The Mechanical Properties of Wood Part 3

(3) It is inversely proportional to the span for beams of the same breadth and depth and not to the cube of this dimension as in stiffness.

The fact that the strength varies as the _square_ of the height and the stiffness as the _cube_ explains the relationship of bending to thickness. Were the law the same for strength and stiffness a thin piece of material such as a sheet of paper could not be bent any further without breaking than a thick piece, say an inch board.

|-------------------------------------------------------------------------------------| | TABLE IX | |-------------------------------------------------------------------------------------| | RESULTS OF STATIC BENDING TESTS ON SMALL CLEAR BEAMS OF 49 WOODS IN GREEN CONDITION | | (Forest Service Cir. 213) | |-------------------------------------------------------------------------------------| | | Fibre | | | Work in Bending | | COMMON NAME | stress at | Modulus | Modulus |-------------------------------| | OF SPECIES | elastic | of | of | To | To | | | | limit | rupture | elasticity | elastic | maximum | Total | | | | | | limit | load | | |-----------------+-----------+----------+------------+----------+----------+---------| | | | | | In.-lbs. | In.-lbs. | In.-lb. | | | Lbs. per | Lbs. per | Lbs. per | per cu. | per cu. | per | | | sq. in. | sq. in. | sq. in. | inch | inch | inch | | | | | | | | | | Hardwoods | | | | | | | | | | | | | | | | Ash, black | 2,580 | 6,000 | 960,000 | 0.41 | 13.1 | 38.9 | | white | 5,180 | 9,920 | 1,416,000 | 1.10 | 20.0 | 43.7 | | Ba.s.swood | 2,480 | 4,450 | 842,000 | .45 | 5.8 | 8.9 | | Beech | 4,490 | 8,610 | 1,353,000 | .96 | 14.1 | 31.4 | | Birch, yellow | 4,190 | 8,390 | 1,597,000 | .62 | 14.2 | 31.5 | | Elm, rock | 4,290 | 9,430 | 1,222,000 | .90 | 19.4 | 47.4 | | slippery | 5,560 | 9,510 | 1,314,000 | 1.32 | 11.7 | 44.2 | | white | 2,850 | 6,940 | 1,052,000 | .44 | 11.8 | 27.4 | | Gum, red | 3,460 | 6,450 | 1,138,000 | | | | | Hackberry | 3,320 | 7,800 | 1,170,000 | .56 | 19.6 | 52.9 | | Hickory, | | | | | | | | big sh.e.l.lbark | 6,370 | 11,110 | 1,562,000 | 1.47 | 24.3 | 78.0 | | bitternut | 5,470 | 10,280 | 1,399,000 | 1.22 | 20.0 | 75.5 | | mockernut | 6,550 | 11,110 | 1,508,000 | 1.50 | 31.7 | 84.4 | | nutmeg | 4,860 | 9,060 | 1,289,000 | 1.06 | 22.8 | 58.2 | | pignut | 5,860 | 11,810 | 1,769,000 | 1.12 | 30.6 | 86.7 | | s.h.a.gbark | 6,120 | 11,000 | 1,752,000 | 1.22 | 18.3 | 72.3 | | water | 5,980 | 10,740 | 1,563,000 | 1.29 | 18.8 | 52.9 | | Locust, honey | 6,020 | 12,360 | 1,732,000 | 1.28 | 17.3 | 64.4 | | Maple, red | 4,450 | 8,310 | 1,445,000 | .78 | 9.8 | 17.1 | | sugar | 4,630 | 8,860 | 1,462,000 | .88 | 12.7 | 32.0 | | Oak, post | 4,720 | 7,380 | 913,000 | 1.39 | 9.1 | 17.4 | | red | 3,490 | 7,780 | 1,268,000 | .60 | 11.4 | 26.0 | | swamp white | 5,380 | 9,860 | 1,593,000 | 1.05 | 14.5 | 37.6 | | tanbark | 6,580 | 10,710 | 1,678,000 | 1.49 | | | | white | 4,320 | 8,090 | 1,137,000 | .95 | 12.1 | 36.7 | | yellow | 5,060 | 8,570 | 1,219,000 | 1.20 | 11.7 | 30.7 | | Osage orange | 7,760 | 13,660 | 1,329,000 | 2.53 | 37.9 | 101.7 | | Sycamore | 2,820 | 6,300 | 961,000 | .51 | 7.1 | 13.6 | | Tupelo | 4,300 | 7,380 | 1,045,000 | 1.00 | 7.8 | 20.9 | | | | | | | | | | Conifers | | | | | | | | | | | | | | | | Arborvitae | 2,600 | 4,250 | 643,000 | .60 | 5.7 | 9.5 | | Cedar, incense | 3,950 | 6,040 | 754,000 | | | | | Cypress, bald | 4,430 | 7,110 | 1,378,000 | .96 | 5.1 | 15.4 | | Fir, alpine | 2,366 | 4,450 | 861,000 | .66 | 4.4 | 7.4 | | amabilis | 4,060 | 6,570 | 1,323,000 | | | | | Douglas | 3,570 | 6,340 | 1,242,000 | .59 | 6.6 | 13.6 | | white | 3,880 | 5,970 | 1,131,000 | .77 | 5.2 | 14.9 | | Hemlock | 3,410 | 5,770 | 917,000 | .73 | 6.6 | 12.9 | | Pine, lodgepole | 3,080 | 5,130 | 1,015,000 | .54 | 5.1 | 7.4 | | longleaf | 5,090 | 8,630 | 1,662,000 | .88 | 8.1 | 34.8 | | red | 3,740 | 6,430 | 1,384,000 | .59 | 5.8 | 28.0 | | shortleaf | 4,360 | 7,710 | 1,395,000 | | | | | sugar | 3,330 | 5,270 | 966,000 | .66 | 5.0 | 11.6 | | west, yellow | 3,180 | 5,180 | 1,111,000 | .52 | 4.3 | 15.6 | | White | 3,410 | 5,310 | 1,073,000 | .62 | 5.9 | 13.3 | | Redwood | 4,530 | 6,560 | 1,024,000 | | | | | Spruce, | | | | | | | | Engelmann | 2,740 | 4,550 | 866,000 | .50 | 4.8 | 6.1 | | red | 3,440 | 5,820 | 1,143,000 | .62 | 6.0 | | | white | 3,160 | 5,200 | 968,000 | .58 | 6.6 | | | Tamarack | 4,200 | 7,170 | 1,236,000 | .84 | 7.2 | 30.0 | |-------------------------------------------------------------------------------------|

