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THE MECHANICAL PROPERTIES OF WOOD

Frontispiece.

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.

THE MECHANICAL PROPERTIES OF WOOD

Including a Discussion

of the Factors Affecting the Mechanical Properties,

and Methods of Timber Testing

BY

SAMUEL J. RECORD, M.A., M.F.

ASSISTANT PROFESSOR OF FOREST PRODUCTS, YALE UNIVERSITY

FIRST EDITION

FIRST THOUSAND

1914

BY THE SAME AUTHOR

Identification of the Economic Woods of the United States.

8vo, vi + 117 pages, 15 figures. Cloth, $1.25 net.

TO THE STAFF OF THE

FOREST PRODUCTS LABORATORY, AT MADISON, WISCONSIN

IN APPRECIATION OF THE MANY OPPORTUNITIES

AFFORDED AND COURTESIES EXTENDED

THE AUTHOR

PREFACE

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.

CONTENTS

PART I

THE MECHANICAL PROPERTIES OF WOOD

INTRODUCTION

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.

FUNDAMENTAL CONSIDERATIONS AND DEFINITIONS

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.

(



P ) Unit stress = ---



A

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

l

0.1



--- = ----- = 0.01 inch per inch of length. L

10





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.

Figure 1

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.

(



unit stress ) E = -------------



unit strain



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.)

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.

TENSILE STRENGTH

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.

TABLE II RATIO OF STRENGTH OF WOOD IN TENSION AND IN COMPRESSION (Bul. 10, U. S. Div. of Forestry, p. 44) KIND OF WOOD Ratio:

R =

Tensile strength

---------------------

compressive strength A stick 1 square inch in cross section.

Weight required to— Pull apart Crush endwise Hickory 3.7 32,000 8,500 Elm 3.8 29,000 7,500 Larch 2.3 19,400 8,600 Longleaf Pine 2.2 17,300 7,400 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.

TABLE III 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 Hardwoods



Ash, white 645 671 Basswood 226 303 Beech 633 969 Birch, yellow 446 526 Elm, slippery 765 832 Hackberry 661 786 Locust, honey 1,133 1,445 Maple, sugar 610 864 Oak, post 714 924 red 639 874 swamp white 757 909 white 622 749 yellow 728 929 Sycamore 540 781 Tupelo 472 796 Conifers



Arborvitæ 241 235 Cypress, bald 242 251 Fir, white 213 304 Hemlock 271 323 Pine, longleaf 240 298 red 179 205 sugar 239 304 western yellow 230 252 white 225 285 Tamarack 236 274

COMPRESSIVE OR CRUSHING STRENGTH

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

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.

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 IV 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 Osage orange 2,260 265.0 Honey locust 1,684 197.5 Black locust 1,426 167.2 Post oak 1,148 134.6 Pignut hickory 1,142 133.9 Water hickory 1,088 127.5 Shagbark hickory 1,070 125.5 Mockernut hickory 1,012 118.6 Big shellbark hickory 997 116.9 Bitternut hickory 986 115.7 Nutmeg hickory 938 110.0 Yellow oak 857 100.5 White oak 853 100.0 Bur oak 836 98.0 White ash 828 97.1 Red oak 778 91.2 Sugar maple 742 87.0 Rock elm 696 81.6 Beech 607 71.2 Slippery elm 599 70.2 Redwood 578 67.8 Bald cypress 548 64.3 Red maple 531 62.3 Hackberry 525 61.6 Incense cedar 518 60.8 Hemlock 497 58.3 Longleaf pine 491 57.6 Tamarack 480 56.3 Silver maple 456 53.5 Yellow birch 454 53.2 Tupelo 451 52.9 Black cherry 444 52.1 Sycamore 433 50.8 Douglas fir 427 50.1 Cucumber tree 408 47.8 Shortleaf pine 400 46.9 Red pine 358 42.0 Sugar pine 353 41.1 White elm 351 41.2 Western yellow pine 348 40.8 Lodgepole pine 348 40.8 Red spruce 345 40.5 White pine 314 36.8 Engelman spruce 290 34.0 Arborvitæ 288 33.8 Largetooth aspen 269 31.5 White spruce 262 30.7 Butternut 258 30.3 Buckeye (yellow) 210 24.6 Basswood 209 24.5 Black willow 193 22.6

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.

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 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.

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 demonstrated 4 that the ultimate strength in compression parallel to the grain is very nearly the same as the extreme fibre stress at the elastic limit in bending. (See Table 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 V RELATION OF FIBRE STRESS AT ELASTIC LIMIT (r) IN BENDING TO THE CRUSHING STRENGTH (C) OF BLOCKS CUT THEREFROM, IN POUNDS PER SQUARE INCH (Forest Service Bul. 70, p. 90) LONGLEAF PINE 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 SPRUCE 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 Jaccard 6 the folding of the cells is accompanied by characteristic alterations of their walls which seem to split them into extremely thin layers. When greatly magnified, these layers appear in longitudinal sections as delicate threads without any definite arrangements, while on cross section they appear as numerous concentric strata. This may be explained on the ground that the growth of a fibre is by successive layers which, under the influence of compression, are sheared apart. This is particularly the case with thick-walled cells such as are found in late wood.

