the deflections rises more and more rapidly, until with 41.9 cwts. it becomes as much as 5 145 inches, or 13 13 times the normal amount, showing that practically the strength of the bar is broken-down, although the bar may not be actually broken. With Mr = 4000 lbs., Rule (328) gives W = 113 × 4000 ÷ (3 x 112) 40.2 cwts. Breaking-down weight, which agrees with the experimental results in Table 70.

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We may therefore admit for plain bars of Wrought-iron Mr 4000 lbs. for the Breaking-down weight; 2000 ibs. for the "Limit of Elasticity," and 1330 lbs. for the safe Working dead load.

TABLE 70.-Of the MEAN DEFLECTION of 3 BARS of WROUGHT IRON, 14 inch square, 3 feet long between supports, loaded in the centre.

Calculated Breaking-down weight = 402 cwt.: "Limit of Elasticity" 20.1 cwt.

(375.) When wrought iron is rolled into L, I, and L sections, the properties of the material are somewhat changed: it would appear that the maltreatment experienced by being crushed into these forms damages the fibrous texture, as proved by the fact that it breaks shorter or more suddenly than plain rectangular sections. The transverse strength of such iron is also considerably less than that of plain bars, as shown by the experiments in Table 71, which give 3208 lbs. as the mean value of Mr. All these bars were loaded to their ultimate strength; two of

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them were literally broken, and it will be observed that these gave the maximum and minimum values of MT, the former being 3720 and the latter 2750 lbs. ; the mean of the two 3235 lbs., or nearly the mean of the six experiments, which was 3208 lbs. For rolled and I bars, plate-iron girders, and tubular beams, we may take the value of MT 3200 lbs. for the breaking-down weight, 1500 lbs. for the "limit of Elasticity" and Proof Strain, and 1120 lbs. for the safe working dead load.

It is remarkable that taking 3200 lbs. for the Ultimate transverse strength, the Rule (500) or (639) gives 3200 × 18÷ 2240 25.7 tons for the maximum ultimate tensile strain, which happens to be precisely the mean strength of British bar iron by Table 1, &c.

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(376.) "Steel."-The transverse strength of steel, like that of wrought iron, may be determined most satisfactorily by a Diagram, as in Fig. 211, which shows that, up to 1450 lbs., the elasticity is almost perfect. Taking that as the "limit of elasticity," we have 5600 lbs. or 2 tons as the value of MT, with which Rule (328) becomes W

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1.0543 x 5600 ÷ 4.5

1457 lbs., and is indicated by a on the diagram. Then, for the value of M, for the breaking-down load, we have the experiments of Mr. Fairbairn, in Table 107, the mean of which = 6663 lbs., or say 3 tons = 6720 lbs.

We may therefore take, as the value of MT for Steel bars, 6720 lbs. or 3 tons for the breaking-down weight; 5600 lbs. or 2 tons for the "limit of elasticity" or "Proof strain ;" and say 3360 lbs. or 11⁄2 ton for the safe working dead load.

SPECIAL RULES FOR WROUGHT IRON.

(377.) "Wrought-iron and T Beams."-The resistances of wrought iron to tensile and crushing strains, and the corresponding extensions and compressions are nearly equal to one another up to 12 or 13 tons per square inch, as shown by Table 91 and Diagram, Fig. 215. The transverse strength of bars might, therefore, be calculated by the ordinary rules in (323) or (510) but for the fact that the great ductility of the metal causes it to have but little stiffness under compressive strains, so that a thin rib becomes undulated or wrinkled with a strain very much less

than the crushing strength of the metal. Thus, while as the Diagram shows, a plain solid bar will bear about 13 tons per square inch; a thin plate may fail by wrinkling with 5 tons or less. Special rules, therefore, become necessary where a thin plate or rib occurs, as in tubular beams of plate-iron (405) and insections, and this arises, not because of the inherent weakness of wrought iron in resisting crushing, but from its tendency to fail by wrinkling.

Tubular beams of plate-iron are frequently made of large dimensions, and are extensively used for the most important structures. The calculation of their strength on exact principles becomes, therefore, highly necessary; the Wrinkling strain, by which that strength is potentially governed, is considered at large (319) in Chapter IX., and the results are applied to such beams in (406), &c. But for ordinary and I sections, it will suffice to give Empirical rules by which the strength may be calculated with sufficient precision for practical purposes.

(378.) The best rule we can give is to calculate D2 x B from the edge of that part of the section which is subjected to tension, or from the bottom in the case of a beam supported at both ends and loaded in the usual way. This, it will be observed, is just the reverse of the mode of calculating Cast-iron beams (341).

Fig. 87 is the section of a beam (No. 5 in Table 71) which,

with a length of 10 feet between bearings, failed with 14 cwt. in the centre. The flange being uppermost, and under compression, we must calculate from the bottom of the section or from the line N. A.; then D2 x B becomes for the rib 212 × 3 = 1·9; and for the top flange (212 212) × 2 = 2.975. The sum of the two = 1.9+2.975 4.875, hence with 3200 lbs. for the value of MT, the rule (324) becomes 4.875 × 3200 ÷ 10 = 1560 lbs. breaking weight: experiment gave 14 cwt. or 1568 lbs., as in col. 6 of Table 71.

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In the reversed position, or flange downwards, as in Fig. 88, we have still to calculate from the bottom of the section or from the line N. A., and for the bottom flange we have 12 x 20.156; for the vertical web (212 - 12) × 3 = 2·32. The sum of the two 2.476, and we obtain 2.476 × 3200 10792 lbs. breaking weight, or about half the strength in the other position, which we calculated to be 1560 lbs.

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(379.) Table 72 gives the safe or working load for Standard sizes of wrought-iron T beams, the application of which is very simple. Thus, say that we require the central safe load for a bar 4 x 4 x inch thick, with a length of 12 feet; the Table gives 156 cwt. for 1 foot long; hence 156 ÷ 12 = 13 cwt. for 12 feet long. The deflection by the rules (697) for this safe 122 x .0235 load would be d =846 inch for a load spread

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4

equally all over we should have 26 cwt., and ⚫846 × 10÷8 = 1.06 inch deflection, &c.

Again, say that we require a bar to carry 20 cwt. in the centre with a length of 73 feet: this is equal to 20 x 7.5 = 150 cwt. with a length of 1 foot, for which Table 72 gives 31 x 31 x inch, or 4 x 4 x inch. These are the sizes for a dead load; with a moving or rolling load we should require double strength, or say 300 cwt. for 1 foot long, and the bar should then be, say 5 × 5 × 1 inch.

TABLE 72.-Of the TRANSVERSE STRENGTH of WROUGHT BEAMS 1 foot long, flange uppermost.

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(380.) The strength of the bar 4 x 4 × 3 inch in the normal position T is given by Table 72 at 156 cwt.:-in the reversed position, the bottom flange would give 32 x 456; the vertical web (42 – 5.94; the sum of the two = 6.5, and taking the value of Mr for safe load in cwts. (375) at 9·5, we obtain 6.5 x 9.5 62 cwt. breaking weight; hence the ratio of strength in the two positions is 15662 = 2.5 to 1.0, and this may be taken as a general ratio for all the bars in Table 72. The variations in the position of bar, distribution of load, &c., are rather confusing; the following statement gives

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