Table A6.3

Formulae for Torsional Deflection and Stress*

Angle of twist per unit length

T = Torque

G = Modulus of rigidity

K = Apparent polar moment of inertia (given in table below)

Solid Section


Max. Shear Stress

Ellipse with major axis = 2a and minor axis = 2b

(at ends of minor axis)

Square of side = a

(at midpoint of each side)

Rectangle of long side = 2a and short side = 2b

(at midpoint of long side)

Equilateral triangle of
side = a

(at midpoint of each side)

* This is Table A6.3 in Chapter A6 of "Analysis and Design of Flight Vehicle Structures", by Bruhn.

A more enxtensive list of formulae for various solid and hollow shapes can be found in "Formulas for Stress and Strain", by Roark, 1954 Ed.