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.

Compression across the grain is 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

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 projection of 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.

When wood is used for columns, props, posts, and spokes, the weight of the load tends to shorten the material endwise. This is endwise 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.

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 compression members of trusses. The strength of a column also depends to a considerable extent upon whether the ends are free to turn or are fixed.

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).

Figure 7

Figure 7

Endwise compression of a short column.

It has been demonstrated⁴ 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 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.

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 Jaccard⁶ 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.

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.

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.

Figure 10

Figure 10

Example of shear along the grain.

Figure 11

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.

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

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).

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 with the axis of the specimen. In this case,

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

Figure 13

Figure 13

Oblique shear in a short column.

Figure 14

Figure 14

Failure of short column by oblique shear.

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 plane intermediate between them—the neutral plane. (N₁P in Fig. 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 the neutral axis (N A in Fig. 15.) of the section.

Figure 15

Figure 15

Diagram of a simple beam. N₁P = neutral plane, N A = neutral axis of section R 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 the transverse shear (or in the case of beams, vertical shear).