_Kinds of Loads_

There are various ways in which beams are loaded, of which the following are the most important:

(1) ~Uniform load~ occurs where the load is spread evenly over the beam.

(2) ~Concentrated load~ occurs where the load is applied at single point or points.

(3) ~Live~ or ~immediate load~ is one of momentary or short duration at any one point, such as occurs in crossing a bridge.

(4) ~Dead~ or ~permanent load~ is one of constant and indeterminate duration, as books on a shelf. In the case of a bridge the weight of the structure itself is the dead load. All large beams support a uniform dead load consisting of their own weight.

The effect of dead load on a wooden beam may be two or more times that produced by an immediate load of the same weight.

Loads greater than the elastic limit are unsafe and will generally result in rupture if continued long enough. A beam may be considered safe under permanent load when the deflections diminish during equal successive periods of time. A continual increase in deflection indicates an unsafe load which is almost certain to rupture the beam eventually.

Variations in the humidity of the surrounding air influence the deflection of dry wood under dead load, and increased deflections during damp weather are c.u.mulative and not recovered by subsequent drying. In the case of longleaf pine, dry beams may with safety be loaded permanently to within three-fourths of their elastic limit as determined from ordinary static tests.

Increased moisture content, due to greater humidity of the air, lowers the elastic limit of wood so that what was a safe load for the dry material may become unsafe.

