t }$$

$$\large{ I_{y1} = 3 \pi r^3 t }$$

Torsional Constant of a Thin Walled Circle formula

$$\large{ J = 2 \pi r^3 t }$$

Where:

$$\large{ A }$$ = area

$$\large{ C_x, C_y }$$ = distance from centroid

$$\large{ d }$$ = diameter

$$\large{ I }$$ = moment of inertia

$$\large{ J }$$ = torsional constant

$$\large{ k }$$ = radius of gyration

$$\large{ P }$$ = perimeter

$$\large{ r }$$ = radius

$$\large{ S }$$ = elastic section modulus

$$\large{ Z }$$ = plastic section modulus

$$\large{ \pi }$$ = Pi