- Article Link - Geometric Properties of Structural Shapes
area of a Thin Walled Circle formula |
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| \( A \;=\; 2 \cdot \pi \cdot r \cdot t \) | ||
| Symbol | English | Metric |
| \( A \) = area | \( in^2 \) | \( mm^2 \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( t \) = thickness | \( in \) | \( mm \) |
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.
Perimeter of a Thin Walled Circle formula |
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\( P \;=\; 2 \cdot \pi \cdot r \) (Outside) \( P \;=\; 2 \cdot \pi \cdot ( r - t ) \) (Inside) |
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| Symbol | English | Metric |
| \( P \) = perimeter | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( t \) = thickness | \( in \) | \( mm \) |
Radius of a Thin Walled Circle formula |
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\( r \;=\; \sqrt{ \dfrac{ 2 \cdot A }{ \pi } } \) (Radius of a Thin Walled Circle) \( A \;=\; \dfrac{ r^2 \cdot \pi }{ 2 } \) |
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| Symbol | English | Metric |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( A \) = area | \( in^2 \) | \( mm^2 \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
Distance from Centroid of a Thin Walled Circle formulas |
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\( C_x \;=\; r \) \( C_y \;=\; r \) |
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| Symbol | English | Metric |
| \( C_x, C_y \) = distance from centroid | \( in \) | \( mm \) |
| \( r \) = inside radius | \( in \) | \( mm \) |
Elastic Section Modulus of a Thin Walled Circle formula |
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\( S \;=\; \dfrac{ 2 \cdot \pi \cdot r \cdot t }{ 3 }\) (Elastic Section Modulus of a Thin Walled Circle) \( r \;=\; \dfrac{ S \cdot 3 }{ 2 \cdot \pi \cdot t }\) \( t \;=\; \dfrac{ S \cdot 3 }{ 2 \cdot \pi \cdot r }\) |
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| Symbol | English | Metric |
| \( S \) = elastic section modulus | \( in^3 \) | \(mm^3\) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( t \) = thickness | \( in \) | \( mm \) |
Plastic Section Modulus of a Thin Walled Circle formula |
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\( Z \;=\; \pi \cdot r^2 \cdot t \) (Plastic Section Modulus of a Thin Walled Circle) \( r \;=\; \sqrt{ \dfrac{ Z }{ \pi \cdot t } } \) \( t \;=\; \dfrac{ Z }{ \pi \cdot r^2 }\) |
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| Symbol | English | Metric |
| \( Z \) = plastic section modulus | \( in^3 \) | \(mm^3 \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( t \) = thickness | \( in \) | \( mm \) |
Polar Moment of Inertia of a Thin Walled Circle formulas |
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\( J_{z} \;=\; 2\cdot \pi \cdot r^3 \cdot t \) \( J_{z1} \;=\; 6 \cdot \pi \cdot r^3 \cdot t \) |
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| Symbol | English | Metric |
| \( J \) = torsional constant | \( in^4 \) | \(mm^4 \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( t \) = thickness | \( in \) | \( mm \) |
Radius of Gyration of a Thin Walled Circle formulas |
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\( k_{x} \;=\; \dfrac{ \sqrt{2} }{ 2 } \cdot r \) \( k_{y} \;=\; \dfrac{ \sqrt{2} }{ 2 } \cdot r \) \( k_{z} \;=\; r \) \( k_{x1} \;=\; \dfrac{ \sqrt{6} }{ 2 } \cdot r \) \( k_{y1} \;=\; \dfrac{ \sqrt{6} }{ 2 } \cdot r \) \( k_{z1} \;=\; \sqrt {3} \cdot r \) |
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| Symbol | English | Metric |
| \( k \) = radius of gyration | \( in \) | \( mm \) |
| \( r \) = inside radius | \( in \) | \( mm \) |
Second Moment of Area of a Thin Walled Circle formulas |
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\( I_{x} \;=\; \pi \cdot r^3 \cdot t \) \( I_{x1} \;=\; 3\cdot \pi \cdot r^3 \cdot t \) \( I_{y1} \;=\; 3\cdot \pi \cdot r^3 \cdot t \) |
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| Symbol | English | Metric |
| \( I \) = moment of inertia | \( in^4 \) | \(mm^4 \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( t \) = thickness | \( in \) | \( mm \) |
Torsional Constant of a Thin Walled Circle formula |
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\( J \;=\; 2\cdot \pi \cdot r^3 \cdot t \) (Torsional Constant of a Thin Walled Circle) \( r \;=\; \left( \dfrac{ J }{ 2 \cdot \pi \cdot t } \right)^{ \frac{1}{3} } \) \( t \;=\; \dfrac{ J }{ 2 \cdot \pi \cdot r^3 } \) |
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| Symbol | English | Metric |
| \( J \) = torsional constant | \( in^4 \) | \(mm^4 \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( t \) = thickness | \( in \) | \( mm \) |