When a dead load not great enough to rupture a beam has been removed, the beam tends gradually to recover its former shape, but the recovery is not always complete. If specimens from such a beam are tested in the ordinary testing machine it will be found that the application of the dead load did not affect the stiffness, ultimate strength, or elastic limit of the material.

In other words, the deflections and recoveries produced by live loads are the same as would have been produced had not the beam previously been subjected to a dead load.[11]

[Footnote 11: See Tiemann, Harry D.: Some results of dead load bending tests of timber by means of a recording deflectometer.

Proc. Am. Soc. for Testing Materials. Phila. Vol. IX, 1909, pp.

534-548.]

~Maximum load~ is the greatest load a material will support and is usually greater than the load at rupture.

~Safe load~ is the load considered safe for a material to support in actual practice. It is always less than the load at elastic limit and is usually taken as a certain proportion of the ultimate or breaking load.

The ratio of the breaking to the safe load is called the factor of safety. (Factor of safety = ultimate strength / safe load) In order to make due allowance for the natural variations and imperfections in wood and in the aggregate structure, as well as for variations in the load, the factor of safety is usually as high as 6 or 10, especially if the safety of human life depends upon the structure. This means that only from one-sixth to one-tenth of the computed strength values is considered safe to use. If the depth of timbers exceeds four times their thickness there is a great tendency for the material to twist when loaded.

It is to overcome this tendency that floor joists are braced at frequent intervals. Short deep pieces shear out or split before their strength in bending can fully come into play.

_Application of Loads_

There are three[12] general methods in which loads may be applied to beams, namely:

[Footnote 12: A fourth might be added, namely, ~vibratory~, or ~harmonic repet.i.tion~, which is frequently serious in the case of bridges.]

(1) ~Static loading~ or the gradual imposition of load so that the moving parts acquire no appreciable momentum. Loads are so applied in the ordinary testing machine.

(2) ~Sudden imposition of load without initial velocity.~ "Thus in the case of placing a load on a beam, if the load be brought into contact with the beam, but its weight sustained by external means, as by a cord, and then this external support be _suddenly_ (instantaneously) removed, as by quickly cutting the cord, then, although the load is already touching the beam (and hence there is no real impact), yet the beam is at first offering no resistance, as it has yet suffered no deformation.

Furthermore, as the beam deflects the resistance increases, but does not come to be equal to the load until it has attained its normal deflection. In the meantime there has been an unbalanced force of gravity acting, of a constantly diminishing amount, equal at first to the entire load, at the normal deflection. But at this instant the load and the beam are in motion, the hitherto unbalanced force having produced an accelerated velocity, and this velocity of the weight and beam gives to them an energy, or _vis viva_, which must now spend itself in overcoming an _excess_ of resistance over and above the imposed load, and the whole ma.s.s will not stop until the deflection (as well as the resistance) has come to be equal to _twice_ that corresponding to the static load imposed. Hence we say the effect of a suddenly imposed load is to produce twice the deflection and stress of the same load statically applied. It must be evident, however, that this case has nothing in common with either the ordinary 'static' tests of structural materials in testing-machines, or with impact tests."[13]

[Footnote 13: Johnson, J.B.: The materials of construction, pp.

81-82.]

(3) ~Impact, shock,~ or ~blow.~[14] There are various common uses of wood where the material is subjected to sudden shocks and jars or impact. Such is the action on the felloes and spokes of a wagon wheel pa.s.sing over a rough road; on a hammer handle when a blow is struck; on a maul when it strikes a wedge.

[Footnote 14: See Tiemann, Harry D.: The theory of impact and its application to testing materials. Jour. Franklin Inst., Oct., Nov., 1909, pp. 235-259, 336-364.]

Resistance to impact is resistance to energy which is measured by the product of the force into the s.p.a.ce through which it moves, or by the product of one-half the moving ma.s.s which causes the shock into the square of its velocity. The work done upon the piece at the instant the velocity is entirely removed from the striking body is equal to the total energy of that body. It is impossible, however, to get all of the energy of the striking body stored in the specimen, though the greater the ma.s.s and the shorter the s.p.a.ce through which it moves, or, in other words, the greater the proportion of weight and the smaller the proportion of velocity making up the energy of the striking body, the more energy the specimen will absorb. The rest is lost in friction, vibrations, heat, and motion of the anvil.

