508 



CARPENTRY. 



Theory of OP. The strain is the simple load A, laid on at the 

 Carpentry. point Q, an d the strength resisting it is as the depth 

 ^-^Y-*" or area of the section OP, as mentioned in the sec- 

 tion on lateral resistance. 



Practical We would have proceeded to compare the theore- 

 estimatw. tical investigation just given with the resulta of expe- 

 riment ; but, as we have already stated, there are 

 few of that kind recorded, which can be turned to 

 any good purpose. The compressibility and dilati- 

 bility of the timber has been seldom thought of, at 

 least so far as to subject it to experiment. We can 

 therefore infer little from the numerous experiments 

 on the transverse strength. The various series of 

 experiments by Belidor, Duhamel, BufFoti, &c. seem 

 in general to confirm the truth of the strength being 

 in proportion to the breadth and square of the depth, 

 directly and inversely as the length. Those, indeed, 

 of Buffon, by far the most valuable that are on re- 

 cord, and which, by being made on large scantlings, 

 were free from the irregularities unavoidable in small 

 Specimens, would show that the strength diminishes 

 in a ratio greater than the inverse proportion of the 

 length ; and reasons might perhaps be given why it 

 should be so. But we have already occupied too 

 much time on this subject; and perhaps it will be 

 better to give the practical carpenter a simple arith- 

 metical rule derived from these experiments, the re- 

 sult of which very nearly coincides with them, for 

 finding the weight which will Break a bar of any 

 scantling. 



Divide the number 651 by the length in feet, sub- 

 tract 10 from the quotient, multiply the remainder 

 by the breadth into the square of the depth, both ex- 

 pressed in inches. The result is the greatest load in 

 pounds. This rule applies only to scantlings of oak. 

 Example, Required the weight necessary to break 

 an oak beam of 8 inches square, and 18 feet long, be- 

 tween the supports. 



651 



-^-10=26.16 and 26.16x8x8x8=13384. 



The experiments of Buffon gives 13200. 



Ex. 2. Required the weight for a 4 inch bar of 7 

 feet long. 



7)651(93 

 10 



83 X 64=s5312. Buffon's experiment gives 

 S312. 



Observe, that this weight is that which will break 

 the beam in a few minutes. One half of this load 

 may be safely laid on the beam, but will give it a set 

 which it does not recover. One third may be laid on 

 it for any length of time without injury. 



It is to be regretted, that we have no series of ex- 

 periments on the other kinds of timber. Fir is said 

 by Buffon to be -f^ of the strength of oak ; Emer- 

 son makes it -| ; Parent -i. We shall adopt the pro- 

 portion ^-ds as a sort of mean. 



Required the load which will break a beam of fir 

 ^f 14 feet long and 3 inches broad, by 5 deep. 



14)651(46.5 

 10 



36.5 X 5 X 5 X 3=2737 weight to break 



2 an oak beam, 



3)5475 



f of this, or 1825 Ibs. to break the 

 fir beam. 



Required the load which may be borne by the same Theory of 

 beam with safety at 4 feet from one end. Carpentry. 



4 X 10 : 7 X 7 : : 40 : 49 : : 1825 : 2235 Ibs. will I*"-* 



break the beam there. One third of this, or 745 Ibs. 

 may be borne with safety. 



According to Emerson's experiments, a rod of 

 good oak, one inch square and one yard long, sup- 

 ported at both ends, will bear in the middle a load of 

 330 Ibs. avoirdupois ; but this only for a short time, 

 and it breaks with more. The rule above mentioned 

 would only give 207 Ibs. ; and, as Emerson says, that 

 or of this load only may be depended on, we 

 think, on the whole, the rule above given from Buf- 

 fon may be safely trusted to in practice. Emerson 

 also states the relative strength of other timber a 

 follows : 



Oak, plumb-tree, yew, II 



Ash, elm, .- 8| 



Thorn, walnut, 7 



Apple, elder, red fir, cherry, and plane, . . 7 

 Beech, cherry, hazle, 



Alder, asp, birch, white fir, willow, 

 He adds to these 



Iron, 



Brass, . . . 



Bone, * 



Lead, 



107 

 50 



22 



Fine freestone, 1 



V. Of the Resistance to Twisting. 



This is the strain that is of most importance in Twisting- - 

 the axles of mills or other machinery, in screws of all 

 kinds, and in the rudders of ships ; it frequently also 

 occurs in masts. If we suppose the twist to be con- 

 fined to one plane of section passing directly across 

 the axle, as to the joints between the two parts of a 

 flute, we must suppose the resistance to arise from the 

 force of cohesion in the particles, and to have some 

 relation to their number. It is clear that the parti- 

 cles on the outside of the axle will be more strained 

 than those nearer the centre. As heretofore, we may- 

 suppose them exerting proportionably greater forces. 

 The section will give way when the exterior particles 

 begin to give way ; for a particle nearer the centre, 

 though strained to the same degree, acts by a short- 

 er leverage. When the section begins to give way, 

 therefore, we may suppose each particle to be exert- 

 ing a force proportional to the distance from the cen- 

 tre. The number of particles in any ring or circie r 

 is as the distance of that circle from the centre. 

 Wherefore the effect of each ring will be as the 

 square of its radius. But the number of rings is also 

 as the radius of the axle. Wherefore we find a very 

 simple rule for the strength of axles, viz. It is pro- 

 portional to the cube of the diameter. 



We may draw several useful conclusions from this 

 principle, even before we endeavour to determine the 

 amount of the resistance to twisting, by drawing it 

 from the direct cohesion. 



It is plain that the interior parts of the axle are not Useful 

 acting so powerfully as those towards the outside, inference, 

 Suppose we bore out the heart of the axle as far as 

 half the diameter, the strength of the remainder will 

 be as the difference of the cubes of 1 and 2, that is, 

 it will be of the entire piece, but the stuff is dimi- 

 nished one fourth. A saving is therefore practica- 



