Photomicrograph of a small block of western hemlock. At the top is the cross section showing to the right the late wood of one season's growth, to the left the early wood of the next season. The other two sections are longitudinal and show the fibrous character of the wood. To the left is the radial section with three rays crossing it. To the right is the tangential section upon which the rays appear as vertical rows of beads. × 35. Photo by the author.
This book was written primarily for students of forestry to whom a knowledge of the technical properties of wood is essential. The mechanics involved is reduced to the simplest terms and without reference to higher mathematics, with which the students rarely are familiar. The intention throughout has been to avoid all unnecessarily technical language and descriptions, thereby making the subject-matter readily available to every one interested in wood.
Part I is devoted to a discussion of the mechanical properties of wood—the relation of wood material to stresses and strains. Much of the subject-matter is merely elementary mechanics of materials in general, though written with reference to wood in particular. Numerous tables are included, showing the various strength values of many of the more important American woods.
Part II deals with the factors affecting the mechanical properties of wood. This is a subject of interest to all who are concerned in the rational use of wood, and to the forester it also, by retrospection, suggests ways and means of regulating his forest product through control of the conditions of production. Attempt has been made, in the light of all data at hand, to answer many moot questions, such as the effect on the quality of wood of rate of growth, season of cutting, heartwood and sapwood, locality of growth, weight, water content, steaming, and defects.
Part III describes methods of timber testing. They are for the most part those followed by the U.S. Forest Service. In schools equipped with the necessary machinery the instructions will serve to direct the tests; in others a study of the text with reference to the illustrations should give an adequate conception of the methods employed in this most important line of research.
The appendix contains a copy of the working plan followed by the U.S. Forest Service in the extensive investigations covering the mechanical properties of the woods grown in the United States. It contains many valuable suggestions for the independent investigator. In addition four tables of strength values for structural timbers, both green and air-seasoned, are included. The relation of the stresses developed in different structural forms to those developed in the small clear specimens is given.
In the bibliography attempt was made to list all of the important publications and articles on the mechanical properties of wood, and timber testing. While admittedly incomplete, it should prove of assistance to the student who desires a fuller knowledge of the subject than is presented here.
The writer is indebted to the U.S. Forest Service for nearly all of his tables and photographs as well as many of the data upon which the book is based, since only the Government is able to conduct the extensive investigations essential to a thorough understanding of the subject. More than eighty thousand tests have been made at the Madison laboratory alone, and the work is far from completion.
The writer also acknowledges his indebtedness to Mr. Emanuel Fritz, M.E., M.F., for many helpful suggestions in the preparation of Part I; and especially to Mr. Harry Donald Tiemann, M.E., M.F., engineer in charge of Timber Physics at the Government Forest Products Laboratory, Madison, Wisconsin, for careful revision of the entire manuscript.
SAMUEL J. RECORD.
YALE FOREST SCHOOL, July 1, 1914.
The mechanical properties of wood are its fitness and ability to resist applied or external forces. By external force is meant any force outside of a given piece of material which tends to deform it in any manner. It is largely such properties that determine the use of wood for structural and building purposes and innumerable other uses of which furniture, vehicles, implements, and tool handles are a few common examples.
Knowledge of these properties is obtained through experimentation either in the employment of the wood in practice or by means of special testing apparatus in the laboratory. Owing to the wide range of variation in wood it is necessary that a great number of tests be made and that so far as possible all disturbing factors be eliminated. For comparison of different kinds or sizes a standard method of testing is necessary and the values must be expressed in some defined units. For these reasons laboratory experiments if properly conducted have many advantages over any other method.
One object of such investigation is to find unit values for strength and stiffness, etc. These, because of the complex structure of wood, cannot have a constant value which will be exactly repeated in each test, even though no error be made. The most that can be accomplished is to find average values, the amount of variation above and below, and the laws which govern the variation. On account of the great variability in strength of different specimens of wood even from the same stick and appearing to be alike, it is important to eliminate as far as possible all extraneous factors liable to influence the results of the tests.
The mechanical properties of wood considered in this book are: (1) stiffness and elasticity, (2) tensile strength, (3) compressive or crushing strength, (4) shearing strength, (5) transverse or bending strength, (6) toughness, (7) hardness, (8) cleavability, (9) resilience. In connection with these, associated properties of importance are briefly treated.
