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### Cross Shaft Torsional Deflection, Stress Equation and Calculator

**Beam Deflection and Stress Equation and Calculators**

Torsional Deformation and Stress of a Cross Shaft Equations and Calculator

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Torque Applied Deformation and Stress of a Cross Shaft Section Calculator

K = 2Cs^{4}

Varies with s / r as follows

For:

0 ≤ r / s ≤ 0.9

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

Shear Stress Maximum

At M Location:

Where B_{M} varies with r / s as follows:

for 0.1 ≤ r / s ≤ 0.5

At N Location:

Where B_{N} varies with r / s as follows:

for 0.3≤ r / s ≤ 0.9

Note: B_{N} > B_{M} for r / s > 0.32

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, s = Dimension as Indicated (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.

Related:

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