and 2 centre-plates in the cellular one give 0637 × 6 = ·3822 also.

Calculating as in (254); the logarithm of 8.1 or 0.908485 x 3.6 = 3.270546, the natural number due to which is 1864-4; then the logarithm of 7.9089 or 0.898117 × 3.6 = 3.233221, the natural number due to which is 1711. The rule in (230), namely F = Mp X (S3-6 — 83.6)÷L2, becomes in our case 498500 × (1864.4 1711) ÷ 102 = 749700 lbs. F.

=

Reducing for incipient wrinkling, the rule in (250) namely Ww = (√t÷ √b) × 80, becomes (√·09555 ÷ √8·1) × 80, or (3092.846) x 80 8.686 tons per square inch, and the area being as before 3·551 square inches, C becomes 8.686 × 2240 × 3.551 = 69090 lbs., and Cw = 51820 lbs. Then the rule in (252), namely Pw Fx C÷(F+3 Cw) becomes 74970069090 (749700+ 51820) 64620 lbs.

=

=

=

Now the cellular pillar of the same external size, length, and area or weight of metal, gave 72280 lbs., or 72280÷64620 1.1185 or 11.85 per cent. in excess of the plain pillar. The advantage of the cellular form is thus shown to be the greatest in the case of short pillars; see (265), which gave 48.3 per cent. (267.) "Steel Pillars."-The only experiments we have, are three by Mr. Hodgkinson, the results of which are given in Table 44, Nos. 28 to 30. Under these circumstances, all we can do is to assume that steel pillars follow the same laws as those of wrought iron in (196), (225), &c.: the values of Mp are given by Table 34, and are based on the experiments. It will be observed that they follow the ratio 1, 2, 3 exactly, which agrees almost precisely with the experimental ratios when correction is made for incipient crushing.

=

=

In Table 44, col. 9 has been calculated by the rule Mp X D3 ̈÷L3 :—thus with No. 30, having both ends flat for D36 we have the logarithm of 87 1.939519 x 3.6 1.782268, the natural number due to which is 6058; then 325500 × ⚫6058 6.25 31550 lbs. F, as in col. 9. (268.) Correcting for incipient crushing, we have the same difficulty as with wrought iron (503) in determining the crushing strength of Steel. From experiments on the transverse

=

strength (507) we found it to be 61.48 tons per square inch:— if we adopt that for steel pillars, only the one with two ends flat in the experiments requires correction for incipient crushing (164), and applying it to that one, we obtain a result too high by 6.7 per cent. For reasons indicated in (504), &c., the crushing strength of malleable metals appears to be less in pillars than in beams :-thus experiments on the transverse strength of wrought iron (520) seem to give C = 24 tons per square inch, but in pillars we found by the experiments (201) that C = 19 tons only. Following the same course with steel, we find the crushing strength in pillars to be 52 tons, or 116,480 lbs. per square inch.

With this value for C, we obtain for our pillar ·87 inch diameter, 872 x 7854 × 116480 = 69240 lbs. for the value of Cp, and 51,930 lbs. for Cp; hence (31550 × 69240) ÷ (31550 +51,930) = 26070 lbs., col. 7, breaking weight, or practically the same as by experiment, which gave 26,059 lbs., col. 6.

(269.) To compare the relative strength of wrought iron and steel pillars we must observe that the ratio will not be constant, but will vary with the length. With long pillars breaking merely by flexure, the ratios are simply those of the respective multipliers in Table 34; thus for pillars with both ends pointed, we obtain 108500 ÷ 95848 = 1·132, or 13.2 per cent. in favour of Steel:-by theory based on the transverse strength and deflection, we obtained 9 per cent. (300). But with very short pillars, where the strength is dominated almost exclusively by the crushing strain, the ratio will be 52 to 19, or nearly 3 to 1 in favour of steel. The ratio will vary between those extremes, dependent on the length of the pillar in proportion to the diameter.

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(270.) The length of steel pillars with which the correction for incipient crushing becomes nil (169) may be found by the rule (203). Thus, for pillars 1 inch diameter, Cp=7854 x 52 40.84 tons, therefore Cp = 10.21 tons, and the rule becomes for those with two pointed ends (48.44 × 136 ÷ 10·21) √ × 26.1 inches long:-for those with one end flat and one pointed (96.88 x 13610.21) × 12 37 inches; and for those with both ends flat (145.3 × 136 10.21) √ × 12

12

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=

=

45 26 inches, &c. But these ratios of length to diameter will vary with the diameter, as shown by (148) and Table 39, which has been calculated by the rule (203).

