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Torsional Deformation Stress Hollow Elliptical Section Equation and Calculator

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Torsional Deformation and Stress Hollow Elliptical Section Equations and Calculator. Hollow elliptical section, outer and inner boundaries similar ellipses

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Torsional Deformation and Stress Eccentric Hollow Elliptical Section Calculator

Where:

q = a_o / a = b_o / b

Wall thickness is not constant

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

Shear Stress

τ_max = 2 T / [ π a b² ( 1 - q⁴ ) ] at end of monor axis on outer surface

Where:

θ = angle of twist (radians)
α = degrees
T = Twisting or torque moment force-length, (in-lbs, N-mm)
L = Length (in, mm)
a, b = Diameter (in, mm)
τ = Unit shear stress force / area (lbs/in², N/mm²)
G = Modulus of rigidity force / area (lbs/in², N/mm²)
K = Polar Moment of Inertia (in⁴, mm⁴) for section

Reference:
Roarks Formulas for Stress and Strain, 7th Edition, Table 10.1 Formulas for torsional deformation and stress.