Bending strains due to the weights, degree of tension, and the directions of line wires, plus those resulting from wind-pressure, are the chief causes that lead to the mechanical failure of insulator pins. Considering the unbalanced component of these forces at right angles to the axis of the pin, which alone produce bending, each pin may be considered as a beam of circular cross section secured at one end and loaded at the other. For this purpose the secured end of the beam is to be taken as the point where the pin enters its cross-arm, and the loaded end of the beam is the point where the line wire is attached to the insulator. The distance between these two points is the length of the beam. The maximum strain in the outside fibres of a pin measured in pounds per square inch of its cross section, represented by S, may be found from the formula, S = P X .0982 D3 where P is the pull of the wire in pounds, D is the diameter of the pin at any point, and X is the distance in inches of that point from the wire. Inspection of this formula shows that S, the maximum strain at any point in the fibres of a pin, when the pull of the line-wire, P, is constant, increases directly with the distance, X, from the wire to the point where the strain, S, takes place. This strain, S, with a constant pull of the line wire, decreases as the cube of the diameter, D, at the point on the pin where S occurs increases. That cross section of a pin just at the top of its hole in the cross-arm is thus subject to the greatest strain, if the pin is of uniform diameter, because this cross section is more distant from the line wire than any other that is exposed to the bending strain. For this reason it is not necessary to give a pin a uniform diameter above its cross-arm, and in practice it is always tapered toward its top. Notwithstanding this taper, the weakest point in pins as usually made is just at the top of the cross-arm, and it is at this cross section where pins usually break. This break comes just below the shoulder that is D3 = P .0982 S X. Where the pin is tapered so that S is constant for all cross sections, then for any pull, P, of the line wire on the pin the quantity (P.0982 S) must be constant at every diameter, D, distant any number of inches, X, from the point where the wire is attached. If the constant, (P.0982 S) is found for any one cross section of a pin, therefore, the diameter at each other cross section with the same maximum stress, S, may be readily found by substituting the value of this constant in the formula. The so-called “standard” wooden pin that has been very generally used for ordinary distribution lines, and to some extent even on high-voltage transmission lines, has a diameter of nearly 1.5 inches just below the shoulder. The distance of the line wire above this shoulder varies between about 4.5 and 6 inches, according to the type of insulator used, and to whether the wire is tied at the side or top of the insulator. If the line wire is tied to the insulator 5 inches above the shoulder of one of the standard pins, then X becomes 5, and D becomes 1.5 in the formula last given. From that formula by transposition and substitution P.0982 S = D3X = (1.5)35 = 0.675. Substituting 0.675 for the quantity P0.0982 S in the formula D3 = P0.0982 S X gives the formula D3 = 0.675 X, from which the diameters at all cross sections of a tapered pin above its shoulder, that will
A pin twenty-one inches long between the line wire and the cross-arm will have a uniform strength to resist the pull of the wire if it has the diameter given in this table at the corresponding distances below the line wire. From this it follows that a pin of any length between wire and cross-arm corresponding to X in the table will be equally strong to resist a pull of the line wire as a standard 1.5-inch diameter pin with its wire five inches above the cross-arm. In other words, if a pin that is twenty-one inches long between the line wire and the cross-arm
In order rightly to appreciate the utility of this table of proposed standard pins, it is necessary to have in mind the fact that all the dimensions are based on the assumption that a wooden pin with a shank of one and one-half inches diameter, and with its line wire attached five inches above the cross-arm, is strong enough for general use on transmission lines. Such an assumption covers a wide range of practice, but its truth may well be doubted for many cases. That this assumption Thus, on the sixty-five-mile line between CaÑon Ferry and Butte, Mont., each conductor is of copper and has a cross section of 106,500 cm., while on the older line between Niagara Falls and Buffalo each copper conductor has a cross section of 350,000 cm. Evidently with equal conditions as to length of span, amount of sag, and sharpness of angles on these two lines, pins ample in strength for the smaller wire might be much too weak for the larger wire. A little consideration will show that it is neither rational nor desirable to adopt pins of uniform strength for all transmission lines, but that several degrees of strength are necessary to correspond with the range in sizes of conductors in regular use. The size of pins for use on any transmission line, when the maximum bending strain exerted by the conductors has been determined, should be found by calculation and experiment, or by experiment alone. According to Trautwine, the average compressive strength of yellow locust is 9,800 pounds, of hickory 8,000 pounds, and of white oak 7,000 pounds per square inch in the direction of the grain. These