Instead of writing "safe stress in pounds per square inch" for tension, compression, or shear, the symbols St, Se, and S, are used. So if A = area in square inches, then the load W which can be carried safely Area X safe stress per square inch or = A X St = W (tension) AX S. W (compression) = A X S = W (shear) Or, in general, for all stresses In designing a part of a is to carry is known. AX machine, however, the load that the part The question is to determine its size. Having decided on the safe stress that the material will stand, we see at once that the load divided by the safe stress per square inch will give the area in square inches required to carry the load, or, Knowing the area, it is a simple problem to calculate the diameter, or the dimensions of the piece. 126. Strength of Bolts.-There is a well-known saying that "a chain is only as strong as its weakest link." This means, in general, that any mechanism must be so designed that its weakest part will be strong enough to stand the greatest load that may come on it. In the design of a bolt it is quite clear that the weakest section of the bolt is at the root of the threads where the cross-sectional area is the least. The area at the root of the threads, therefore, must not be less than the area required to support the load safely, as found by the formula, A = W The bolt used should have an area, at the root of the threads, nearest to but not less than the required area. Example: What size of steel eyebolt will support a weight of 5000 lb.? Take 12,000 lb. as the safe load in tension. The necessary area to support the weight, therefore, is .416 sq. in. Of course, the example could be completed by saying .7854 D2 = = .416 sq. in., where D diameter at the root of the thread. By then solving for D we would get the diameter at the root of the threads. But the Bolt Tables afford an easier method than this. In the following table .4193 is given as the area of a -in. bolt at the root of the thread. Therefore, a 3-in. eyebolt would probably be used. In figuring the allowable loads for steel bolts, it is best not to allow over 12,000 lb. stress per square inch, and 10,000 lb. is perhaps even more usual on account of the sharp root of the threads, which makes a bolt liable to develop cracks at this point. 127. 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 = .7854 X 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 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. Find the safe load on a hemp rope of in. diameter. D = 1 and D2 = 1 × = 1 4 128. 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. 129. Strength of Chains. It has been demonstrated by repeated tests that a welded joint cannot be safely loaded so heavily as a solid piece of material. Of course, there are welds that are practically as strong as the stock, but it is not safe to depend upon 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 A 2 X .7854 X D2 = Combining the constant numbers, this can be simplified into 130. 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 10 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. PROBLEMS 205. A small hoist is so designed that the maximum load will cause a pull of about 1750 lb. in the hoisting rope. What diameter hemp rope should be used? 206. What would be the safe load for a 3-in. chain? 207. The boiler of Fig. 92 is suspended from the steel beams by four rods, each rod being threaded at the top and secured by a nut. When the boiler is completely set up and operating, the total weight supported by the rods will be about 15,000 lb. Determine the diameter of the rods, allowing a safe tensile stress of 12,000 lb. per square inch. 208. A manufacturer of jackscrews states that a 24-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 compressive stress per square inch in the screw when carrying 28 tons? 209. 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? 210. The cylinder head of a small steam engine, Fig. 93, having a cylinder diameter of 7 in. is held on by six studs of 2-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? 211. With a cylinder diameter of 10 in. and an air pressure of 100 lb. per square inch, find the greatest weight that can be lifted by the air hoist shown in Fig. 94. Also find the size of piston rod necessary, assuming that it is screwed into the piston. 212. Work out a formula for the strength of crucible steel cables on the same plan as that given for hemp rope. |