(271.) "Steel Piston-rods.”—With long rods, or rather where the length is great in proportion to the diameter, the advantage of a steel pillar over a wrought iron one is not very great, as shown by (300). But strength is not the only, nor indeed the principal quality in which steel is superior as a piston-rod :the continued action of passing to-and-fro through the gland, has a tendency to "score" the surface and wear longitudinal furrows in it; in resisting this tendency, the superior hardness of steel gives it a great advantage over wrought iron. For these reasons steel is used almost exclusively for first-class work, and as it is now so much reduced in price, it is probable that its use will become still more general for engines of all classes.

(272.) It is shown in (210) that a piston-rod is subjected alternately to tensile and compressive strains, both of which must be considered in calculating the strength :—also that the area at the screw or key-way is half only of that due to the diameter of the body of the rod. The mean tensile strength of Steel may be taken at 96,000 lbs. per square inch, hence the maximum strain admissible on the body of the rod is 48,000 lbs. per square inch, and the second column of Table 56 has been thus calculated. In any case where we are certain from the shortness of the rod, &c., that its strength will be governed by the tensile strain, we may find the area necessary direct by the rule:

(273.)

Area Wx Mr÷ 48000.

F

In which W = the strain on the rod due to the area of piston, pressure of steam, &c., and My = the "Factor of Safety" (880). For the strength to resist the compressive strain at the upstroke, the rod may be taken as a pillar flat at one end and pointed at the other, namely, flat at the piston, and pointed at the cross-head. Then taking M, from col. 2 of Table 34 at 217,000 lbs., the rule in (197) becomes :—

(274.)

In which F

P

F = 217000 × D3·6 ÷ L3.

the breaking weight by flexure in lbs., L = the maximum length unsupported in feet, or the distance from the

gland of the cylinder to the centre of the cross-head at the top of the stroke, and D = the diameter in inches.

(275.) In many cases the results of this rule require correction for incipient crushing by the rule (164); taking the absolute crushing strain, or C, in Steel at 52 tons or 116,480 lbs. per square inch, we obtain the value of Cp in the third column of Table 56.

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Thus, for a steel rod 3 inches diameter, 7 feet long, taking 3136 at 90.9 from col. 3 of Table 35, the rule (274) becomes 217000 × 90.949 402500 lbs. F, or the breaking weight by flexure. Then Cp being by the third column, 1,121,000 lbs., Cp 840500 lbs., and the rule (164), or Pc =F × Cp ÷ (F +Cp), becomes 402500 x 1121000÷(402500 + 840500) = 363000 lbs., as in Table 56.

(276.) When the strength as a pillar as thus calculated exceeds the tensile strength as given in the second column, the latter governs the case and limits the strength (211). Table 56 has been calculated by a combination of the rules for flexure (274), incipient crushing (164), and tensile strength (272): thus with the 3-inch rod, the lengths 3, 4, 5 feet give strengths all alike, being limited by the tensile strength, or 461,800 lbs., as given by the second column. For the lengths 9 and 10 feet, the breaking weights are those due with flexure simply by the rule in (274), while the strains for the intermediate lengths of 6, 7, and 8 feet have been reduced for incipient crushing by the rule (164), &c.

(277.) Table 49 gives the particulars of steel piston-rods in practice; col. 6 has been calculated by the rules, and col. 7 gives the "Factor of Safety" (880), or the ratio of the breaking to the working strain: it will be observed that it is very variable, which is due to the fact, that the sizes of piston-rods are usually fixed by "rule of thumb." The mean value of the Factor may be taken at 14, and we have thus obtained the sizes given by col. 8, with the help of Table 56:-as in most cases the actual lengths were intermediate between those in the Table, the nearest diameter had to be estimated, and will not be exact, but will usually be sufficiently so for practical purposes.

(278.) "Timber Pillars."- By the experiments of Mr.

TABLE 56.-Of the STRENGTH of STEEL PISTON-RODS to resist TENSILE and COMPRESSIVE STRAINS.

763,400*

603,200 1,464,000|

41 680,960 1,652,000
44 763,400 1,852,000

912,500 2,287,000
51,140,400 2,767,000
1,357,200 3,293,000
61,517,400 3,865,000

7 1,847,300 4,483,000

NOTE. The strains marked * are limited by the tensile strength in col. 2; those marked † are due to flexure simply. The rest have been reduced for incipient crushing by the rule in (164), with the value of Cp given by col. 3.

457,500 386,500
551,300
763,400* 656,600 560,600