Hollow Circle

on . Posted in Plane Geometry

  • circle hollow 4Two 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.

Hollow Circle Index

 

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 \(3.141 592 653 ...\)

 

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Tags: Structural Steel Circle