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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 ALL calculators require a Premium Membership

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Torque Applied Deformation and Stress of a Cross Shaft Section Calculator

K = 2Cs4

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 BM varies with r / s as follows:

for 0.1 ≤ r / s ≤ 0.5 At N Location: Where BN varies with r / s as follows:

for 0.3≤ r / s ≤ 0.9 Note: BN > BM 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/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) 