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 hollow circle is a structural shape used in construction.
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area of a Hollow Circle formula
| \(\large{ A = \pi \; \left( R^2 - r^2 \right) }\) |
|
Where:
| Units |
English |
Metric |
| \(\large{ A }\) = area |
\(\large{ in^2 }\) |
\(\large{ mm^2 }\) |
| \(\large{ r }\) = inside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ R }\) = outside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ \pi }\) = Pi |
\(\large{3.141 592 653 ...}\) |
Circumference of a Hollow Circle formulas
| \(\large{ C = 2 \; \pi \; R }\) |
(outside) |
| \(\large{ C = 2 \; \pi \; r }\) |
(inside) |
Where:
| Units |
English |
Metric |
| \(\large{ C }\) = circumference |
\(\large{ in }\) |
\(\large{ mm }\) |
| \(\large{ r }\) = inside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ R }\) = outside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ \pi }\) = Pi |
\(\large{3.141 592 653 ...}\) |
Where:
\(\large{ C }\) = circumference
\(\large{ r }\) = inside radius
\(\large{ R }\) = outside radius
\(\large{ \pi }\) = Pi
Distance from Centroid of a Hollow 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 Hollow Circle formula
| \(\large{ S = \frac{ \pi \; \left( R^4 \;-\; r^4 \right) }{ 4\;R } }\) |
|
Where:
| Units |
English |
Metric |
| \(\large{ S }\) = elastic section modulus |
\(\large{\frac{lbf}{in^2}}\) |
\(\large{Pa}\) |
| \(\large{ r }\) = inside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ R }\) = outside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ \pi }\) = Pi |
\(\large{3.141 592 653 ...}\) |
Plastic Section Modulus of a Hollow Circle formula
| \(\large{ Z = \frac { 4 \; \left( R^3 \;-\; r^3 \right) } { 3 } }\) |
|
Where:
| Units |
English |
Metric |
| \(\large{ Z }\) = plastic section modulus |
\(\large{ in^4 }\) |
\(\large{mm^4 }\) |
| \(\large{ r }\) = inside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ R }\) = outside radius |
\(\large{ in }\) |
\(\large{mm }\) |
Polar Moment of Inertia of a Hollow Circle formulas
| \(\large{ J_{z} = \frac { \pi }{2} \; \left( R^4 - r^4 \right) }\) |
|
| \(\large{ J_{z1} = \frac { \pi }{2} \; \left( R^4 - r^4 \right) + 2\; \pi \; R^2 \left( R^2 - r^2 \right) }\) |
|
Where:
| Units |
English |
Metric |
| \(\large{ J }\) = torsional constant |
\(\large{ in^4 }\) |
\(\large{mm^4 }\) |
| \(\large{ r }\) = inside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ R }\) = outside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ \pi }\) = Pi |
\(\large{3.141 592 653 ...}\) |
Radius of a Hollow Circle formula
| \(\large{ r = \sqrt {\frac {2 \; A } {\pi} } }\) |
|
Where:
| Units |
English |
Metric |
| \(\large{ A }\) = area |
\(\large{ in^2 }\) |
\(\large{mm^2 }\) |
| \(\large{ r }\) = inside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ \pi }\) = Pi |
\(\large{3.141 592 653 ...}\) |
Radius of Gyration of a Hollow Circle formulas
| \(\large{ k_{x} = \frac {1}{2} \; \sqrt { R^2 + r^2 } }\) |
|
| \(\large{ k_{y} = \frac {1}{2} \; \sqrt { R^2 + r^2 } }\) |
|
| \(\large{ k_{z} = \frac { \sqrt { 2 } }{2} \; \sqrt { R^2 + r^2 } }\) |
|
| \(\large{ k_{x1} = \frac {1}{2} \; \sqrt { 5 \; R^2 + r^2 } }\) |
|
| \(\large{ k_{y1} = \frac {1}{2} \; \sqrt { 5 \; R^2 + r^2 } }\) |
|
| \(\large{ k_{z1} = \frac { \sqrt { 2 } }{2} \; \sqrt { 5 \; R^2 + r^2 } }\) |
|
Where:
| Units |
English |
Metric |
| \(\large{ k }\) = radius of gyration |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ r }\) = inside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ R }\) = outside radius |
\(\large{ in }\) |
\(\large{mm }\) |
Second Moment of Area of a Hollow circle formulas
| \(\large{ I_{x} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) }\) |
|
| \(\large{ I_{y} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) }\) |
|
| \(\large{ I_{x1} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) + \pi \; R^2 \left( R^2 - r^2 \right) }\) |
|
| \(\large{ I_{y1} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) + \pi \; R^2 \left( R^2 - r^2 \right) }\) |
|
Where:
| Units |
English |
Metric |
| \(\large{ I }\) = moment of inertia |
\(\large{ in^4 }\) |
\(\large{mm^4 }\) |
| \(\large{ r }\) = inside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ R }\) = outside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ \pi }\) = Pi |
\(\large{3.141 592 653 ...}\) |
Sector of a Hollow Circle formula
| \(\large{ A = \frac{\pi \; \Delta \; \left( r^2 \;-\; R^2 \right) }{360} }\) |
|
Where:
| Units |
English |
Metric |
| \(\large{ A }\) = sector area |
\(\large{ in^2 }\) |
\(\large{mm^2 }\) |
| \(\large{ \Delta }\) = angle |
\(\large{ deg }\) |
\(\large{rad }\) |
| \(\large{ r }\) = inside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ R }\) = outside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ \pi }\) = Pi |
\(\large{3.141 592 653 ...}\) |
Torsional Constant of a Hollow Circle formulas
| \(\large{ J = \frac { \pi \; \left( R^4 \;-\; r^4 \right) } { 2 } }\) |
|
| \(\large{ J = \frac { \pi \; \left( D^4 \;-\; d^4 \right) } { 32 } }\) |
|
Where:
| Units |
English |
Metric |
| \(\large{ J }\) = torsional constant |
\(\large{ in^4 }\) |
\(\large{mm^4 }\) |
| \(\large{ d }\) = inside diameter |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ D }\) = outside diameter |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ r }\) = inside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ R }\) = outside radius |
\(\large{ in }\) |
\(\large{mm }\) |
| \(\large{ \pi }\) = Pi |
\(\large{3.141 592 653 ...}\) |
