Fig. 7, the extensometers being arranged first with the mirror at the lower end and then at the upper end and the mean of these readings taken, so that errors due to bending of the specimen were eliminated, as described above. All the tests were carried out in a uniform manner. Two or more extensometers being set in position, an initial load of 100 pounds was applied to the specimen; the load was increased to its maximum value several times and then brought back to its initial value. The zeros of the extensometers were then set and readings taken at 5000, 10,000, 15,000, and 20,000 pounds respectively in the case of the single-angles and 15,000, 20,000, 25,000, and 30,000 pounds respectively in the case of the doubleangle. The load was then brought back to its initial value and the zeros of the extensometers checked. No sets were allowed to pass in which the extensometers failed to return to their initial readings. All observations were repeated at least once before the extensometers were removed to other positions. The uniformity of the results was remarkable. It was found that the specimen could be taken out of the machine and replaced without the extensometer readings for a given load being appreciably altered. 1 100 The lateral deflections of the specimens were carefully measured by means of telescopes and scales reading to inch. These deflections were allowed for in reducing the results, as will be explained later. The Emery machine was calibrated by levers during the period of the tests and was found to be reading correctly to within I per cent. at all loads. The sequence of tests was as follows: (1) Specimen I.-Single, 3 inches x 3 inches x 14 inch angle with lock angle. Line of pull on end plate in line with back of main angle. (2) Same specimen, with lock angle removed. (3) Specimen II.-Single, 3 inches x 3 inches × 4 inch angle with lock angle. Line of pull on end plate in line with centroid of main section. (4) Same specimen with lock angle removed. (5) Same specimen with line of pull on end plate changed so as to be in line with rivets. VOL. CLXXX, No. 1076-12 (6) Specimen III.-Double, 3 inches x 3 inches x 14 inch angle section, space of 3% inch between angles, with lock angles. Line of pull in line with unconnected legs of main angles. (7) Same specimen with lock angles removed. The stresses corresponding to the extensometer readings are given in Tables I to III, pp. 153-155, the values of E being calculated from the readings and the total load, as will be described later. The curves of stress distribution are shown in Figs. 8 to 21. PART III.-ANALYSIS OF THE EXPERIMENTAL RESULTS. §1. The Planar Distribution of Stress. The theory described in Part I of this paper is based upon the assumption that the distribution of stress over a cross-section normal to the axis of load follows a linear law. That this is true for members of the type considered in this paper has already been shown by the writer.10 It is also evident from the curves shown in Figs. 8 to 21. These represent the actual mean extensometer readings for the various cases, the mean straight line through the experimental points being drawn and continued so as to give the maximum strains, which occur at one or other of the corners of the angles. It will be noticed that in every case the mean straight lines for readings 1 to 5, on being produced to the corner of the angle, agree exactly with those for readings 6 to 10. The deviations of the experimental points from the straight lines are in nearly all cases so small as to be unimportant, especially considering that the specimens were ordinary shop products. Where deviations do occur they are usually regular and apparently denote a slight actual departure from planar distribution. They are most marked at the end sections and are probably due to warping produced by the end constraints. In one case only do they become important,-i.e., at the end of the doubleangle specimen (Figs. 19 and 21). For this section the mean straight lines could not be drawn and the results have not been reduced. These deviations, however, entirely vanish at the central section of the same specimen, and are thus probably due to the great