152 APPLIED MECHANICS 
Taking the maximum stress at 10,000 lbs. per square inch, find the diameter of 
the shaft. 
9. The external diameter of a hollow shaft is 15 inches, and the internal 
diameter is 10 inches. The shaft is subjected to a bending moment equal to 
the twisting moment, and the maximum stress is 10,500 lbs. per square inch, 
Find the horse-power transmitted at 85 revolutions per minute. 
10. A shaft 5 inches diameter is subjected to a thrust of 15 tons along its 
axis. There isa bending moment on the shaft equal to half the twisting moment. 
The maximum compressive stress is 13,000 lbs. per square inch. Find the horse- 
power transmitted at 120 revolutions per minute. 
11. Referring to Figs. 197 and 198, page 146. If the forces P and Q are 
each 9000 lbs., and the angles PBF 
and QDH are each 60°, what must 
be the diameters of the crank pin B F Ss 
and the shaft at C if the maximum - 
stress is 9000 Ibs. per square inch ? wl 
12. The centre lines of the crank 
shaft of a single-cylinder engine are | 
shown in Fig. 209. When the crank <aeT bE 
and connecting-rod are at right 
angles, the effective force on the rod 
is 80 tons. . The work is entirely 
taken off at the right-hand end, and Fria. 209. 
the bearings may be assumed to $6 
exercise no restraint on the shaft, Calculate the bending moment and twisting 
moment on the crank pin, and find the maximum direct stress induced, the pin 
being 12 inches Q a ; 
internal and 21 Cc Q 
inches external 
diameter, [U.L.] 
13. Thecranked 
shaft (Fig. 210) 
turns in bearings 
at Aand B. The Pp 
cranks C and D 
are in the same 
plane, and the forces P and Q act at right angles to that plane. P= 2000 lbs., 
and Q=2400 Ibs. Find the equivalent twisting moments in inch-lbs. on the 
shaft at A and on the crank pin at C. 
; 14. Same as the preceding exercise, except that the crank C and the force Q 
are turned through a right angle, as shown in Fig. 211. 
15. A three-throw cranked shaft used for working a set of three deep well 
pumps is shown in Fig. 212. The rods are so long that the forces on the crank 
pins may be as- 
sumed as acting 
vertically. The 
shaft turns in 
bearings at A 
and EK, and it 
is driven by 
pure _ twisting 
at the end A. 
The cranks 
make angles of Fria. 212. 
120° with one 
another. Allowing for bending and twisting, determine the diameters (in 
inches) of the three crank pins for the given loads when the shaft is in the 
given position (a) by the Rankine formula, and (b) by the Guest formula. 
Maximum tensile stress, 9000 lbs. per square inch. 
16. A wooden beam, 3 inches deep and 2 inches wide, when tested, gave way 
by shearing along the neutral surface when the load at the centre of the span 
reached 2760 lbs. What was the intensity of the longitudinal shear stress in the 
plane of fracture, assuming that the distribution of stress at fracture is the same 
as within the elastic limit? 
Fia. 210. Fig. 211. 
