Half Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • circle half 4Half 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.

Structural Shapes

area of a Half Circle  formula

\(\large{ A_{area} =  \frac   { \pi \; r^2 } {2}   }\)

\(\large{ A_{area} = \frac { \pi \; d^2} {8} }\)

Where:

\(\large{ A_{area} }\) = area

\(\large{ d }\) = diameter

\(\large{ r }\) = radius

\(\large{ \pi }\) = Pi

Circumference of a Half Circle formula

\(\large{ C = \frac {\pi \; d} {2}  }\)

Where:

\(\large{ C }\) = circumference

\(\large{ d }\) = diameter

\(\large{ \pi }\) = Pi

Perimeter of a Half Circle formula

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

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

Where:

\(\large{ P }\) = perimeter

\(\large{ d }\) = diameter

\(\large{ r }\) = radius

\(\large{ \pi }\) = Pi

Radius of a Half Circle formula

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

Where:

\(\large{ r }\) = radius

\(\large{ A_{area} }\) = area

\(\large{ \pi }\) = Pi

Distance from Centroid of a Half Circle formula

\(\large{ C_x =  0   }\)

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

Where:

\(\large{ C_x, C_y }\) = distance from centroid

\(\large{ r }\) = radius

\(\large{ \pi }\) = Pi

Elastic Section Modulus of a Half Circle formula

\(\large{ S =  \frac { I_x }  { C_y  }  }\)

Where:

\(\large{ S }\) = elastic section modulus

\(\large{ C_x, C_y }\) = distance from centroid

Polar Moment of Inertia of a Circle formula

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

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

Where:

\(\large{ J }\) = torsional constant

\(\large{ r }\) = radius

\(\large{ \pi }\) = Pi

Radius of Gyration of a Half Circle formula

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

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

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

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

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

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

Where:

\(\large{ k }\) = radius of gyration

\(\large{ r }\) = radius

\(\large{ \pi }\) = Pi

Second Moment of Area of a Half circle formula

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

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

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

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

Where:

\(\large{ I }\) = moment of inertia

\(\large{ r }\) = radius

\(\large{ \pi }\) = Pi

 

Tags: Equations for Moment of Inertia Equations for Structural Steel Equations for Modulus