Mechanics of Materials: Torsion
Vital Cocolot José Artemio
Torsional Deformation
In the field
of solid mechanics, torsion is the twisting of an
object due to an applied torque.
Torsion is expressed in either the Pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m)
or foot-pound force (ft·lbf). In sections perpendicular to
the torque axis, the resultant shear stress in this
section is perpendicular to the radius.
In non-circular cross-sections, twisting
is accompanied by a distortion called warping, in which transverse sections do
not remain plane. For shafts of uniform cross-section unrestrained against
warping, the torsion is:
where:
T: is the applied torque or moment of torsion in Nm.
t: (tau) is the maximum shear stress at the outer surface
JT : is the torsion constant for the section.
r: is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface).
ℓ: is the length of the object to or over which the torque is being applied.
φ:(phi) is the angle of twist in radians.
G: is the shear modulus.
Fig.1 Torque applied to a steel bar. |
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Fig.2 The angle lets us determine the shear strain at any point along the cross section. |
Bibliographic
[1] |
Douglas P. Holmes, «Mechanics of Materials: Torsion,» [En
línea]. Available: https://www.bu.edu/moss/mechanics-of-materials-torsion/.
[Último acceso: 15 Agosto 2021]. |
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