Quarter Circle

Written by Jerry Ratzlaff 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.

 

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arc Length of a Quarter Circle formula

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

 

area of a Quarter Circle formula

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

 

Distance from Centroid of a Quarter Circle formulas

\(\large{ C_x =  \frac {4 \; r} {3 \; \pi}  }\)

\(\large{ C_y =  \frac   {4 \; r}  {3 \; \pi}   }\)

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

 

Elastic Section Modulus of a Quarter Circle formula

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

 

Perimeter of a Quarter Circle formulas

\(\large{ P =  \frac {2 \;  \pi \; r} {4} + 2 \; r   }\) 

\(\large{ P =  L + 2 \; r   }\) 

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

 

Polar Moment of Inertia of a Circle formulas

\(\large{ J_{z} = \left(    \frac { \pi}{ 8 } - \frac { 8 }{ 9 \; \pi } \right)   r^4   }\) 

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

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

 

Radius of a Quarter Circle formula

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

 

Radius of Gyration of a Half Circle formulas

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

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

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

\(\large{ k_{x1} =   \frac {  r  }  { 2  }    }\)

\(\large{ k_{y1} =   \frac {  r  }  { 2  }   }\)

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

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

 

Second Moment of Area of a Half circle formulas

\(\large{ I_{x} =   \left(    \frac { \pi}{ 16 } - \frac { 4 }{ 9 \; \pi } \right)  \; r^4     }\) 

\(\large{ I_{y} =  \left(    \frac { \pi}{ 16 } - \frac { 4 }{ 9 \; \pi } \right) \;  r^4 }\) 

\(\large{ I_{x1} =   \frac {  \pi \;  r^4}{ 16 }  }\) 

\(\large{ I_{y1} =  \frac { \pi \; r^4}{ 8 }  }\)

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

 

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Tags: Inertia Equations Structural Steel Equations Modulus Equations