THE MECHANICAL PROPERTIES OF WOOD INCLUDING A DISCUSSION OF THE FACTORS AFFECTING THE MECHANICAL PROPERTIES, AND METHODS OF TIMBER TESTING TEXT

| Red pine | 358 | 42.0 | | Sugar pine | 353 | 41.1 | | White elm | 351 | 41.2 | | Western yellow pine | 348 | 40.8 | | Lodgepole pine | 348 | 40.8 | | Red spruce | 345 | 40.5 | | White pine | 314 | 36.8 | | Engelman spruce | 290 | 34.0 | | Arborvitæ | 288 | 33.8 | | Largetooth aspen | 269 | 31.5 | | White spruce | 262 | 30.7 | | Butternut | 258 | 30.3 | | Buckeye (yellow) | 210 | 24.6 | | Basswood | 209 | 24.5 | | Black willow | 193 | 22.6 | |-------------------------------------------------------| The complexity of the computations depends upon the way in which the stress is applied and the manner in which the stick bends. Ordinarily where the length of the test specimen is not greater than four diameters and the ends are squarely faced (see Fig. 7), the force acts uniformly over each square inch of area and the crushing strength is equal to the maximum load (P) divided { P } by the area of the cross-section (A). { C = --- } { A } [Illustration: FIG. 7.--Endwise compression of a short column.] It has been demonstrated[4] that the ultimate strength in compression parallel to the grain is very nearly the same as the extreme fibre stress at the elastic limit in bending. (See Table V.) In other words, the transverse strength of beams at elastic limit is practically equal to the compressive strength of the same material in short columns. It is accordingly possible to calculate the approximate breaking strength of beams from the compressive strength of short columns except when the wood is brittle. Since tests on endwise compression are simpler, easier to make, and less expensive than transverse bending tests, the importance of this relation is obvious, though it does not do away with the necessity of making beam tests. [Footnote 4: See Circular No. 18, U.S. Division of Forestry: Progress in timber physics, pp. 13-18; also Bulletin 70, U.S. Forest Service: Effect of moisture on the strength and stiffness of wood, pp. 42, 89-90.] |-------------------------------------------------------------------------------| | TABLE V | |-------------------------------------------------------------------------------| | RELATION OF FIBRE STRESS AT ELASTIC LIMIT (r) IN BENDING TO THE CRUSHING | | STRENGTH (C) OF BLOCKS CUT THEREFROM, IN POUNDS PER SQUARE INCH | | (Forest Service Bul. 70, p. 90) | |-------------------------------------------------------------------------------| | LONGLEAF PINE | |-------------------------------------------------------------------------------| | | Soaked | Green | 14 | 11.5 | 9.5 | Kiln-dry | | MOISTURE CONDITION | 50 per | 23 per | per | per | per | 6.2 per | | | cent | cent | cent | cent | cent | cent | | -------------------------+--------+--------+-------+-------+-------+----------| | Number of tests averaged | 5 | 5 | 5 | 5 | 4 | 5 | | _r_ in bending | 4,920 | 5,944 | 6,924 | 7,852 | 9,280 | 11,550 | | _C_ in compression | 4,668 | 5,100 | 6,466 | 7,466 | 8,985 | 10,910 | | Per cent _r_ is in | | | | | | | | excess of _C_ | 5.5 | 16.5 | 7.1 | 5.2 | 3.3 | 5.9 | |-------------------------------------------------------------------------------| | SPRUCE | |-------------------------------------------------------------------------------| | | Soaked | Green | 10 | 8.1 | Kiln-dry | | MOISTURE CONDITION | 30 per | 30 per | per | per | 3.9 per | | | cent | cent | cent | cent | cent | |----------------------------------+--------+--------+-------+-------+----------| | Number of tests averaged | 5 | 4 | 5 | 3 | 4 | | _r_ in bending | 3,002 | 3,362 | 6,458 | 8,400 | 10,170 | | _C_ in compression | 2,680 | 3,025 | 6,120 | 7,610 | 9,335 | | Per cent _r_ | | | | | | | is in excess of _C_ | 12.0 | 11.1 | 5.5 | 10.4 | 9.0 | |-------------------------------------------------------------------------------| When a short column is compressed until it breaks, the manner of failure depends partly upon the anatomical structure and partly upon the degree of humidity of the wood. The fibres (tracheids in conifers) act as hollow tubes bound closely together, and in giving way they either (1) buckle, or (2) bend.