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### Shaft with One Spline Deflection, Stress Equation and Calculator

Beam Deflection and Stress Equation and Calculators

Torque Applied Deformation and Stress of a Shaft with One Spline Equations and Calculator

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Torque Applied Deformation and Stress of a Shaft with One Spline Section Calculator

K = 2Cr4

Varies with b / r as follows

For:

0   ≤   b / r ≤   0.5

Where 0.2  ≤   a / b   ≤   1.4

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

Shear Stress Maximum

At M:

Where B varies with b / r as follows:

for 0 ≤ b / r ≤ 0.5

for 0.2 ≤ a / b ≤ 1.4

Where:

θ = angle of twist (radians),
T = Twisting or torque moment force-length, (in-lbs, N-mm),
L = Length of Section (in, mm),
h = Length as Indicated (in, mm),
r = radius (in, mm),
a,b = Distance as shown (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.

Related:

The Shaft Design Book (Design Charts and Calculations for Torsional Properties of Non-Circular Shafts)

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