Related Resources: calculators

Circular Section Deformation and Stress Torsional Deformation Stress Equation and Calculator

Beam Deflection and Stress Equation and Calculators

Torsional Deformation and Stress Circular Section Equations and Calculator.

ALL calculators require a Premium Membership

Preview

Torsional Deformation and Stress Solid Circular Sector Calculator

K = Cr⁴ where C varies with α / π as follows:

For 0 ≤ α / π ≤ 2.0

C = 0.0034 - 0.0697 (α / π) + 0.5825 (α / π)² - 0.2950 (α / π)³ + 0.0874 (α / π)⁴ - 0.0111 (α / π)⁵

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

Shear Stress

For 0 ≤ α / π ≤ 1.0

B = 0.0117 - 0.2137 (α / π) + 2.2475 (α / π)² - 4.6709 (α / π)³ + 5.1764 (α / π)⁴ - 2.2000 (α / π)⁵

τ_max = T / B r³ on a radial boundary

Where:

θ = angle of twist (radians)
α = degrees
T = Twisting or torque moment force-length, (in-lbs, N-mm)
L = Length (in, mm)
r = Radius (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.