Half Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • circle half 4circle half 8Half of the interior of a circle having a straight chord and an arc.
  • Center of a circle having all points on the line circumference are at equal distance from the center point.
  • A half circle is a structural shape used in construction.

 

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Arc Length of a Half Circle formula

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

   

Area of a Half Circle formula

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

 

Perimeter of a Half Circle formula

\(\large{ P =  \frac{2 \; \pi \; r}{2} + 2 \; r   }\) 
Symbol English Metric
\(\large{ P }\) = perimeter \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{mm  }\)

   

Radius of a Half Circle formula

\(\large{ r = \sqrt   {\frac {2 \; A_{area}} {\pi} }   }\) 
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 Half Circle formulas

\(\large{ C_x =  0   }\)

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

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 Half Circle formula

\(\large{ S =  \frac { I_x }  { C_y  }  }\) 
Symbol English Metric
\(\large{ S }\) = elastic section modulus \(\large{ in^3 }\) \(\large{ mm^3 }\)
\(\large{ C_x, C_y }\) = distance from centroid \(\large{ in }\) \(\large{ mm }\)

 

Polar Moment of Inertia of a Circle formulas

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

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

Symbol English Metric
\(\large{ J }\) = torsional constant \(\large{ in^4 }\) \(\large{mm^4  }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{mm  }\)

 

Radius of Gyration of a Half Circle formulas

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

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

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

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

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

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

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

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

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

\(\large{ I_{x1} =   \frac {  \pi \; r^4}{ 8 }  }\) 

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

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