130. Strength of Hemp Ropes.-It is quite common in calculating the strength of ropes and cables to assume that the section of the rope is a solid circle. Of course, the strands of the rope do not completely fill the circle but, if we find by test the allowable safe strength per square inch on this basis, it will be perfectly safe to make calculations for other sizes of ropes on the same basis. The safe working stress based on the full area of the circle is 1420 lb. per square inch. The Nominal Area (as the area of the full circle by which the rope is designated is called) is A =.7854X D2. The safe stress is 1420 lb. per square inch and, consequently, the weight that can be supported by a rope of diameter D is W=SXA =1420X.7854X D2 Here we have two constant numbers (1420 and .7854) that would be used every time we were to calculate the safe strength of a rope. If this were to be done often we would not want to multiply these together every time, so we can combine them now, once and for all. Hence 1420.7854-1120, approximately W=1120X Da Example: Find the safe load on a hemp rope of in. diameter. 131. Wire Ropes and Cables.-For wire ropes made of crucible steel, a safe working load of 15,000 lb. per square inch of nominal area is allowable. For cables of Swedish iron but half this value should be used. 132. Strength of Chains.-It has been demonstrated by repeated tests that a welded joint cannot be safely loaded as heavily as a solid piece of material. Of course, there are often welds that are practically as strong as the stock, but it is not safe to depend on them. For this reason, the safe working load per square inch for chain links is often given as 9000 lb., which is just of 12,000 lb. If D = the diameter of the rod of which the links are made Combining the constant numbers, this can be simplified into W=14,000 × D2 This is used in the same way as the formula for a rope. 133. Columns.-The previous examples were cases of tension. The size of a rod or timber subjected to compression is computed in the same way unless it is long in comparison with its thickness. When a bar under compression has a length greater than ten times its least thickness, it is called a Column and must be considered by the use of complicated formulas which take account of its length. It can be seen by taking a yardstick, or similar piece, that it is much easier to break than a piece of shorter length but otherwise of the same dimensions. A long piece, when compressed, will buckle in the center and break under a light thrust or compression. An example of this can be found in the piston rod on a steam engine, where, on account of the length of the rod, it is necessary to use much lower stresses than those given in the tables. The compressive stress allowed in piston rods varies with the judgment of different designers but is generally about 5000 lb. per square inch, using a pressure on the piston of 125 lb. per square inch. Example: Find the size of rod for a 30 in. by 52 in. Corliss engine with 125 lb. steam pressure. 30 in. is the diameter of the cylinder and 52 in. is the stroke, which is not considered in the problem except in that it has reduced the allowable stress in the rod. .7854×302=706.86 sq. in., area of piston. 706.86X125=88357.5 lb., total pressure on piston. Using 5000 lb. per square inch, allowable stress in the rod. 883585000=17.67 sq. in. sectional area of rod, From the table of areas of circles, it is seen that this is the area of a circle nearly 4 in. in diameter, so we would use a 4 in. rod. PROBLEMS Note. In all examples involving screw threads, to get areas at root of thread, use the table given in this chapter. Give sizes of bolts always as diameters. 219. If the generator frame shown in Fig. 84 weighs 3000 lb., what size steel eyebolt should be used for lifting it, allowing a stress of 10,000 lb. at the root of the thread? 220. What would be the safe load for a in. chain? 221. What size hemp rope would be necessary to lift a load of 4000 lb.? EYEBOLT FIG. 84. 222. What force would be necessary to shear off a bar of machinery steel 2 in. in diameter? 223. A certain manufacturer of jack screws states that a 2 in. screw is capable of raising 28 tons. If the diameter of the screw at the base of the threads is 1.82 in., what is the stress per square inch at the bottom of the threads when carrying 28 tons? 224. A soft steel test bar having a diameter of .8 in. is pulled in two by a load of 31,500 lb. What was the breaking tensile stress per square inch? 125 lbs. per sq. in. 7" FIG. 85. 225. The cylinder head of a small steam engine (Fig. 85) having a cylinder diameter of 7 in. is held on by 6 studs of in. diameter. When there is a steam pressure of 125 lb. per square inch in the cylinder, what will be the pull on each stud? And what will be the stress per square inch in each stud, due to the steam pressure? 226. With a cylinder diameter of 10 in. and an air pressure of 100 lb. per square inch, find the greatest weight that can be safely lifted by the air hoist, shown in Fig. 86. Also find the size of piston rod necessary, assuming that it is screwed into the piston. Notice that this rod is subject only to tension and, therefore, a greater stress is allowable than in steam engine piston rods. 227. Work out a formula for the strength of crucible steel cables on the same plan as that given for hemp rope. 228. What is the greatest load that should be lifted with a pair of tackle blocks having 3 pulleys in the movable block and 2 in the fixed block, and INDEX Addition of decimals, 35 Air compressors, 149 steam and, 159 Allowances for shrink fits, 171 Analyzing practical problems in fractions, 22 Area of a circle, 77 Areas of circles, table of, 101 Arrangement of pulleys, 142 Belting, horse power of, 139 rules for, 141 Belt joints, 143 Belts, grain and flesh sides, 143 speeds of, 141 tension per inch of width, 141 thickness of, 141 width of, 140 Blocks, types of tackle, 123 Bolts, strength of, 175 Bolt table, U. S. S. threads, 176 Cables, strength of wire rope and, 177 Cancellation, 19 Casting, weight of, 83 Centigrade thermometers, 164 Chains, strength of, 177 Circle, area of, 77 circumference of, 51 diameter of, 51 radius of, 51 Circumference of a circle, 51 Circumferences of circles, table of, 101 Circumferential speeds, 54 Classes of levers, 117 Coefficient of linear expansion, 169 Columns, 178 Common denominator, 9 fractions reduced to decimals, 39 Complex decimals, 40 Compound fractions, 21 gear and pulley trains, 68 Contraction, expansion and, 168 |