[5] [Footnote 5: See Bulletin 70, _op. cit._, p. 129.] The first is typical of any dry thin-walled cells, as is usually the case in seasoned white pine and spruce, and in the early wood of hard pines, hemlock, and other species with decided contrast between the two portions of the growth ring. As a rule buckling of a tracheid begins at the bordered pits which form places of least resistance in the walls. In hardwoods such as oak, chestnut, ash, etc., buckling occurs only in the thinnest-walled elements, such as the vessels, and not in the true fibres. According to Jaccard[6] the folding of the cells is accompanied by characteristic alterations of their walls which seem to split them into extremely thin layers. When greatly magnified, these layers appear in longitudinal sections as delicate threads without any definite arrangements, while on cross section they appear as numerous concentric strata. This may be explained on the ground that the growth of a fibre is by successive layers which, under the influence of compression, are sheared apart. This is particularly the case with thick-walled cells such as are found in late wood. [Footnote 6: Jaccard, P.: Étude anatomique des bois comprimés. Mit. d. Schw. Centralanstalt f.d. forst. Versuchswesen. X. Band, 1. Heft. Zurich, 1910, p. 66.] |-------------------------------------------------------| | TABLE VI | |-------------------------------------------------------| | RESULTS OF ENDWISE COMPRESSION TESTS ON SMALL CLEAR | | PIECES OF 40 WOODS IN GREEN CONDITION | | (Forest Service Cir. 213) | |-------------------------------------------------------| | | Fibre | | Modulus | | COMMON NAME | stress at | Crushing | of | | OF SPECIES | elastic | strength | elasticity | | | limit | | | |-------------------+-----------+----------+------------| | | Lbs. per | Lbs. per | Lbs. per | | | sq. inch | sq. inch | sq. inch | | | | | | | Hardwoods | | | | | | | | | | Ash, white | 3,510 | 4,220 | 1,531,000 | | Basswood | 780 | 1,820 | 1,016,000 | | Beech | 2,770 | 3,480 | 1,412,000 | | Birch, yellow | 2,570 | 3,400 | 1,915,000 | | Elm, slippery | 3,410 | 3,990 | 1,453,000 | | Hackberry | 2,730 | 3,310 | 1,068,000 | | Hickory, | | | | | big shellbark | 3,570 | 4,520 | 1,658,000 | | bitternut | 4,330 | 4,570 | 1,616,000 | | mockernut | 3,990 | 4,320 | 1,359,000 | | nutmeg | 3,620 | 3,980 | 1,411,000 | | pignut | 3,520 | 4,820 | 1,980,000 | | shagbark | 3,730 | 4,600 | 1,943,000 | | water | 3,240 | 4,660 | 1,926,000 | | Locust, honey | 4,300 | 4,970 | 1,536,000 | | Maple, sugar | 3,040 | 3,670 | 1,463,000 | | Oak, post | 2,780 | 3,330 | 1,062,000 | | red | 2,290 | 3,210 | 1,295,000 | | swamp white | 3,470 | 4,360 | 1,489,000 | | white | 2,400 | 3,520 | 946,000 | | yellow | 2,870 | 3,700 | 1,465,000 | | Osage orange | 3,980 | 5,810 | 1,331,000 | | Sycamore | 2,320 | 2,790 | 1,073,000 | | Tupelo | 2,280 | 3,550 | 1,280,000 | | | | | | | Conifers | | | | | | | | | | Arborvitæ | 1,420 | 1,990 | 754,000 | | Cedar, incense | 2,710 | 3,030 | 868,000 | | Cypress, bald | 3,560 | 3,960 | 1,738,000 | | Fir, alpine | 1,660 | 2,060 | 882,000 | | amabilis | 2,763 | 3,040 | 1,579,000 | | Douglas | 2,390 | 2,920 | 1,440,000 | | white | 2,610 | 2,800 | 1,332,000 | | Hemlock | 2,110 | 2,750 | 1,054,000 | | Pine, lodgepole | 2,290 | 2,530 | 1,219,000 | | longleaf | 3,420 | 4,280 | 1,890,000 | | red | 2,470 | 3,080 | 1,646,000 | | sugar | 2,340 | 2,600 | 1,029,000 | | western yellow | 2,100 | 2,420 | 1,271,000 | | white | 2,370 | 2,720 | 1,318,000 | | Redwood | 3,420 | 3,820 | 1,175,000 | | Spruce, Engelmann | 1,880 | 2,170 | 1,021,000 | | Tamarack | 3,010 | 3,480 | 1,596,000 | |-------------------------------------------------------| The second case, where the fibres bend with more or less regular curves instead of buckling, is characteristic of any green or wet wood, and