It is not therefore surprising, from a consideration of the foregoing, to find that most formulae professing to give the ultimate strength of a column or strut are based upon constants derived from experimental research, although it must be confessed that up to the present time the experimental data available, especially as regards mild steel, do not by any means cover the whole of the ground, or solve all the problems which will present themselves to the designer in the course of his practice.

It is proposed, then, to give in the few pages following a summary in a graphic form of some of the principal experiments on columns of wrought iron and steel - so far as they approximate to the ordinary conditions of practical construction - to be followed by working details of column construction, with explanatory remarks.

In Fig. 126 are plotted the experiments on the compressive resistance of wrought-iron rectangular bars and hollow circular tubes, carried out by Eaton Hodgkinson, and described in the Appendix to the Report of the Commissioners appointed to inquire into the application of iron to railway structures, and carried out in 1846-47.

The rectangular bars varied in length from 3¾ inches to 10 feet, with a sectional area ranging from 1.04 to 5.8 square inches. They were tested in a vertical position, with their ends made perfectly flat and well bedded against two parallel and horizontal crushing surfaces. The proportions of length to least radius of gyration were in several cases extreme, and beyond the range of practice; as, for example, in the case of a bar 10 feet long and half an inch thick. Ratios beyond the value of 400 to 1 are not plotted in the diagram, but the dotted mean curve has been laid down, with the aid of experiments, with a value of beyond that limit. In this diagram, as in those to be further described, all the individual experiments are plotted, and the reader is in a position to judge for himself of the probable accuracy of the dotted mean curve, which has been drawn to represent the average value of the ultimate resistance to compression for various proportions of length to least radius of gyration. In these experiments all the rectangular bars, with the exception of those having a value of l/r, less than 50 to 1 failed by flexure.

Fig. 126.

The circular tubes ranged from 1½ inches to 6|- inches in diameter, and from 2 feet 4 inches to 10 feet in length, the sectional area of the tubes ranging between 0.44 square inch to 2.9 square inches, and the thickness of metal from 1/10 inch to ¼ inch.

Fig. 127 gives the results of a series of tests1 made at Water-town Arsenal on wrought iron rectangular bars, forty-seven in number, nominally 3 inches square (varying from 8.70 to 8'94 square inches in area), and of various lengths from 2 feet 6 inches to 15 feet, centre to centre of pins. The iron of which the bars were manufactured was found to have an average ultimate tensile strength of 22.56 tons per square inch, with an elastic limit in tension of 10.67 tons, an elongation in 20 inches of 21½- per cent., with a contraction of area of 31 per cent.

Chemical analysis gave the following results: carbon, 0.05 ; phosphorus, 0.22; sulphur, 0 048; silicon, 0.084; manganese, 0218.

In those experiments which are plotted in Fig. 127, the bars were in each case provided with l½-inch diameter pins at each end, arranged as shown in the figure.

The bars were tested horizontally, the pins being vertical, while the weight of the longer bars was counter-weighted.

In all cases failure took place through lateral flexure, and in every case but one the plane of flexure was perpendicular to the axis of the pins - that is to say, in the plane in which the ends of the bar were free to move round the pin.

It is to be observed that up to a length of about 24 diameters, or a proportion of length to least radius of gyration of about 83 : 1, the lateral flexure was gradual and without sudden springing, but that beyond this length, after the flexure had attained a certain amount, a sudden increase of deflection occurred, accompanied by a rapid fall in resisting power. This fact is perhaps not without value in the consideration of the proper proportion of length to least dimension, and is an argument in favour of an increased factor of safety in long columns.

1 Report of tests, Watertown Arsenal, 1883.

Fig. 127.

Selecting bars of the same length, and tested under the same conditions, except as regards the nature of the end bearings, we are enabled to make the following comparisons, each result being the mean of two experiments: -

We may also observe the influence of the size of the pin from the following results, each being, as before, the mean of two experiments : -

It will be seen that the pin-ended strut, with 2 ¼-inch pins, gives a result similar to that with one flat end and one pin end, and is not much below the strut with two flat ends, the tendency of increasing the size of the pins being to approximate to the conditions of a flat-ended strut, when the frictional conditions of the pin surface in contact remain the same.

The observed deflections of flat-ended bars 10 feet in length in the above series, when loaded beyond their limit of ultimate resistance, give a curve which closely approximates to that required by theory, being of triple flexure, while the tangent to the curve at the ends is nearly, if not quite, square to the plane of the abutting surface.

Pin-ended bars give indication of an approximation to the same curve, the difference in the form of curve becoming less as the size of the pin increases.