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_ the part A is round and of diameter d, the part B is square 
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SIMPLE STRAINS AND STRESSES 79 
bar is 6 inches wide and } inch thick. Determine the lowest efficiency of this 
joint, and describe how it will give way. 
18. A tie-bar 5 inches wide and 4 inch thick has a lap joint in it, as shown in 
Fig. 97. The rivets at A and B have a diameter d, and those at C and D have a 
diameter d,. Find the best values of d and d, (to the nearest sixteenth of an 
inch) so that the efficiencies may be as nearly as possible equal to one another. 
Give the efficiencies. ' 
14. Taking the joint referred to in the preceding exercise, but making all 
the rivets of the same diameter, plot on squared paper the various efficiencies of 
the joint for different sizes of rivets up to 1} inches diameter. 
15. Determine the best diameter of rivets (to the nearest ,’, inch) for a tie- 
bar butt joint with double cover straps, and 12 rivets in all, arranged as in Fig. 
87, p. 75. Width of bar, 9 inches; thickness, § inch. f;=O°8f;. Resistance 
of rivets in double shear=1-75 times their resistance in single shear. Find the 
lowest efliciency of the joint. 
16. A cylindrical boiler shell is 7 feet in diameter, and the plates are # inch 
thick. The longitudinal riveted joints have a tearing efficiency of 70 per cent, 
Find the steam pressure which will cause a tensile stress of 5 tons per square 
inch in the plates between the rivets. Also, what tensile stress will this steam 
pressure produce in the plates between the rivets of the circumferential joints 
which havé a tearing efficiency of 60 per cent. ? 
17. The end plates of a boiler shell are ,% inch thick, and are dished to 
a radius of 6 feet. Find the tensile stress in these plates due to a steam 
ure of 150 lbs. per square inch. If the thickness is altered from 4%; inch to 
i inch, to what radius must the end plates be curved so that the stress shall be 
unaltered under the same steam pressure ? 
18. Find the centrifugal tension (in Ibs. per square inch) in the rim of a 
cast-iron fly-wheel 25 feet in diameter when running at 250 revolutions per 
minute. Weight of cast-iron=0°26 lb. per cubic inch. 
19. Determine the speed, in revolutions per minute, of a cast-iron fly-wheel 
20 feet in diameter when the centrifugal tension in the rim 
is 4250 lbs. per square inch. Weight of 1 cubic inch of cast- 
iron =0°26 Ib. ; 
20. Fig. 98 shows the lower end of a foundation bolt ; 
in cross section, s being the side of thesquare. ‘The effective 
width of the cotter C is 6, and its thickness ¢. Taking 
fi=8, fs=6, and f-=15, all in tons per square inch, express 
the dimensions s, b, and ¢ in terms of d. 
21. Referring to the bolt of the preceding exercise, if 
c=16ft, f-=0°8f, fi=5 tons per square inch, and P= 10 tons. 
ind the dimensions d, s, b, and ¢ in inches, Fia. 98 
22. net to the joint shown in Fig. 92, p. 77, if SRY 
Sc= 15, Lak and f,= 6, all in tons per square inch, determine d), b, ¢, D, and D; in 
terms of d. 
94. Simple Torsion.—If two equal and opposite parallel forces P 
and Q act at opposite ends of a straight lever (Fig. 99) which is fixed 
to a shaft S, and which lies in a 
plane at right angles to the axis 
of the shaft, then, the forces P 
and Q cannot be balanced by any 
single force, i.e. they have no 
single force for their resultant, 
from which it follows that the 
forces P and Q will only tend to 
rotate the shaft about its axis. 
If the lines of action of P and Q be at perpendicular distances a and b 
respectively from the axis of the shaft, then the turning moment, twisting 
Fig. 99. 
_ moment, or torque will be measured by Pa+Qb=T. But since P=Q, 
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