In making use of figures indicating the strength or other mechanical properties of wood for the purpose of comparing the relative merits of different species, the fact should be borne in mind that there is a considerable range in variability of each individual material and that small differences, such as a few hundred pounds in values of 10,000 pounds, cannot be considered as a criterion of the quality of the timber. In testing material of the same kind and grade, differences of 25 per cent between individual specimens may be expected in conifers and 50 per cent or even more in hardwoods. The figures given in the tables should be taken as indications rather than fixed values, and as applicable to a large number collectively and not to individual pieces.
Study of the mechanical properties of a material is concerned mostly with its behavior in relation to stresses and strains, and the factors affecting this behavior. A stress is a distributed force and may be defined as the mutual action (1) of one body upon another, or (2) of one part of a body upon another part. In the first case the stress is external; in the other internal. The same stress may be internal from one point of view and external from another. An external force is always balanced by the internal stresses when the body is in equilibrium.
If no external forces act upon a body its particles assume certain relative positions, and it has what is called its natural shape and size. If sufficient external force is applied the natural shape and size will be changed. This distortion or deformation of the material is known as the strain. Every stress produces a corresponding strain, and within a certain limit (see elastic limit, page 5) the strain is directly proportional to the stress producing it.1 The same intensity of stress, however, does not produce the same strain in different materials or in different qualities of the same material. No strain would be produced in a perfectly rigid body, but such is not known to exist.
Stress is measured in pounds (or other unit of weight or force). A unit stress is the stress on a unit of the sectional area.
For instance, if a load (P) of one hundred pounds is uniformly supported by a vertical post with a cross-sectional area (A) of ten square inches, the unit compressive stress is ten pounds per square inch.
Strain is measured in inches (or other linear unit). A unit strain is the strain per unit of length. Thus if a post 10 inches long before compression is 9.9 inches long under the compressive stress, the total strain is 0.1 inch, and the unit strain is
|---||=||-----||=||0.01 inch per inch of length.|
As the stress increases there is a corresponding increase in the strain. This ratio may be graphically shown by means of a diagram or curve plotted with the increments of load or stress as ordinates and the increments of strain as abscissæ. This is known as the stress-strain diagram. Within the limit mentioned above the diagram is a straight line. (See Fig. 1.) If the results of similar experiments on different specimens are plotted to the same scales, the diagrams furnish a ready means for comparison. The greater the resistance a material offers to deformation the steeper or nearer the vertical axis will be the line.
Stress-strain diagrams of two longleaf pine beams. E.L. = elastic limit. The areas of the triangles 0(EL)A and 0(EL)B represent the elastic resilience of the dry and green beams, respectively.
There are three kinds of internal stresses, namely, (1) tensile, (2) compressive, and (3) shearing. When external forces act upon a bar in a direction away from its ends or a direct pull, the stress is a tensile stress; when toward the ends or a direct push, compressive stress. In the first instance the strain is an elongation; in the second a shortening. Whenever the forces tend to cause one portion of the material to slide upon another adjacent to it the action is called a shear. The action is that of an ordinary pair of shears. When riveted plates slide on each other the rivets are sheared off.
These three simple stresses may act together, producing compound stresses, as in flexure. When a bow is bent there is a compression of the fibres on the inner or concave side and an elongation of the fibres on the outer or convex side. There is also a tendency of the various fibres to slide past one another in a longitudinal direction. If the bow were made of two or more separate pieces of equal length it would be noted on bending that slipping occurred along the surfaces of contact, and that the ends would no longer be even. If these pieces were securely glued together they would no longer slip, but the tendency to do so would exist just the same. Moreover, it would be found in the latter case that the bow would be much harder to bend than where the pieces were not glued together—in other words, the stiffness of the bow would be materially increased.
Stiffness is the property by means of which a body acted upon by external forces tends to retain its natural size and shape, or resists deformation. Thus a material that is difficult to bend or otherwise deform is stiff; one that is easily bent or otherwise deformed is flexible. Flexibility is not the exact counterpart of stiffness, as it also involves toughness and pliability.
