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### Torsional Deformation Stress Hollow Elliptical Section Equation and Calculator

**Beam Deflection and Stress Equation and Calculators**

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 b^{2} ( 1 - q^{4} ) ] 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/in^{2}, N/mm^{2})

G = Modulus of rigidity force / area (lbs/in^{2}, N/mm^{2})

K = Polar Moment of Inertia (in^{4}, mm^{4}) for section

Reference:

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