Thin Wall 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 thin wall circle is a structural shape used in construction.
- See Article Link - Geometric Properties of Structural Shapes
area of a Thin Walled Circle formula |
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\(\large{ A = 2\; \pi \;r\; t }\) (Area of a Thin Walled Circle) \(\large{ r = \frac{ A }{ 2 \; \pi \; t } }\) \(\large{ t = \frac{ A }{ 2 \; \pi \; r } }\) |
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Solve for A
Solve for r
Solve for t
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| Symbol | English | Metric |
| \(\large{ A }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ t }\) = thickness | \(\large{ in }\) | \(\large{mm }\) |
Perimeter of a Thin Walled Circle formula |
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\(\large{ P = 2\; \pi \;r }\) (outside) \(\large{ P = 2\; \pi \; \left( r - t \right) }\) (inside) |
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| Symbol | English | Metric |
| \(\large{ P }\) = perimeter | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ t }\) = thickness | \(\large{ in }\) | \(\large{mm }\) |
Radius of a Thin Walled Circle formula |
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\(\large{ r = \sqrt{ \frac { 2 \; A }{ \pi } } }\) (Radius of a Thin Walled Circle) \(\large{ A = \frac {r^2 \; \pi }{ 2 } }\) |
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| 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 |
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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 Thin Walled Circle formula |
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\(\large{ S = \frac{ 2 \; \pi \; r \; t }{ 3 } }\) (Elastic Section Modulus of a Thin Walled Circle) \(\large{ r = \frac{ S \; 3 }{ 2 \; \pi \; t } }\) \(\large{ t = \frac{ S \; 3 }{ 2 \; \pi \; r } }\) |
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| Symbol | English | Metric |
| \(\large{ S }\) = elastic section modulus | \(\large{in^3}\) | \(\large{mm^3}\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ t }\) = thickness | \(\large{ in }\) | \(\large{mm }\) |
Plastic Section Modulus of a Thin Walled Circle formula |
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\(\large{ Z = \pi \; r^2 \; t }\) (Plastic Section Modulus of a Thin Walled Circle) \(\large{ r = \sqrt{ \frac{ Z }{ \pi \; t } } }\) \(\large{ t = \frac{ Z }{ \pi \; r^2 } }\) |
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| Symbol | English | Metric |
| \(\large{ Z }\) = plastic section modulus | \(\large{ in^3 }\) | \(\large{mm^3 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ t }\) = thickness | \(\large{ in }\) | \(\large{mm }\) |
Polar Moment of Inertia of a Thin Walled Circle formulas |
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\(\large{ J_{z} = 2\; \pi \;r^3 \;t }\) \(\large{ J_{z1} = 6\; \pi \;r^3 \;t }\) |
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| Symbol | English | Metric |
| \(\large{ J }\) = torsional constant | \(\large{ in^4 }\) | \(\large{mm^4 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ t }\) = thickness | \(\large{ in }\) | \(\large{mm }\) |
Radius of Gyration of a Thin Walled Circle formulas |
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\(\large{ k_{x} = \frac { \sqrt {2} } { 2 } \; r }\) \(\large{ k_{y} = \frac { \sqrt {2} } { 2 } \; r }\) \(\large{ k_{z} = r }\) \(\large{ k_{x1} = \frac { \sqrt {6} } { 2 } \; r }\) \(\large{ k_{y1} = \frac { \sqrt {6} } { 2 } \; r }\) \(\large{ k_{z1} = \sqrt {3} \; r }\) |
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| 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 |
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\(\large{ I_{x} = \pi \;r^3 \;t }\) \(\large{ I_{x1} = 3\; \pi \;r^3 \;t }\) \(\large{ I_{y1} = 3\; \pi \;r^3 \;t }\) |
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| Symbol | English | Metric |
| \(\large{ I }\) = moment of inertia | \(\large{ in^4 }\) | \(\large{mm^4 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ t }\) = thickness | \(\large{ in }\) | \(\large{mm }\) |
Torsional Constant of a Thin Walled Circle formula |
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\(\large{ J = 2\; \pi \;r^3 \; t }\) (Torsional Constant of a Thin Walled Circle) \(\large{ r = \left( \frac{ J }{ 2 \; \pi \; t } \right)^{ \frac{1}{3} } }\) \(\large{ t = \frac{ J }{ 2 \; \pi \; r^3 } }\) |
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| Symbol | English | Metric |
| \(\large{ J }\) = torsional constant | \(\large{ in^4 }\) | \(\large{mm^4 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ t }\) = thickness | \(\large{ in }\) | \(\large{mm }\) |
