to the steam pressure alone. As a simple instance take the case of a long double-ended boiler, a steam-space stay placed too close to the shell plate (fig. 150). The stay's duty is to support the surrounding flat plate; but, on account of the longitudinal contraction of the shell, the stay will be in compression and actually assist the steam pressure in forcing out the plate, thereby seriously increasing the load on the adjoining stays, and increasing the bending stresses in the flange.

Screwed Stays near Flanges. The reverse action is met with at the edges of the combustion-chamber backs. Evidently there is a pull in one direction at the flange, which is balanced by the pull on the stay (see fig. 151). This load Q, is proportional to the mean of the

4

Q1

FIG. 151

pitches 12 and 1,, and if the latter dimension is the maximum which practice has shown to be safe, then the distance x, measured from the centre of the flange, is found by the formula

where a is the width of the water-space between the two combustion chambers.

The following list contains most of the experiments that have been made on flat plates:

W. Fairbairn, 1856, pp. 194 and 197. -in. copper and g-in. iron plates, 5-in. and 4-in. pitches.

R. H. Thurston, 'Franklin Inst.,' 1872, iii. vol. lxiii. p. 93. 1-in. iron plate, 83-in. and 9-in. pitch.

L. E. Fletcher, Rep. M. S. U. A.,' Oct. 1876, p. 31. Admiralty experiments on Thunderer' boiler.

W. Boyd, M. E.,' 1878, p. 223.

pitch.

-in. iron,-in. steel plates, 9-in.

C. Bach and R. Wilson (see p. 178). Unstayed plates.

D. Greig and Max Eryth, M. E.,' 1879, p. 272, 8-in. and-in. plates, 4-in. pitch,

W. S. Hutton, p. 180.

Board of Trade experiments on mild steel, 'Parl. Rep.,' 1881 (c. 2897), 1885 (c. 4572).

German Admiralty, Danzig, 1884-92.

Of these experiments the last two are undoubtedly the most important, and as the reports contain the necessary drawings, they might be used for a more thorough analysis of the subject than has yet been attempted, but a short summary is all that can be given here. In the Board of Trade experiments the pressures are noted when the first permanent set took place (p1). Also the pressure (p2) at which the scale fell off near the stays; this would correspond with an elongation or compression of the outside of the plate of about 5 per cent. pressure (p3) was noted when cracking noises were heard, and the total bulging and the permanent set at these pressures are also noted.

Board of Trade Experiments on Stayed Flat Steel Plates

The

From these experiments it would appear as if the diameter of the

stay were of more importance than the thickness of the plate, pointing to the same conclusion as the more theoretical investigations that the maximum stresses are to be found near the stay holes. In these experiments the stays were comparatively short, and their elastic elongations or contractions were too short to be measured, so that no data are available as to the load on each stay.

In the German Admiralty experiments the stays were about 6 feet long between the inside nuts; they had plus threads and were turned over their full lengths. As they were strained beyond their elastic limits their elongations were no accurate indication of the pull on each, but after the maximum pressure had been removed, elastic contraction took place, which amounted to about in., and this could be measured with great accuracy, permitting of the load on each stay being calculated. The stays were iron and the modulus of elasticity has been assumed to be 20,000 kilo. = 28,800,000 pounds. The estimated loads have been divided by the test pressures which produced them, and the square roots of areas thus found are given in the last columns of the following tables, p. 190. While carrying out these calculations it was found that the different stays were often very unequally loaded. The most probable explanation being, that on account of the lengths of the stays the end plates acquired very appreciable deformations, and as soon as the elastic limit had been passed it is probable that sometimes one stay would stretch, then another, etc., while at the same time the surrounding plate might give way either elastically or plastically. Naturally, one stay might be more heavily loaded than its neighbour, while at the next highest pressure it might be more lightly loaded. As an example, the test I b was carefully investigated. In this case the two plates were stayed by 12 stays pitched 11.8 ins. apart. The distance from the outer stays to the circumferential guard ring of the flange was 8 ins. The test pressures at which readings were taken were 30, 40, 50, 60, and 65 kilos. per square millimetre, i.e. about one atmosphere each (427, 569, 711, 853, 925, pounds per square inch). The areas supported by each stay at each of these pressures are given below, the groups of figures corresponding with the positions of the stays. The square of 118 is 139-4, and if each stay had borne its due load these figures would all have been 139.4 square inches.

It will be seen that at the low pressures the stays carry more than their apportioned load, while as the pressure increases the circumferential support of the plate seems to relieve the stays; but even then each of the centre stays supports on an average 163 square inches, whereas their proper share is only 139 square inches. The important point to be noted is the change of distribution with each increment of pressure. Thus No. 1 stay starts by supporting 114 square inches, and at the fourth test supports 148 square inches; while No. 4 stay starts by supporting 202 square inches, and at the fourth test only supports 75 square inches. For fuller details the original papers must be consulted, but as each one of the 14 experiments has resulted in the record of between 500 and 700 gaugings, an analysis should not be undertaken lightly. The more important results are contained in the following table. The elongation of every stay, as well as the deformations of the front plate, F, and the back plate, B, between the stays were carefully gauged. The manhole was situated in the back plate, and frequently leaked, as did the various seams. The cylindrical shell was 52 ins. internal diameter and 2 in. thick. It was not considered safe to subject it to a higher pressure than 80 atmospheres (1,137 lbs. per square inch). This was the limit for experiments III a and IV b. Both end plates were bolted to the cylinder flanges by means of 52 turned bolts 1 in. diameter. The pitch line was 58 ins. diameter. There was also a guard ring for each plate. The stays had double nuts at each end, with small washers at the back end, while at the front end there were sometimes small washers, sometimes riveted ones.

0

Ida

Curved Beams. An originally curved beam behaves very much in the same way as a straight one, except that the stresses are not distributed so uniformly. Let the line OP (fig. 152) be the neutral fibre, which does not alter its length while being bent. For any short length p. da the elongation of the fibres above or below this line is proportional to their distances from it. But not so the strains, for, as the outer fibres are longer than the inner ones, so will the strains, and consequently also the stresses, be proportionately greater the nearer they are to the centre of curvature. Let po and p be the radii of curvature of the neutral fibre before and after bending, and let r be the distance of any

--

FIG. 152

fibre from this line; then, if E is the modulus of elasticity, it is easily shown that the stress is

Then, on carrying out the necessary algebraical operations, n (figs. 153 and 154), the distance of the neutral fibre from the concave side of the rectangular beam, is found.