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
- Tags: Structural Steel Circle
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 |
||
| \( A \;=\; \pi \; ( R^2 - r^2 ) \) | ||
| Symbol | English | Metric |
| \( A \) = area | \( in^2 \) | \( mm^2 \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
| \( R \) = outside radius | \( in \) | \( mm \) |
| \( r \) = inside radius | \( in \) | \( mm \) |
Circumference of a Hollow Circle formulas |
||
|
\( C \;=\; 2 \; \pi \; r \) (inside) \( C \;=\; 2 \; \pi \; R \) (outside) |
||
| Symbol | English | Metric |
| \( C \) = circumference | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( R \) = outside radius | \( in \) | \( mm \) |
Distance from Centroid of a Hollow Circle formulas |
||
|
\( C_x \;=\; r\) \( C_y \;=\; r\) |
||
| 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 |
||
| \( S \;=\; \pi \; ( R^4 - r^4 ) \;/\; 4\;R \) | ||
| Symbol | English | Metric |
| \( S \) = elastic section modulus | \(in^3\) | \(mm^3\) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( R \) = outside radius | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
Plastic Section Modulus of a Hollow Circle formula |
||
| \( Z \;=\; 4 \; ( R^3 - r^3 ) \;/\; 3 \) | ||
| 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 |
||
|
\( J_{z} \;=\; ( \pi \;/\; 2 ) \; ( R^4 - r^4 ) \) \( J_{z1} \;=\; [ \; ( \pi \;/\; 2 ) \; ( R^4 - r^4 ) \; ] + [ 2\; \pi \; R^2 \; ( R^2 - r^2 ) \; ] \) |
||
| Symbol | English | Metric |
| \( J \) = torsional constant | \( in^4 \) | \(mm^4 \) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( R \) = outside radius | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
Radius of a Hollow Circle formula |
||
|
\( r \;=\; C \;/\; 2 \; \pi \) \(R \;=\; C \;/\;2 \; \pi \) |
||
| Symbol | English | Metric |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( R \) = outside radius | \( in \) | \( mm \) |
| \( C \) = circumference | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
Radius of Gyration of a Hollow Circle formulas |
||
|
\( k_{x} \;=\; \frac{1}{2} \; \sqrt { R^2 + r^2 } \) \( k_{y} \;=\; \frac{1}{2} \; \sqrt { R^2 + r^2 } \) \( k_{z} \;=\; ( \sqrt{ 2 } \;/\; 2) \; \sqrt{ R^2 + r^2 } \) \( k_{x1} \;=\; \frac{1}{2} \; \sqrt{ 5 \; R^2 + r^2 } \) \( k_{y1} \;=\; \frac{1}{2} \; \sqrt{ 5 \; R^2 + r^2 } \) \( k_{z1} \;=\; ( \sqrt{ 2 } \;/\; 2) \; \sqrt{ 5 \; R^2 + r^2 } \) |
||
| 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 |
||
|
\( I_{x} \;=\; ( \pi \;/\; 4) \; ( R^4 - r^4 ) \) \( I_{y} \;=\; ( \pi \;/\; 4) \; ( R^4 - r^4 ) \) \( I_{x1} \;=\; [ \; ( \pi \;/\; 4 ) \; ( R^4 - r^4 ) \; ] + [ \pi \; R^2 \; ( R^2 - r^2 ) \; ] \) \( I_{y1} \;=\; [ \; ( \pi \;/\; 4 ) \; ( R^4 - r^4 ) \; ] + [ \pi \; R^2 \; ( R^2 - r^2 ) \; ] \) |
||
| Symbol | English | Metric |
| \( I \) = moment of inertia | \( in^4 \) | \( mm^4 \) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( R \) = outside radius | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
Sector of a Hollow Circle formula |
||
| \( A \;=\; \pi \; \Delta \; ( r^2 - R^2 ) \;/\; 360 \) | ||
| 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 | \(3.141 592 653 ...\) | |
Torsional Constant of a Hollow Circle formulas |
||
|
\( J \;=\; \pi \; ( R^4 - r^4 ) \;/\; 2 \) \( J \;=\; \pi \; ( D^4 - d^4 ) \;/\; 32 \) |
||
| 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 | \(3.141 592 653 ...\) | |
Tags: Structural Steel Circle