This heat of combustion is then utilized as much as possible to heat the water in the boiler and thus generate steam. Finally, the steam is conducted to an engine and there performs its work.

In such a process but very little of the heat generated in the firebox is turned into work at the engine, because of the large amount that is lost. Some of it goes up the chimney, some escapes into the boiler room, a considerable amount of it is lost at the engine by radiation and by condensation in the cylinder, and a very large amount is carried away by the exhaust steam.

The average coal burned under boilers, when burned as completely as possible, will generate about 12,500 B.t.u.'s per pound of coal. However, in the average power plant, for each pound of coal fired, only about 7500 B.t.u.'s are absorbed by the boiler, and only about 600 B.t.u.'s are transformed into work at the engine flywheel. We see from this that for every 12,500 B.t.u.'s supplied to the power plant, only about 600 B.t.u.'s are delivered as work. The average over-all efficiency of a power plant is, therefore, about

Considering the boiler (including furnace) and engine separately, it is plain that the average boiler delivers to the engine about 7500 B.t.u.'s (in the steam) for each 12,500 B.t.u.'s supplied to the boiler, and the average engine delivers up as work about 600 B.t.u.'s of the 7500 B.t.u.'s supplied to it. Their respective efficiencies then are as follows:

Boiler efficiencies over 80 have been obtained, but 50% is more common, and it is probable that there are many cases where boiler efficiencies are still lower. Steam engine efficiencies greater than 20% have also been obtained.

PROBLEMS

197. In testing direct-current generators, it is customary to specify that under full load the temperature of the armature shall not rise more than 40° C. above a room temperature of 25° C.; that is, the

temperature of the armature under these conditions should not exceed 65° C. In making a test a Fahrenheit thermometer was used. The room was at a temperature of 77° F. and the temperature of the armature at the end of the run was 180° F. Did the generator meet the specifications? What was the temperature change in Centigrade degrees?

198. The steel rails to be laid in a railroad track are each 30 ft. in length. If the maximum temperature variation from summer to winter is 140° F., what allowance in inches must be made for the expansion in each rail?

199. If we wished to maintain a tempering bath at a temperature of 500° F., what should be the reading on a Centigrade pyrometer?

200. In erecting a long steam line that will have a variation in temperature of 320° F., how far apart should the expansion joints be placed if each joint can take care of a movement of 3 in.?

201. If a brass bushing measures 2 in. just after boring, when its temperature is 95° F., what will it measure when it has cooled to 65° F.? 202. A steel link 2 ft. long is made in. too short for the slot in the flywheel rim into which it is to be shrunk. How hot must the link be before it will go into the slot if its temperature before heating is 65° F.?

203. A horizontal steam turbine and dynamo are to be direct-connected, their shaft centers being 31⁄2 ft. above the bedplate. If the bearings are lined up at a temperature of 70° F., how much will they be out of alignment under running conditions when the temperature of the dynamo frame is 80° F. and that of the turbine is 215° F., both frames being of cast iron?

204. A steam power plant during a period of 1 mo. burned an average of 2 lb. of coal per developed horsepower-hour. If 1 hp.-hr. is equivalent to 2550 B.t.u., what was the overall efficiency of the plant, assuming the coal had an average heating value of 12,000 B.t.u. per pound.

CHAPTER XVIII

STRENGTH OF MATERIALS

122. Stress. When a load or force is applied to any piece of material it tends to alter the shape of the piece. This can easily be demonstrated with an ordinary piece of rubber. A pull will stretch the rubber, making it longer and thinner, and a pressure will squeeze it into a shorter and thicker piece. Other materials, such as wood, iron, etc., change in shape under a load, the same as rubber, but the change is so slight, in most cases, as to be invisible to the naked eye.

If a 1-in. manila rope is used to suspend a load of 800 lb., the stretch in the rope produced by the load will be an appreciable amount, and in all probability the rope will be very near the breaking point. At any point in the rope each fiber will be stretched taut, indicating that the tendency of the load is to tear the fibers apart. The fibers themselves resist being stretched and torn apart, and this resisting force in the rope itself, counteracting the pull of the load, is called "stress." Thus we see that the load on the rope sets up a stress in every fiber.

In the same manner a load or force applied to any piece of material sets up an internal resistance, or stress, in the piece itself which opposes the tendency of the load to alter its shape or rupture the piece entirely. In the above case, if we could cut the-in. rope at any point and attach the cut ends to a spring scale, the scale would read 800 lb., showing that the load tends to pull the rope apart at any section with a force of 800 lb. It follows, then, that the total internal resistance or stress exerted by the fibers to keep them from pulling apart must equal the load, or 800 lb.

There are three different kinds of stresses that can be produced, depending upon how the load is applied.

1. Tensile stress (pulling stress).

2. Compressive stress (crushing stress).
3. Shearing stress (cutting stress).

Figure 91 shows how these different stresses are produced. There are two other kinds of stresses, but they are really special cases of the three just given. They are:

(a) Bending stress (really a combination of tension on one side and compression on the other).

(b) Torsional or twisting stress (a form of shearing stress). 123. Unit Stress.-"Unit stress" is the stress on a unit area; for example, if the cross-sectional area of a bar is 10 sq. in.

FIG. 91. Simple illustrations of tension, compression, and shear. and the total stress on this section is 700 lb., the unit stress will be 700 divided by 10, or 70 lb. per square inch. It is apparent, then, that the total stress equals the unit stress times the area of the section, and, therefore, that the load equals the unit stress times the area. Letting S stand for unit stress, W for load, and A for area, we get

The foregoing statements apply only to the simple stresses (1, 2, and 3 of Art. 122), that is, to such cases of simple, direct stress as are illustrated in Fig. 91. In Fig. 91 suppose that the post under compression is a square timber 10 in. on a side, and the load W is 16,000 lb. The cross-sectional area is then 10 X 100 sq. in. and the unit stress will be,

10

=

124. Ultimate Strength.-By taking specimens of different materials and loading them until they break it has been possible to find out just what stress each kind of material will stand. The unit stress to which a material must be subjected in order to break it is called the ultimate strength of the material. The strength of most materials differs for the different methods of loading as shown in Fig. 91.

The unit stress at which a material will break under tension is called the "tensile strength," or the ultimate strength in tension. The unit stress at which a material will break in compression is called the "compressive strength," or the ultimate strength in compression.

The unit stress at which a material will break in shear is called the "shearing strength," or the ultimate strength in shear. The following table gives the average values for the most used materials.

ULTIMATE STRENGTHS (POUNDS PER SQUARE INCH)

125. Safe Working Stresses.-The unit stress which exists in a member while under load is usually referred to as the "working stress." When parts for machines, structures, bridges, etc. are being designed, the customary procedure is to determine first what unit stress the material for any particular part can stand with safety. This is called the "safe working stress" or "safe stress," and its determination is largely a matter of judgment and experience. The "safe working stress" is generally found by dividing the ultimate strength by some number called a "factor of safety." A factor of safety of 5 is one that is used quite commonly for parts subjected to steady loads.

The following table gives the average range of safe working stresses for some of the most used materials. From the table we note that for cast iron the safe stress in tension is 3000–4000, which means between 3000 and 4000 lb. per square inch.