to be due to the fibres being broken at right angles to their length, whereas in a gradual fracture time is given for the fibres to stretch. The question naturally arises whether the phenomena observed in the Wöhler-Bauschinger tests are due to fatigue or impact, or to both these causes combined. We are certainly not able to assert that the impact of the load did not contribute to some extent in causing the bars to fail with a reduced load. It is known that the sudden application of a load to a beam produces, for an instant only, twice the deflection as the same load applied gradually. The deflections of railway bridges with live loads passing over them are about 20 per cent. greater than with the same load standing on the bridge. The bridge appears to recover from the first effect of the live load as it advances and covers the whole bridge, but the dynamic effect is, however, most probably much greater than 20 per cent., as this only includes the average of the vertical movements, some of which may exceed this amount, while others may be less, while the horizontal vibrations are not included at all. If we apply the Wöhler-Bauschinger results to railway bridges, we may imagine trains to pass over them in rapid succession without appreciable impact or friction, and, if the results are to form the basis of the determination of working-stresses, without a separate allowance for impact, we must assume that the millions of repetitions in these experiments are about equivalent to the effect of impact and the slower repetitions of stresses which occur in railway bridges. The rule which still exists in the regulations of the British Board of Trade for railway bridges is simply to limit the workingstresses in iron to 5 tons per square inch in tension and 4 tons in compression. For steel the limiting stress is 6 tons. No account is taken of the variable range of stress or of impact. The rule obviously gives excessive strength for those parts of a bridge where the range of stress is small, as in plate web boxgirders of 150 feet span, while it would be dangerous if applied to those parts of structures where both the range of stress and the impact are large, as in the longitudinals, floor beams, suspenders, and other members of bridges liable to sudden loading. In America and Europe, and to some extent in England, the practice is to make the working-stress depend upon the range of stress, or upon the impact, or both these causes combined. Thus in the New York Elevated Railroad the flanges of the girders were designed for a stress of 3-6 tons per square inch, the web bracing for 3-4 tons per square inch, and for members subjected to alternating stresses a stress of only 2 tons per square inch was allowed. In the numerous elaborate specifications which have been written by American engineers to govern the design of important railway bridges,1 rules are given for limiting the intensity of the working-stresses in various parts of the structure more or less in accordance with the impact which they are likely to sustain and the results given in Table V. The following table was prepared by Mr. J. A. Macdonald, engineer for bridges, New South Wales, for general office use in connection with the design of highway bridges; it gives the ultimate breaking-strength for various ranges of stress as given by Launhardt's and Weyrauch's formulæ. TABLE VI. STRENGTH OF WROUGHT IRON UNDER VARYING STRESS FOR IRON HAVING Similar tables could be prepared, if thought desirable, for mild steel. The working-stress for cast iron may be taken as follows, if the statical strength is taken as 10 tons per square inch :- 'Mr. Theodore Cooper's specifications, for example. For a dead load, 2.50 tons per square inch. For a live load, 1.20 tons per square inch. For alternating stresses equal in amount, 0·83 tons per square inch. Intermediate cases may be treated in the same way as for wrought iron and steel. Launhardt's and Weyrauch's formulæ may be expressed in a more simple manner thus― Some American engineers use this form of the formula for determining the working-stresses in bridges, including both fatigue and impact; thus for wrought-iron eye-bars Intensity of working stress in pounds per square inch Others allow more for the impact of the live load, and use the following formula : In the new regulations1 issued by the French Government for ensuring the safety of bridges, the following rules are given for determining the admissible stresses in the various members. The maximum allowable stress for wrought iron in tons per square inch is By taking account of the change of sign when the stresses change from tension to compression, the above rules will, according to the new regulations, be applicable to members subject to alternating stresses. 1 Engineering, January 5, 1892. CHAPTER II. STRENGTH AND ELASTICITY OF TIMBER. THE strength and elasticity of timber is largely influenced by a variety of circumstances, such as the climate, kind of soil, whether grown on mountain ridges or on low-lying ground, the time when the tree was felled, the age of the tree, the seasoning, etc. A much greater variation is observed in the results of testing timbers than occurs in the case of iron and steel, and timbers of the same name differ widely in their physical properties. In testing timber it is well known that specimens of large scantling give much lower results than specimens of small scantling, which latter, however useful they may be in showing the relative values of different timbers, are of very little value in furnishing data for application to large-sized scantlings. In testing timber in tension it is very difficult to get trustworthy results with soft woods, and the shoulders of the specimen held in the shackles of the testing-machine must be, according to Professor Lanza, at least five times as long as the length under test in order to prevent shearing along the fibre, even when the stress is applied axially, and then considerable lateral pressure must be applied to the portions held in the shackles. The sectional areas of the pieces tested by Lanza were about one square inch. Tensile tests of timber are of very little practical value, as the timber more frequently fails by transverse, compressive, or shearing stress, as they are less than that required in tension. The author has tested nearly all the varieties of Australian timbers in tension, but these are hard woods, and may be tested by preparing them to a similar form to that generally used for testing round specimens of wrought iron and steel. The average result of testing red pine and per spruce in tension from specimens cut from the circumference and heart of the tree is about 10,000 lbs. per square inch, while most of the Australian timbers exceeded 20,000 lbs. square inch. There is no defined modulus of direct elasticity for timber, the slight stretching which occurs being exceedingly irregular. Compressive Strength and Elasticity. The compressive strength of timber is useful not only in designing timber compression members in a structure, but, according to Professor Bauschinger, in determining the quality of the timber, and the influence of seasoning, of the time of felling, and other circumstances of its growth, as the tests are easily made and the results trustworthy. He recommends that prisms one and a half times the length of the side should be properly cut from the various parts of the tree to give a true average, and then tested at a standard dryness, which he fixes as 15 per cent. of moisture. Professor Lanza1 has tested a large number of American timbers of large scantling in 12-feet and 2-feet lengths, of circular and rectangular sections, with the results that the columns all gave way by direct crushing, the strength of the columns being found, in the proportions experimented upon, by multiplying the sectional area by the crushing strength, the lateral deflections observed being too small to exert any appreciable effect. The averages of these experiments are as follows: Another series of tests made at the Watertown Arsenal, and the averages plotted by Mr. Edward F. Ely, gave the following rules for the breaking-strength of columns of white and yellow pine with flat ends, the load being evenly distributed over the ends: Lanza, "App. Mech.," p. 669. |