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.
  • See Geometric Properties of Structural Shapes

area of a Circle Segment formula

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

Where:

\(\large{ A_{area} }\) = area

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

\(\large{ r }\) = radius

Perimeter of a Circle Segment formula

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

Where:

\(\large{ P }\) = perimeter

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

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

\(\large{ r }\) = radius

Distance from Centroid of a Circle Segment formula

\(\large{ C_x =  0  }\)

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

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

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 formula

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

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

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

Where:

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

\(\large{ A_{area} }\) = area

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

Second Moment of Area of a Circle Segment 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:

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

\(\large{ r }\) = radius

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

 

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