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The Mechanical Properties of Wood Part 1

The Mechanical Properties of Wood.

by Samuel J. Record.

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_.

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_, in FUNDAMENTAL CONSIDERATIONS AND DEFINITIONS, above) 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.

[Footnote 1: This is in accordance with the discovery made in 1678 by Robert Hooke, and is known as _Hooke's law_.]

Stress is measured in pounds (or other unit of weight or force).

A ~unit stress~ is the stress on a unit of the sectional { P } area. { Unit stress = --- } For instance, if a load (P) of one { A } 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 l 0.1 strain is --- = ----- = 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 abscissae. 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.

[Illustration: FIG. 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.)

[Footnote 2: If the straight portion does not pass through the origin, a parallel line should be drawn through the origin, and the load at elastic limit taken from this line. (See Fig. 32.)]

~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 abscissae 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 { unit stress } length. { E = ------------- } It is a number indicative of { unit strain } 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 arborvitae 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 ------------------------------------------------------------------------------ Sp. Modulus of Tensile Crushing Modulus MATERIAL gr., elasticity strength strength of dry in bending rupture -------------------------+----- +------------+----------+----------+---------- Lbs. per Lbs. per Lbs. per Lbs. per sq. in. sq. in. sq. in. 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. ------------------------------------------------------------------------------

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