TABLE VI 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 Hardwoods





Ash, white 3,510 4,220 1,531,000 Basswood 780 1,820 1,016,000 Beech 2,770 3,480 1,412,000 Birch, yellow 2,570 3,400 1,915,000 Elm, slippery 3,410 3,990 1,453,000 Hackberry 2,730 3,310 1,068,000 Hickory, big shellbark 3,570 4,520 1,658,000 bitternut 4,330 4,570 1,616,000 mockernut 3,990 4,320 1,359,000 nutmeg 3,620 3,980 1,411,000 pignut 3,520 4,820 1,980,000 shagbark 3,730 4,600 1,943,000 water 3,240 4,660 1,926,000 Locust, honey 4,300 4,970 1,536,000 Maple, sugar 3,040 3,670 1,463,000 Oak, post 2,780 3,330 1,062,000 red 2,290 3,210 1,295,000 swamp white 3,470 4,360 1,489,000 white 2,400 3,520 946,000 yellow 2,870 3,700 1,465,000 Osage orange 3,980 5,810 1,331,000 Sycamore 2,320 2,790 1,073,000 Tupelo 2,280 3,550 1,280,000 Conifers





Arborvitæ 1,420 1,990 754,000 Cedar, incense 2,710 3,030 868,000 Cypress, bald 3,560 3,960 1,738,000 Fir, alpine 1,660 2,060 882,000 amabilis 2,763 3,040 1,579,000 Douglas 2,390 2,920 1,440,000 white 2,610 2,800 1,332,000 Hemlock 2,110 2,750 1,054,000 Pine, lodgepole 2,290 2,530 1,219,000 longleaf 3,420 4,280 1,890,000 red 2,470 3,080 1,646,000 sugar 2,340 2,600 1,029,000 western yellow 2,100 2,420 1,271,000 white 2,370 2,720 1,318,000 Redwood 3,420 3,820 1,175,000 Spruce, Engelmann 1,880 2,170 1,021,000 Tamarack 3,010 3,480 1,596,000

The second case, where the fibres bend with more or less regular curves instead of buckling, is characteristic of any green or wet wood, and in dry woods where the fibres are thick-walled. In woods in which the fibre walls show all gradations of thickness—in other words, where the transition from the thin-walled cells of the early wood to the thick-walled cells of the late wood is gradual—the two kinds of failure, namely, buckling and bending, grade into each other. In woods with very decided contrast between early and late wood the two forms are usually distinct. Except in the case of complete failure the cavity of the deformed cells remains open, and in hardwoods this is true not only of the wood fibres but also of the tube-like vessels. In many cases longitudinal splits occur which isolate bundles of elements by greater or less intervals. The splitting occurs by a tearing of the fibres or rays and not by the separation of the rays from the adjacent elements.

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 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.

SHEARING STRENGTH

Whenever forces act upon a body in such a way that one portion tends to slide upon another adjacent to it the action is called a shear. 8 In wood this shearing action may be (1) along the grain, or (2) across the grain. A tenon breaking out its mortise is a familiar example of shear along the grain, while the shoving off of the tenon itself would be shear across the grain. The use of wood for pins or tree-nails involves resistance to shear across the grain. Another common instance of the latter is where the steel edge of the eye of an axe or hammer tends to cut off the handle. In Fig. 10 the action of the wooden strut tends to shear off along the grain the portion AB of the wooden tie rod, and it is essential that the length of this portion be great enough to guard against it. Fig. 11 shows characteristic failures in shear along the grain.

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 VII 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 Hardwoods



Ash, black 876 832 white 1,360 1,312 Basswood 560 617 Beech 1,154 1,375 Birch, yellow 1,103 1,188 Elm, slippery 1,197 1,174 white 778 872 Hackberry 1,095 1,161 Hickory, big shellbark 1,134 1,191 bitternut 1,134 1,348 mockernut 1,251 1,313 nutmeg 1,010 1,053 pignut 1,334 1,457 shagbark 1,230 1,297 water 1,390 1,490 Locust, honey 1,885 2,096 Maple, red 1,130 1,330 sugar 1,193 1,455 Oak, post 1,196 1,402 red 1,132 1,195 swamp white 1,198 1,394 white 1,096 1,292 yellow 1,162 1,196 Sycamore 900 1,102 Tupelo 978 1,084 Conifers



Arborvitæ 617 614 Cedar, incense 613 662 Cypress, bald 836 800 Fir, alpine 573 654 amabilis 517 639 Douglas 853 858 white 742 723 Hemlock 790 813 Pine, lodgepole 672 747 longleaf 1,060 953 red 812 741 sugar 702 714 western yellow 686 706 white 649 639 Spruce, Engelmann 607 624 Tamarack 883 843

Both shearing stresses may act at the same time. Thus the weight carried by a beam tends to shear it off at right angles to the axis; this stress is equal to the resultant force acting perpendicularly at any point, and in a beam uniformly loaded and supported at either end is maximum at the points of support and zero at the centre. In addition there is a shearing force tending to move the fibres of the beam past each other in a longitudinal direction. (See Fig. 12.) This longitudinal shear is maximum at the neutral plane and decreases toward the upper and lower surfaces.

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





P shear = -----.



2 A

When the value of the angle θ is less than 45 degrees,





P

the shear along the plane = --- sin θ cos θ.



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 VIII 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 Ash 6,280 Hickory 7,285 Beech 5,223 Locust 7,176 Birch 5,595 Maple 6,355 Cedar (white) 1,372 Oak 4,425 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 Chestnut 1,536 Pine (southernyellow) 5,735 Dogwood 6,510 Pine (very resinous yellow) 5,053 Ebony 7,750 Poplar 4,418 Gum 5,890 Spruce 3,255 Hemlock 2,750 Walnut (black) 4,728 Hickory 6,045 Walnut (common) 2,830 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.

TRANSVERSE OR BENDING STRENGTH: BEAMS

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 9 ] proportional to their distances from a plane intermediate between them—the neutral plane. (N 1 P 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

Diagram of a simple beam. N 1 P = 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.

Beams

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.)

Figure 16

Three common forms of beams. 1. Simple. 2. Cantilever. 3. Continuous.

Stiffness of Beams

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: 10





P' l 3 E = -----------



4 D b h 3





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 h 3 Necessary weight (P') = ----------



l 3

In this case the values for E are read from tables prepared from data obtained by experimentation on the given material.

