1623. The table from which the above has been reduced to English measures, is extended to pieces of 31 ·980 in. square, and 47.97 ft. long; but as such scantlings rarely if ever occur in practice, unless strengthened by means of trussing, we have not considered it necessary to proceed beyond the scantling of 20-25 in. by 21-320 in., and 32 ft. long.

1624. Though the table is founded upon experiments on oak, it will serve for all sorts of wood, whose primitive strength is known, and the proportion they bear to oak. In order to facilitate calculations of that nature, the following table has been constructed, in which will be found the absolute and primitive strengths of the several sorts of timber, ordinarily used in carpentry, as also of some few others.

TABLE VII.

For applying the preceding Table to the Woods undermentioned. The primitive horizontal or transverse Strength of Oak is taken at 1000; its supporting or primitive vertical Strength at 807; and its cohesive or absolute Strength at 1821; being deduced from Pieces 19-188 lines English square.

Method of using the above Table for horizontal Timbers.

1625. To find the strength of a beam of fir 23.98 ft. long and 5.330 by 9.594 in. Against these dimensions in the Table VI. we find 10378 as the breaking weight. In the Table VII. we find the primitive horizontal strength of oak is to that of fir as 1000 to 918. Hence 1000 918::10378 to a fourth term which 9527; which expresses the greatest strength of such a beam of fir, or that which would break it. Cutting off the last figure on the right hand, that is, taking one tenth, we have 952 for the greatest weight with which such a beam should be loaded.

1626. If the beam be of chesnut, whose primitive strength is 957, the proportion becomes 1000: 957::10378 9931 the greatest strength of such a piece, and 9931 the greatest weight with which it should be loaded.

Method of Application for the vertical bearing Strength.

10

1627. To find the vertical strength of an oak post 9.594 in. square, and 9.594 ft. high, we shall find in Table VII. for the primitive vertical strength, 807 for 19-188 lines English superficial. But as this strength diminishes as the relative height of the post increases, which in this case is 12 times, we must (1601.), take only of 807, according to the progression there given, that is, 672.

13254 756

1628. The post being 9.594 in. square, its area will be 9.594×12|2 = 13254-756, and 9-155692·34, and 692·34 × 672·5=465000, which divided by 10=46500; is the weight with which without risk the post may be loaded.

19-188

1629. If the post be of fir, whose primitive vertical strength to that of oak is as 851 to 807, we have only to use the proportion 807: 465000::851 : 490980, which divided by 10=49098; the greatest weight with which it should be loaded.

Method for obtaining the absolute or cohesive Strength.

1630. In respect of this species of strength, which is that with which timber resists being drawn asunder in the direction of its fibres by weights acting at its ends, it is only necessary to multiply the area of the section of the piece reduced to lines by the tabular number 1821. if it be oak, and divide the product by 19.188, and the quotient will show the greatest effort it can bear.

13254 75 × 1821

1631. Thus for a piece of oak 9.594 in. square, we have 19-188 =1260700 (in round numbers), which divided by 10 gives the greatest weight that should be suspended to the piece.

1632. From Table VII. it will be seen that in the direction of the absolute strength, beech

is the strongest wood, and that strength will be 13254-75 × 2480 (the tabular number) =1363850,

19.188

which will give 136385 for the greatest weight to be attached.

Of the Strength of Timbers in an inclined Position.

1633. If we suppose the vertical piece AB to become inclined to the base, experiment proves that its strength to resist (fig. 614.) a vertical effort diminishes as its inclination increases; so that, if from the upper part in D a vertical Df be

let fall, and from the points of the base the horizontal line BC A
be drawn, the strength of the piece diminishes as Bf in-
creases whence, I. The strength of a vertical piece is to that
of an inclined piece of the same length and scantling as the
length AB is to Bf, or as the radius is to the sine of the in-
clination of the piece. II. Vertical pieces have the greatest
strength to resist a weight, and the weakest are pieces which
lie horizontally.

ƒ Fig. 614.

1634. The first of these results furnishes an easy method of finding, by the aid of the last table, the strength of a piece B of timber whose length and inclination are known. Thus, suppose a piece of oak inclined 4·692 feet and 9-594 feet long; its size being 8.528 by 9.594 inches, whose area, therefore, is 11781 74 lines. This must be divided by the tabular number 19·188, and the quotient will be 614. In table VII., 807 is the primitive vertical strength of oak for 19.188 lines superficial of section; but as the piece is more than 12 times the width of its base, we are, as before observed, to take only of 807, or 672.5, which is to be multiplied by 614, and the product is 41 2915. Then the proportion 9.594 4.692::412915: 843400 is the strength, which, divided by 10=84340, is the greatest load to which the inclined piece ought to be subjected.

1635. In a section of a following chapter, that on PRACTICAL or CONSTRUCTIVE CARPENTRY, tables of scantlings for timbers will be given, more immediately useful to the practical architect than those deducible from the above rules.