Circle Segment

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • circle segment 6Circle segment is an interior part of a circle bound by a chord and an arc.
  • Center of a circle having all points on the line circumference are at equal distance from the center point.

 

Structural Shapes

 

Arc Length of a Circle Segment formula

\(\large{ l =   \theta \; \frac{\pi}{180} \; r }\)   

Where:

\(\large{ l }\) = arc length

\(\large{ \theta }\) = angle

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

\(\large{ r }\) = radius

 

area of a Circle Segment formulas

\(\large{ A_{area} =   \frac {r^2} {2} \; \left( \theta  -  sin \; \theta   \right)   }\)   
\(\large{ A_{area} =   \frac {r^2 \; \left( \theta  \;-\;  sin \; \theta   \right) }{ 2 }       }\)  

Where:

\(\large{ A_{area} }\) = area

\(\large{ \theta }\) = angle

\(\large{ r }\) = radius

 

Distance from Centroid of a Circle Segment formulas

\(\large{ C_x =  0  }\)   
\(\large{ C_y =  \frac {4 \; r}{3} \; \left(  \frac {sin^3 \; \frac{\theta}{2} } {\theta \; - \; sin \; \theta}    \right)  }\)   

Where:

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

\(\large{ \theta }\) = angle

\(\large{ r }\) = radius

 

Elastic Section Modulus of a Circle Segment formula

\(\large{ S =  \frac{ I_x }{ C_y \;-\; r \; cos \; \left(  \frac {\theta}{2}   \right)  }  }\)   

Where:

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

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

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

\(\large{ r }\) = radius

\(\large{ \theta }\) = angle

 

Perimeter of a Circle Segment formula

\(\large{ P = \theta \; r   + 2r \; sin \;  \frac { \theta }{2} }\)   

Where:

\(\large{ P }\) = perimeter

\(\large{ \theta }\) = angle

\(\large{ r }\) = radius

 

Polar Moment of Inertia of a Circle Segment formula

\(\large{ J_{z} =   \frac {r^4}{4} \; \left(  \theta - sin \; \theta  + \frac  {2}{3}  \; sin \; \theta \; sin^2 \; \frac {\theta}{2}  \right)    }\)   

Where:

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

\(\large{ r }\) = radius

\(\large{ \theta }\) = angle

 

Radius of Gyration of a Circle Segment formulas

\(\large{ k_{x} =    \sqrt {   \frac {I_x}{A_{area}}   }   }\)   
\(\large{ k_{y} =   \sqrt {   \frac {I_y}{A_{area}} }   }\)   
\(\large{ k_{z} =   \sqrt {   k_{x}{^2}  +  k_{y}{^2}   }        }\)   

Where:

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

\(\large{ A_{area} }\) = area

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

 

Second Moment of Area of a Circle Segment formulas

\(\large{ I_{x} =   \frac {r^4}{8} \;  \left(  \theta - sin \;  \theta +  2 \; sin \; \theta \; sin^2 \; \frac {\theta}{2}  \right)    }\)   
\(\large{ I_{y} =   \frac {r^4}{24} \; \left(  3 \; \theta - 3 \; sin \;  \theta  -  2 \; sin \; \theta \; sin^2 \; \frac {\theta}{2}  \right)    }\)   

Where:

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

\(\large{ r }\) = radius

\(\large{ \theta }\) = angle

 

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