compressive strengths are less than the tensile strengths of the same woods, and should therefore be employed in calculation, since the fibres on one side of a bending pin are compressed while the fibres on the other side are elongated. Substituting 1,000 for the value of S in the formula, S = P X.0982 D3, and also 5 for the value of X, and 11/2 for the value of D, the resulting value of P is found to be 736.5 pounds. This result shows that with a locust pin of 11/2 inches diameter at the shank, and with its line wire attached five inches above the shoulder, the unbalanced side pull of the wire that will break the pin by bending is 736 pounds, provided that the wood of the pin has a strength of 1,000 pounds per square inch in compression. As all of the The calculation just made takes no account of the fact that the actual diameter of the shank of each pin just below the shoulder is 1/32 inch less than the nominal diameter, but this of course reduces the strength somewhat. Trautwine states that the figures above given for the compressive strengths of wood are only averages and are subject to much variation. Of course no pin should be knowingly loaded in regular practice to the breaking point, and to provide against variations in the strength of wood, and for unexpected strains, a liberal factor of safety, say four, should be adopted in fixing the maximum strains on insulator pins. Applying this factor to the calculations just made, it appears that the maximum pull of the line wire at the top of any one of the above proposed standard pins should not exceed 736 ÷ 4 = 184 pounds in regular work. A little calculation will readily show that the side pull of some of the larger conductors now in use on transmission lines will greatly exceed 184 pounds under conditions, as to sag, angles and wind pressure, that are frequently met in practice. On page 448, Vol. xx., A. I. E. E., some tests are reported on six locust wood pins with shank diameters of 17/16 to 11/2 inches. Each of these pins was tested by inserting its shank in a hole of 11/2 inches diameter in a block of hard wood, and then applying a strain at about right angles to the pin and about 41/2 inches from the block by means of a Seller’s machine. The pull on each pin was applied gradually, and in most of the pins the fibres of the wood began to part when the side pull reached 700 to 750 pounds, though the maximum loads sustained were about ten per cent above these figures. The average calculated value of S, the compressive strength of the wood in these pins, was 11,130 pounds per square inch on the basis of the loads at which the fibres of the wood began to break, and 13,623 pounds per square inch for the loads at which the pins gave way. On pages 650 to 653 of the volume last cited, results are reported of tests on twenty-two pins of eucalyptus wood, which is generally used for this purpose in California. Twelve of these pins were of a size much used in California on lines where the voltage is not above 30,000. Each of the twelve pins was 67/8 inches long in the stem, 45/8 inches long in the shank, 11/2 inches in diameter at the shank, 2 inches in diameter at the square shoulder where the shank joins the stem, and 13/8 inches in diameter at the top of the thread. The For a single pin, the lowest breaking strain was 705 pounds, the largest 1,360 pounds, and the average for the twelve pins was 1,085 pounds. Unfortunately, the exact distance of the cable from the cross-arm is not stated, but as the cable was wound about the side groove of the insulator it was probably either in line with or a little below the top of the pin. It seems probable also that the diameter of these pins at the shoulder—that is, two inches—may have increased the breaking strain somewhat by giving the shoulder a good bearing on the cross-arm. The ten other pins were of the size in use on the 60,000-volt line between Colgate power-house and Oakland, Cal. Each of these pins had a length of 53/8 inches and a maximum diameter of 21/8 inches in the shank, and a length of 103/8 inches in the stem, with a diameter of 21/2 inches at the shoulder. This shoulder was not square, but its surface formed an angle of forty-five degrees with the axis of the pin, and this bevel shoulder took up 1/4 inch of the length just given for the stem of the pin. At 21/2 inches from its threaded end the stem of the pin had a diameter of 115/16 inches, and the diameter slopes to 13/8 inches at two inches from the end. The two inches of length at the top of the stem has the uniform diameter of 13/8 inches, and is threaded with four threads per inch for the insulator. Each of these ten pins was tested, as already described, until it broke, but the break in this case started as a split at the lower end of the threaded portion and ran down the stem to the shoulder in a line nearly parallel with the axis of the pin. The pull on the cable at right angles to the axis of each pin had a maximum value of 1,475 pounds in one case, and a corresponding value of 3,190 pounds in another, while the average breaking strain for the ten pins was 2,310 pounds. Unfortunately, the report of this test above named does not distinctly state just how far the testing cable was attached above the shank of each of these large pins; but it seems probable that the same insulator was used with the larger as with the smaller pins, and if this was so the testing cable was attached near the end of each pin, as this cable was wound about the side groove of the insulator used on the smaller pins. With the types of insulator |