Half Circle

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.

Half Circle Index

 

Arc Length of a Half Circle formula

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

   

Area of a Half Circle formula

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

 

Perimeter of a Half Circle formula

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

   

Radius of a Half Circle formula

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

   

Distance from Centroid of a Half Circle formulas

\( C_x \;=\; 0   \)

\( C_y \;=\; 4 \; r \;/\; 3 \; \pi  \) 

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

   

Elastic Section Modulus of a Half Circle formula

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

 

Polar Moment of Inertia of a Circle formulas

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

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

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

 

Radius of Gyration of a Half Circle formulas

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

\( k_{y} \;=\;    r \;/\;  2 \) 

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

\( k_{x1} \;=\;    r \;/\;  2 \) 

\( k_{y1} \;=\;    r \;/\;  2 \) 

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

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

 

Second Moment of Area of a Half circle formulas

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

\( I_{y} \;=\; \pi \; r^4\;/\; 8 \)

\( I_{x1} \;=\; \pi \; r^4\;/\; 8 \)

\( I_{y1} \;=\; \pi \; r^4\;/\; 8 \)

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

 

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Tags: Structural Steel Circle