Carrying Capacity and Deflection of Helical Springs of Round Steel,-(Continued). d = 5%" | d = 9/16" | d = 1⁄2" | d = 7/16" | d=" d = 5/16" D 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 W W W 2.00 2.25 2.50 2.75 3.00 3.25 .1029.1297.1606.1963.2367 .0858 .1081.1338.1635.1972 3.50 3.75 4.00 4.50 5.00 644 596 544 486 432 .0617 .0772.0960.1423.2016 .0529 .0661.0823.1220.1728 .0441 .0551.0686.1017.1440 D 2.00 2.25 2.50 2.75 .0030 .0048 .0071 .0101 .0139 .0185 .0240 .0305.0381.0569.0810 2.50 W❘ 2163 D W 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 5.00 5.50 1916 1720 1560 1427 1315 1220 1137 1065 945 849 .0056 .0081 .0112 .0151 .0197 .0252 .0316 .0390.0474.0679.0935 .0048 .0070 .0096 .0129 .0169 .0216 .0040 .0058 .0080 .0108 .0141 .0180 2.50 2.75 3.00 3.25 3.50 3.75 .0271 .0334.0406.0582.0801 .0225 .0278.0339.0485.0668 4.00 4.25 4.50 5.00 5.50 1701 1587 1484 1315 1180 .0196 .0243.0297.0427.0591 .0168 .0208.0254.0366.0506 .0140 .0173.0212.0305.0422 d = 1" d = " d = 3⁄44" W D 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.50 6.00 4418 3976 3615 3313 3058 2840 2651 2485 2339 2093 1893 .0028 .0038 .0051 .0066 .0084 .0105 .0129 .0157.0189 .0264.0356 .0024 0033 .0044 .0057 .0072 .0090 .0111 .0135 .0162.0226.0305 .0020 .0027 .0036 .0047 .0060 .0075 .0093 .0113.0135 .0188.0254 The formulæ for deflection or compression given by Clark, Hartneli, and Begtrup, although very different in form, show a substantial agreement when reduced to the same form. Let d = diameter of wire in inches, D1 = mean diameter of coil, n the number of coils, w the applied weight in pounds, and C a coefficient, then The coefficient Creduced from Hartnell's formula is 8 x 180,000 1,440,000; according to Clark, 164 × 22 = 1,441,792, and according to Begtrup (using 12,000,000 for the torsional modulus of elasticity) = 12,000,000 ÷ 8 = 1,500,000. 12,566nfr2 Rankine's formula for greatest safe extension, v1 = may take cd if we use 30,000 and 12,000,000 as the values for f the form v1 = .7854n D, 2 and c respectively. The several formulæ for safe load given above may be thus compared, letting d = diameter of wire, and D mean diameter of coil, Rankine, .3927 Sd3 ; Begtrup, W= ; Hartnell, D1 Substituting for ƒ the value 30,000 given by Rankine, and for .196fd3 W = ; Clark, W = ↑ 12000₫3 3(d × 16)9 W 73 S, 60,000 as given by Begtrup, we have W = : 11,760 Rankine; 12,238 Taking from the Pennsylvania Railroad specifications the capacity when closed of the following springs, in which d= diameter of wire, D diameter outside of coil. D1 = Dd, c capacity, H height when free, and h height when closed, all in inches. and substituting the values of c in the formula c = W = xD1 we find x, the ds D1 coefficient of to be respectively 32,000; 38,000; 32,400; 24,888; 34,560; 42,140, average 34,000. d3 D1 Taking 12,000 as the coefficient of according to Rankine and Clark for safe load, and 24,000 as the coefficient according to Begtrup and Hartnell, we have for the safe load on these springs, as we take one or the other coefficient, J. W. Cloud (Trans. A. S. M. E., v. 173) gives the following: deflection of spring under load. Mr. Cloud takes S 80,000 and G = 12,600,000. The stress in a helical spring is almost wholly one of torsion. For method of deriving the formulæ for springs from torsional formula see Mr. Cloud's paper, above quoted. ELLIPTICAL SPRINGS, SIZES, AND PROOF TESTS. Pennsylvania Railroad Specifications, 1896. | | | | | | | | | 20 || 20 20 20 | | | | | | | 2010 | 2. p.t. (a) ins. (a) Between bands; (b) over all; a.p.t., auxiliary plates touching. PHOSPHOR-BRONZE SPRINGS. Wilfred Lewis (Engineers' Club, Philadelphia, 1887) made some tests with phosphor-bronze wire, .12 