TABLE 149.-Of the VARIABLENESS in the STRENGTH of MATERIALS in resisting different STRAINS.

TABLE 149.-Of the VARIABLENESS in the STRENGTH of MATERIALS in resisting different STRAINS-continued.

(958.) "Agreement of Rules with Experiment."—There are very great difficulties in preparing a Practical Work on the Strength of Materials, as compared, or rather contrasted, with a purely Theoretical one. Theorists follow fundamental Laws, which are as fixed and inflexible as the laws of gravitation, and the accuracy of their conclusions can be mathematically demonstrated. But when confronted with the results of experiment many of these correct laws are found to lead to manifestly erroneous conclusions, and have to be relinquished in favour of Empirical Rules, for which nothing can be said, except that they are correct as proved by Experiment.

(959.) Many of the Rules in this work are of a more or less Empirical character; in most cases the Theoretical laws were first taken as a basis, but had to be laboriously modified tentatively, by the teachings of experience. In almost all cases,

their correctness is shown at every point by comparison with experiment. It will be interesting, however, to collect a few of the most important of these in the form of a table, which is done in Table 150.

In some cases the agreement of the Rules with Experiment is remarkable, partaking evidently more or less of an accidental character: some of these are given in paragraphs 21, 139, 375, 685, 777, 878, &c.

(960.) "Real and Apparent Factor of Safety."-Essentially, the "Factor of Safety" is, or should be, the Ratio of the Breaking weight to the Safe Load, the latter being 1.0, and its special object is to give a margin of strength to cover unknown and unexpected contingencies. But this simple purpose becomes complicated by the fact that the breaking weight varies with the character of the strain: thus for a Cast-iron beam, it is shown by Table 141, that the breaking weight for constant dead load being 1.0, it is reduced to for an Intermittent dead load, or one acting in one direction only, or off-and-on continuously without shock; and to for a similar Alternating load, or one acting in both directions, up-and-down continuously. Say that the constant dead load = 18 tons Breaking weight: then the Intermittent Breaking weight becomes 18 x = 6 tons, and the Alternating Breaking weight, 18 x 3 tons.

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Now, if we take 3 for the Factor of Safety, and apply it to these three loads, we obtain 6, 2, and 1 ton respectively, as the Safe loads, which are equal to }, }, and of the constant dead load, the Apparent Factor of Safety becoming 3, 9, and 18 for the three cases, while the real Factor is the same in all, namely 3.

Illustrations of the application of these principles to cases in practice are given in (923), &c.: thus with Wrought-iron beams, the Dynamic rolling load is of the equivalent dead constant load, and with Factor 3 becomes 3x1th of that dead load. Similarly, with Cast Iron, the Dynamic rolling load is th of the equivalent dead constant load, and with the same Factor, 3, becomes÷3 th of that dead load: the apparent Factor = 18, although the real Factor is 3, as before. Again, with Timber, the Dynamic rolling load, which with Factor 5

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becomes 5th of the dead constant Breaking weight, the apparent Factor being 20, while the real Factor is 5 only, &c.

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In many cases it is convenient to use the apparent rather than the real Factor of Safety, and this course has been adopted frequently throughout this work: thus for Railway Bridges, the Factor used by most Engineers is 6, which is in fact the apparent Factor: being an intermittent strain with wrought iron, the Real Factor is 6 × 3 = 4. Thus, say we have a Bridge whose calculated breaking weight 600 tons, then with Factor 4, we obtain 600÷ 4 = 150 tons dead Safe load, or 150 × 100 tons intermittent Safe load: evidently we should have obtained the same result more easily by using the apparent Factor 6, which gives 600 ÷ 6 100 tons, as before. (961.) "Strength of Flat Cover to Boiler."-A circular Boiler in America, 48 inches diameter, was provided with a plain, flat cover of cast iron 17 inch thick, and was subjected to a steam pressure of 160 to 170 lbs. per square inch, which it bore for about 6 months and then burst:-breaking at the edge all round. By Rule (367) we obtain Р = 172 × 148390482 or 3.5156 x 148390 2304 227 lbs. per square inch: but applying the correction for thickness of metal as given in (931) and taking the value of z for say 2 inches thick at 74, we obtain 227 × 74 168 lbs. bursting pressure per square inch, or practically the pressure with which the cover actually burst, so that it is surprising that it did not fail before.

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(962.) "Low Resilience of Slate, &c."-Slate and York paving are frequently used for flooring in cases where they are supported at the ends only and act as beams: as there will always be a probability of a blow from the load falling on the floor, and those materials are excessively weak in resisting Impact, that fact should be borne in mind and extra strength provided to guard against failure. Table 67 shows by col. 6, that a Castiron plate of a given thickness, &c., will bear a safe falling load 6.782 = 34 times the safe falling load for a similar plate of Slate; and 6·78·06 113 times!! the safe falling load for York paving.

(963.) "Graphic Ratios of Strength, &c."-Figures give, of course, very precise information as to the Specific Strengths of