C A R P K N T R V. 



407 



Theory of er. But, as ill great works, there arc numberless, 

 and ofti-n imperceptible defect* of solidity, it will be 



V *"*V"**' safest not only to disregard the additional strength 

 arising in this way, but also, even in this simplest 

 kind of strain, never to load the piece of timber above 

 half, or even one-third, of what the first propor- 

 tions would suppose it equal to bear. 



II. O/'//tf Resistance to Compression in Length. 



Timber, when so placed, that the strain tends to 

 compress the piece lengthwise, is perhaps in the 

 most favourable position for taking advantage of its 

 strength. We can be absolutely certain, that the 

 whole of the fibres arc called into action, and we may, 

 by forming the joint exactly at right angles to the 

 strain, be ensured of the uniform action of each. 

 When drawn in length, on the other hand, it fre- 

 quently happens, that bolts, mortices, or joggles, are 

 the only way in which we have a hold of the beam ; 

 and, that so far from having the strength of the 

 whole transverse section to depend on, we have only 

 the lateral cohesion and friction of those fibres, which 

 form the heel of the mortice, or shoulder of the jog- 

 gle. While, therefore, long heels and joggles, deep 

 scarfing, or stout bolts and straps, are the chief ob- 

 iects to be attended to in the one case, the same dif- 

 ficulties do not occur in the other, and we have not 

 the same chance of failure from defective workman- 

 ship. We have, therefore, much hesitation in ad- 

 mitting the maxim of an author, to whom this de- 

 partment of engineering is greatly indebted, that ties 

 are in general better than struts. It is true indeed 

 as he says, that a small iron rod will support a load 

 as a tie, which could not resist a moment were it 

 compressed by a similar strain. But this does not 

 arise from the mere circumstance of its acting as a 

 tie ; for the strength of cohesion must be pretty 

 much the same either way, it is only from the chance 

 of bending, and becoming thereby subjected to pow- 

 erful cross strains, where the small diameter of the 

 iron rod enables the distant strain to act by the en- 

 ergy of a powerful lever. When bending is altoge- 

 ther prevented, as in the case of an iron truss inclo- 

 sed between the two halves of a girder, we know 

 that the resistance to compression may be safely re- 

 lied on. And, when with the same area of section, 

 the power of leverage is diminished, as by shorten- 

 ing the length of the strut, or by increasing its dia- 

 meter, as by deep flanging, or forming the rod into 

 a hollow tube, we know the resistance to compres- 

 sion is at least as powerful as in any form of a tie. 



In investigating, therefore, the resistance to com- 

 pression, and especially in endeavouring to obviate 

 those unavoidable weaknesses which this position in- 

 volves, we must attend carefully to the mode in which 

 the strain is propagated through the parts of the beam. 

 We would recommend to the inquisitive reader, to 

 study what we have said in the article BOSCOVICH'S 

 THEORY, on the mutual action of points of matter: he 

 will find it greatly facilitate his acquiring correct no- 

 tions of this subject. We sli^ll hereafter have occa- 

 sion to refer more particularly to that article ; but, in 

 the mean time, we would wish to give the intelligent 

 practitioner some simple ideas of this matter, which 

 may possibly tend to assist and direct his practice. 



VOL. V. PART II. 



depends 

 much on 

 how the 

 strain is 

 propaga- 

 ted. 



It is to be regretted, that the experiment! on the 

 strength of timber against compression, are still fewer 

 than those which refer to the first mentioned it rain, 

 although they are certainly of equal importance. 



When we press a rod of soft clay or wax endwise* 

 it bulges out in the middle ; a beam of wood crip- 

 ples, swells out in the middle, the fibres lose their co- 

 hesion, rents appear, and it speedily yields to the strain. 



Take a bundle of small rods, or even rushes, set 

 them on end loosely and compress them, they will se- 

 parate from each other in the middle, bulge out, and 

 speedily give way ; bind them firmly at two or three 

 places, their strength is greatly increased ; wrap them 

 up entirely from end to end, they are stronger still : 

 the resistance, therefore, to compression, depends in- 

 timately on the lateral adhesion. Separate trie whole 

 into several smaller parcels, of which, while some are 

 firmly wrapped up, let others be held more loosely ; 

 place the loose parcels on one side, and repeat the 

 compression, the looser part will yield, the others 

 following will be bent, and may snap with a much 

 smaller force than they would have resisted alone, be- 

 cause the bending enables the strain to act with the 

 energy of a powerful lever. The exterior fibre, which 

 is most bent" and strained, gives way first, ere the 

 strength of the others can be acted on. 



It is evident that the fibres, which are twisted, 

 must resist compression much less than those which 

 are straight. And accordingly, if the experiments 

 of Muschenbroek are to be relied on, oak will hang 

 more than twice as much as fir, yet the latter will 

 support nearly three times as much as the former. 



The resistance to compression, therefore, depends 

 greatly on the power by which bending is prevented, 

 either in the individual fibre, or in the entire piece. 

 Now suppose that a bar of an inch square can sup- 

 port a given quantity M as a ton, then it is evident, 

 that before we produce the same strain in the fibres 

 of a bar of two inches, we must at least lay on four 

 tons N. But, in truth, we may lay on a great deal 

 more ; for, supposing this smaller beam has been bent 

 a little, until the fibres on the weaker side were just 

 as much compressed, and those on the stronger just 

 as much dilated, as could be done with safety, then 

 we may say, that there is some intermediate place, 

 which, having neither suffered dilatation nor com- 

 pression, may be considered as the fulcrum or centre 

 of conversion about which this motion has taken 

 place. Let this be the point A, or a, it is evident, 

 that the distance of the exterior, or any other resist- 

 ing fibre from the centre A, will be to the distance 

 of every similar fibre from a, as the diameter BC to 

 b c. The fibres of the large bar, therefore, in so far 

 as bending is concerned, are not in the same situation 

 with those of the smaller, and before they arrive at it, 

 the weight N must be farther increased in the ratio 

 of the diameters of the bars ; that is, N must be to 

 M in the ratio of the cubes of BC and b c. Indeed 

 there is reason to believe, from the experiments of 

 Muschenbroek, and the investigations of Euler, that 

 the resistance to compression increases in a still high- 

 er degree than this, perhaps in the ratio of the fourth 

 powers of the diameters, at least for those of which 

 the fibres are ridged, as fir, &c. and which were found 

 by Muschenbroek far better adapted to this purpose 

 than the oak, and others of which the fibres are twisted. 

 SR 



Theory of 

 Carpentry. 



On the 

 prevention 

 of bending. 

 PLATE 

 CXII. 

 Fig. 1. 



