796 



APPLIED MECHANIC* 



[TENSION. 



condition in some respects, for it lias happened that very 

 few writers have discussed it as a whole. Of those who 

 have discussed portions of it, some may be said to have 

 done so, with too little regard to its practical application ; 

 while others have erred in the opposite direction, giving 

 mere empirical rules without theoretical reasons for 

 tlu-ir vstalilishmont. We shall endeavour to steer a 

 middle course between these extremes, trying to show, as 

 clearly as possible, the reasons for conclusions that have 

 been arrived at, and quoting from the best authorities 

 the results of experiments in a form that may render 

 them conveniently applicable in practice. 



1. TENSION'. We niiiy consider that every body sub- 

 jected to tension consists of numerous fibres laid side by 

 side, and extending over the whole length of the body. 

 Even if the body be not of a fibrous constitution, we 

 may conceive its particles to be arranged in longitudinal 

 rows, each particle being held to the next by some force 

 which we call attraction of cohesion. A row of particles 

 BO held together, exactly corresponds with our notion of 

 a fibre ; and we are therefore warranted in treating all 

 bodies as fibrous while we discuss their strength to resist 

 tension. 



Let us suppose that we have a rope ca- ^^ 

 pable of sustaining a hundredweight, and K 

 no more, without breaking. We should "** "^** 

 call the absolute cohesive strength of that 

 rope one hundredweight, or 112 Ibs. The 

 length of the rope by which the weight is 

 suspended has evidently no influence on 

 its strength ; for if any one part of its 

 length be capable of sustaining the strain, 

 and if it be uniform, every other part will 

 be equally capable of sustaining it. It 

 is true that were it hanging vertically, additions to its 

 length would increase the weight, stretching its upper 

 portion, because each portion of added length becomes 

 an added weight But considering the weight of the 

 rope itself as part of the stretching force, we say that 

 the given rope has an absolute cohesive strength of 

 112 Ibs., whatever be its length. 



Now, if any number of such ropes were suspended in 

 a row (Fig. 54), each might have a hundredweight at- 



tif.lt, 



of ropes, reckoning; each as having the strength of a 

 hundredweight. Whether we deal with ropes, however, 

 of hemp, or rods of wood or of iron, or of any other 

 material, if we know the strength of one such rod, and 

 the number of them sustaining equal weights, we know 

 the total weight sustained by them all ; that is to say, 

 their combined strength. Let us assume, instead of 

 ropes, that we experiment with square bars of iron 

 measuring an inch each way, or having a square inch of 

 sectional area. Whether a number of these bars, such 

 as nine of them, be suspended in a row, of which A 

 (Fig. 55) is the plan, with intervals between them ; or 

 in a close row with no intervals as in B, and forming a 

 bar nine inches wide by one thick ; or in a square, C, 

 measuring three inches each way ; there can be no dif- 

 ference in their combined strength, or in the total weight 

 carried by the whole number of bars, however they m;iy 

 be arranged. 



If, then, we know the weight sustained by a bar or rod 



of any material having a sectional area of one square 



inch, we can estimate the weight that can be sustained 



by any other bar of the same material, by calculating 



Fig. 55. 



n 



f 



tached to it without breaking, and the absolute cohesive 

 strength of all together would be expressed by the num- 

 ber of hundredweight* sustained ; that is, by the number 



the number of square inches in its sectional area, and 

 allowing the known strength for each square inch. For 

 example : let us suppose that we find by experiment the 

 average strength of a bar of wrought-iron, 1 square inch 

 in section, to be 30 tons, or 67,200 Ibs. ; let us ascertain 

 the strength of a bar 10 inches wide and 10 inches thick. 

 Since the sectional area is 10 in. X 10 in., or 100 square 

 inches, the strength is 30 tons X 100 sq. in., or 3,000 

 tons; or 67,200 Ibs. X 100 sq. in., viz., 6,720,000 Ibs. 

 The strength of a round bar 1 inch in diameter would 

 be estimated in the same way ; for as the area of a circle 

 1 inch in diameter is '7854 sq. in. , the strength of the 

 round bar 1 inch in diameter would be 30 tons x 0-7854 

 sq. in., about 23J tons ; or 67, 200 Ibs. X 0'7854 sq. in., 

 about 52,780 Ibs. 



Farther, as the areas of circles are in proportion to 

 the squares of their respective diameters, the strength 

 of a round bar of iron of any diameter is 23J tons, or 

 52, 780 Ibs., multiplied by the square of the diameter in 

 inches. Thus, a round bar of 10 inches in diameter has 

 a strength of 23J tons X 100 = 2,350 tons ; for the area 

 of a circle 10 inches in diameter is 100 times that of a 

 circle 1 inch in diameter. All this mode of calculation 

 manifestly proceeds on the simple principle, that every 

 equal fibre or row of particles is supposed to act equally 

 in resisting strain ; and that as the number of such fibres 

 or rows is proportional to the area of section, the strength 

 of different bars or rods is therefore proportional to 

 their areas of section. 



So far the theoretical principle of cohesive strength 

 appears very simple, and easily applicable in practice. 

 It now becomes our business to inquire how far practical 

 results agree with the theoretical principle. Many 

 engineers have devoted great care to experiments on 

 this subject ; and although the results present consider- 

 able differences, yet all of them seem to bear out the 

 principle we have laid down. As an example of the 

 near approach which practical results make to the theo- 

 retical law, we may select some experiments made on 

 round copper bars, as shown in the following table. The 

 first column contains the diameters of the bars in inches ; 

 the second the sectional areas in square inches, or deci- 

 mal parts of a square inch ; the third contains the 

 weights in tons, and decimal parts of tons, which were 

 required to break the bars ; and the fourth column con- 

 tains the weights in tons per square inch of sectional 



