498 



CARPENTRY. 



Theory of 

 Carpentry. 



And on 



the area. 



The relative strengths are by him for a bar 4- feet 

 long, T 7 {j- inch square. ibs. 



Fir 226 

 Linden 20C 

 Beech 146 

 Oak 86 



which are very different from the order in which 

 these woods resist being drawn in length. 



Oak has borne a pressure of 4000 Ibs. per square 

 inch. Six of the pieces of oak in Girard's experiments, 

 broke with 271 Olbs. pressure per square inch ; but 

 15 others bore much more. A great deal depends 

 on the length and uniform soundness of the pieces. 



Perronet gives the following proportions from ex- 

 periment : 



Oak 124 



Willow 9f 



Fir 9rr 



Poplar 7|- 



Ash ' 74 



Elm 7 



His experiments were made on short specimens. 



Muschenbroek says, the relative strength of pieces 

 of wood against compression, is as the cube of their 

 diameter directly and inversely as the square of the 

 length. This is after some investigations of Euler. 

 They are founded upon principles that are somewhat 

 dubious. He merely assumes a certain value for 

 what he calls the rigour of the beam or post, with- 

 out much inquiry as to the way in which that rigour 

 is effected. 



The resistance increases much faster than the area 

 of the section ; and in so far as the failure arises from 

 bending, this observation becomes of the utmost im- 

 portance. We can frequently confine the bending to 

 one direction only, in which, by placing the greater 

 dimension, we will vastly strengthen the post with- 

 out increasing the scantling. This principle has been 

 forced upon the attention of the carpenter in the 

 case of cross strains ; and joists and rafters have gra- 

 dually become thinner and deeper. But we doubt 

 whether the majority of carpenters have even thought 

 whether a square upright, in a partition of 6 inches, 

 or one of 4 inches by 9, is the best. Yet the latter 

 will be trussed sidewise in the building, and its resist- 

 ance to bending in the direction of its breadth, is at 

 least three times as great as the other. 



We shall have occasion to resume this subject. 

 Our investigations respecting it can be pursued with 

 much more facility, when we comprehend the prin- 

 ciples of the transverse strength of timber. 



Experiments on this kind of strain should be mul- 

 tiplied. It is that against which we must guard in 

 the most difficult and delicate cases which come un- 

 der the consideration of the engineer. But such ex- 

 periments must be entrusted to men of science ; for 

 we see that the modifications arising from bending, 

 &c. are so great, that a set of them made in the form 

 most likely to be adopted, would be so completely 

 anomalous, as to afford no rule of practice whatever, 

 We must attend particularly to the manner in which 

 the fracture is produced ; we must endeavour to dis- 

 cover the means of opposing it. Thus we know, 

 that friable matter, as stone, cracks obliquely under 

 pressure, and the pieces slide along the surface of 



fracture ; that fibrous matter, as wood, splits longitu- Theory of 

 dinally, and bulges out. Now, both of these may be t-'arpcmry. 

 prevented by hooping, and that even loosely. On S T"" IP ' / 

 the other hand, should the interior fibres of the tim- 

 ber yield, by penetrating through the softer parts, 

 we may condense the whole, by driving the hoops 

 tight along a very gentle taper. By this means again, 

 we diminish the diameter of the strained part, and, 

 consequently, expose it more to the risk of bending. 

 This last may be obviated by thin flanges, cross 

 bridles, and trusses. An increase of the diameter 

 acts both as a hoop againat bulging out, and as a truss 

 against bending. 



If, by these several or by similar precautions, we 

 can reduce the strain to an absolute crush, there is no 

 question but we shall have resistances vastly greater 

 than what have been usually experienced, and to 

 which, in truth, it is difficult to perceive any limit. 

 The science of carpentry consists, indeed, entirely in 

 the reductioa of all strains to this one ; and after all 

 we do not yet know in what situation this resistance 

 acts most favourably. There is a most extensive 

 field here for research, but all that can be done by 

 an individual is to regret, that while so little progress 

 has been made in forwarding this enquiry, the neces- 

 sary experiments are beyond the means of a private 

 person. We shall at present, therefore, take it for 

 granted, that the resistance to compression among- 

 the particles, is much the same as that against dis- 

 tension. It is highly probable, that this is the case 

 just at the beginning of the strain. And although 

 this principle, when applied to practice, becomes liable 

 to great modifications for the strength increases ra- 

 pidly with an increased diameter, while it diminishes 

 greatly by increasing the length yet we shall per- 

 ceive the reason of these modifications much more 

 distinctly, as we proceed in our investigations respect- 

 ing other strains. 



III. Of the Lateral Resistance. 



The piece may be crushed across, as when a pin ^ IC i atera j 

 or a tenon fails, or a joist gives way at the wall, where resistance 

 we have the strength of one section to overcome ; or much the 

 when a piece is torn out crosswise by a square ed- s * me a8 

 ged tool ; in which case we have the united strength dircct * 

 of the two sections. Some experiments were made 

 by the late Dr Robison, with a view to determine 

 the resistance to this strain. 



Two iron bars were disposed horizontally, at an 

 inch distance ; a third hung perpendicularly between, 

 them, being supported by a pin made of the substance 

 to be examined. This pin was made of a prismatic 

 form, so as to fit exactly iu the holes in the three bars> 

 which were made very exact, and of the same size 

 and shape. A scale was suspended at the lower end 

 of the perpendicular bar, and loaded till it tore out 

 that part of the pin which filled the middle hole. 

 This weight was evidently the measure of the later- 

 al cohesion of two sections. The side bars were 

 made to grasp the middle bar pretty strongly between 

 them, that there mighl^be no distance interposed be- 

 tween the opposite pressures. This would have com- 

 bined the energy of a lever with the purely transverse 

 pressure. For the same reason, it was necessary that 



