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In a Nut Shell:
Shear Stress in an Torsion Member
The shear stress.
τ, in a torsion member (under the assumptions that each circular
cross-section
remains plane,
perpendicular to its axis, and for elastic response, τ = G γ ) is given by the
expression
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τ
= T ρ / J |
τmax =
T c / J
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where T is the torque acting on the member at
the location where the shear stress is to be
calculated, ρ is
the radial distance from the centroidal axis to
the “fiber” where the
shear stress is
calculated, J is the polar moment of
inertia of the entire cross-section, and
c
is the radius of the
cross-section. The shear stress is
zero on the axis of the member and
maximum at the outer fiber (outer radius, c) and
varies linearly for elastic response.
Click here for notes on
calculating the polar moment of inertia, J.
Common units for shear
stress are psi, ksi, MPa, N/mm2 (English/Metric)
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