COMPRESSIVE OR CRUSHING STRENGTH

The tensile strength of wood parallel to the grain depends upon the strength of the fibres and is affected not only by the nature and dimensions of the wood elements but also by their arrangement. It is greatest in straight-grained specimens with thick-walled fibres. Cross grain of any kind materially reduces the tensile strength of wood, since the tensile strength at right angles to the grain is only a small fraction of that parallel to the grain.

TABLE IIRATIO OF STRENGTH OF WOOD IN TENSION AND IN COMPRESSION(Bul. 10, U. S. Div. of Forestry, p. 44)KIND OF WOODRatio:R =Tensile strength---------------------compressive strengthA stick 1 square inch in cross section.Weight required to—Pull apartCrush endwiseHickory3.732,0008,500Elm3.829,0007,500Larch2.319,4008,600Longleaf Pine2.217,3007,400NOTE.—Moisture condition not given.

Failure of wood in tension parallel to the grain occurs sometimes in flexure, especially with dry material. The tension portion of the fracture is nearly the same as though the piece were pulled in two lengthwise. The fibre walls are torn across obliquely and usually in a spiral direction. There is practically no pulling apart of the fibres, that is, no separation of the fibres along their walls, regardless of their thickness. The nature of tension failure is apparently not affected by the moisture condition of the specimen, at least not so much so as the other strength values.3

Tension at right angles to the grain is closely related to cleavability. When wood fails in this manner the thin fibre walls are torn in two lengthwise while the thick-walled fibres are usually pulled apart along the primary wall.

TABLE IIITENSILE STRENGTH AT RIGHT ANGLES TO THE GRAIN OF SMALL CLEAR PIECES OF 25 WOODS IN GREEN CONDITION(Forest Service Cir. 213)COMMON NAME OF SPECIESWhen surface of failure is radialWhen surface of failure is tangentialLbs. per sq. inchLbs. per sq. inchHardwoodsAsh, white645671Basswood226303Beech633969Birch, yellow446526Elm, slippery765832Hackberry661786Locust, honey1,1331,445Maple, sugar610864Oak, post714924red639874swamp white757909white622749yellow728929Sycamore540781Tupelo472796ConifersArborvitæ241235Cypress, bald242251Fir, white213304Hemlock271323Pine, longleaf240298red179205sugar239304western yellow230252white225285Tamarack236274

Compression across the grainis very closely related to hardness and transverse shear. There are two ways in which wood is subjected to stress of this kind, namely, (1) with the load acting over the entire area of the specimen, and (2) with a load concentrated over a portion of the area. (See Fig. 2.) The latter is the condition more commonly met with in practice, as, for example, where a post rests on a horizontal sill, or a rail rests on a cross-tie. The former condition, however, gives the true resistance of the grain to simple crushing.]

Figure 2

Compression across the grain.

The first effect of compression across the grain is to compact the fibres, the load gradually but irregularly increasing as the density of the material is increased. If the specimen lies on a flat surface and the load is applied to only a portion of the upper area, the bearing plate indents the wood, crushing the upper fibres without affecting the lower part. (See Fig. 3.) As the load increases the projecting ends sometimes split horizontally. (See Fig. 4.) The irregularities in the load are due to the fact that the fibres collapse a few at a time, beginning with those with the thinnest walls. The projectionof the ends increases the strength of the material directly beneath the compressing weight by introducing a beam action which helps support the load. This influence is exerted for a short distance only.

Figure 3

Side view of failures in compression across the grain, showing crushing of blocks under bearing plate. Specimen at right shows splitting at ends.

Figure 4

End view of failures in compression across the grain, showing splitting of the ends of the test specimens.

TABLE IVRESULTS OF COMPRESSION TESTS ACROSS THE GRAIN ON 51 WOODS IN GREEN CONDITION, AND COMPARISON WITH WHITE OAK(U. S. Forest Service)COMMON NAME OF SPECIESFibre stress at elastic limit perpendicular to grainFiber stress in per cent of white oak, or 853 pounds per sq. in.Lbs. per sq. inchPer centOsage orange2,260265.0Honey locust1,684197.5Black locust1,426167.2Post oak1,148134.6Pignut hickory1,142133.9Water hickory1,088127.5Shagbark hickory1,070125.5Mockernut hickory1,012118.6Big shellbark hickory997116.9Bitternut hickory986115.7Nutmeg hickory938110.0Yellow oak857100.5White oak853100.0Bur oak83698.0White ash82897.1Red oak77891.2Sugar maple74287.0Rock elm69681.6Beech60771.2Slippery elm59970.2Redwood57867.8Bald cypress54864.3Red maple53162.3Hackberry52561.6Incense cedar51860.8Hemlock49758.3Longleaf pine49157.6Tamarack48056.3Silver maple45653.5Yellow birch45453.2Tupelo45152.9Black cherry44452.1Sycamore43350.8Douglas fir42750.1Cucumber tree40847.8Shortleaf pine40046.9Red pine35842.0Sugar pine35341.1White elm35141.2Western yellow pine34840.8Lodgepole pine34840.8Red spruce34540.5White pine31436.8Engelman spruce29034.0Arborvitæ28833.8Largetooth aspen26931.5White spruce26230.7Butternut25830.3Buckeye (yellow)21024.6Basswood20924.5Black willow19322.6