Strength of Beams

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 R = ---------



b h 2





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 (P 1 ) 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.

TABLE IX 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 Hardwoods











Ash, black 2,580 6,000 960,000 0.41 13.1 38.9 white 5,180 9,920 1,416,000 1.10 20.0 43.7 Basswood 2,480 4,450 842,000 .45 5.8 8.9 Beech 4,490 8,610 1,353,000 .96 14.1 31.4 Birch, yellow 4,190 8,390 1,597,000 .62 14.2 31.5 Elm, rock 4,290 9,430 1,222,000 .90 19.4 47.4 slippery 5,560 9,510 1,314,000 1.32 11.7 44.2 white 2,850 6,940 1,052,000 .44 11.8 27.4 Gum, red 3,460 6,450 1,138,000





Hackberry 3,320 7,800 1,170,000 .56 19.6 52.9 Hickory, big shellbark 6,370 11,110 1,562,000 1.47 24.3 78.0 bitternut 5,470 10,280 1,399,000 1.22 20.0 75.5 mockernut 6,550 11,110 1,508,000 1.50 31.7 84.4 nutmeg 4,860 9,060 1,289,000 1.06 22.8 58.2 pignut 5,860 11,810 1,769,000 1.12 30.6 86.7 shagbark 6,120 11,000 1,752,000 1.22 18.3 72.3 water 5,980 10,740 1,563,000 1.29 18.8 52.9 Locust, honey 6,020 12,360 1,732,000 1.28 17.3 64.4 Maple, red 4,450 8,310 1,445,000 .78 9.8 17.1 sugar 4,630 8,860 1,462,000 .88 12.7 32.0 Oak, post 4,720 7,380 913,000 1.39 9.1 17.4 red 3,490 7,780 1,268,000 .60 11.4 26.0 swamp white 5,380 9,860 1,593,000 1.05 14.5 37.6 tanbark 6,580 10,710 1,678,000 1.49



white 4,320 8,090 1,137,000 .95 12.1 36.7 yellow 5,060 8,570 1,219,000 1.20 11.7 30.7 Osage orange 7,760 13,660 1,329,000 2.53 37.9 101.7 Sycamore 2,820 6,300 961,000 .51 7.1 13.6 Tupelo 4,300 7,380 1,045,000 1.00 7.8 20.9 Conifers











Arborvitæ 2,600 4,250 643,000 .60 5.7 9.5 Cedar, incense 3,950 6,040 754,000





Cypress, bald 4,430 7,110 1,378,000 .96 5.1 15.4 Fir, alpine 2,366 4,450 861,000 .66 4.4 7.4 amabilis 4,060 6,570 1,323,000





Douglas 3,570 6,340 1,242,000 .59 6.6 13.6 white 3,880 5,970 1,131,000 .77 5.2 14.9 Hemlock 3,410 5,770 917,000 .73 6.6 12.9 Pine, lodgepole 3,080 5,130 1,015,000 .54 5.1 7.4 longleaf 5,090 8,630 1,662,000 .88 8.1 34.8 red 3,740 6,430 1,384,000 .59 5.8 28.0 shortleaf 4,360 7,710 1,395,000





sugar 3,330 5,270 966,000 .66 5.0 11.6 west, yellow 3,180 5,180 1,111,000 .52 4.3 15.6 White 3,410 5,310 1,073,000 .62 5.9 13.3 Redwood 4,530 6,560 1,024,000





Spruce, Engelmann 2,740 4,550 866,000 .50 4.8 6.1 red 3,440 5,820 1,143,000 .62 6.0

white 3,160 5,200 968,000 .58 6.6

Tamarack 4,200 7,170 1,236,000 .84 7.2 30.0

Kinds of Loads

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

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

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

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

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

The effect of dead load on a wooden beam may be two or more times that produced by an immediate load of the same weight. Loads greater than the elastic limit are unsafe and will generally result in rupture if continued long enough. A beam may be considered safe under permanent load when the deflections diminish during equal successive periods of time. A continual increase in deflection indicates an unsafe load which is almost certain to rupture the beam eventually.

Variations in the humidity of the surrounding air influence the deflection of dry wood under dead load, and increased deflections during damp weather are 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. 11

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.

(



ultimate strength ) Factor of safety

= -------------------





safe load



In order to make due allowance for the natural variations and imperfections in wood and in the aggregate structure, as well as for variations in the load, the factor of safety is usually as high as 6 or 10, especially if the safety of human life depends upon the structure. This means that only from one-sixth to one-tenth of the computed strength values is considered safe to use. If the depth of timbers exceeds four times their thickness there is a great tendency for the material to twist when loaded. It is to overcome this tendency that floor joists are braced at frequent intervals. Short deep pieces shear out or split before their strength in bending can fully come into play.

Application of Loads

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

(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." 13

(3) Impact, shock, or blow. 14 There are various common uses of wood where the material is subjected to sudden shocks and jars or impact. Such is the action on the felloes and spokes of a wagon wheel 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.

