Hollow Circle
- 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.
- See Article Link - Geometric Properties of Structural Shapes
Hollow Circle Index
- Area of a Hollow Circle
- Circumference of a Hollow Circle
- Distance from Centroid of a Hollow Circle
- Elastic Section Modulus of a Hollow Circle
- Plastic Section Modulus of a Hollow Circle
- Polar Moment of Inertia of a Hollow Circle
- Radius of a Hollow Circle
- Radius of Gyration of a Hollow Circle
- Second Moment of Area of a Hollow Circle
- Sector of a Hollow Circle
- Torsional Constant of a Hollow Circle
area of a Hollow Circle formula |
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\(\large{ A = \pi \; \left( R^2 - r^2 \right) }\) (Area of a Hollow Circle) \(\large{ R = \sqrt{ \frac{ A \;-\; \pi \; r^2 }{ \pi } } }\) \(\large{ r = \sqrt{ R^2 - \frac{ A}{\pi} } }\) |
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Solve for A
Solve for R
Solve for r
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| Symbol | English | Metric |
| \(\large{ A }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ R }\) = outside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
Circumference of a Hollow Circle formulas |
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\(\large{ C = 2 \; \pi \; r }\) (inside) \(\large{ C = 2 \; \pi \; R }\) (outside) |
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Solve for C
Solve for r
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| Symbol | English | Metric |
| \(\large{ C }\) = circumference | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ R }\) = outside radius | \(\large{ in }\) | \(\large{mm }\) |
Distance from Centroid of a Hollow Circle formulas |
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\(\large{ C_x = r}\) \(\large{ C_y = r}\) |
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| 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 Hollow Circle formula |
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| \(\large{ S = \frac{ \pi \; \left( R^4 \;-\; r^4 \right) }{ 4\;R } }\) | ||
| Symbol | English | Metric |
| \(\large{ S }\) = elastic section modulus | \(\large{in^3}\) | \(\large{mm^3}\) |
| \(\large{ r }\) = 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 |
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| \(\large{ Z = \frac { 4 \; \left( R^3 \;-\; r^3 \right) } { 3 } }\) | ||
| Symbol | English | Metric |
| \(\large{ Z }\) = plastic section modulus | \(\large{ in^3 }\) | \(\large{mm^3 }\) |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ R }\) = outside radius | \(\large{ in }\) | \(\large{mm }\) |
Polar Moment of Inertia of a Hollow Circle formulas |
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\(\large{ J_{z} = \frac { \pi }{2} \; \left( R^4 - r^4 \right) }\) \(\large{ J_{z1} = \frac { \pi }{2} \; \left( R^4 - r^4 \right) + 2\; \pi \; R^2 \left( R^2 - r^2 \right) }\) |
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| Symbol | 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 |
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\(\large{ r = \frac{C}{2 \; \pi} }\) \(\large{ R = \frac{C}{2 \; \pi} }\) |
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Solve for r
Solve for C
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| Symbol | English | Metric |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ R }\) = outside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ C }\) = circumference | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
Radius of Gyration of a Hollow Circle formulas |
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\(\large{ k_{x} = \frac {1}{2} \; \sqrt { R^2 + r^2 } }\) \(\large{ k_{y} = \frac {1}{2} \; \sqrt { R^2 + r^2 } }\) \(\large{ k_{z} = \frac { \sqrt { 2 } }{2} \; \sqrt { R^2 + r^2 } }\) \(\large{ k_{x1} = \frac {1}{2} \; \sqrt { 5 \; R^2 + r^2 } }\) \(\large{ k_{y1} = \frac {1}{2} \; \sqrt { 5 \; R^2 + r^2 } }\) \(\large{ k_{z1} = \frac { \sqrt { 2 } }{2} \; \sqrt { 5 \; R^2 + r^2 } }\) |
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| Symbol | 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 |
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\(\large{ I_{x} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) }\) \(\large{ I_{y} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) }\) \(\large{ I_{x1} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) + \pi \; R^2 \left( R^2 - r^2 \right) }\) \(\large{ I_{y1} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) + \pi \; R^2 \left( R^2 - r^2 \right) }\) |
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| Symbol | 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 |
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| \(\large{ A = \frac{\pi \; \Delta \; \left( r^2 \;-\; R^2 \right) }{360} }\) | ||
| Symbol | 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 |
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\(\large{ J = \frac { \pi \; \left( R^4 \;-\; r^4 \right) } { 2 } }\) \(\large{ J = \frac { \pi \; \left( D^4 \;-\; d^4 \right) } { 32 } }\) |
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| Symbol | 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 | \(\large{3.141 592 653 ...}\) | |
Tags: Inertia Structural Steel Modulus