Geometrical Properties of Circular Segment

Radius - r =   m

Angle - α =   °

k = π180

a =  2·r²·(1 – cos(α)) m

h =  r² – a²4 m

Area

A = r²2·(α·k – sin(α)) m²

Centroid

y_c = a2 m

z_c = 4·r3·sin(α2)³α·k – sin(α) – h m

Perimeter

P = α·k·r + a m

Second moments of area

I_y = r⁴8·(α·k – sin(α) + 2·sin(α)·sin(α2)²) – (h + z_c)²·A m⁴

I_z = r⁴24·(3·α·k – 3·sin(α) – 2·sin(α)·sin(α2)²) m⁴

Polar moment of area

I_x = I_y + I_z m⁴

Radii of gyration

r_y =  I_yA m

r_z =  I_zA m

r_x =  I_xA m