If successively larger loads are applied to a body and then removed it will be found that at first the body completely regains its original form upon release from the stress—in other words, the body is elastic. No substance known is perfectly elastic, though many are practically so under small loads. Eventually a point will be reached where the recovery of the specimen is incomplete. This point is known as the elastic limit, which may be defined as the limit beyond which it is impossible to carry the distortion of a body without producing a permanent alteration in shape. After this limit has been exceeded, the size and shape of the specimen after removal of the load will not be the same as before, and the difference or amount of change is known as the permanent set.
Elastic limit as measured in tests and used in design may be defined as that unit stress at which the deformation begins to increase in a faster ratio than the applied load. In practice the elastic limit of a material under test is determined from the stress-strain diagram. It is that point in the line where the diagram begins perceptibly to curve.2 (See Fig. 1.)
Resilience is the amount of work done upon a body in deforming it. Within the elastic limit it is also a measure of the potential energy stored in the material and represents the amount of work the material would do upon being released from a state of stress. This may be graphically represented by a diagram in which the abscissæ represent the amount of deflection and the ordinates the force acting. The area included between the stress-strain curve and the initial line (which is zero) represents the work done. (See Fig. 1.) If the unit of space is in inches and the unit of force is in pounds the result is inch-pounds. If the elastic limit is taken as the apex of the triangle the area of the triangle will represent the elastic resilience of the specimen. This amount of work can be applied repeatedly and is perhaps the best measure of the toughness of the wood as a working quality, though it is not synonymous with toughness.
Permanent set is due to the plasticity of the material. A perfectly plastic substance would have no elasticity and the smallest forces would cause a set. Lead and moist clay are nearly plastic and wood possesses this property to a greater or less extent. The plasticity of wood is increased by wetting, heating, and especially by steaming and boiling. Were it not for this property it would be impossible to dry wood without destroying completely its cohesion, due to the irregularity of shrinkage.
A substance that can undergo little change in shape without breaking or rupturing is brittle. Chalk and glass are common examples of brittle materials. Sometimes the word brash is used to describe this condition in wood. A brittle wood breaks suddenly with a clean instead of a splintery fracture and without warning. Such woods are unfitted to resist shock or sudden application of load.
The measure of the stiffness of wood is termed the modulus of elasticity (or coefficient of elasticity). It is the ratio of stress per unit of area to the deformation per unit of length.
It is a number indicative of stiffness, not of strength, and only applies to conditions within the elastic limit. It is nearly the same whether derived from compression tests or from tension tests.
A large modulus indicates a stiff material. Thus in green wood tested in static bending it varies from 643,000 pounds per square inch for arborvitæ to 1,662,000 pounds for longleaf pine, and 1,769,000 pounds for pignut hickory. (See Table IX.) The values derived from tests of small beams of dry material are much greater, approaching 3,000,000 for some of our woods. These values are small when compared with steel which has a modulus of elasticity of about 30,000,000 pounds per square inch. (See Table I.)
|COMPARATIVE STRENGTH OF IRON, STEEL, AND WOOD|
|MATERIAL||Sp. gr.,dry||Modulus of elasticity in bending||Tensile strength||Crushing strength||Modulus of rupture|
|Lbs. per sq. in.||Lbs. per sq. in.||Lbs. per sq. in.||Lbs. per sq. in.|
|Cast iron, cold blast (Hodgkinson)||7.1||17,270,000||16,700||106,000||38,500|
|Bessenger steel, high grade (Fairbain).||7.8||29,215,000||88,400||225,600|
|Longleaf pine, 3.5% moisture (U.S.)||.63||2,800,000||13,000||21,000|
|Redspruce, 3.5% moisture (U.S.)||.41||1,800,000||8,800||14,500|
|Pignut hickory, 3.5% moisture (U.S.)||.86||2,370,000||11,130||24,000|
|NOTE.—Great variation may be found in different samples of metals as well as of wood. The examples given represent reasonable values.|
Tension results when a pulling force is applied to opposite ends of a body. This external pull is communicated to the interior, so that any portion of the material exerts a pull or tensile force upon the remainder, the ability to do so depending upon the property of cohesion. The result is an elongation or stretching of the material in the direction of the applied force. The action is the opposite of compression.
Wood exhibits its greatest strength in tension parallel to the grain, and it is very uncommon in practice for a specimen to be pulled in two lengthwise. This is due to the difficulty of making the end fastenings secure enough for the full tensile strength to be brought into play before the fastenings shear off longitudinally. This is not the case with metals, and as a result they are used in almost all places where tensile strength is particularly needed, even though the remainder of the structure, such as sills, beams, joists, posts, and flooring, may be of wood. Thus in a wooden truss bridge the tension members are steel rods.