in. diaineter, coiled in the form of a spiral spring, 14 in. diameter from ceutre to centre, making 52 coils. Such a spring of steel, according to the practice of the P. R. R., might be used for 40 lbs. A load of 30 lbs. gradually applied gave a permanent set. With a load of 21 lbs. in 30 hours the spring engthened from 205 inches to 21% inches, and in 200 hours to 2114 inches. It was concluded that 21 lbs. was too great for durability. For a given load the extension of the bronze spring was just double the extension of a similar steel spring, that is, for the same extension the steel spring is twice as strong. SPRINGS TO RESIST TORSIONAL FORCE. Flat spiral or helical spring... P = S bh2 f = R = 12 PIR Round helical spring ........ P = 32 R π Ed1 32 P R21 TG d 3PR2l b2+h2 ; f = Rd = 16 R S 3R √b2 + h2 G 6343 P force applied at end of radius or lever-arm R; & = = angular motion at end of radius R; S = permissible maximum stress, = 4/5 of permissible stress in flexure; E = modulus of elasticity in tension; G = torsional modu lus, = 2/5 E; 1 = developed length of spiral, or length of bar; d = diameter of wire; b = breadth of flat bar; h = thickness. HELICAL SPRINGS-SIZES AND CAPACITIES. *The subscript 1 means the outside coil of a concentric group or cluster; 2 and 3 are inner coils. 8 814 RIVETED JOINTS. Fairbairn's Experiments. (From Report of Committee on The earliest published experiments on riveted joints are contained in the memoir by Sir W. Fairbairn in the Transactions of the Royal Society. Making certain empirical allowances, he adopted the following ratios as expressing the relative strength of riveted joints: These well-known ratios are quoted in most treatises on riveting, and are still sometimes referred to as having a considerable authority. It is singular, however, that Sir W. Fairbairn does not appear to have been aware that the proportion of metal punched out in the line of fracture ought to be different in properly designed double and single riveted joints. These celebrated ratios would therefore appear to rest on a very unsatisfactory analysis of the experiments on which they were based. Loss of Strength in Punched Plates.-A report by Mr. W. Parker and Mr. John, made in 1878 to Lloyd's Committee, on the effect of punching and drilling, showed that thin steel plates lost comparatively little from punching, but that in thick plates the loss was very considerable. The following table gives the results for plates punched and not annealed or reamed: The effect of increasing the size of the hole in the die-block is shown in the following table: The plates were from 0.675 to 0.712 inch thick. When %-in. punched holes were reamed out to 1% in. diameter, the loss of tenacity disappeared, and the plates carried as high a stress as drilled plates. Annealing also restores to punched plates their original tenacity. Strength of Perforated Plates. (P. D. Bennett, Eng'g, Feb. 12, 1886, p. 155.) Tests were made to determine the relative effect produced upon tensile strength of a flat bar of iron or steel: 1. By a 34-inch hole drilled to the required size; 2. by a hole punched inch smaller and then drilled to the size of the first hole; and, 3, by a hole punched in the bar to the size of the drilled bar. The relative results in strength per square inch of original area were as follows: In tests 2 and 4 the holes were filled with rivets driven by hydraulic pressure. The increase of strength per square inch caused by drilling is a phenomenon of similar nature to that of the increased strength of a grooved bar over that of a straight bar of sectional area equal to the smallest section of the grooved bar. Mr. Bennett's tests on an iron bar 0.84 in. diameter, 10 in. |