Axial Members under Loading

Typical axial members with applied torque, T, include tapered, constant, and abrupt members.

Admissible cross-sections include circular and annular.

In a Nut Shell: Deformation (Angle of twist) for an Axial Member, φ

For an axial member, of constant cross-section, the angle of twist is φ = TL/JG .

Note it depends directly on the torque and length of the member and inversely on

the polar moment of inertia and material. Common units are radians.

Key limitations are that cross-sections remain plane and perpendicular to the centroidal axis

and the stress does not exceed the proportional limit τ = Gγ .

The angle of twist, φ, for tapered, axial members (γ is a function of x and τ = Gγ)

φ = ∫ (T dx/JG) where integration is over the length of the member

Deformations for members with abrupt changes in section and material

δ = Σ T_iL_i / J_i G_i

T_i is the torque in section i, L_i is the length of section i,

J_i is the polar moment of inertia of section i, and G_i is the shearing modulus for section i

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