When wood is used for columns, props, posts, and spokes, the weight of the load tends to shorten the material endwise. This isendwise compression, or compression parallel to the grain. In the case of long columns, that is, pieces in which the length is very great compared with their diameter, the failure is by sidewise bending or flexure, instead of by crushing or splitting. (See Fig. 5.) A familiar instance of this action is afforded by a flexible walking-stick. If downward pressure is exerted with the hand on the upper end of the stick placed vertically on the floor, it will be noted that a definite amount of force must be applied in each instance before decided flexure takes place. After this point is reached a very slight increase of pressure very largely increases the deflection, thus obtaining so great a leverage about the middle section as to cause rupture.

Figure 5

Testing a buggy spoke in endwise compression, illustrating the failure by sidewise bending of a long column fixed only at the lower end.Photo by U. S. Forest Service

The lateral bending of a column produces a combination of bending with compressive stress over the section, the compressive stress being maximum at the section of greatest deflection on the concave side. The convex surface is under tension, as in an ordinary beam test. (See Fig. 6.) If the same stick is braced in such a way that flexure is prevented, its supporting strength is increased enormously, since the compressive stress acts uniformly over the section, and failure is by crushing or splitting, as in small blocks. In all columns free to bend in any direction the deflection will be seen in the direction in which the column is least stiff. This sidewise bending can be overcome by making pillars and columns thicker in the middle than at the ends, and by bracing studding, props, and compressionmembers of trusses. The strength of a column also depends to a considerable extent upon whether the ends are free to turn or are fixed.

Figure 6

Unequal distribution of stress in a long column due to lateral bending.

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 by the area of the cross-section (A).

(P)C=---A

Figure 7

Endwise compression of a short column.

It has been demonstrated4that the ultimate strength in compression parallel to the grain is very nearly the same as the extremefibre stress at the elastic limit in bending. (See Table 5.) 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.

TABLE VRELATION 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 PINEMOISTURE CONDITIONSoaked 50 per centGreen 23 per cent14 per cent11.5 per cent9.5 per centKiln-dry 6.2 per centNumber of tests averaged555545rin bending4,9205,9446,9247,8529,28011,550Cin compression4,6685,1006,4667,4668,98510,910Per centris in excess ofC5.516.57.15.23.35.9SPRUCEMOISTURE CONDITIONSoaked 30 per centGreen 30 per cent10 per cent8.1 per centKiln-dry 3.9 per centNumber of tests averaged54534rin bending3,0023,3626,4588,40010,170Cin compression2,6803,0256,1207,6109,335Per centris in excess ofC12.011.15.510.49.0

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

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 Jaccard6the 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 withoutany 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.

TABLE VIRESULTS OF ENDWISE COMPRESSION TESTS ON SMALL CLEAR PIECES OF 40 WOODS IN GREEN CONDITION(Forest Service Cir. 213)COMMON NAME OF SPECIESFibre stress at elastic limitCrushing strengthModulus of elasticityLbs. per sq. inchLbs. per sq. inchLbs. per sq. inchHardwoodsAsh, white3,5104,2201,531,000Basswood7801,8201,016,000Beech2,7703,4801,412,000Birch, yellow2,5703,4001,915,000Elm, slippery3,4103,9901,453,000Hackberry2,7303,3101,068,000Hickory, big shellbark3,5704,5201,658,000bitternut4,3304,5701,616,000mockernut3,9904,3201,359,000nutmeg3,6203,9801,411,000pignut3,5204,8201,980,000shagbark3,7304,6001,943,000water3,2404,6601,926,000Locust, honey4,3004,9701,536,000Maple, sugar3,0403,6701,463,000Oak, post2,7803,3301,062,000red2,2903,2101,295,000swamp white3,4704,3601,489,000white2,4003,520946,000yellow2,8703,7001,465,000Osage orange3,9805,8101,331,000Sycamore2,3202,7901,073,000Tupelo2,2803,5501,280,000ConifersArborvitæ1,4201,990754,000Cedar, incense2,7103,030868,000Cypress, bald3,5603,9601,738,000Fir, alpine1,6602,060882,000amabilis2,7633,0401,579,000Douglas2,3902,9201,440,000white2,6102,8001,332,000Hemlock2,1102,7501,054,000Pine, lodgepole2,2902,5301,219,000longleaf3,4204,2801,890,000red2,4703,0801,646,000sugar2,3402,6001,029,000western yellow2,1002,4201,271,000white2,3702,7201,318,000Redwood3,4203,8201,175,000Spruce, Engelmann1,8802,1701,021,000Tamarack3,0103,4801,596,000

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.