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.
|RATIO OF STRENGTH OF WOOD IN TENSION AND IN COMPRESSION|
|(Bul. 10, U. S. Div. of Forestry, p. 44)|
|KIND OF WOOD|| Ratio:
| A stick 1 square inch in cross
|Weight required to—|
|Pull apart||Crush endwise|
|NOTE.—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.
|TENSILE STRENGTH AT RIGHT ANGLES TO THE GRAIN OF SMALL CLEAR PIECES OF 25 WOODS IN GREEN CONDITION|
|(Forest Service Cir. 213)|
|COMMON NAME OF SPECIES||When surface of failure is radial||When surface of failure is tangential|
|Lbs. per sq. inch||Lbs. per sq. inch|
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.]
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.
Side view of failures in compression across the grain, showing crushing of blocks under bearing plate. Specimen at right shows splitting at ends.
End view of failures in compression across the grain, showing splitting of the ends of the test specimens.
|RESULTS OF COMPRESSION TESTS ACROSS THE GRAIN ON 51 WOODS IN GREEN CONDITION, AND COMPARISON WITH WHITE OAK|
|(U. S. Forest Service)|
|COMMON NAME OF SPECIES||Fibre stress at elastic limit perpendicular to grain||Fiber stress in per cent of white oak, or 853 pounds per sq. in.|
|Lbs. per sq. inch||Per cent|
|Big shellbark hickory||997||116.9|
|Western yellow pine||348||40.8|
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.
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 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.
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).
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.
|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)|
|MOISTURE CONDITION||Soaked 50 per cent||Green 23 per cent||14 per cent||11.5 per cent||9.5 per cent||Kiln-dry 6.2 per 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|
|MOISTURE CONDITION||Soaked 30 per cent||Green 30 per cent||10 per cent||8.1 per cent||Kiln-dry 3.9 per 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
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.
|RESULTS OF ENDWISE COMPRESSION TESTS ON SMALL CLEAR PIECES OF 40 WOODS IN GREEN CONDITION|
|(Forest Service Cir. 213)|
|COMMON NAME OF SPECIES||Fibre stress at elastic limit||Crushing strength||Modulus of elasticity|
|Lbs. per sq. inch||Lbs. per sq. inch||Lbs. per sq. inch|
|Hickory, big shellbark||3,570||4,520||1,658,000|
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.
Failures of short columns of green spruce.
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.
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.
Example of shear along the grain.
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.
|SHEARING STRENGTH ALONG THE GRAIN OF SMALL CLEAR PIECES OF 41 WOODS IN GREEN CONDITION|
|(Forest Service Cir. 213)|
|COMMON NAME OF SPECIES||When surface of failure is radial||When surface of failure is tangential|
|Lbs. per sq. inch||Lbs. per sq. inch|
|Hickory, big shellbark||1,134||1,191|
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.
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,
When the value of the angle θ is less than 45 degrees,
|the shear along the plane||=||---||sin θ cos θ.|
Oblique shear in a short column.
Failure of short column by oblique shear.
|SHEARING STRENGTH ACROSS THE GRAIN OF VARIOUS AMERICAN WOODS|
|(J.C. Trautwine. Jour. Franklin Institute. Vol. 109, 1880, pp. 105-106)|
|KIND OF WOOD||Lbs. per sq. inch||KIND OF WOOD||Lbs. per sq. inch|
|Cedar (white)||1,519||Oak (live)||8,480|
|Cedar (Central Amer.)||3,410||Pine (white )||2,480|
|Cherry||2,945||Pine (northern yellow)||4,340|
|Dogwood||6,510||Pine (very resinous yellow)||5,053|
|NOTE.—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 directly] 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.
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).
In addition to this there is a shearing stress, tending to move the fibres past one another in an axial direction, which is called longitudinal shear (or in the case of beams, horizontal shear). This stress must be taken into consideration in the design of timber structures. It is maximum at the neutral plane and decreases to zero at the outer elements of the section. The shorter the span of a beam in proportion to its height, the greater is the liability of failure in horizontal shear before the ultimate strength of the beam is reached.
There are three common forms of beams, as follows:
(1) Simple beam—a bar resting upon two supports, one near each end. (See Fig. 16, No. 1.)
