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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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 |
\(\large{3.141 592 653 ...}\) |
Tags:
Equations for Perimeter
Equations for Inertia
Equations for Structural Steel
Equations for Modulus