Circle Segment

Written by Jerry Ratzlaff on . Posted in Plane Geometry

area of a Circle Segment formula

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

Center of a Circle Segment

A point at a fixed equal distance from all points of the circumference of a circle.

Perimeter of a Circle Segment formula

\(\large{ P =   \frac {\pi \; \theta \; r}{180}   + 2 \; r \; sin \;  \frac { \theta }{2} }\)

Distance from Centroid of a Circle Segment formula

\(\large{ C_x =  0   }\)

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

Elastic Section Modulus of a Circle Segment formula

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

Polar Moment of Inertia of a Circle Segment formula

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

Radius of Gyration of a Circle Segment formula

\(\large{ k_{x} =    \sqrt {   \frac {I_x}{A}   }   }\)

\(\large{ k_{y} =   \sqrt {   \frac {I_y}{A} }   }\)

\(\large{ k_{z} =   \sqrt {   k_{x}{^2}  +  k_{y}{^2}   }        }\)

Second Moment of Area of a Circle Segment formula

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

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

 

Where:

\(\large{ A }\) = area

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

\(\large{ d }\) = diameter

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

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

\(\large{ P }\) = perimeter

\(\large{ r }\) = radius

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

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

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

 

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