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Torque Applied Deformation and Stress of a T-Section Calculator

For b ≥ d

K = K₁ + K₂ + αD⁴

Where:

t = b if b < d,
t = d if d < b,
t₁ = b if b > d,
t₁ = d if d > b

for b < 2(d + r)

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

Shear Stress Maximum

A = a b + d c + (r - πr²/4)

Where:

θ = angle of twist (radians),
α = degrees,
T = Twisting or torque moment force-length, (in-lbs, N-mm),
L = Length of Section (in, mm),
a, b, c, d = Length as Indicated (in, mm),
D = Diameter (in, mm),
r = radius (in, mm),
A = area of section (in², mm²)
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.