In impact the stresses produced become very complex and difficult to measure, especially if the velocity is high, or the ma.s.s of the beam itself is large compared to that of the weight.

The difficulties attending the measurement of the stresses beyond the elastic limit are so great that commonly they are not reckoned. Within the elastic limit the formulae for calculating the stresses are based on the a.s.sumption that the deflection is proportional to the stress in this case as in static tests.

A common method of making tests upon the resistance of wood to shock is to support a small beam at the ends and drop a heavy weight upon it in the middle. (See Fig. 40.) The height of the weight is increased after each drop and records of the deflection taken until failure. The total work done upon the specimen is equal to the area of the stress-strain diagram plus the effect of local inertia of the molecules at point of contact.

The stresses involved in impact are complicated by the fact that there are various ways in which the energy of the striking body may be spent:

(_a_) It produces a local deformation of both bodies at the surface of contact, within or beyond the elastic limit. In testing wood the compression of the substance of the steel striking-weight may be neglected, since the steel is very hard in comparison with the wood. In addition to the compression of the fibres at the surface of contact resistance is also offered by the inertia of the particles there, the combined effect of which is a stress at the surface of contact often entirely out of proportion to the compression which would result from the action of a static force of the same magnitude. It frequently exceeds the crushing strength at the extreme surface of contact, as in the case of the swaging action of a hammer on the head of an iron spike, or of a locomotive wheel on the steel rail. This is also the case when a bullet is shot through a board or a pane of gla.s.s without breaking it as a whole.

(_b_) It may move the struck body as a whole with an accelerated velocity, the resistance consisting of the inertia of the body.

This effect is seen when a croquet ball is struck with a mallet.

(_c_) It may deform a fixed body against its external supports and resistances. In making impact tests in the laboratory the test specimen is in reality in the nature of a cushion between two impacting bodies, namely, the striking weight and the base of the machine. It is important that the ma.s.s of this base be sufficiently great that its relative velocity to that of the common centre of gravity of itself and the striking weight may be disregarded.

(_d_) It may deform the struck body as a whole against the resisting stresses developed by its own inertia, as, for example, when a baseball bat is broken by striking the ball.

|-------------------------------------------------------| | TABLE X | |-------------------------------------------------------| | RESULTS OF IMPACT BENDING TESTS ON SMALL CLEAR BEAMS | | OF 34 WOODS IN GREEN CONDITION | | (Forest Service Cir. 213) | |-------------------------------------------------------| | | Fibre | | Work in | | COMMON NAME | stress at | Modulus of | bending | | OF SPECIES | elastic | elasticity | to | | | limit | | elastic | | | | | limit | |-------------------+-----------+------------+----------| | | | | In.-lbs. | | | Lbs. per | Lbs. per | per cu. | | | sq. in. | sq. in. | inch | | | | | | | Hardwoods | | | | | | | | | | Ash, black | 7,840 | 955,000 | 3.69 | | white | 11,710 | 1,564,000 | 4.93 | | Ba.s.swood | 5,480 | 917,000 | 1.84 | | Beech | 11,760 | 1,501,000 | 5.10 | | Birch, yellow | 11,080 | 1,812,000 | 3.79 | | Elm, rock | 12,090 | 1,367,000 | 6.52 | | slippery | 11,700 | 1,569,000 | 4.86 | | white | 9,910 | 1,138,000 | 4.82 | | Hackberry | 10,420 | 1,398,000 | 4.48 | | Locust, honey | 13,460 | 2,114,000 | 4.76 | | Maple, red | 11,670 | 1,411,000 | 5.45 | | sugar | 11,680 | 1,680,000 | 4.55 | | Oak, post | 11,260 | 1,596,000 | 4.41 | | red | 10,580 | 1,506,000 | 4.16 | | swamp white | 13,280 | 2,048,000 | 4.79 | | white | 9,860 | 1,414,000 | 3.84 | | yellow | 10,840 | 1,479,000 | 4.44 | | Osage orange | 15,520 | 1,498,000 | 8.92 | | Sycamore | 8,180 | 1,165,000 | 3.22 | | Tupelo | 7,650 | 1,310,000 | 2.49 | | | | | | | Conifers | | | | | | | | | | Arborvitae | 5,290 | 778,000 | 2.04 | | Cypress, bald | 8,290 | 1,431,000 | 2.71 | | Fir, alpine | 5,280 | 980,000 | 1.59 | | Douglas | 8,870 | 1,579,000 | 2.79 | | white | 7,230 | 1,326,000 | 2.21 | | Hemlock | 6,330 | 1,025,000 | 2.19 | | Pine, lodgepole | 6,870 | 1,142,000 | 2.31 | | longleaf | 9,680 | 1,739,000 | 3.02 | | red | 7,480 | 1,438,000 | 2.18 | | sugar | 6,740 | 1,083,000 | 2.34 | | western yellow | 7,070 | 1,115,000 | 2.51 | | white | 6,490 | 1,156,000 | 2.06 | | Spruce, Engelmann | 6,300 | 1,076,000 | 2.09 | | Tamarack | 7,750 | 1,263,000 | 2.67 | |-------------------------------------------------------|