TABLE X 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 Hardwoods





Ash, black 7,840 955,000 3.69 white 11,710 1,564,000 4.93 Basswood 5,480 917,000 1.84 Beech 11,760 1,501,000 5.10 Birch, yellow 11,080 1,812,000 3.79 Elm, rock 12,090 1,367,000 6.52 slippery 11,700 1,569,000 4.86 white 9,910 1,138,000 4.82 Hackberry 10,420 1,398,000 4.48 Locust, honey 13,460 2,114,000 4.76 Maple, red 11,670 1,411,000 5.45 sugar 11,680 1,680,000 4.55 Oak, post 11,260 1,596,000 4.41 red 10,580 1,506,000 4.16 swamp white 13,280 2,048,000 4.79 white 9,860 1,414,000 3.84 yellow 10,840 1,479,000 4.44 Osage orange 15,520 1,498,000 8.92 Sycamore 8,180 1,165,000 3.22 Tupelo 7,650 1,310,000 2.49 Conifers





Arborvitæ 5,290 778,000 2.04 Cypress, bald 8,290 1,431,000 2.71 Fir, alpine 5,280 980,000 1.59 Douglas 8,870 1,579,000 2.79 white 7,230 1,326,000 2.21 Hemlock 6,330 1,025,000 2.19 Pine, lodgepole 6,870 1,142,000 2.31 longleaf 9,680 1,739,000 3.02 red 7,480 1,438,000 2.18 sugar 6,740 1,083,000 2.34 western yellow 7,070 1,115,000 2.51 white 6,490 1,156,000 2.06 Spruce, Engelmann 6,300 1,076,000 2.09 Tamarack 7,750 1,263,000 2.67

Impact testing is difficult to conduct satisfactorily and the data obtained are of chief value in a relative sense, that is, for comparing the shock-resisting ability of woods of which like specimens have been subjected to exactly identical treatment. Yet this test is one of the most important made on wood, as it brings out properties not evident from other tests. Defects and brittleness are revealed by impact better than by any other kind of test. In common practice nearly all external stresses are of the nature of impact. In fact, no two moving bodies can come together without impact stress. Impact is therefore the commonest form of applied stress, although the most difficult to measure.

Failures in Timber Beams

If a beam is loaded too heavily it will break or fail in some characteristic manner. These failures may be 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. 15

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.

Figure 17

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.

Figure 18

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).

TABLE XI 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 Tension Compression Shear Longleaf pine:







green 17 18 24 58 dry 9 22 22 56 Douglas fir:







green 191 27 72 1 dry 91 19 76 5 Shortleaf pine:







green 48 27 56 17 dry 13 54

46 Western larch:







green 62 23 71 6 dry 52 54 19 27 Loblolly pine:







green 111 40 53 7 dry 25 60 12 28 Tamarack:







green 30 37 53 10 dry 9 45 22 33 Western hemlock:







green 39 21 74 5 dry 44 11 66 23 Redwood:







green 28 43 50 7 dry 12 83 17

Norway pine:







green 49 18 76 6 dry 10 30 60 10 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: TORSION

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.

Figure 19

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.

Figure 20

Effect of torsion on different grades of hickory. Photo by U. S. Forest Service.

HARDNESS

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.

TABLE XII 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 Pounds Pounds Pounds Pounds Hardwoods







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 9 Beech 942 1,012 897 918 10 Sugar maple 937 992 918 901 11 Rock elm 910 954 883 893 12 Hackberry 799 829 795 773 13 Slippery elm 788 919 757 687 14 Yellow birch 778 827 768 739 15 Tupelo 738 814 666 733 16 Red maple 671 766 621 626 17 Sycamore 608 664 560 599 18 Black ash 551 565 542 546 19 White elm 496 536 456 497 20 Basswood 239 273 226 217 Conifers







1 Longleaf pine 532 574 502 521 2 Douglas fir 410 415 399 416 3 Bald cypress 390 460 355 354 4 Hemlock 384 463 354 334 5 Tamarack 384 401 380 370 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. 16 Tests for abrasion are made by wearing down wood with sandpaper or by means of a sand blast.

CLEAVABILITY

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.

Figure 21

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.

TABLE XIII 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 Hardwoods



Ash, black 275 260 white 333 346 Bashwood 130 168 Beech 339 527 Birch, yellow 294 287 Elm, slippery 401 424 white 210 270 Hackberr 422 436 Locust, honey 552 610 Maple, red 297 330 sugar 376 513 Oak, post 354 487 red 380 470 swamp white 428 536 white 382 457 yellow 379 470 Sycamore 265 425 Tupelo 277 380 Conifers



Arborvitæ 148 139 Cypress, bald 167 154 Fir, alpine 130 133 Douglas 139 127 white 145 187 Hemlock 168 151 Pine, lodgepole 142 140 longleaf 187 180 red 161 154 sugar 168 189 western yellow 162 187 white 144 160 Spruce, Engelmann 110 135 Tamarack 167 159

PART II

FACTORS AFFECTING THE MECHANICAL PROPERTIES OF WOOD

INTRODUCTION

Wood is an organic product—a structure of infinite variation of detail and design. 17 It is on this account that no two woods are alike—in reality no two specimens from the same log are identical. There are certain properties that characterize each species, but they are subject to considerable variation. Oak, for example, is considered hard, heavy, and strong, but some pieces, even of the same species of oak, are much harder, heavier, and stronger than others. With hickory are associated the properties of great strength, toughness, and resilience, but some pieces are comparatively weak and brash and ill-suited for the exacting demands for which good hickory is peculiarly adapted.

It follows that no definite value can be assigned to the properties of any wood and that tables giving average results of tests may not be directly applicable to any individual stick. With sufficient knowledge of the intrinsic factors affecting the results it becomes possible to infer from the appearance of material its probable variation from the average. As yet too little is known of the relation of structure and chemical composition to the mechanical and physical properties to permit more than general conclusions.

RATE OF GROWTH

To understand the effect of variations in the rate of growth it is first necessary to know how wood is formed. A tree increases in diameter by the formation, between the old wood and the inner bark, of new woody layers which envelop the entire stem, living branches, and roots. Under ordinary conditions one layer is formed each year and in cross section as on the end of a log they appear as rings—often spoken of as annual rings. These growth layers are made up of wood cells of various kinds, but for the most part fibrous. In timbers like pine, spruce, hemlock, and other coniferous or softwood species the wood cells are mostly of one kind, and as a result the material is much more uniform in structure than that of most hardwoods. (See Frontispiece.) There are no vessels or pores in coniferous wood such as one sees so prominently in oak and ash, for example. (See Fig. 22.)

