1294
THEORY AND PRACTICE OF ENGINEERING.
Cook II.
Oak -
-
-
- 1672
Poplar -
-
-
981
-
- 1766
Plane -
-
- 1821
-, Dantzic
_
- 1457
Sycamore
.
- 1608
Fine, pitch
- 1632
Teak
- 2151
-, red
-
- 1341
By the above table, to find the weight which will produce fracture, on a rectangularbeam, supported at the two ends, when it is loaded in the centre, we must multiply thebreadth by the square of the depth, and again by four times the constant value S: thenthis product, divided by the length in inches, w*ill give the weight required. For example,it is required to know what w*eight would break a beam of English oak, 10 inches deep,
. . 4 x 6 x 10 s x 16/2
G inches in breadth, and 20 feet long:-——-= 1G720 lbs.
® 240
"When the beam is fixed at one end, and loaded at the other, then the co-efficient 4 isomitted, and the weight is thus found,
6 x 10* x 1672---=4180 lbs.
240
When the beam is uniformly loaded throughout, and supported at both ends,
4x6 x 10 2 x 1672 „ 00 „
-—--x 2 = 33440 lbs.
240
The application of the numbers given in the table to the preceding formula will affordthe means of finding the weight that will produce fracture, and this weight diminished one-tenth, by cutting off one figure on the right hand, will give the weight in pounds thatit ought to carry, and the timber should never be subjected to more ; indeed it is neversafe to put timber to the utmost of its efforts ; a fourth of the breaking weight is in manycases considered sufficient.
To ascertain the weight or load any timber will bear when laid horizontally, the length andscantling being given, we must seek in the table for the breaking weight which correspondsto the length and scantling, and find the primitive horizontal strength of the timber in thesecond table. Thus, for a piece of oak 12-792 by 18-122, and 27*18 feet long, we find thebreaking weight to be 85461 : when fir is to be substituted, look into the second table forits primitive horizontal strength, which is 918. Then as 1000 : 918 :: 85461 : 78453, whichexpresses in pounds avoirdupois the weight that would break the piece of fir ; diminishthis weight one-tenth, and then 7845 lbs. is the weight it should be subjected to, or be madeto carry.
Resistance to Compression in the Direction of its Lengthy or its Vertical Bearing Strength. —This power is as great as that which would tear it asunder, though, under some circum-stances, it exerts a greater strength when used as a tie than as a strut; in the latter case,it is sometimes apt to bend, which it cannot do when pulled in the direction of its length.The resistance to compression is increased according to the position in which the strutor support is placed: when the weight applied begins to overpower it, the centrefibres swell, and the outer ones in consequence burst or lose their cohesion, and yield tothe strain: resistance to such an effect depends on the lateral adhesion of the fibres,which may be resembled to a bundle of rods, which would not yield if bound roundfirmly together. Timber which has its fibre cross-grained offers still less resistance;therefore it is that a fir-post is capable of carrying three times as much as one of oak,although for a tie the oak is the strongest. The relative strength of timber against com-pression is as the cube of their diameters directly, and inversely as the square of its length ;but the area of its section may be modified to produce greater strength ; for a post in someplaces 9 by 4 is stronger than another 6 by 6; the stiffest post is that which has its sides inthe proportion of 10 to 6.
Rondelet found the most simple method of ascertaining the absolute strength of oak, orits proportion for different lengths when lying between two points of support, was tomultiply the area of the section by half the absolute strength, and to divide the productby the number of times its depth is contained in the length between the points of support,wherever beams are placed horizontally, and have a bearing at the two ends; those ofequal depth diminish in strength, in proportion to the distance given between their supports :where the lengths are equal, their relative strengths are as their widths and squares oftheir depths.
The follow’ing tables, taken from Rondelet, and converted by Mr. Gwilt into English dimensions and weights, are of the greatest value in estimating the results of the variousexperiments made by Buffon upou timber. The first column gives the proportion thatthe depth has to the length; the second the length of each piece in English feet; thethird the greatest strength of each piece in pounds avoirdupois.