Segment of a Circle
Segment is an interior part of a circle bound by a chord and an arc.
- Angle (\(\Delta\)) - Two rays sharing a common point.
- Center (cp) - Having all points on the line circumference are at equal distance from the center point.
- Chord (c) - Also called long chord (LC), is between any two points on a circular curve.
- Circle - All points are at a fixed equal distance from a radius point (rp).
- Circumference (C) - The outside of a circle or a complete circular arc.
- Height (h) - Length of radius from radius center to midpoint of chord.
- Height (h') - Length of radius from midpoint of chord to point on circular curve.
- Length (L) - Total length of any circular curve measured along the arc.
- Major Arc - The longest of two arcs of a circle or ellipse.
- Minor Arc - The shorter of two arcs of a circle or ellipse.
- Radius (r) - Half the diameter of a circle. A line segment between the center point and a point on a circle or sphere.
- Radius Point (rp) - Radius center point of circular curve.
- Sector is a fraction of the area of a circle with a radius on each side and an arc.
- Tangent (T) - A line that touches a curve at just one point such that it is perpendicular to a radius line of the curve.
Article Links
Arc Length of a Segment formula |
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\(\large{ L = \Delta \; \frac{\pi}{180} \; r }\) | ||
Symbol | English | Metric |
\(\large{ L }\) = arc length | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ \Delta }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
\(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Area of a Segment formula |
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\(\large{ A = \frac {r^2} {2} \; \left( \Delta - sin \; \Delta \right) }\) \(\large{ A = \frac {r^2 \; \left( \Delta \;-\; sin \; \Delta \right) }{ 2 } }\) \(\large{ A = r^2 \; \left( \frac { \Delta \; \pi }{ 360 } \;-\; \frac { sin \; \Delta }{ 2 } \right) }\) \(\large{ A = \frac { 1 }{ 2 } \; r^2 \; \left( \; \frac {\pi}{180} \Delta \;-\; sin \; \Delta \; \right) \;\; }\) |
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Symbol | English | Metric |
\(\large{ A }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
\(\large{ \Delta }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
\(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Distance from Centroid of a Segment formulas |
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\(\large{ C_x = 0 }\) \(\large{ C_y = \frac {4 \; r}{3} \; \left( \frac {sin^3 \; \frac{\Delta}{2} } {\Delta \; - \; sin \; \Delta} \right) }\) |
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Symbol | English | Metric |
\(\large{ C_x, C_y }\) = distance from centroid | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ \Delta }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Elastic Section Modulus of a Segment formula |
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\(\large{ S = \frac{ I_x }{ C_y \;-\; r \; cos \; \left( \frac {\Delta}{2} \right) } }\) | ||
Symbol | English | Metric |
\(\large{ S }\) = elastic section modulus | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
\(\large{ C_x, C_y }\) = distance from centroid | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ \Delta }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
\(\large{ I }\) = moment of inertia | \(\large{\frac{lbm}{ft^2-sec} }\) | \(\large{\frac{kg}{m^2} }\) |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Height of a Segment formulas |
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\(\large{ h = r \; \left( 1 - cos \; \frac{ \Delta }{2} \right) }\) \(\large{ h = r - \sqrt{ r^2 - \frac{ l^2 }{4} } }\) |
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Symbol | English | Metric |
\(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ \Delta }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
\(\large{ l }\) = chord | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Length of a Segment formulas |
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\(\large{ c = 2 \; r \; sin \; \frac{ \Delta }{2} }\) \(\large{ c = r \; \sqrt{ 2 - 2 \; cos \; \Delta } }\) |
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Symbol | English | Metric |
\(\large{ l }\) = chord | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ \Delta }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Perimeter of a Segment formula |
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\(\large{ P = \Delta \; r + 2r \; sin \; \frac { \Delta }{2} }\) | ||
Symbol | English | Metric |
\(\large{ P }\) = perimeter | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ \Delta }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Polar Moment of Inertia of a Segment formula |
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\(\large{ J_{z} = \frac {r^4}{4} \; \left( \Delta - sin \; \Delta + \frac {2}{3} \; sin \; \Delta \; sin^2 \; \frac {\Delta}{2} \right) }\) | ||
Symbol | English | Metric |
\(\large{ J }\) = torsional constant | \(\large{ in^4 }\) | \(\large{ mm^4 }\) |
\(\large{ \Delta }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Radius of Gyration of a Segment formulas |
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\(\large{ k_{x} = \sqrt { \frac {I_x}{A} } }\) \(\large{ k_{y} = \sqrt { \frac {I_y}{A} } }\) \(\large{ k_{z} = \sqrt { k_{x}{^2} + k_{y}{^2} } }\) |
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Symbol | English | Metric |
\(\large{ k }\) = radius of gyration | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ A }\) = area | \(\large{ deg }\) | \(\large{ rad }\) |
\(\large{ I }\) = moment of inertia | \(\large{ in^4 }\) | \(\large{ mm^4 }\) |
Second Moment of Area of a Segment formulas |
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\(\large{ I_{x} = \frac {r^4}{8} \; \left( \Delta - sin \; \Delta + 2 \; sin \; \Delta \; sin^2 \; \frac {\Delta}{2} \right) }\) \(\large{ I_{y} = \frac {r^4}{24} \; \left( 3 \; \Delta - 3 \; sin \; \Delta - 2 \; sin \; \Delta \; sin^2 \; \frac {\Delta}{2} \right) }\) |
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Symbol | English | Metric |
\(\large{ I }\) = moment of inertia | \(\large{ in^4 }\) | \(\large{ mm^4 }\) |
\(\large{ \Delta }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Tags: Inertia Structural Steel Modulus