(2) Cantilever beam—a bar resting upon one support or fulcrum, or that portion of any beam projecting out of a wall or beyond a support. (See Fig. 16, No. 2.)
(3) Continuous beam—a bar resting upon more than two supports. (See Fig. 16, No. 3.)
Three common forms of beams. 1. Simple. 2. Cantilever. 3. Continuous.
The two main requirements of a beam are stiffness and strength. The formulæ for the modulus of elasticity (E) or measure of stiffness of a rectangular prismatic simple beam loaded at the centre and resting freely on supports at either end is:
|4 D b h3|
|b||=||breadth or width of beam, inches.|
|h||=||height or depth of beam, inches.|
|l||=||span (length between points of supports) of beam, inches.|
|D||=||deflection produced by load P', inches.|
|P'||=||load at or below elastic limit, pounds.|
From this formulæ it is evident that for rectangular beams of the same material, mode of support, and loading, the deflection is affected as follows:
(1) It is inversely proportional to the width for beams of the same length and depth. If the width is tripled the deflection is one-third as great.
(2) It is inversely proportional to the cube of the depth for beams of the same length and breadth. If the depth is tripled the deflection is one twenty-seventh as great.
(3) It is directly proportional to the cube of the span for beams of the same breadth and depth. Tripling the span gives twenty-seven times the deflection.
The number of pounds which concentrated at the centre will deflect a rectangular prismatic simple beam one inch may be found from the preceding formulæ by substituting D = 1" and solving for P'. The formulæ then becomes:
|4 E b h3|
|Necessary weight (P')||=||----------|
The measure of the breaking strength of a beam is expressed in terms of unit stress by a modulus of rupture, which is a purely hypothetical expression for points beyond the elastic limit. The formulæ used in computing this modulus is as follows:
|1.5 P l|
|b, h, l||=||breadth, height, and span, respectively, as in preceding formulæ.|
|R||=||modulus of rupture, pounds per square inch.|
|P||=||maximum load, pounds.|
In calculating the fibre stress at the elastic limit the same formulæ is used except that the load at elastic limit (P1) is substituted for the maximum load (P).
From this formulæ it is evident that for rectangular prismatic beams of the same material, mode of support, and loading, the load which a given beam can support varies as follows:
(1) It is directly proportional to the breadth for beams of the same length and depth, as is the case with stiffness.
(2) It is directly proportional to the square of the height for beams of the same length and breadth, instead of as the cube of this dimension as in stiffness.
(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.
|RESULTS OF STATIC BENDING TESTS ON SMALL CLEAR BEAMS OF 49 WOODS IN GREEN CONDITION|
|(Forest Service Cir. 213)|
|COMMON NAME OF SPECIES||Fibre stress at elastic limit||Modulus of rupture||Modulus of elasticity||Work in Bending|
|To elastic limit||To maximum load||Total|
|Lbs. per sq. in.||Lbs. per sq. in.||Lbs. per sq. in.||In.-lbs. per cu. inch||In.-lbs. per cu. inch||In.-lbs. per cu. inch|
|Hickory, big shellbark||6,370||11,110||1,562,000||1.47||24.3||78.0|
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 cumulative 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.
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
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.
(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 mass 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."
(3) Impact, shock, or blow. 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 passing over a rough road; on a hammer handle when a blow is struck; on a maul when it strikes a wedge.
Resistance to impact is resistance to energy which is measured by the product of the force into the space through which it moves, or by the product of one-half the moving mass 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 mass and the shorter the space 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 mass 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 formulæ for calculating the stresses are based on the assumption 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 glass 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 mass 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.
|RESULTS OF IMPACT BENDING TESTS ON SMALL CLEAR BEAMS OF 34 WOODS IN GREEN CONDITION|
|(Forest Service Cir. 213)|
|COMMON NAME OF SPECIES||Fibre stress at elastic limit||Modulus of elasticity||Work in bending to elastic limit|
|Lbs. per sq. in.||Lbs. per sq. in.||In.-lbs. per cu. inch|
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.
If a beam is loaded too heavily it will break or fail in some characteristic manner. These failures may be classified 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.
Within the elastic limit the elongations and shortenings are equal, and the neutral plane lies in the middle of the beam. (See page 23.) 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 classification 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.
