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