THE MECHANICAL PROPERTIES OF WOOD
[Illustration: Frontispiece. _Photo by the author_.
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. X 35.]
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
PREFACE
PART I THE MECHANICAL PROPERTIES OF WOOD
Introduction
Fundamental considerations and definitions
Tensile strength
Compressive or crushing strength
Shearing strength
Transverse or bending strength: Beams
Toughness: Torsion
Hardness
Cleavability
PART II FACTORS AFFECTING THE MECHANICAL PROPERTIES OF
WOOD
Introduction
Rate of growth
Heartwood and sapwood
Weight, density, and specific gravity
Color
Cross grain
Knots
Frost splits
Shakes, galls, pitch pockets
Insect injuries
Marine wood-borer injuries
Fungous injuries
Parasitic plant injuries
Locality of growth
Season of cutting
Water content
Temperature
Preservatives
PART III TIMBER TESTING
Working plan
Forms of material tested
Size of test specimens
Moisture determination
Machine for static tests
Speed of testing machine
Bending large beams
Bending small beams
Endwise compression
Compression across the grain
Shear along the grain
Impact test
Hardness test: Abrasion and indentation
Cleavage test
Tension test parallel to the grain
Tension test at right angles to the grain
Torsion test
Special tests
Spike pulling test
Packing boxes
Vehicle and implement woods
Cross-arms
Other tests
APPENDIX
Sample working plan of United States Forest
Service
Strength values for structural timbers
BIBLIOGRAPHY
Part I: Some general works on mechanics, materials of
construction, and testing of materials
Part II: Publications and articles on the mechanical
properties of wood, and timber testing
Part III: Publications of the United States Government on
the mechanical properties of wood, and timber
testing
ILLUSTRATIONS
Frontispiece Photomicrograph of a small block of western
hemlock
1. Stress-strain diagrams of two longleaf pine beams
2. Compression across the grain
3. Side view of failures in compression across the
grain
4. End view of failures in compression across the
grain
5. Testing a buggy-spoke in endwise compression
6. Unequal distribution of stress in a long column due
to lateral bending
7. Endwise compression of a short column
8. Failures of a short column of green spruce
9. Failures of short columns of dry chestnut
10. Example of shear along the grain
11. Failures of test specimens in shear along the
grain
12. Horizontal shear in a beam
13. Oblique shear in a short column
14. Failure of a short column by oblique shear
15. Diagram of a simple beam
16. Three common forms of beams--(1) simple,
(2) cantilever, (3) continuous
17. Characteristic failures of simple beams
18. Failure of a large beam by horizontal shear
19. Torsion of a shaft
20. Effect of torsion on different grades of hickory
21. Cleavage of highly elastic wood
22. Cross-sections of white ash, red gum, and eastern
hemlock
23. Cross-section of longleaf pine
24. Relation of the moisture content to the various
strength values of spruce
25. Cross-section of the wood of western larch showing
fissures in the thick-walled cells of the late
wood
26. Progress of drying throughout the length of a
chestnut beam
27. Excessive season checking
28. Control of season checking by the use of S-irons
29. Static bending test on a large beam
30. Two methods of loading a beam
31. Static bending test on a small beam
32. Sample log sheet, giving full details of a
transverse bending test on a small pine beam
33. Endwise compression test
34. Sample log sheet of an endwise compression test on
a short pine column
35. Compression across the grain
36. Vertical section of shearing tool
37. Front view of shearing tool
38. Two forms of shear test specimens
39. Making a shearing test
40. Impact testing machine
41. Drum record of impact bending test
42. Abrasion machine for testing the wearing qualities
of woods
43. Design of tool for testing the hardness of woods
by indentation
44. Design of tool for cleavage test
45. Design of cleavage test specimen
46. Designs of tension test specimens used in United
States
47. Design of tension test specimen used in New South
Wales
48. Design of tool and specimen for testing tension at
right angles to the grain
49. Making a torsion test on hickory
50. Method of cutting and marking test specimens
51. Diagram of specific gravity apparatus
TABLES
I. Comparative strength of iron, steel, and wood
II. Ratio of strength of wood in tension and in
compression
III. Right-angled tensile strength of small clear
pieces of 25 woods in green condition
IV. Results of compression tests across the grain on
51 woods in green condition, and comparison with
white oak
V. Relation of fibre stress at elastic limit in
bending to the crushing strength of blocks cut
therefrom in pounds per square inch
VI. Results of endwise compression tests on small
clear pieces of 40 woods in green condition
VII. Shearing strength along the grain of small clear
pieces of 41 woods in green condition
VIII. Shearing strength across the grain of various
American woods
IX. Results of static bending tests on small clear
beams of 49 woods in green condition
X. Results of impact bending tests on small clear
beams of 34 woods in green condition
XI. Manner of first failure of large beams
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
XIII. Cleavage strength of small clear pieces of 32
woods in green condition
XIV. Specific gravity, and shrinkage of 51 American
woods
XV. Effect of drying on the mechanical properties of
wood, shown in ratio of increase due to reducing
moisture content from the green condition to
kiln-dry
XVI. Effect of steaming on the strength of green
loblolly pine
XVII. Speed-strength moduli, and relative increase in
strength at rates of fibre strain increasing in
geometric ratio
XVIII. Results of bending tests on green structural
timbers
XIX. Results of compression and shear tests on green
structural timbers
XX. Results of bending tests on air-seasoned
structural timbers
XXI. Results of compression and shear tests on
air-seasoned structural timbers
XXII. Working unit stresses for structural timber
expressed in pounds per square inch
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 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.
