112 APPLIED MECHANICS 
and the lever is symmetrical about vertical and horizontal longitudinal 
sections. 
10. Same as Exercise 8, except that the load is 6000 lbs., and is uniformly 
‘distributed. : 
11. Same as Exercise 9, except that the load is 6000 Ibs., and is uniformly 
distributed. 
12. An overhung steel crank-pin journal has a diameter d and length. The 
total load on the journal is 62,500 Ibs. uniformly distributed. The pressure on the 
journal is to be 600 lbs. per square inch of projected area (projected area=d/). 
The maximum bending stress is to be 10,000 lbs. per square inch. Find d and J. 
13. Same as Exercise 12, except that there is a hole through the pin having 
a diameter equal to 4d, the axis of the hole coinciding with the axis of the pin. 
14. Acast-iron flanged beam resting on supports 12 feet apart carries a central 
load of 12 tons, and a load of 5 tons uniformly distributed over the whole length. 
The total depth of the beam is 13 inches. The area of the cross section of the 
bottom flange is to be four times the area of that of the top flange, and the stress 
in the bottom flange is to be 2 tons per square inch. Find the area of the top 
flange and the stress in it, assuming that the modulus of the cross section is equal 
to the area of one flange multiplied by the total depth of the beam. 
15. Professor Goodman in his ‘‘ Mechanics Applied to Engineering” gives 
the proportions for cast-iron flanged beams shown in Fig. 152, Show that, for 
this form of section, neglecting the fillets between the 
flanges and the web, the moment of resistance to bending 
is 0°077d*f, where d is the total depth, and f the maximum 
tensile stress in the larger flange. 
16. Determine the horse-power which may be safely 
transmitted by a spur-pinion 12, inches diameter, having 
20 teeth, when running at 200 revolutions per minute. 
Breadth of teeth 2} times the pitch.* 
17. Find the pitch and number of teeth for a spur-wheel 
4 feet in diameter, which when running at 90 revolutions 
per minute transmits 150 horse-power. Breadth of teeth 
3 times the pitch.* Fig. 152. 
18. At what speed, in revolutions per minute, must a 
spur-wheel 3 feet in diameter run when transmitting 80 horse-power. Number 
of teeth 40, breadth of teeth 7 inches.* 
19. A horizontal steel shaft 5 inches in diameter projects 36 inches beyond a 
supporting bearing. At the free end there is a vertical load of P lbs., and at a 
point 9 inches from the free end there is an equal load acting in a horizontal 
direction at right angles to the shaft. If the maximum tensile stress in the shaft 
is 12,000 lbs. per square inch, find the force P. 
20. A ferro-concrete beam, rectangular in section, is 12 inches wide and 
24 inches deep. The reinforcement consists of four steel bars, each # inch in 
diameter, their axes being at a depth of 22 inches below the top or compression 
face of the beam. Taking the modulus of elasticity of the steel as 10 times that 
of the concrete, find the depth of the neutral axis of the section from the top. 
If the beam rests on supports 18 feet apart, what load, in tons, uniformly distri- 
buted, will this beam carry when the maximum compressive stress produced in 
the concrete is 600 lbs. per square inch, and what will then be the tensile stress 
in the steel in lbs. per square inch? . 
21. A concrete beam of rectangular section, 11 inches wide, is to be reinforced 
by steel bars whose axes are to be 20 inches from the compression face of the 
beam. If the modulus of elasticity of the steel is 11 times that of the concrete, 
find the total area of the steel bars, so that when the tensile stress in the steel 
is 11,000 lbs. per square inch, the maximum compressive stress in the concrete 
is 500 lbs. per square inch? Find also the distance of the neutral surface of the 
beam from the compression face. 
* Use the formula P=200np, where P is the driving force at the pitch line in 
re p os pitch of the teeth in inches, and n the breadth of the teeth divided by 
the pitch. 
