Quarter Circle

on . Posted in Plane Geometry

  • circle quarter 52 overlapping circles 1A part of the interior of a circle having two radius boundries at a 90° angle and an arc.
  • Center of a circle having all points on the line circumference are at equal distance from the center point.
  • A quarter circle is a structural shape used in construction.

Quarter Circle Index

 

arc Length of a Quarter Circle formula

\( L \;=\; 2 \; \pi \; r\;/\;4 \) 
Symbol English Metric
\( L \) = arc length \( in \) \( mm \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = radius \( in \) \( mm \)

 

area of a Quarter Circle formula

\( A \;=\; \pi \; r^2 \;/\;4 \) 
Symbol English Metric
\( A \) = area \( in^2 \) \( mm^2 \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = radius \( in \) \( mm \)

 

Distance from Centroid of a Quarter Circle formulas

\( C_x \;=\; 4 \; r\;/\;3 \; \pi \)

\( C_y \;=\; 4 \; r\;/\;3 \; \pi \)

Symbol English Metric
\( C_x, C_y \) = distance from centroid \( in \) \( mm \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = radius \( in \) \( mm \)

 

Elastic Section Modulus of a Quarter Circle formula

\( S \;=\; I_x \;/\; C_y \) 
Symbol English Metric
\( S \) = elastic section modulus \(in^3\) \(mm^3\)
\( I \) = moment of inertia \(lbm\;/\;ft^2-sec\) \(kg\;/\;m^2\)

 

Perimeter of a Quarter Circle formulas

\( P \;=\; (2 \; \pi \; r\;/\;4)+ 2 \; r  \) 

\( P \;=\; L + 2 \; r  \) 

Symbol English Metric
\( P \) = perimeter \( in \) \( mm \)
\( L \) = arc length \( in \) \( mm \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = radius \( in \) \( mm \)

 

Polar Moment of Inertia of a Circle formulas

\( J_{z} \;=\; [\; ( \pi\;/\; 8 ) - ( 8 \;/\; 9 \; \pi ) \;] \;  r^4  \) 

\( J_{z1} \;=\; \pi \; r^4 \;/\; 8 \) 

Symbol English Metric
\( L \) = arc length \( in \) \( mm \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = radius \( in \) \( mm \)

 

Radius of a Quarter Circle formula

\( r \;=\; \sqrt{ 2 \; A \;/\; \pi }  \) 
Symbol English Metric
\( r \) = radius \( in \) \( mm \)
\( A \) = area \( in^2 \) \( mm^2 \) 
\( \pi \) = Pi \(3.141 592 653 ...\)

 

Radius of Gyration of a Half Circle formulas

\( k_{x} \;=\;   r  \; \sqrt{  ( 1 \;/\; 4 )  -  ( 16 \;/\; 9 \;  \pi^2)  }  \) 

\( k_{y} \;=\;   r  \; \sqrt{  ( 1 \;/\; 4 )  -  ( 16 \;/\; 9 \;  \pi^2)  }  \)

\( k_{z} \;=\;   r  \; \sqrt{  ( 1 \;/\; 2 )  -  ( 16 \;/\; 9 \;  \pi^2)  }  \)

\( k_{x1} \;=\;   r  \;/\; 2  \)

\( k_{y1} \;=\;   r  \;/\; 2  \)

\( k_{z1} \;=\; ( \sqrt {2} \;/\; 2 ) \; r  \)

Symbol English Metric
\( k \) = radius of gyration \( in \) \( mm \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = radius \( in \) \( mm \)

 

Second Moment of Area of a Half circle formulas

\( I_{x} \;=\; [\; ( \pi\;/\; 16 ) - ( 4 \;/\; 9 \; \pi ) \;]  \; r^4  \) 

\( I_{y} \;=\; [\; ( \pi\;/\; 16 ) - ( 4 \;/\; 9 \; \pi ) \;]  \; r^4  \)

\( I_{x1} \;=\; \pi \; r^4\;/\; 16 \)

\( I_{y1} \;=\; \pi \; r^4\;/\; 8 \)

Symbol English Metric
\( I \) = moment of inertia  \( in^4 \) \( mm^4 \)
\( \pi \) = Pi \(3.141 592 653 ...\)
\( r \) = radius \( in \) \( mm \)

 

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Tags: Structural Steel Circle