in dry woods where the fibres are thick-walled. In woods in which the fibre walls show all gradations of thickness--in other words, where the transition from the thin-walled cells of the early wood to the thick-walled cells of the late wood is gradual--the two kinds of failure, namely, buckling and bending, grade into each other. In woods with very decided contrast between early and late wood the two forms are usually distinct. Except in the case of complete failure the cavity of the deformed cells remains open, and in hardwoods this is true not only of the wood fibres but also of the tube-like vessels. In many cases longitudinal splits occur which isolate bundles of elements by greater or less intervals. The splitting occurs by a tearing of the fibres or rays and not by the separation of the rays from the adjacent elements. [Illustration: FIG. 8.--Failures of short columns of green spruce.] [Illustration: FIG. 9.--Failures of short columns of dry chestnut.] Moisture in wood decreases the stiffness of the fibre walls and enlarges the region of failure. The curve which the fibre walls make in the region of failure is more gradual and also more irregular than in dry wood, and the fibres are more likely to be separated. In examining the lines of rupture in compression parallel to the grain it appears that there does not exist any specific type, that is, one that is characteristic of all woods. Test blocks taken from different parts of the same log may show very decided differences in the manner of failure, while blocks that are much alike in the size, number, and distribution of the elements of unequal resistance may behave very similarly. The direction of rupture is, according to Jaccard, not influenced by the distribution of the medullary rays.[7] These are curved with the bundles of fibres to which they are attached. In any case the failure starts at the weakest points and follows the lines of least resistance. The plane of failure, as visible on radial surfaces, is horizontal, and on the tangential surface it is diagonal. [Footnote 7: This does not correspond exactly with the conclusions of A. Thil, who says ("Constitution anatomique du bois," pp. 140-141): "The sides of the medullary rays sometimes produce planes of least resistance varying in size with the height of the rays. The medullary rays assume a direction more or less parallel to the lumen of the cells on which they border; the latter curve to the right or left to make room for the ray and then close again beyond it. If the force acts parallel to the axis of growth, the tracheids are more likely to be displaced if the marginal cells of the medullary rays are provided with weak walls that are readily compressed. This explains why on the radial surface of the test blocks the plane of rupture passes in a direction nearly following a medullary ray, whereas on the tangential surface the direction of the plane of rupture is oblique--but with an obliquity varying with the species and determined by the pitch of the spirals along which the medullary rays are distributed in the stem." See Jaccard, _op. cit._, pp. 57 _et seq._] SHEARING STRENGTH Whenever forces act upon a body in such a way that one portion tends to slide upon another adjacent to it the action is called a ~shear~.[8] In wood this shearing action may be (1) ~along the grain~, or (2) ~across the grain~. A tenon breaking out its mortise is a familiar example of shear along the grain, while the shoving off of the tenon itself would be shear across the grain. The use of wood for pins or tree-nails involves resistance to shear across the grain. Another common instance of the latter is where the steel edge of the eye of an axe or hammer tends to cut off the handle. In Fig. 10 the action of the wooden strut tends to shear off along the grain the portion _AB_ of the wooden tie rod, and it is essential that the length of this portion be great enough to guard against it. Fig. 11 shows characteristic failures in shear along the grain. [Footnote 8: Shear should not be confused with ordinary cutting or incision.] [Illustration: FIG. 10.