(2) Cross-grained tension, in which the fracture is caused by a tensile force acting oblique to the grain. (See Fig. 17, No. 2.) This is a common form of failure where the beam has diagonal, spiral or other form of cross grain on its lower side. Since the tensile strength of wood across the grain is only a small fraction of that with the grain it is easy to see why a cross-grained timber would fail in this manner.
(3) Splintering tension, in which the failure consists of a considerable number of slight tension failures, producing a ragged or splintery break on the under surface of the beam. (See Fig. 17, No. 3.) This is common in tough woods. In this case the surface of fracture is fibrous.
(4) Brittle tension, in which the beam fails by a clean break extending entirely through it. (See Fig. 17, No. 4.) It is characteristic of a brittle wood which gives way suddenly without warning, like a piece of chalk. In this case the surface of fracture is described as brash.
Compression failure (see Fig. 17, No. 5) has few variations except that it appears at various distances from the neutral plane of the beam. It is very common in green timbers. The compressive stress parallel to the fibres causes them to buckle or bend as in an endwise compressive test. This action usually begins on the top side shortly after the elastic limit is reached and extends downward, sometimes almost reaching the neutral plane before complete failure occurs. Frequently two or more failures develop at about the same time.
Characteristic failures of simple beams.
Horizontal shear failure, in which the upper and lower portions of the beam slide along each other for a portion of their length either at one or at both ends (see Fig. 17, No. 6), is fairly common in air-dry material and in green material when the ratio of the height of the beam to the span is relatively large. It is not common in small clear specimens. It is often due to shake or season checks, common in large timbers, which reduce the actual area resisting the shearing action considerably below the calculated area used in the formulæ for horizontal shear. (See page 98 for this formulæ.) For this reason it is unsafe, in designing large timber beams, to use shearing stresses higher than those calculated for beams that failed in horizontal shear. The effect of a failure in horizontal shear is to divide the beam into two or more beams the combined strength of which is much less than that of the original beam. Fig. 18 shows a large beam in which two failures in horizontal shear occurred at the same end. That the parts behave independently is shown by the compression failure below the original location of the neutral plane.
Failure of a large beam by horizontal shear. Photo by U. S, Forest Service.
Table XI gives an analysis of the causes of first failure in 840 large timber beams of nine different species of conifers. Of the total number tested 165 were air-seasoned, the remainder green. The failure occurring first signifies the point of greatest weakness in the specimen under the particular conditions of loading employed (in this case, third-point static loading).
|MANNER OF FIRST FAILURE OF LARGE BEAMS|
|(Forest Service Bul. 108, p. 56)|
|COMMON NAME OF SPECIES||Total number of tests||Per cent of total failing by|
|NOTE.—These tests were made on timbers ranging in cross section from 4" × 10" to 8" × 16", and with a span of 15 feet.|
Toughness is a term applied to more than one property of wood. Thus wood that is difficult to split is said to be tough. Again, a tough wood is one that will not rupture until it has deformed considerably under loads at or near its maximum strength, or one which still hangs together after it has been ruptured and may be bent back and forth without breaking apart. Toughness includes flexibility and is the reverse of brittleness, in that tough woods break gradually and give warning of failure. Tough woods offer great resistance to impact and will permit rougher treatment in manipulations attending manufacture and use. Toughness is dependent upon the strength, cohesion, quality, length, and arrangement of fibre, and the pliability of the wood. Coniferous woods as a rule are not as tough as hardwoods, of which hickory and elm are the best examples.
Torsion of a shaft.
The torsion or twisting test is useful in determining the toughness of wood. If the ends of a shaft are turned in opposite directions, or one end is turned and the other is fixed, all of the fibres except those at the axis tend to assume the form of helices. (See Fig. 19.) The strain produced by torsion or twisting is essentially shear transverse and parallel to the fibres, combined with longitudinal tension and transverse compression. Within the elastic limit the strains increase directly as the distance from the axis of the specimen. The outer elements are subjected to tensile stresses, and as they become twisted tend to compress those near the axis. The elongated elements also contract laterally. Cross sections which were originally plane become warped. With increasing strain the lateral adhesion of the outer fibres is destroyed, allowing them to slide past each other, and reducing greatly their power of resistance. In this way the strains on the fibres nearer the axis are progressively increased until finally all of the elements are sheared apart. It is only in the toughest materials that the full effect of this action can be observed. (See Fig. 20.) Brittle woods snap off suddenly with only a small amount of torsion, and their fracture is irregular and oblique to the axis of the piece instead of frayed out and more nearly perpendicular to the axis as is the case with tough woods.