Figure 22

Cross sections of a ring-porous hardwood (white ash), a diffuse-porous hardwood (red gum), and a non-porous or coniferous wood (eastern hemlock). × 30. Photomicrographs by the author.

The structure of the hardwoods is more complex. They are more or less filled with vessels, in some cases (oak, chestnut, ash) quite large and distinct, in others (buckeye, poplar, gum) too small to be seen plainly without a small hand lens. In discussing such woods it is customary to divide them into two large classes—ring-porous and diffuse-porous. (See Fig. 22.) In ring-porous species, such as oak, chestnut, ash, black locust, catalpa, mulberry, hickory, and elm, the larger vessels or pores (as cross sections of vessels are called) become localized in one part of the growth ring, thus forming a region of more or less open and porous tissue. The rest of the ring is made up of smaller vessels and a much greater proportion of wood fibres. These fibres are the elements which give strength and toughness to wood, while the vessels are a source of weakness.

In diffuse-porous woods the pores are scattered throughout the growth ring instead of being collected in a band or row. Examples of this kind of wood are gum, yellow poplar, birch, maple, cottonwood, basswood, buckeye, and willow. Some species, such as walnut and cherry, are on the border between the two classes, forming a sort of intermediate group.

If one examines the smoothly cut end of a stick of almost any kind of wood, he will note that each growth ring is made up of two more or less well-defined parts. That originally nearest the centre of the tree is more open textured and almost invariably lighter in color than that near the outer portion of the ring. The inner portion was formed early in the season, when growth was comparatively rapid and is known as early wood (also spring wood); the outer portion is the late wood, being produced in the summer or early fall. In soft pines there is not much contrast in the different parts of the ring, and as a result the wood is very uniform in texture and is easy to work. In hard pine, on the other hand, the late wood is very dense and is deep-colored, presenting a very decided contrast to the soft, straw-colored early wood. (See Fig. 23.) In ring-porous woods each season's growth is always well defined, because the large pores of the spring abut on the denser tissue of the fall before. In the diffuse-porous, the demarcation between rings is not always so clear and in not a few cases is almost, if not entirely, invisible to the unaided eye. (See Fig. 22.)

Figure 23

Cross section of longleaf pine showing several growth rings with variations in the width of the dark-colored late wood. Seven resin ducts are visible. × 33. Photomicrograph by U.S. Forest Service.

If one compares a heavy piece of pine with a light specimen it will be seen at once that the heavier one contains a larger proportion of late wood than the other, and is therefore considerably darker. The late wood of all species is denser than that formed early in the season, hence the greater the proportion of late wood the greater the density and strength. When examined under a microscope the cells of the late wood are seen to be very thick-walled and with very small cavities, while those formed first in the season have thin walls and large cavities. The strength is in the walls, not the cavities. In choosing a piece of pine where strength or stiffness is the important consideration, the principal thing to observe is the comparative amounts of early and late wood. The width of ring, that is, the number per inch, is not nearly so important as the proportion of the late wood in the ring.

It is not only the proportion of late wood, but also its quality, that counts. In specimens that show a very large proportion of late wood it may be noticeably more porous and weigh considerably less than the late wood in pieces that contain but little. One can judge comparative density, and therefore to some extent weight and strength, by visual inspection.

The conclusions of the U.S. Forest Service regarding the effect of rate of growth on the properties of Douglas fir are summarized as follows:

"1. In general, rapidly grown wood (less than eight rings per inch) is relatively weak. A study of the individual tests upon which the average points are based shows, however, that when it is not associated with light weight and a small proportion of summer wood, rapid growth is not indicative of weak wood.

"2. An average rate of growth, indicated by from 12 to 16 rings per inch, seems to produce the best material.

"3. In rates of growths lower than 16 rings per inch, the average strength of the material decreases, apparently approaching a uniform condition above 24 rings per inch. In such slow rates of growth the texture of the wood is very uniform, and naturally there is little variation in weight or strength.

"An analysis of tests on large beams was made to ascertain if average rate of growth has any relation to the mechanical properties of the beams. The analysis indicated conclusively that there was no such relation. Average rate of growth [without consideration also of density], therefore, has little significance in grading structural timber." 18 This is because of the wide variation in the percentage of late wood in different parts of the cross section.

Experiments seem to indicate that for most species there is a rate of growth which, in general, is associated with the greatest strength, especially in small specimens. For eight conifers it is as follows: 19



Rings per inch Douglas fir 24 Shortleaf pine 12 Loblolly pine 6 Western larch 18 Western hemlock 14 Tamarack 20 Norway pine 18 Redwood 30

No satisfactory explanation can as yet be given for the real causes underlying the formation of early and late wood. Several factors may be involved. In conifers, at least, rate of growth alone does not determine the proportion of the two portions of the ring, for in some cases the wood of slow growth is very hard and heavy, while in others the opposite is true. The quality of the site where the tree grows undoubtedly affects the character of the wood formed, though it is not possible to formulate a rule governing it. In general, however, it may be said that where strength or ease of working is essential, woods of moderate to slow growth should be chosen. But in choosing a particular specimen it is not the width of ring, but the proportion and character of the late wood which should govern.

In the case of the ring-porous hardwoods there seems to exist a pretty definite relation between the rate of growth of timber and its properties. This may be briefly summed up in the general statement that the more rapid the growth or the wider the rings of growth, the heavier, harder, stronger, and stiffer the wood. This, it must be remembered, applies only to ring-porous woods such as oak, ash, hickory, and others of the same group, and is, of course, subject to some exceptions and limitations.

