SIMPLE STRAINS AND STRESSES 85 
neglecting the couplings, find the percentage saving of weight by the substitu- 
a tion, assuming She the steel is 2 per cent. heavier than the wrought-iron. 
G 10. A steel shaft 24 inches diameter, which is subjected to pure twisting, is 
_ 60 feet long, and is driven at one end, while the power is taken off at the other. 
One end of the shaft moves 30° in advance of the other, Find (1) the maximum 
_ shear stress, (2) the torque, and (3) the horse-power transmitted at 180 revolu- 
per minute. C=13,000,000 lbs. per square inch, 
11. A wrought-iron shaft 3 inches diameter and 40 feet long is subjected to 
pure twisting by couples at its ends. The maximum shear stress is 9000 lbs. 
ao inch, and the speed is 120 revolutions per minute. Determine the 
. power transmitted, and the angle of twist in degrees, C=10,500,000 lbs. 
square inch. 
12. Find the diameter of a steel shaft which will transmit 15 horse-power at 
180 revolutions per minute with an angle of twist amounting to 1° in a length 
_ equal to twenty times the diameter. Find also the maximum shear stress. 
_ ©=13,000,000 Ibs. per square inch. 
13. Determine the diameter of a solid shaft which shall have the same stiff- 
ness, under the same twisting moment, as a hollow shaft of the same material 
whose external and internal diameters are 9 inches and 6 inches respectively. 
Find also the ratio of the maximum shear stresses in the two shafts. 
14. A steel shaft 24 inches in diameter is driven by a 20 horse-power gas- 
engine at 100 revolutions per minute. The shaft is supported by three bearings, 
spaced 15 feet apart between centres, and the centre of the driving pulley is 
6 inches beyond the centre of one of the end bearings. Pulleys are arranged, 
as shown on the sketch (Fig. 105), to work certain machines, and the horse- 
" 45H.P. E 12 HP. 
18 Diameter—>F) _10 Diameter. anP acs 24 Diameter —>F 
' Ag ' B ] Cc 
ey a Tae toes 
__ Spat ps gota | es 
Fia. 105. 
pe taken off each of these pulleys is shown on the sketch; in addition, each 
ng absorbs 4 horse-power. Assuming that all the loads are applied at the 
centres of the respective pulleys and bearings, calculate the angle of twist in 
the shaft at each of these points, reckoning from either end of the shaft. The 
modulus of rigidity is 12,500,090 lbs. per square inch. [B.E.] 
15.—T wo closely coiled spiral springs were made out of round steel wire 
Z inch diameter. The one spring, A, had a mean diameter of coil of 4 inches, 
_ and the other, B, had a mean diameter of coil of 5 inches, both springs had 12 
__- complete coils. These two springs were tested by loads extending them axially, 
___ and the results of the tests are shown in the table below :— 
WwW 2 4 6 8 10 12 14 16 18 20 
x, 0:26 | 0°52 | 0°79 | 1:06 | 1:32 | 1°59 | 1°86 | 2°12 2°39 | 2°66 
® | O51 | 1°02) 1°53 | 2°04 | 255) 3:06 | 3:57 | 4°09 | 4:60 | 5°12 
Where W is the axial load in pounds, and a, and zg are the extensions in 
inches of the springs A and B respectively. 
Plot the results on squared paper. 
Given that the law connecting the extension of these springs with their mean 
diameter of coil is of the form 
Extension of B_ (nee diameter of coil of B\" 
Extension of A \mean diameter of coil of i) 
what is the probable value of n? 
' ine from these experiments the average value of the modulus of shear 
elasticity C for this quality of steel wire. [B.E.] 
16. A closely coiled helical spring is made out of round steel wire } inch in 
diameter, the coils having a mean diameter of 3 inches. What axial pull will 
produce a shear’ stress of 20,000 Ibs. per square inch? If the modulus of 
7 