--Example of shear along the grain.] [Illustration: FIG. 11.--Failures of test specimens in shear along the grain. In the block at the left the surface of failure is radial; in the one at the right, tangential] |---------------------------------------------| | TABLE VII | |---------------------------------------------| | SHEARING STRENGTH ALONG THE GRAIN OF SMALL | | CLEAR PIECES OF 41 WOODS IN GREEN CONDITION | | (Forest Service Cir. 213) | |---------------------------------------------| | | When | When | | COMMON NAME | surface of | surface of | | OF SPECIES | failure is | failure is | | | radial | tangential | |-------------------+------------+------------| | | Lbs. per | Lbs. per | | | sq. inch | sq. inch | | | | | | Hardwoods | | | | | | | | Ash, black | 876 | 832 | | white | 1,360 | 1,312 | | Basswood | 560 | 617 | | Beech | 1,154 | 1,375 | | Birch, yellow | 1,103 | 1,188 | | Elm, slippery | 1,197 | 1,174 | | white | 778 | 872 | | Hackberry | 1,095 | 1,161 | | Hickory, | | | | big shellbark | 1,134 | 1,191 | | bitternut | 1,134 | 1,348 | | mockernut | 1,251 | 1,313 | | nutmeg | 1,010 | 1,053 | | pignut | 1,334 | 1,457 | | shagbark | 1,230 | 1,297 | | water | 1,390 | 1,490 | | Locust, honey | 1,885 | 2,096 | | Maple, red | 1,130 | 1,330 | | sugar | 1,193 | 1,455 | | Oak, post | 1,196 | 1,402 | | red | 1,132 | 1,195 | | swamp white | 1,198 | 1,394 | | white | 1,096 | 1,292 | | yellow | 1,162 | 1,196 | | Sycamore | 900 | 1,102 | | Tupelo | 978 | 1,084 | | | | | | Conifers | | | | | | | | Arborvitæ | 617 | 614 | | Cedar, incense | 613 | 662 | | Cypress, bald | 836 | 800 | | Fir, alpine | 573 | 654 | | amabilis | 517 | 639 | | Douglas | 853 | 858 | | white | 742 | 723 | | Hemlock | 790 | 813 | | Pine, lodgepole | 672 | 747 | | longleaf | 1,060 | 953 | | red | 812 | 741 | | sugar | 702 | 714 | | western yellow | 686 | 706 | | white | 649 | 639 | | Spruce, Engelmann | 607 | 624 | | Tamarack | 883 | 843 | |---------------------------------------------| Both shearing stresses may act at the same time. Thus the weight carried by a beam tends to shear it off at right angles to the axis; this stress is equal to the resultant force acting perpendicularly at any point, and in a beam uniformly loaded and supported at either end is maximum at the points of support and zero at the centre. In addition there is a shearing force tending to move the fibres of the beam past each other in a longitudinal direction. (See Fig. 12.) This longitudinal shear is maximum at the neutral plane and decreases toward the upper and lower surfaces. [Illustration: FIG. 12.--Horizontal shear in a beam.] Shearing across the grain is so closely related to compression at right angles to the grain and to hardness that there is little to be gained by making separate tests upon it. Knowledge of shear parallel to the grain is important, since wood frequently fails in that way. The value of shearing stress parallel to the grain is found by dividing the maximum load in pounds (P) by the area of the cross section in inches (A). { P } { Shear = --- } { A } Oblique shearing stresses are developed in a bar when it is subjected to direct tension or compression. The maximum shearing stress occurs along a plane when it makes an angle of 45 degrees P with the axis of the specimen. In this case, shear = -----. When 2 A the value of the angle [Greek: theta] is less than 45 degrees, P the shear along the plane = --- sin [Greek: theta] cos [Greek: A theta]. (See Fig. 13.) The effect of oblique shear is often visible in the failures of short columns. (See Fig. 14.) [Illustration: FIG. 13.--Oblique shear in a short column.] [Illustration: FIG. 14.--Failure of short column by oblique shear.] |---------------------------------------------------------------------------| | TABLE VIII | |---------------------------------------------------------------------------| | SHEARING STRENGTH ACROSS THE GRAIN OF VARIOUS AMERICAN WOODS |