Chap. XXII.

STRENGTH OF TIMBER.

130S

48 times, a sixth ; 60 times, a twelfth ; and at 72 times the height of its base, its strengthis only a 24th part. It results from the above experiments that we ought never to makea post in height more than ten times its diameter or width at the base; and in calculatingits strength, at the rate of 10*80 pounds for every 1*066 line superficial of base, which isnot a quarter of the weight that would crush it, we find that a post whose sides are1*066 feet, and containing 22104*576 lines English , would sustain a weight of 238729pounds avoirdupois, or 106 tons. When a post is made in height equal to ten times itswidth of base, it should never have in practice a weight of more than 5 pounds per 1 *066line imposed upon it: and when fms height is 15 times the base, 4 pounds; and when20 times, not more than 3 pounds for the same proportion : all posts should havetheir bases extended, or their area made proportionate to the weight they have to sustain:they ought also to have a stability given them, in reference to their situation andisolation ; this stability is in proportion to the base, the diameter of which, as comparedwith the height, may vary as 7 to 10.

For Timbers placed vertically , as Posts, See. — To find the vertical strength of an oak post9*594 inches square and 9*594 feet high, seek in the preceding table for the primitivevertical strength of oak, which is 807 for 19*188 lines superficial of base ; but as this strengthshould diminish in a ratio of the number of times that the width of the base is contained inthe width of the post, which in the present case is 12, only ^ of 807 must be taken,or 672J. This post, which is 9*594 inches, or 115*128 lines square, has an area of 13254*756square lines, which being divided by 19*188 will give 692*34; and for the greatest weightit can bear before breaking, 692*34 x 672*5 = 465,OOOlbs., and this divided by 10 gives46,500 pounds as the weight the post may be loaded w ith : when the post is of fir, theprimitive vertical strength of which is as 851 to 807, to have its greatest strength, it is onlynecessary to make the proportions, as 807: 465000:: 851 : 490980, which divided by 10gives 49,098 pounds as the utmost weight it should be loaded w*ith.

To find the absolute or cohesive Strength. — This strength by which timber resists whendrawn at the two ends is ascertained by multiplying the area of the section, reduced tolines, by 1821 for oak, which is its tabular number, and dividing the product by 19*188,and the quotient will indicate the greatest weight that it ought to bear.

13254*75 x 1821

For oak, 9*594 inches square, —-——— -— 1*260,700, which divided by 10 gives

19*188

126,070 pounds for the greatest weight it should be subjected to.

We find by the table that beech has the greatest absolute strength, so that apiece of timber of the same dimensions as the preceding would have a strength by13°54*75 x 1^480

—----=1,363,850, which will give 136,385, as the greatest weight to which it

Fig. 2038.

ought to be subject.

To find the Strength of Timber when in an inclined Position. — If it be supposed that apiece of vertical timber, as A B, be inclined on its base, experience proves that its strengthto support a vertical effort diminishes in proportion to its inclination,so that if from its upper extremity a vertical Df be lowered, andfrom the points of the base B a horizontal line B C be drawn, thestrength of the piece will be less in proportion as B/is larger : whenceit results that the strength of a piece of vertical timber is to that of aninclined piece of the same scantling, as the length AB is to B f, or asthe radius to the size of the inclination of the timber.

Secondly, the vertical pieces have the greater power to support aweight, and the horizontal the less; the first of these results gives aneasy method by means of the preceding table, to find the strength of apiece of timber, the length and inclination of which are known: for ex-ample; a piece of oak 9*594 feet long, inclined 4*692 feet, its dimen-sions being 8*528 by 9*594 inches, whose area therefore is 11781*74 lines; this must bedivided by the tabular number, 19*188, and the quotient will be 614.

In the preceding table 807 is the primitive vertical strength of oak for 19*188 linessuperficial of section; but as the length of this piece is more than twelve times the width ofthe base, we must only take ^ of 807, viz. 672^, which multiplied by 614 gives 412915.Then 9*594 : 4*692 : : 412915 : 843400 ; this divided by 10 gives 84,340 for the utmostload to which the inclined piece should be loaded.

Joints and Joining Timbers. — As timber cannot always be obtainedof sufficient length for tie-beams or bridges, it is necessary to showthe method usually employed to unite two or more pieces togetherby their ends, which is called scarfing, and is differently performedby carpenters: the roost common means is lapping or halving, oras it is sometimes called ship-lapping. This is nothing more than Fig . 20o9.

cutting away a part of the thickness of one piece, and an equal quan-

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