- Torsion constant
The torsion constant is a geometrical property of a beam's cross-section which determines the relationship between angle of twist and applied torque.
For a beam of uniform cross-section along its length:
is the angle of twist in radians
T is the applied torque
L is the beam length
J is the torsion constant
G is the modulus of rigidity of the materialFor non-circular cross-sections, there are no exact analytical equations for finding J. Approximate solutions have been found for many shapes.
Examples for specific cross-sectional shapes
Circle
Roark's Formulas for stress & Strain, 6th Edition, Warren C. Young]
r is the radius
This is identical to thepolar moment of inertia and is exact.Hollow concentric circular tube
]
is the outer radius
is the inner radius
This is identical to thepolar moment of inertia and is exact.Square
a is the side lengthRectangle
a is the length of the long side
b is the length of the short side
is found from the following table: [Advanced Strength and Applied Elasticity, Ugural & Fenster, Elsevier, ISBN 0-444-00160-3]
Alternatively the following equation can be used with an error of not greater than 4%:
]Thin walled closed tube of uniform thickness
]
A is the mean of the areas enclosed by the inner and outer boundaries
t is the wall thickness
U is the length of the median boundaryThin walled open tube of uniform thickness
]
t is the wall thickness
U is the length of the median boundaryCircular thin walled open tube of uniform thickness
This is a tube with a slit cut longitudinally through its wall.
]
t is the wall thickness
r is the mean radius
This is derived from the above equation for an arbitrary thin walled open tube of uniform thickness.References
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