Impact testing is difficult to conduct satisfactorily and the data obtained are of chief value in a relative sense, that is, for comparing the shock-resisting ability of woods of which like specimens have been subjected to exactly identical treatment.

Yet this test is one of the most important made on wood, as it brings out properties not evident from other tests. Defects and brittleness are revealed by impact better than by any other kind of test. In common practice nearly all external stresses are of the nature of impact. In fact, no two moving bodies can come together without impact stress. Impact is therefore the commonest form of applied stress, although the most difficult to measure.

_Failures in Timber Beams_

If a beam is loaded too heavily it will break or fail in some characteristic manner. These failures may be cla.s.sified according to the way in which they develop, as tension, compression, and horizontal shear; and according to the appearance of the broken surface, as brash, and fibrous. A number of forms may develop if the beam is completely ruptured.

Since the tensile strength of wood is on the average about three times as great as the compressive strength, a beam should, therefore, be expected to fail by the formation in the first place of a fold on the compression side due to the crushing action, followed by failure on the tension side. This is usually the case in green or moist wood. In dry material the first visible failure is not infrequently on the lower or tension side, and various attempts have been made to explain why such is the case.[15]

[Footnote 15: See Proc. Int. a.s.sn. for Testing Materials, 1912, XXIII_{2}, pp. 12-13.]

Within the elastic limit the elongations and shortenings are equal, and the neutral plane lies in the middle of the beam.

(See TRANSVERSE OR BENDING STRENGTH: BEAMS, above.) Later the top layer of fibres on the upper or compression side fail, and on the load increasing, the next layer of fibres fail, and so on, even though this failure may not be visible. As a result the shortenings on the upper side of the beam become considerably greater than the elongations on the lower side. The neutral plane must be presumed to sink gradually toward the tension side, and when the stresses on the outer fibres at the bottom have become sufficiently great, the fibres are pulled in two, the tension area being much smaller than the compression area.

The rupture is often irregular, as in direct tension tests.

Failure may occur partially in single bundles of fibres some time before the final failure takes place. One reason why the failure of a dry beam is different from one that is moist, is that drying increases the stiffness of the fibres so that they offer more resistance to crushing, while it has much less effect upon the tensile strength.

There is considerable variation in tension failures depending upon the toughness or the brittleness of the wood, the arrangement of the grain, defects, etc., making further cla.s.sification desirable. The four most common forms are:

(1)~Simple tension,~ in which there is a direct pulling in two of the wood on the under side of the beam due to a tensile stress parallel to the grain, (See Fig. 17, No. 1.) This is common in straight-grained beams, particularly when the wood is seasoned.