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Circular Shaft Opposite Sides flattened Torsional Deformation Stress Equation and Calculator

Beam Deflection and Stress Equation and Calculators

Torsional Deformation and Stress Circular shaft with opposite sides flattened Equations and Calculator.

Torsional Deformation and Stress Circular shaft with opposite sides flattened Equations and Calculator

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Torsional Deformation and Stress Circular shaft with opposite sides flattened Calculator

h = r - w

K = 2Cr4 where C varies with h / r as follows:

For two flat sides 0 ≤ h / r ≤ 0.8

C = .7854 - 0.4053 (h / r) - 3.5810 (h / r)2 + 5.2708 (h / r)3 - 2.0772 (h / r)4

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

Shear Stress

For 0 ≤ h / r ≤ 0.6

B = 0.6366 + 2.5303 (h / r) - 11.157 (h / r)2 + 49.568 (h / r)3 - 85.886 (h / r)4 + 69.849 (h / r)5

τmax = T B / r3

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.


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