This section is from the book "Notes On Construction In Mild Steel", by Henry Fidler. Also available from Amazon: Notes On Construction In Mild Steel.
We may now lastly observe from experiments Nos. 63 to 74 inclusive the influence of eccentric loading upon the ultimate strength of the column.
Comparing experiments 63 and 64 with 65 and 66, we have two sets of columns, similar in length, cross-section, and details of ends, and differing only in the position of the point of application of the load. In the former (Nos. 63 and 64) the load is applied at the centre of gravity of the unsymmetrical cross-section, with a mean ultimate resistance of 12.13 tons per square inch. In the latter (Nos. 65 and 66) the load is applied at the centre of figure, 1.60 inches out of the centre of gravity, or, say, one-fifth of the width of the column, with a mean ultimate resistance of only 7.74 tons per square inch.
The reduction of strength due to eccentric loading is therefore in this case 36 per cent.
Again, comparing Nos. 73 and 74 with Nos. 71 and 72, we find a mean reduction of 39 per cent., the eccentric loading being about one-sixth of the width of the column from the centre of gravity of the section.
It is noteworthy that a measurable amount of lateral flexure is observed at a much earlier stage in the history of the test in the case of the eccentric load, and the total loads required to cause a given degree of lateral flexure are much less in the eccentric load than in the case of that applied at the centre of gravity, a result which is in consonance with theoretical requirements.
If we endeavour to trace the influence of the form of crosssection upon the ultimate strength as between the H-shaped, the box with plate webs, and the box with lattice webs, it is found that there is little difference between the two latter, the lattice-webbed column being practically as strong as the plate-webbed for all values of l/r. The H-shape appears, however, to fall short of the ultimate resistances of the other sections, more especially as the value of l/r becomes greater. Further evidence is, however, required.
The results of the pin- and flat-ended experiments are plotted in Fig. 128. It is not surprising, from a consideration of the foregoing remarks, that the average results are to be represented rather by an area than by a mean line, the varying elements of resistance in a built-up column being more likely to show considerable variations in strength than solid rectangular plates or bars, or simple rolled sections.
Comparing pin-ended with flat-ended columns, we find, with nearly equal values of l/r, that the pin-ended columns give an ultimate resistance but little less than that of flat ends.
Thus the mean of experiments 31, 32, 37, and 38 is 15.02 tons per square inch, while the mean of Nos. 25, 26, 45, 46, 52, 55, and 56 is 14.88 tons per square inch. It is probable that the size of pins was not without influence in the ultimate resistance of the pin-ended columns, while, on the other hand, the local buckling of the plates in some of the flat-ended specimens probably lowered the resistance of those columns as a whole.
The well-known experiments of Mr. James Christie, M.Am.-Soc.C.E., on wrought-iron and steel struts, are plotted in Figs. 129 to 132, and Figs. 134, 135, but for a complete description of the whole of the details of these valuable series of experiments the student is referred to the original record.1
In Fig. 129 are plotted the results of compression tests on flat- and fixed-ended angles and tees, these forms of struts being of the type-sections shown in Figs. 142 and 147. The angles experimented upon ranged in section from 1" X 1" X ⅛" to 4" X 4" x ⅜", while the lengths of the struts ranged from 515/16" to 15' 5 ⅜ ", giving a proportion of - which varied between 14 and 481.
1 Transactions of the American Society of Civil Engineers, vol. xiii., April, 1884.
The tees, of which the experimental compressive results are plotted in the same figure, varied from 1" X 1" to 4" X 4" in section, and from 6" to 15' O⅝" in length, giving a proportion of - ranging between 14 and 420.
The results of experiments on fixed-ended angles are plotted in the same figure. The fixing of the ends was obtained by means of clamps, and it is probable that the theoretical conditions of a fixed-ended strut were more nearly obtained in this series than in flat-ended struts. It will be observed from the diagram that when l/r exceeds about 150, the fixed-ended struts show generally a greater compressive resistance than the flat-ended.
Fig. 130 gives the results of compression tests upon hinged and round-ended angles and tees, both sections being plotted in the same figure. In this case, in the large majority of instances, the hinged ends consisted of ball and socket bearings, a semi-spherical ball of from 1 inch to 2 inches in diameter bearing upon a semi-spherical socket, the specimens being so arranged that the centres of balls were as nearly as practicable coincident with the centre of gravity of the cross-section.
The influence of the size of the ball (probably due, although lubricated, to frictional resistance in the socket) may be traced in one or two instances in this set of experiments.
For example, a 2½" X 2½" angle, 5 feet 41/16 inches in length, with 2-inch diameter ball, failed at 12.44 tons per square inch, while an angle of the same section and length, with 1-inch diameter ball, failed at 8.18 tons per square inch. Again, an angle 3" x 3" x 7/16", 15 feet 3¾ inches in length, with 2-inch ball, failed at 2.66 tons per square inch, while the same bar with 1-inch ball failed at 1.31 tons per square inch. Another angle, 2" X 2" x 5/16",15 feet 43/16 inches in length, with 2-inch ball, failed at 0 71 ton per square inch, while the same bar with 1-inch ball failed at 0.62 ton per square inch.