end constraints in this case. 10 Loc. cit. §2. The Method of Analysis. The planar distribution of stress having been established, the equations of Part I may be applied to determine the position of the load axis at each section. The details of this analysis are given in Table IV. The method, being the same for all cases, may be illustrated by a single example. Consider the central section of Specimen I with lock angle at 20,000 pounds load. The distribution of strain is shown in Fig. 8, and the constants for the section are given at the head of Table I. The results of the TABLE I. Stresses Corresponding to the Mean Extensometer Readings for Specimen I. Distance from centroid to back of angle, 0.85 inch. Compression -. Section 24" from end plate 2,380 3.420 5,020 20,000 - 5.960 360 1,450 2,980 5,020 6,180 5.960 5.520 5,310 5,310 440 3,060 6,040 9.810 12,140 11,560 10,980 10.450 10,310 360 4.510 8.940 14.390 17.720 17,000 16,300 15,540 15,280 70 6,250 11,910 18,810 23,280 22,400 21,440 20,580 20,280 5,000 2,470 - 510 (b) Without lock angle. Central sec tion Section 21⁄2" from end plate 5,000 2,030 580 1.380 2,690 4,290 5.750 5,680 5,600 5.530 5.390 870 calculation are given in the first line of Table IV. Lines through the centroid of the section parallel to the legs of the angle being taken as coördinate axes, the point of zero stress in the angle is seen to have coördinates (1.15, -0.85). This is one point on the neutral axis. Another may be found by calculating where the 6-10 line would cut the x-axis if produced. Thus the neutral axis is found to be inclined to the x-axis at an angle of tan - 6.93. This is tana in the notation of Part I. Substituting this value, the coördinates of the point of zero stress and ƒ = o in equations (2) and (3), the coördinates (x, y) of the load axis are found to be (-0.76, 0.37). All the values of (x, y) given in Table IV were calculated in a similar manner. The coördinates (x, y) give the position of the load axis relative to the cross-section considered. This depends, to some extent, upon the lateral deflection TABLE II. Stresses Corresponding to the Mean Extensometer Readings for Specimen II. Distance from centroid to back of angle, 0.85 inch. Stresses in pounds per square inch. Tension +. Compression-. 5,000 Central sec 10,000 tion 15,000 20,000 Section 2" from end plate 2,100 310 1,250 3,040 4.590 6,300 6,230 5.990| 5.990 5.920 3,890 310 2,650 5.920 9,180 12,380 12,300 12,070 12,070 11,980 5.130 150 4,200 8,950 13.610 18,350 18,290 18,120 17,980 17,810 6,850 540 5.760 11,980 18,130 24,200 24,150 23,900 23,810 23,500 5,000 2,340 780 780 2,490 4,050 6,150 6,150 6,300 6,300 6,780 10,000 4.510 -1,400 1,870 5,370 8,480 12,450 12,370 12,510 12,770 13,210 15,000 6,620 1,870 2,960 8,250 12,830 18,750 18,500 18,750 18,990 19,600 20,000 8,560 -2,100 4,440 11,280 17,280 24,900 24,650 24,750 24.970 25,680 5.000 Section 22" 10,000 from end 15,000 plate 20,000 2,250 - 700 5.600 1,320 860 930 2,410 4.040 6,230 6,150 6,230| 6,230 6,230 2,020 5,140 8,100 12,210 12,210 12,380 12,430 12,430 3,270 7,860 12,100 18,220 18,290 18,430 18,600 18,680 4.590 10,500 15,880 23,800 24,100 24,280 24,680 24,820 2,410 - (c) Load axis on gusset plate changed to line of rivets. 780 1,010 2,490 4,360 6,300 6,300 6,300 6,300 6,300 1,400 2,260 5.290 8,640 12,450 12,480 12,480 12,680 12,480 7,160 1,630 3,660 7,860 12,820 18,290 18,420 18,590 18,810 18,810 8,7101,550 5,130 10,670 16,950 23,800 24,250 24.420 24,800 24,980 5,000- 3,190 1,170 620 2,410 4.510 6,460 6,460 6,530 6,530 6,850 10,000 6,230 -2,180 1,480 5,060 9,100 12,900 12,730 12,900 13,130 13,600 15,000 8.950 -2,880, 2,640 7.780 13.520 19,120 19,050 19,210 19,520 20,300 20,000-11,280 -3,500 3,680 10,420 18,280 25,200 25, 120 25,280 25,750 26.420 of the section, so that, in order to find the position of the load axis where the load enters the angle, it is necessary to correct for this deflection. Column (4) of Table IV gives the mean deflections of the centroids of the sections under the different loads measured as described above, and column (5) gives the values of (x, y) referred to the end sections of the specimens taken as being the middle section of the riveted ends. |