816 



APPLIED MECHANICS. 



[SI! RAKING STRAIN CXJCPUNCa. 



the motal of the plate U (horn cleanly round the circum- 

 e of the hole ; ami the force required to effect tho 

 operation, appears to be the same aa would be required 

 to shear a plate of the same material ami thickness an 

 that punched, over a length equal to that of the cir- 

 cumference of the hole. 



\amplo of shearing strain occurring in prac- 

 tice, is that to which the pins uniting the limbs of a 

 chain are subject (Fig. %). 1. If the joint consist of single 

 limbs united by a pin, a strain applied to the limb longi- 

 tudinally tends to shear the pin across at one place. 

 Fig. M. 



Z. If the links be double and single alternately, the pin 

 is exposed to be shorn at two places. 3. Where the links 

 are three and two alternately, the shearing must take 

 place at four places ; and, generally, whatever be the num- 

 ber of links embracing each other at both sides, the m 

 number of places at which the pin must be shorn is " 

 double the smaller number of links. We naturally 

 conclude that, if a certain power be required to 

 shear a pin at one place, it would require double 

 the force to shear it at two, triple at three, ;;IM 

 so on, an additional force being required for I 

 each additional separation of the substance made. " 

 Practically, this is found to be true. Carrying 

 the same reasoning to the consideration of the strains 

 required for shearing pins of different sizes, we conclude 

 that if wo double the area of section that is, the surface 

 where the separation is effected or the number of fibres 

 shorn we have to double the force necessary to shear it. 

 We, therefore, conclude that the strength to resist shear- 

 ing, or the force required to shear, is proportional to the 

 area of the body shorn at the place where the separation 

 is effected : and here, also, our reasoning is borne out by 

 experiment. A pin of iron 2 inches in diameter, requires 

 4 times the force to shear it that a pin 1 inch in diameter 

 requires, because the area of the circle 2 inches is 4 times, 

 or 2 x 2 times, tho area of a circle 1 inch in diameter. 



It is not uncommon, in machinery, to couple two rods 

 A and B in the manner indicated in Fig. 97. The ends 

 of the rods being turned truly cylindrical, and a socket 

 ! bored to fit on them, the ends are inserted in the 

 socket, and keys D and E are driven into slits cut 

 through the socket and the rods. On a great longitudinal 

 strain being applied to the rods, so as to pull them out of the 

 socket, fracture may occur in one of the following ways : 



1. Either of the rods, or the socket itself, may give 

 way under tho effort of direct tension ; and if go, they 

 must yield at the weakest place, which is manifestly 

 where the keys pass through them, part of their sec- 

 tional area being occupied by the keys, which add no- 

 thing to the cohesive strength. 



2. Either of the keys may be shorn across at the two 

 places where they leave the socket, and enter the rods. 



.ither of the rods may have the material between 

 the key and its end drawn out, so as to leave an open- 

 ing F, the material forced out being punched or shorn 

 at both sides by the strain on the key. 



r end of the socket may have tho material at 

 O drawn out in a similar way. 



Now, if the material be of the same quality through, 

 out, the strength to resist fracture in the 2nd, 3rd, and 



ways may be equalised, because they are all shearing 

 strains of tho same kind, and wo have only to make tho 

 several areas of the part, that would be shorn, all equal ; 

 that i* to say, the sectional area of each key D and K 



should be equal to that of the end part F of each rod, 

 because the shearing would separate two surfaces in 

 Fi f . 87. 



TRANSVERSE 



SECTION. 



either case ; and tho area of tho part G of the socket 

 need be only half that, because four surfaces would bo 

 separated. But we have as yet established no relation 

 between the strength to resist tensive strain and that to 

 resist shearing, and cannot, therefore, without further 

 information, compute the proportional strength of the 

 effective transverse sections of the rods and socket where 

 the keys pass through them. The truth is, that very 

 few experiments have been made upon the strength of 

 materials to resist a shearing strain. Such as have been 

 made with malleable iron, seem to show that it is pre- 

 cisely equal to the strength to resist tension. We be- 

 lieve that with other materials this law may be very 

 safely assumed as correct As the tensive strength is 

 also proportional to the area of section, the areas to re- 

 sist equal tensive and shearing strains should be equal. 

 Accordingly, we should make tho transverse sections of 

 the rods and socket such, that the area of each part, 

 on either side of the key, shall be equal to the trans- 

 verse section of the key ; for the key would be shorn 

 at two places, and the rod or socket would be pulled 

 asunder at tho two places on either side of the key. 

 On examining the figure, it will at once suggest itself 

 that the keys should be made narrow and broad (measur- 

 ing the breadth in the direction of the rods lengthways), 

 so as to trench as little as possible upon the sectional 

 area of the socket and rods. 



Although for round or square pins, or bars, the law 

 Fife. 98. that the strength to resist shearing, 



is very nearly the same as the cohe- 

 sive strength, yet there is Jittle 

 doubt that by increasing the depth 

 of a bar exposed to be shorn, the 

 breadth being diminished so as to 

 retain the same area, the strength is 

 materially increased. If we placed 

 a bar of iron having 2 ins. X 1 in. of 

 sectional area under a shearing 

 strain edgeways, it would certainly resist more than 

 when placed sideways. We are not aware, IH.WCV.T, 

 that experiments have been made to a .-.ulli. icnt ex- 

 tent to warrant us in laying down any law as to this. 