Effect of torsion on different grades of hickory. Photo by U. S. Forest Service.
The term hardness is used in two senses, namely: (1) resistance to indentation, and (2) resistance to abrasion or scratching. In the latter sense hardness combined with toughness is a measure of the wearing ability of wood and is an important consideration in the use of wood for floors, paving blocks, bearings, and rollers. While resistance to indentation is dependent mostly upon the density of the wood, the wearing qualities may be governed by other factors such as toughness, and the size, cohesion, and arrangement of the fibres. In use for floors, some woods tend to compact and wear smooth, while others become splintery and rough. This feature is affected to some extent by the manner in which the wood is sawed; thus edge-grain pine flooring is much better than flat-sawn for uniformity of wear.
|HARDNESS OF 32 WOODS IN GREEN CONDITION, AS INDICATED BY THE LOAD REQUIRED TO IMBED A 0.444-INCH STEEL BALL TO ONE-HALF ITS DIAMETER|
|(Forest Service Cir. 213)|
|COMMON NAME OF SPECIES||Average||End surface||Radial surface||Tangential surface|
|1 Osage orange||1,971||1,838||2,312||1,762|
|2 Honey locust||1,851||1,862||1,860||1,832|
|3 Swamp white oak||1,174||1,205||1,217||1,099|
|4 White oak||1,164||1,183||1,163||1,147|
|5 Post oak||1,099||1,139||1,068||1,081|
|6 Black oak||1,069||1,093||1,083||1,031|
|7 Red oak||1,043||1,107||1,020||1,002|
|8 White ash||1,046||1,121||1,000||1,017|
|10 Sugar maple||937||992||918||901|
|11 Rock elm||910||954||883||893|
|13 Slippery elm||788||919||757||687|
|14 Yellow birch||778||827||768||739|
|16 Red maple||671||766||621||626|
|18 Black ash||551||565||542||546|
|19 White elm||496||536||456||497|
|1 Longleaf pine||532||574||502||521|
|2 Douglas fir||410||415||399||416|
|3 Bald cypress||390||460||355||354|
|6 Red pine||347||355||345||340|
|7 White fir||346||381||322||334|
|8 Western yellow pine||328||334||307||342|
|9 Lodgepole pine||318||316||318||319|
|10 White pine||299||304||294||299|
|11 Engelmann pine||266||272||253||274|
|12 Alpine fir||241||284||203||235|
|NOTE.—Black locust and hickory are not included in this table, but their position would be near the head of the list.|
Tests for either form of hardness are of comparative value only. Tests for indentation are commonly made by penetrations of the material with a steel punch or ball. Tests for abrasion are made by wearing down wood with sandpaper or by means of a sand blast.
Cleavability is the term used to denote the facility with which wood is split. A splitting stress is one in which the forces act normally like a wedge. (See Fig. 21.) The plane of cleavage is parallel to the grain, either radially or tangentially.
Cleavage of highly elastic wood. The cleft runs far ahead of the wedge.
This property of wood is very important in certain uses such as firewood, fence rails, billets, and squares. Resistance to splitting or low cleavability is desirable where wood must hold nails or screws, as in box-making. Wood usually splits more readily along the radius than parallel to the growth rings though exceptions occur, as in the case of cross grain.
Splitting involves transverse tension, but only a portion of the fibres are under stress at a time. A wood of little stiffness and strong cohesion across the grain is difficult to split, while one with great stiffness, such as longleaf pine, is easily split. The form of the grain and the presence of knots greatly affect this quality.
|CLEAVAGE STRENGTH OF SMALL CLEAR PIECES OF 32 WOODS IN GREEN CONDITION|
|(Forest Service Cir. 213)|
|COMMON NAME OF SPECIES||When surface of failure is radial||When surface of failure is tangential|
|Lbs. per sq. inch||Lbs. per sq. inch|
|PART I THE MECHANICAL PROPERTIES OF WOOD
PART II FACTORS AFFECTING THE MECHANICAL PROPERTIES OF WOOD
PART III TIMBER TESTING