Chap. XXII.
TIMBER AND ITS PROPERTIES.
1293
cubes of their diameters: in rectangular beams, the lateral strengths are to each other asthe breadths and squares of the depths, the strength varying as the breadth multiplied intothe square of the depth.
A piece of timber of the greatest strength that can be cut out from a round tree isobtained by dividing the diameter of the circle into three equal parts, raising perpen-diculars upon it, and prolonging them till they cutthe circumference; a rectangle uniting these pointsshows the form of the strongest beam that can beobtained. The comparative strength of beams, but nottheir actual strength, may be calculated by the fore-going rules: the value of actual strength must beconverted into relative on account of the length andother dimensions being relative ; thrice the length ofa beam, is to its depth, as its absolute cohesion is toits relative strength, to which must be added theweight of the timber.
The strains upon a beam fixed at one end in a walland loaded at the other is four times greater thanwhen the same weight is hung upon the middle of thesame beam, and the latter supported at the two ex-tremities : when a beam is fixed at both its extremitiesand loaded in the middle, its strength is to that whenonly supported at its two ends as 3 to 2 : when a weight is uniformly distributed over abeam, its mechanical action to produce fracture is only one-half of what it is when collectedin the middle.
Let Z = the length in inches :
6 = the breadth in inches :
eZsthe depth in inches :
W = the weight in pounds that would break it:
Ssthe weight requisite to break a piece of similar timber, whoselength, breadth, and depth are eacli 1 inch : then,
as
(W
bd a
S,
which S will be a constant number of reference for computing the strength of any piece oftimber of the same kind, under all variety of dimensions and modes of fixing and loading.For a beam fixed at one end, and loaded at the other,
S bd a
W =
l
For a beam fixed at one end, and loaded uniformly throughout,
w=i^£*
For a beam supported at each end, and loaded in the middle,w _4 Sbd*
For a beam supported as above, and loaded uniformly,
8S bd*
~r~
For a beam fixed at one end, and loaded in the middle,
W _——
For a beam fixed as above, and loaded uniformly,
12 S bd*
' v= ——
The value of S has been deduced from a variety of experiments, and in the followingtable is shown the experimental strength of different timbers, when exposed to a transversestrain.
Value of Cohesive Strength of a Rod an Inch Square.
-
-
- 1590
-
.
- 2355
-, Scotch
-
-
- 1866
-
-
- 1556
-
-
- 1350
Larch
-
-
- 1620
-, very young
-
-
- 1590
-
- 1635
2376
1746
1102
1395
1896
966
1275
1911