In ring-porous woods of good growth it is usually the middle portion of the ring in which the thick-walled, strength-giving fibres are most abundant. As the breadth of ring diminishes, this middle portion is reduced so that very slow growth produces comparatively light, porous wood composed of thin-walled vessels and wood parenchyma. In good oak these large vessels of the early wood occupy from 6 to 10 per cent of the volume of the log, while in inferior material they may make up 25 per cent or more. The late wood of good oak, except for radial grayish patches of small pores, is dark colored and firm, and consists of thick-walled fibres which form one-half or more of the wood. In inferior oak, such fibre areas are much reduced both in quantity and quality. Such variation is very largely the result of rate of growth.

Wide-ringed wood is often called "second-growth," because the growth of the young timber in open stands after the old trees have been removed is more rapid than in trees in the forest, and in the manufacture of articles where strength is an important consideration such "second-growth" hardwood material is preferred. This is particularly the case in the choice of hickory for handles and spokes. Here not only strength, but toughness and resilience are important. The results of a series of tests on hickory by the U.S. Forest Service show that "the work or shock-resisting ability is greatest in wide-ringed wood that has from 5 to 14 rings per inch, is fairly constant from 14 to 38 rings, and decreases rapidly from 38 to 47 rings. The strength at maximum load is not so great with the most rapid-growing wood; it is maximum with from 14 to 20 rings per inch, and again becomes less as the wood becomes more closely ringed. The natural deduction is that wood of first-class mechanical value shows from 5 to 20 rings per inch and that slower growth yields poorer stock. Thus the inspector or buyer of hickory should discriminate against timber that has more than 20 rings per inch. Exceptions exist, however, in the case of normal growth upon dry situations, in which the slow-growing material may be strong and tough." 20

The effect of rate of growth on the qualities of chestnut wood is summarized by the same authority as follows: "When the rings are wide, the transition from spring wood to summer wood is gradual, while in the narrow rings the spring wood passes into summer wood abruptly. The width of the spring wood changes but little with the width of the annual ring, so that the narrowing or broadening of the annual ring is always at the expense of the summer wood. The narrow vessels of the summer wood make it richer in wood substance than the spring wood composed of wide vessels. Therefore, rapid-growing specimens with wide rings have more wood substance than slow-growing trees with narrow rings. Since the more the wood substance the greater the weight, and the greater the weight the stronger the wood, chestnuts with wide rings must have stronger wood than chestnuts with narrow rings. This agrees with the accepted view that sprouts (which always have wide rings) yield better and stronger wood than seedling chestnuts, which grow more slowly in diameter." 21

In diffuse-porous woods, as has been stated, the vessels or pores are scattered throughout the ring instead of collected in the early wood. The effect of rate of growth is, therefore, not the same as in the ring-porous woods, approaching more nearly the conditions in the conifers. In general it may be stated that such woods of medium growth afford stronger material than when very rapidly or very slowly grown. In many uses of wood, strength is not the main consideration. If ease of working is prized, wood should be chosen with regard to its uniformity of texture and straightness of grain, which will in most cases occur when there is little contrast between the late wood of one season's growth and the early wood of the next.

HEARTWOOD AND SAPWOOD

Examination of the end of a log of many species reveals a darker-colored inner portion—the heartwood, surrounded by a lighter-colored zone—the sapwood. In some instances this distinction in color is very marked; in others, the contrast is slight, so that it is not always easy to tell where one leaves off and the other begins. The color of fresh sapwood is always light, sometimes pure white, but more often with a decided tinge of green or brown.

Sapwood is comparatively new wood. There is a time in the early history of every tree when its wood is all sapwood. Its principal functions are to conduct water from the roots to the leaves and to store up and give back according to the season the food prepared in the leaves. The more leaves a tree bears and the more thrifty its growth, the larger the volume of sapwood required, hence trees making rapid growth in the open have thicker sapwood for their size than trees of the same species growing in dense forests. Sometimes trees grown in the open may become of considerable size, a foot or more in diameter, before any heartwood begins to form, for example, in second-growth hickory, or field-grown white and loblolly pines.

As a tree increases in age and diameter an inner portion of the sapwood becomes inactive and finally ceases to function. This inert or dead portion is called heartwood, deriving its name solely from its position and not from any vital importance to the tree, as is shown by the fact that a tree can thrive with its heart completely decayed. Some, species begin to form heartwood very early in life, while in others the change comes slowly. Thin sapwood is characteristic of such trees as chestnut, black locust, mulberry, Osage orange, and sassafras, while in maple, ash, gum, hickory, hackberry, beech, and loblolly pine, thick sapwood is the rule.

There is no definite relation between the annual rings of growth and the amount of sapwood. Within the same species the cross-sectional area of the sapwood is roughly proportional to the size of the crown of the tree. If the rings are narrow, more of them are required than where they are wide. As the tree gets larger, the sapwood must necessarily become thinner or increase materially in volume. Sapwood is thicker in the upper portion of the trunk of a tree than near the base, because the age and the diameter of the upper sections are less.

When a tree is very young it is covered with limbs almost, if not entirely, to the ground, but as it grows older some or all of them will eventually die and be broken off. Subsequent growth of wood may completely conceal the stubs which, however, will remain as knots. No matter how smooth and clear a log is on the outside, it is more or less knotty near the middle. Consequently the sapwood of an old tree, and particularly of a forest-grown tree, will be freer from knots than the heartwood. Since in most uses of wood, knots are defects that weaken the timber and interfere with its ease of working and other properties, it follows that sapwood, because of its position in the tree, may have certain advantages over heartwood.

