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(110.) “Strength of Ropes."— The experiments of Captain Huddart have shown that hand-laid ropes such as are commonly made in small rope-works are not so strong as those made with register and press-block. He also found in the latter greater uniformity of strength among the various sizes: in the handlaid ropes the smaller sizes were proportionately stronger than the larger, ranging from 560 lbs. per circular inch in 3-inch girth, to 421 lbs. in the 8-inch. Those made with the register were nearly uniform in strength, being = 820 lbs. per circular inch in both the 3-inch and 8-inch ropes.

From the deterioration by age and moisture to which ropes are subjected the safe working load should not exceed of the breaking weight for such cases as cranes and pulley-blocks. But where life and limb depend absolutely on the strength of ropes, as in hoists or lifts, &c., and where moreover there is considerable wear-and-tear by constant passing over pulleys, &c., the working load should not exceed {th of the breaking weight.

The proof strain is commonly taken at half the breaking weight, but this seems to be too high in most cases: we have taken it at } in Table 24, which gives the breaking weights by Captain Huddart's experiments, also the proof strain and working load in accordance with varying circumstances.

It is frequently expedient to use two ropes of equivalent strength rather than one large one, and this is commonly done in the teagles or hoists used in the factories of the north of England. Thus, where the weight of cage and load = 30 cwt., we might use by col. 6, one 63-inch, or preferably two 4}-inch

ones, &c.

(111.) Flat Ropes.”—The continual bending of ropes over pulleys is found to be very destructive, especially with small pulleys, and of course ropes of large size suffer the most. For this reason flat ropes are better adapted for such cases; their strength may be found from that of the round ones of which they are composed: thus a flat rope 1} x 6 inches, composed of four round ropes each 1} inch diameter or 4} inches girth, will by col. 6 of Table 24 give a working load 15.3 X 4 = 61 cwt., &c.

(112.) “ Rigidity of Ropes.”—When a rope passes over a

TABLE 24.–Of the STRENGTH and WEIGHT of HEMPEN ROPES.

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2.4 4.9 7.6 11.0 15.0 19:5 24:7 30.5 37.0 44.0 51.5 59.7 69 78 99 122 144 176

39 49 61 70 88 103 119 137 156 198 241 295 351

7 8

77 89 103 117 148 183 221 264

10 11 12

732 886 1054

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pulley, the strain upon it is not only that due to the weight lifted, but also that due to the stiffness or rigidity of the rope itself, and still further to the friction of the pin. Coulomb, Navier, and others have investigated this subject, and the following rule is based on their results :•

·014273 X X X W (113.) w=

D
In which x = ďx 48 for white hempen rope; d

= diameter of rope in inches; D = diameter of pulley in inches measured at the centres of the ropes ; W = the statical weight on the rope in lbs. without motion; and w = the extra weight to overcome the stiffness of the rope and produce motion.

(114.) Thus, let A in Fig. 26 be a pulley 14 inches diameter, with a rope 1 inch diameter having equal weights W, W of 1100 lbs. suspended on each side, the diameter at the centres of the ropes will then be 152 inches. Now, with no rigidity in the rope or friction of axle, the addition of the smallest weight to one side would cause motion, but the rigidity of the rope will require a considerable extra weight to overcome it; in our

case:

{C-0257 + (- 0212 x 48)] x 48) + (-014273 x 48 x 1100)

= 51 lbs. 154 Table 25 has been calculated by the rule (113), col. A by rule A = .014273 x x: and col. B by rule B = [0257 + (0212 x 2)] x x. To use this Table; multiply the number in col. A opposite the given size of rope by the statical strain or weight W; add the number in col. B and divide the sum by the diameter of the pulley in inches, measured at centres of ropes ; the quotient is the extra weight w required to overcome the rigidity and produce motion. Thus for a rope 3 inches girth, or 1 inch diameter, on a 7-inch pulley, or 8 inches centres, and a weight of 1000 lbs., we have from col. A, 6247 x 1000 = 624•7, and from col. B, 41.74, from which we obtain w = (624:7 + 41.74) = 8 83 lbs.: motion would therefore ensue with 1000 lbs, at one side, and 1083 at the other, if there was no friction from the pin.

