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Geometrical Properties of Ellipse


ellipse.png

Dimensions

a = m, b = m

Area

A = π·a·b m2

Centroid

yc = b m, zc = a m

Perimeter (approx.)

P = π·(3·(a + b) – √(3·a + b)·(a + 3·b)) m

Second moments of area

Iy = π·a·b3/4 m4

Iz = π·b·a3/4 m4

Polar moment of area

Ix = Iy + Iz m4

Torsional constant

It = π·a3·b3/(a2 + b2) m4

Torsional section modulus

#If

a > b

Wt = π·a·b2/2 m3

#Else

a < b

Wt = π·b·a2/2 m3

#End If

Radii of gyration

ry = √Iy/A m

rz = √Iz/A m

rx = √Ix/A m


Substitute