137. Angle of Torsion.— If a shaft of diameter D and length I' ij
subjected throughout its entire length to a twisting moment T, one en
will rotate in advance of the other by an angle 6 given by the fonnula-^

where C is the modulus of transverse elasticity of the material of tn
shaft. The above formula gives the angle of torsion in circular measui^
If n is the number of degrees in the angle of torsion, then —

180x32TL .Qo/;i TL
"= 30416^017^ = '''■'' CD^-



I



SHAFTING AND SHAFT COUPLINGS.
99



The value of C may be taken at from 9,000,000 to 10,500,000 for
wrought-iron, and at 11,000,000 for steel.
Mr. D. K. Clark gives as the working hmit of the angle of torsion one
degree for a length equal to twenty diameters. Applying this to the
formula above, we get the following relations —

CDS = 11672-2 T



T =



CDS



11672-2



^-y-



1672-2 T



If in the formula n = 583-61



TL
CD4



C



we substitute the value T from the



equation T =



3-1416



Dy already given, we get the formula w = 114*59



/L



and if we make L = 20 D and substitute the ordinary values of / which
are generally taken in calculating the diameter of a shaft, we find that
the angle of twist is about double that given by Mr. Clark as the working
limit of twist.
For a hollow shaft having an external diameter D^ and an internal
diameter Dg the angle of torsion is —

TL • . ,

in circular measure ;



(9=10-186



w = 583-61



C (D{ - D|)
TL



in degrees.
