Geometrical Properties of Elliptical Pipe

Dimensions

a =   m, b =   m

t =   m

a₁ = a – t m

b₁ = b – t m

Area

A = π·(a·b – a₁·b₁) m²

Centroid

y_c = a m, z_c = b m

Perimeter (approx.)

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

Second moments of area

I_y = π4·(a·b³ – a₁·b₁³) m⁴

I_z = π4·(b·a³ – b₁·a₁³) m⁴

Polar moment of area

I_x = I_y + I_z m⁴

Torsional constant

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I_t = π·a³·b³a² + b²·(1 – k⁴) m⁴

Torsional section modulus

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Radii of gyration

r_y =  I_yA m

r_z =  I_zA m

r_x =  I_xA m