Figure 8

Failures of short columns of green spruce.

Figure 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 wallsmake 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.7These are curved with the bundles of fibres to which they are attached. In any case the failure starts atthe 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.

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 ashear.8In 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. InFig. 10the action of the wooden strut tends to shear off along the grain the portionABof the wooden tie rod, and it is essential that the length of this portion be great enough to guard against it.Fig. 11shows characteristic failures in shear along the grain.

Figure 10

Example of shear along the grain.

Figure 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 VIISHEARING STRENGTH ALONG THE GRAIN OF SMALL CLEAR PIECES OF 41 WOODS IN GREEN CONDITION(Forest Service Cir. 213)COMMON NAME OF SPECIESWhen surface of failure is radialWhen surface of failure is tangentialLbs. per sq. inchLbs. per sq. inchHardwoodsAsh, black876832white1,3601,312Basswood560617Beech1,1541,375Birch, yellow1,1031,188Elm, slippery1,1971,174white778872Hackberry1,0951,161Hickory, big shellbark1,1341,191bitternut1,1341,348mockernut1,2511,313nutmeg1,0101,053pignut1,3341,457shagbark1,2301,297water1,3901,490Locust, honey1,8852,096Maple, red1,1301,330sugar1,1931,455Oak, post1,1961,402red1,1321,195swamp white1,1981,394white1,0961,292yellow1,1621,196Sycamore9001,102Tupelo9781,084ConifersArborvitæ617614Cedar, incense613662Cypress, bald836800Fir, alpine573654amabilis517639Douglas853858white742723Hemlock790813Pine, lodgepole672747longleaf1,060953red812741sugar702714western yellow686706white649639Spruce, Engelmann607624Tamarack883843

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.

Figure 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 maximumshearing stress occurs along a plane when it makes an angle of 45 degrees with the axis of the specimen. In this case,

Pshear=-----.2A

When the value of the angleθis less than 45 degrees,

Pthe shear along the plane=---sinθcosθ.A

(See Fig. 13.) The effect of oblique shear is often visible in the failures of short columns. (See Fig. 14.)

Figure 13

Oblique shear in a short column.

Figure 14

Failure of short column by oblique shear.

TABLE VIIISHEARING STRENGTH ACROSS THE GRAIN OF VARIOUS AMERICAN WOODS(J.C. Trautwine. Jour. Franklin Institute. Vol. 109, 1880, pp. 105-106)KIND OF WOODLbs. per sq. inchKIND OF WOODLbs. per sq. inchAsh6,280Hickory7,285Beech5,223Locust7,176Birch5,595Maple6,355Cedar (white)1,372Oak4,425Cedar (white)1,519Oak (live)8,480Cedar (Central Amer.)3,410Pine (white )2,480Cherry2,945Pine (northern yellow)4,340Chestnut1,536Pine (southernyellow)5,735Dogwood6,510Pine (very resinous yellow)5,053Ebony7,750Poplar4,418Gum5,890Spruce3,255Hemlock2,750Walnut (black)4,728Hickory6,045Walnut (common)2,830NOTE.—Two specimens of each were tested. All were fairly seasoned and without defects. The piece sheared off was 5/8 in. The single circular area of each pin was 0.322 sq. in.

When external forces acting in the same plane are applied at right angles to the axis of a bar so as to cause it to bend, they occasion a shortening of the longitudinal fibres on the concave side and an elongation of those on the convex side. Within the elastic limit the relative stretching and contraction of the fibres is directly9] proportional to their distances from a planeintermediate between them—theneutral plane. (N1PinFig. 15.) Thus the fibres half-way between the neutral plane and the outer surface experience only half as much shortening or elongation as the outermost or extreme fibres. Similarly for other distances. The elements along the neutral plane experience no tension or compression in an axial direction. The line of intersection of this plane and the plane of section is known as theneutral axis(N AinFig. 15.) of the section.

Figure 15

Diagram of a simple beam.N1P= neutral plane,N A= neutral axis of sectionR S.

If the bar is symmetrical and homogeneous the neutral plane is located half-way between the upper and lower surfaces, so long as the deflection does not exceed the elastic limit of the material. Owing to the fact that the tensile strength of wood is from two to nearly four times the compressive strength, it follows that at rupture the neutral plane is much nearer the convex than the concave side of the bar or beam, since the sum of all the compressive stresses on the concave portion must always equal the sum of the tensile stresses on the convex portion. The neutral plane begins to change from its central position as soon as the elastic limit has been passed. Its location at any time is very uncertain.

The external forces acting to bend the bar also tend to rupture it at right angles to the neutral plane by causing one transverse section to slip past another. This stress at any point is equal to the resultant perpendicular to the axis of the forces acting at this point, and is termed thetransverse shear(or in the case of beams,vertical shear).

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