TABLE 25.-Of CONSTANTS for Loss of PowER by RIGIDITY of

HEMP Ropes.

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(115.) The advantage of large diameters for the pulleys will now be apparent, the loss of effect being inversely proportional to the diameter: thus the extra weight due to rigidity for 4, 8, and 16-inch pulleys to raise 1000 lbs. with a 3-inch rope would be 166, 83, and 41:5 lbs., the strain becoming 1000 + 166 = 1166 ; 1000 + 83 = 1083, and 1000 + 41.5=1041.5 lbs. respectively, irrespective of friction.

(116.) “ Loss by Friction.”—The effect of friction may be illustrated by Fig. 26 : the strain on the pin is in that case 1100 + 1151 = 2251 lbs.; taking friction at th of the weight, , we have 2251 - 6 = 375 lbs. friction at the surface of the pin. Taking 2 inches for the diameter of the pin and 15% for the effective diameter of the pulley, we have 375 x 2 : 15.75 = 48 lbs. at the rope. Thus to raise 1100 lbs. we require a strain of 1100 + 51 + 48 = 1199 lbs.: hence 1100 - 1199 = .918, or say 92 per cent. of the power is utilised, 8 per cent. being lost by friction and rigidity of the rope.

(117.) Strains in Common Sheave-blocks.”—The strains on a rope in common sheave-blocks are very complicated, the effect of rigidity and friction accumulating throughout with every additional pulley. Say that we take the case of a pair of 4 and 3-sheave blocks, Fig. 27, with a rope 3 inches in girth and 7-inch pulleys, or 8-inch centres, having pins 14 inch diameter.

Assuming 800 lbs. on the rope h, the extra strain for rigidity on the pulley r by Table 25 and (113) will be (• 6247 x 800) + 41.74

= 68 lbs., and the tension on the 8 rope g would be 868 lbs. if there were not a further loss by friction of the pin. The weight on the pin of the pulley r = 800 + 868 1668 lbs., the friction, 1668 • 6 = 278 lbs. at the surface of the pin, which is reduced to 278 X 11 - 8 43 lbs. at the rope: the tension on g thus becomes 868 + 43 911 lbs.

Similarly, the extra strain from rigidity on the pulley p, is (-6247 x 911) + 41.74

= 76 lbs., which increases the strain 8 on the rope f to 911 + 76 = 987 lbs.: the weight on the pin becomes 911 + 987 = 1898 lbs.: friction (1898 X 11) (6 x 8) = 48 lbs. at the rope, thus increasing the tension on f to 987 +48 1035 lbs., &c., &c. The strains on all the ropes in Fig. 27 have been thus calculated, and from that figure we may now obtain data for any number of pulleys from 1 to 7.

(118.) Thus with a single pulley r, we have 800 - 911 = .878, or say 88 per cent. of the power utilised, hence 12 per cent. is lost: we should obtain the same result from the pulley k, namely, 1727 - 1960 = .881.

With 1 and 2 sheaves, o, p, r, the weight lifted at W is equal to the sum of the strains on the ropes f, g, h, or 1035 + 911 + 800 2746 lbs. But the mechanical power of the combination being 3 to 1, the tension at e should have raised 1177 x 3 3531 lbs. at W; hence we have 2746 = 3531 78, or 78 per cent. utilised, and 22 per cent. lost.

With 2 and 3 sheaves, m, n, o, p, r, the weight lifted is the sum of the strains on the ropes d, e, f, g, h, or 5260 lbs., but the weight due to the strain of 1518 at c is 1518 x 5 7590 lbs., hence 5260 = 7590 = .69, or 69 per cent. is utilised, and 31 per cent. lost.

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