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.

area of a Thin Walled Circle formula

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

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

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

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 $$\large{ in }$$ $$\large{ mm }$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ t }$$ = 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 $$\large{in^3}$$ $$\large{mm^3}$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ t }$$ = 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 $$\large{ in^3 }$$ $$\large{mm^3 }$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ t }$$ = 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 $$\large{ in^4 }$$ $$\large{mm^4 }$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ t }$$ = 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 $$\large{ in^4 }$$ $$\large{mm^4 }$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ t }$$ = 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 $$\large{ in^4 }$$ $$\large{mm^4 }$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{mm }$$