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Geometrical Properties of Circular Segment


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Radius - r = m

Angle - α = °

k = π/180

a = r2·(1 – cos(α)) m

h = r2a2/4 m

Area

A = r2/2·(α·ksin(α)) m2

Centroid

yc = a/2 m

zc = 4·r/3·sin(α/2)3/(α·ksin(α)) – h m

Perimeter

P = α·k·r + a m

Second moments of area

Iy = r4/8·(α·ksin(α) + 2·sin(αsin(α/2)2) – (h + zc)2·A m4

Iz = r4/24·(3·α·k – 3·sin(α) – 2·sin(αsin(α/2)2) m4

Polar moment of area

Ix = Iy + Iz m4

Radii of gyration

ry = √Iy/A m

rz = √Iz/A m

rx = √Ix/A m


Substitute