SIMPLE STRAINS AND STRESSES 83 
— . 
__ d=diameter of solid shaft or internal diameter of hollow shaft in 
ae inches. 
__ D=external diameter of hollow shaft in inches. 
_ f=maximum shear stress on shaft in Ibs. per square inch. 
C= modulus of rigidity of shaft in lbs. per square inch. 
@=angle of twist of shaft in circular measure. 
n=angle of twist of shaft in degrees. 
For both Solid and Hollow Shafts— 
as 2rTN p — 12 x 33000H 
12 x 33000" 2rN j 
For Solid Shafts— 
i kok 
_2fl_ 3277 1360/1 _ 360 x 1677 
Cd wCdt" aCd mCdi * 
For Hollow Shafts— — 
_ © (Dt-d' _ 16TD 
“te 764 D Me fe (D# — dd)" 
gam. 3mm 1, 360ft_ 360 x 167 
CD rC(Dt—di)’ OD 7C(Di— di)’ 
98. Helical Springs.—It has already been shown that if a shaft or 
_ wire of diameter d and length / be subjected to a torque T, the angle 
of twist is ee Also, if f is the maximum shear stress, T=7,0%, 
ee afl 
a 6= ~~ 
and Ca 
_____ Now suppose the wire to be bent round so that its axis forms a semi-_ 
circle of radius R, and let two radial arms AB and CD be connected to the 
Fig. 104. 
~ free ends of the wire, as shown in Fig. 103. If forces PP be applied to 
__ the inner ends of these arms, the forces acting through the centre of the | 