It is really remarkable that the inner heartwood of old trees remains as sound as it usually does, since in many cases it is hundreds of years, and in a few instances thousands of years, old. Every broken limb or root, or deep wound from fire, insects, or falling timber, may afford an entrance for decay, which, once started, may penetrate to all parts of the trunk. The larvæ of many insects bore into the trees and their tunnels remain indefinitely as sources of weakness. Whatever advantages, however, that sapwood may have in this connection are due solely to its relative age and position.

If a tree grows all its life in the open and the conditions of soil and site remain unchanged, it will make its most rapid growth in youth, and gradually decline. The annual rings of growth are for many years quite wide, but later they become narrower and narrower. Since each succeeding ring is laid down on the outside of the wood previously formed, it follows that unless a tree materially increases its production of wood from year to year, the rings must necessarily become thinner. As a tree reaches maturity its crown becomes more open and the annual wood production is lessened, thereby reducing still more the width of the growth rings. In the case of forest-grown trees so much depends upon the competition of the trees in their struggle for light and nourishment that periods of rapid and slow growth may alternate. Some trees, such as southern oaks, maintain the same width of ring for hundreds of years. Upon the whole, however, as a tree gets larger in diameter the width of the growth rings decreases.

It is evident that there may be decided differences in the grain of heartwood and sapwood cut from a large tree, particularly one that is overmature. The relationship between width of growth rings and the mechanical properties of wood is discussed under Rate of Growth. In this connection, however, it may be stated that as a general rule the wood laid on late in the life of a tree is softer, lighter, weaker, and more even-textured than that produced earlier. It follows that in a large log the sapwood, because of the time in the life of the tree when it was grown, may be inferior in hardness, strength, and toughness to equally sound heartwood from the same log.

After exhaustive tests on a number of different woods the U.S. Forest Service concludes as follows: "Sapwood, except that from old, overmature trees, is as strong as heartwood, other things being equal, and so far as the mechanical properties go should not be regarded as a defect." 22 Careful inspection of the individual tests made in the investigation fails to reveal any relation between the proportion of sapwood and the breaking strength of timber.

In the study of the hickories the conclusion was: "There is an unfounded prejudice against the heartwood. Specifications place white hickory, or sapwood, in a higher grade than red hickory, or heartwood, though there is no inherent difference in strength. In fact, in the case of large and old hickory trees, the sapwood nearest the bark is comparatively weak, and the best wood is in the heart, though in young trees of thrifty growth the best wood is in the sap." 23 The results of tests from selected pieces lying side by side in the same tree, and also the average values for heartwood and sapwood in shipments of the commercial hickories without selection, show conclusively that "the transformation of sapwood into heartwood does not affect either the strength or toughness of the wood.... It is true, however, that sapwood is usually more free from latent defects than heartwood." 24

Specifications for paving blocks often require that longleaf pine be 90 per cent heart. This is on the belief that sapwood is not only more subject to decay, but is also weaker than heartwood. In reality there is no sound basis for discrimination against sapwood on account of strength, provided other conditions are equal. It is true that sapwood will not resist decay as long as heartwood, if both are untreated with preservatives. It is especially so of woods with deep-colored heartwood, and is due to infiltrations of tannins, oils, and resins, which make the wood more or less obnoxious to decay-producing fungi. If, however, the timbers are to be treated, sapwood is not a defect; in fact, because of the relative ease with which it can be impregnated with preservatives it may be made more desirable than heartwood. 25

In specifications for structural timbers reference is sometimes made to "boxheart," meaning the inclusion of the pith or centre of the tree within a cross section of the timber. From numerous experiments it appears that the position of the pith does not bear any relation to the strength of the material. Since most season checks, however, are radial, the position of the pith may influence the resistance of a seasoned beam to horizontal shear, being greatest when the pith is located in the middle half of the section. 26

WEIGHT, DENSITY, AND SPECIFIC GRAVITY

From data obtained from a large number of tests on the strength of different woods it appears that, other things being equal, the crushing strength parallel to the grain, fibre stress at elastic limit in bending, and shearing strength along the grain of wood vary in direct proportion to the weight of dry wood per unit of volume when green. Other strength values follow different laws. The hardness varies in a slightly greater ratio than the square of the density. The work to the breaking point increases even more rapidly than the cube of density. The modulus of rupture in bending lies between the first power and the square of the density. This, of course, is true only in case the greater weight is due to increase in the amount of wood substance. A wood heavy with resin or other infiltrated substance is not necessarily stronger than a similar specimen free from such materials. If differences in weight are due to degree of seasoning, in other words, to the relative amounts of water contained, the rules given above will of course not hold, since strength increases with dryness. But of given specimens of pine or of oak, for example, in the green condition, the comparative strength may be inferred from the weight. It is not permissible, however, to compare such widely different woods as oak and pine on a basis of their weights. 27

The weight of wood substance, that is, the material which composes the walls of the fibres and other cells, is practically the same in all species, whether pine, hickory, or cottonwood, being a little greater than half again as heavy as water. It varies slightly from beech sapwood, 1.50, to Douglas fir heartwood, 1.57, averaging about 1.55 at 30° to 35° C., in terms of water at its greatest density 4° C. The reason any wood floats is that the air imprisoned in its cavities buoys it up. When this is displaced by water the wood becomes water-logged and sinks. Leaving out of consideration infiltrated substances, the reason a cubic foot of one kind of dry wood is heavier than that of another is because it contains a greater amount of wood substance. Density is merely the weight of a unit of volume, as 35 pounds per cubic foot, or 0.56 grams per cubic centimetre. Specific gravity or relative density is the ratio of the density of any material to the density of distilled water at 4° C. (39.2° F.). A cubic foot of distilled water at 4° C. weighs 62.43 pounds. Hence the specific gravity of a piece of wood with a density of 35 pounds is

35







-------

=

0.561

.

