It is not difficult to discover from the results of these experiments, and others which will be referred to, the great importance of avoiding structural weakness at the ends of a column which first receive the stress, whether it be a pin-ended, fixed-ended, or a flat-ended connection. The concentration of stress, and what appears to be in some cases of short columns a certain flow of material under extreme loads, may constitute this the weak point in the entire column strength.

In the case now before us the end of the column is strengthened by the addition of three extra eye-plates on each side, forming a total thickness of metal of 3⅜ inches and a total bearing surface for the 3-inch diameter pin of 11.81 square inches. The stress through the eye-plate is transmitted to the body of the column by the rivet's, which have a collective shearing area of 8.4 square inches. But this column (No. 42 in the table) failed by the shearing of these rivets, which did not fill the holes, the longest rivets having the most clearance.

Another source of weakness was found to be the bending of the pin, when the unsupported length was too great, accompanied in some cases by the elongation of the pin-holes.

Riveted columns of the type now under consideration may be stated to consist of a number of component parts, the nature of those components and their liability to individual failure varying with the details of design of the column.

It is conceivable that the ultimate strength of a column will be determined by that of its component parts, and that the full strength of the column as a whole will not be attained when local weakness of the component is present. An example of local weakness at the ends of a column has already been described, and this view is further confirmed by an analysis of the experiments upon the box-shaped columns of the types shown in Fig. 163. Of thirty experiments carried out on this type, nine failed by the buckling of the plates between the rivets, and some instructive details may be gathered upon the important point of the proper pitch of rivets in a riveted column required to ensure the maximum resistance, especially when the column is short. The buckled plate may be considered as a fixed.ended rectangular column, subject to compression in the length of the whole column, the length of this subsidiary or component column being the pitch of the rivets. If, further, this subsidiary column is supposed to be subject to a compressive stress per square inch equal in intensity to that sustained by the whole cross.section, we shall then have the relations expressed in the following table, in which are given the pitch of rivets both crosswise and lengthwise, the thickness of plates, i.e. the least dimension of the column, the ratio of . both of the component and entire columns, and the ultimate strength per square inch, all as derived from the experiments, all the columns excepting the last (No. 38) having failed by buckling the plates between the rivets.

Table No. 34. The Influence Of Rivet Pitch On The Ultimate Strength Of Columns

Number of experiment.

Pitch of rivets in inches.

Mean thickness of plates.

Value of l/r

Ultimate strength.

Tons per square inch.

Nature of end connection.

P.Pin ends. F_flat ends.

Crosswise.

Lengthwise.

Plate between rivets.

Entire column.

25

75

6

0.22

95

49.3

13.98

P

26

7.5

6

0.26

80

49.3

14.15

P

13

8.0

6

0.26

80

46.1

14.16

F

14

8.0

6

0.26

80

46.1

14.98

F

19

10.5

6

0.28

74

471

15.60

F

32

10.25

6

0.31

67

50.8

15.65

F

31

10.25

6

0.32

65

50.9

14.66

F

34

10.25

6

0.33

63

65.5

15.40

F

37

10.25

6

0.44

47

51.1

15.03

F

38

10.25

6

0.49

42

51.1

14.76

F

It will be observed from the above figures that the 6.inch pitch of rivets represented, so far as the buckling of the plates is concerned, a column of greater length in proportion to its least radius of gyration than the column taken as a whole. This preponderance of slenderness is maintained in the first seven experiments, decreasing as the plates thicken; in the next two the proportions of l/r are nearly alike, and it may have been a matter of uncertainty whether the column would fail as a whole by lateral flexure, or by buckling as they did between the rivets. In the last case, however, the thickening of the plate to 0.49 inch has altered the relative proportions of l/r-, and the plate between the rivets is stronger than the column as a whole. Failure takes place, not by buckling of the plate, but by lateral flexure of the whole column, the plates buckling subsequently to the maximum load being attained. The ultimate resistances to buckling may be compared with the results of Hodgkinson's experiments on flat-ended rectangular bars shown in Fig. 126.

The foregoing analysis is subject to the uncertainty which attaches to the influence which the crosswise pitch may have exerted upon the ultimate buckling resistance, but it at least serves to show that the pitch of riveting should not be overlooked in the design of columns, especially those which, by reason of their ratio of l/r, may be expected to give a high ultimate resistance.

In the particular cases cited, it is evident that half an inch was practically the minimum thickness of plate required to prevent buckling with a 6-inch pitch; or, vice versa, that 6 inches was the maximum pitch allowable for -inch plates, when the ratio of length to least radius of gyration for the entire column was about 50 to l.

We may now refer to the results of the experiments of the latticed columns, Nos. 43 to 74 inclusive, of the table on page 190, of which the types are shown in Figs. 150, 151. We obtain from this series some light on the important and difficult subject of the minimum section required for the lattice members of columns of this type and dimension ; the evidence is, it must be admitted, only of a limited and negative character, but is valuable as far as it goes.

These lattice bars formed a single triangulated system, arranged at an angle of about 60 degrees, and secured to the flanges of the channel irons by one ⅝-inch or -inch rivet, the breadth of the bars being 2 inches and 2 inches respectively, and the thickness ⅜ inch. In the absence of any statement in the record of tests to the contrary, we may assume that bars of these scantlings were sufficient to develop the full strength of columns of the lengths and dimensions shown in the table.

The percentage of weight of material used to resist what may be termed the secondary stresses in a column, to counteract local flexure, to provide sufficient bearing area at the ends, or in other ways to meet local weakness, in comparison with the total net theoretic weight of the section subject to direct compression, must always claim attention in a preliminary estimate of the weight of any column or strut, and will vary in accordance with the special conditions of each case. It is obvious that the reduction to a minimum of the scantlings of such a system of latticing as that just referred to is desirable on economical grounds, although the practical conditions of riveted connections and the thickness judged necessary for resisting corrosion will limit the extent to which such reduction can be carried.