62.43









To find the weight per cubic foot when the specific gravity is given, simply multiply by 62.43. Thus, 0.561 × 62.43 = 35. In the metric system, since the weight of a cubic centimetre of pure water is one gram, the density in grams per cubic centimetre has the same numerical value as the specific gravity.

Since the amount of water in wood is extremely variable it usually is not satisfactory to refer to the density of green wood. For scientific purposes the density of "oven-dry" wood is used; that is, the wood is dried in an oven at a temperature of 100°C. (212°F.) until a constant weight is attained. For commercial purposes the weight or density of air-dry or "shipping-dry" wood is used. This is usually expressed in pounds per thousand board feet, a board foot being considered as one-twelfth of a cubic foot.

Wood shrinks greatly in drying from the green to the oven-dry condition. (See Table XIV.) Consequently a block of wood measuring a cubic foot when green will measure considerably less when oven-dry. It follows that the density of oven-dry wood does not represent the weight of the dry wood substance in a cubic foot of green wood. In other words, it is not the weight of a cubic foot of green wood minus the weight of the water which it contains. Since the latter is often a more convenient figure to use and much easier to obtain than the weight of oven-dry wood, it is commonly expressed in tables of "specific gravity or density of dry wood."

TABLE XIV SPECIFIC GRAVITY, AND SHRINKAGE OF 51 AMERICAN WOODS (Forest Service Cir. 213) COMMON NAME OF SPECIES Moisture content Specific gravity oven-dry, based on Shrinkage from green to oven-dry condition Volume when green Volume when oven-dry In volume Radial Tangential Per cent



Per cent Per cent Per cent Hardwoods











Ash, black 77 0.466







white 38 .550 0.640 12.6 4.3 6.4 " 47 .516 .590 11.7



Basswood 110 .315 .374 14.5 6.2 8.4 Beech 61 .556 .669 16.5 4.6 10.5 Birch, yellow 72 .545 .661 17.0 7.9 9.0 Elm, rock 46 .578







slippery 57 .541 .639 15.5 5.1 9.9 white 66 .430







Gum, red 71 .434







Hackberry 50 .504 .576 14.0 4.2 8.9 Hickory, big shellbark 64 .601

17.6 7.4 11.2 " 55 .666

20.9 7.9 14.2 bitternut 65 .624







mockernut 64 .606

16.5 6.9 10.4 " 57 .662

18.9 8.4 11.4 " 48 .666







nutmeg 76 .558







pignut 59 .627

15.0 5.6 9.8 " 54 .667

15.3 6.3 9.5 " 55 .667

16.9 6.8 10.9 " 52 .667

21.2 8.5 13.8 shagbark 65 .608

16.0 6.5 10.2 " 58 .646

18.4 7.9 11.4 " 64 .617







" 60 .653

15.5 6.5 9.7 water 74 .630







Locust, honey 53 .695 .759 8.6



Maple, red 69 .512







sugar 57 .546 .643 14.3 4.9 9.1 " 56 .577







Oak, post 64 .590 .732 16.0 5.7 10.6 red 80 .568 .660 13.1 3.7 8.3 swamp white 74 .637 .792 17.7 5.5 10.6 tanbark 88 .585







white 58 .594 .704 15.8 6.2 8.3 " 62 .603 .696 14.3 4.9 9.0 " 78 .600 .708 16.0 4.8 9.2 yellow 77 .573 .669 14.2 4.5 9.7 " 80 .550







Osage orange 31 .761 .838 8.9



Sycamore 81 .454 .526 13.5 5.0 7.3 Tupelo 121 .475 .545 12.4 4.4 7.9

TABLE XIV (CONT.) SPECIFIC GRAVITY, AND SHRINKAGE OF 51 AMERICAN WOODS (Forest Service Cir. 213) COMMON NAME OF SPECIES Moisture content Specific gravity oven-dry, based on Shrinkage from green to oven-dry condition Volume when green Volume when oven-dry In volume Radial Tangential Per cent



Per cent Per cent Per cent Conifers











Arborvitæ 55 .293 .315 7.0 2.1 4.9 Cedar, incense 80 .363







Cypress, bald 79 .452 .513 11.5 3.8 6.0 Fir, alpine 47 .306 .321 9.0 2.5 7.1 amabilis 117 .383







Douglas 32 .418 .458 10.9 3.7 6.6 white 156 .350 .437 10.2 3.4 7.0 Hemlock (east.) 129 .340 .394 9.2 2.3 5.0 Pine, lodgepole 44 .370 .415 11.3 4.2 7.1 lodgepole 58 .371 .407 10.1 3.6 5.9 longleaf 63 .528 .599 12.8 6.0 7.6 red or Nor 54 .440 .507 11.5 4.5 7.2 shortleaf 52 .447







sugar 123 .360 .386 8.4 2.9 5.6 west yellow 98 .353 .395 9.2 4.1 6.4 " 125 .377 .433 11.5 4.3 7.3 " 93 .391 .435 9.9 3.8 5.8 white 74 .363 .391 7.8 2.2 5.9 Redwood 81 .334







" 69 .366







Spruce, Engelmann 45 .325 .359 10.5 3.7 6.9 " 156 .299 .335 10.3 3.0 6.2 red 31 .396







white 41 .318







Tamarack 52 .491 .558 13.6 3.7 7.4

This weight divided by 62.43 gives the specific gravity per green volume. It is purely a fictitious quantity. To convert this figure into actual density or specific gravity of the dry wood, it is necessary to know the amount of shrinkage in volume. If S is the percentage of shrinkage from the green to the oven-dry condition, based on the green volume; D, the density of the dry wood per cubic foot while green; and d the actual density of oven-dry wood, then

D



---------- = d. 1 - .0 S





This relation becomes clearer from the following analysis: Taking V and W as the volume and weight, respectively, when green, and v and w as the corresponding volume and weight when oven-dry, then,





w





W





V -