[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 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
{ 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 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 |
|------------------------------------------------------------------------------|
| | 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. |
|------------------------------------------------------------------------------|
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) |
|--------------------------------------------------------------|
| | Ratio: | A stick 1 square inch in |
| | | cross section. |
| | Tensile | |
| KIND OF WOOD | strength | Weight required to-- |
| | R = ----------- +----------------------------|
| | compressive | Pull apart | Crush endwise |
| | strength | | |
|---------------+-----------------+------------+---------------|
| 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]
[Footnote 3: See Brush, Warren D.: A microscopic study of the
mechanical failure of wood. Vol. II, Rev. F.S. Investigations,
Washington, D.C., 1912, p. 35.]
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) |
|--------------------------------------------|
| | When | When |
| COMMON NAME | surface of | surface of |
| OF SPECIES | failure is | failure is |
| | radial | tangential |
|------------------+------------+------------|
| | Lbs. per | Lbs. per |
| | sq. inch | 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.
[Illustration: FIG. 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.
[Illustration: FIG. 3.--Side view of failures in compression
across the grain, showing crushing of blocks under bearing
plate. Specimen at right shows splitting at ends.]
[Illustration: FIG. 4.--End view of failures in compression
across the grain, showing splitting of the ends of the test
specimens.]
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.
[Illustration: FIG. 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.
[Illustration: FIG. 6.--Unequal distribution of stress in a long
column due to lateral bending.]
|-------------------------------------------------------|
| TABLE IV |
|-------------------------------------------------------|
| RESULTS OF COMPRESSION TESTS ACROSS THE GRAIN ON |
| 51 WOODS IN GREEN CONDITION, AND COMPARISON WITH |
| WHITE OAK |
| (U. S. Forest Service) |
|-------------------------------------------------------|
| | Fibre stress | Fiber stress |
| COMMON NAME | at elastic | in per cent |
| OF SPECIES | limit | of white oak, |
| | perpendicular | or 853 pounds |
| | to grain | 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 |
|-------------------------------------------------------|
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
{ P }
by the area of the cross-section (A). { C = --- }
{ A }
[Illustration: FIG. 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
V.) 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.
[Footnote 4: See Circular No. 18, U.S. Division of Forestry:
Progress in timber physics, pp. 13-18; also Bulletin 70, U.S.
Forest Service: Effect of moisture on the strength and stiffness
of wood, pp. 42, 89-90.]
|-------------------------------------------------------------------------------|
| 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 |
|-------------------------------------------------------------------------------|
| | Soaked | Green | 14 | 11.5 | 9.5 | Kiln-dry |
| MOISTURE CONDITION | 50 per | 23 per | per | per | per | 6.2 per |
| | cent | cent | cent | cent | cent | 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 |
|-------------------------------------------------------------------------------|
| | Soaked | Green | 10 | 8.1 | Kiln-dry |
| MOISTURE CONDITION | 30 per | 30 per | per | per | 3.9 per |
| | cent | cent | cent | cent | 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]
[Footnote 5: See Bulletin 70, _op. cit._, p. 129.]
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.
[Footnote 6: Jaccard, P.: Étude anatomique des bois comprimés.
Mit. d. Schw. Centralanstalt f.d. forst. Versuchswesen. X. Band,
1. Heft. Zurich, 1910, p. 66.]
|-------------------------------------------------------|
| TABLE VI |
|-------------------------------------------------------|
| RESULTS OF ENDWISE COMPRESSION TESTS ON SMALL CLEAR |
| PIECES OF 40 WOODS IN GREEN CONDITION |
| (Forest Service Cir. 213) |
|-------------------------------------------------------|
| | Fibre | | Modulus |
| COMMON NAME | stress at | Crushing | of |
| OF SPECIES | elastic | strength | elasticity |
| | limit | | |
|-------------------+-----------+----------+------------|
| | Lbs. per | Lbs. per | Lbs. per |
| | sq. inch | sq. inch | 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.
[Illustration: FIG. 8.--Failures of short columns of green
spruce.]
[Illustration: FIG. 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.
[Footnote 7: This does not correspond exactly with the
conclusions of A. Thil, who says ("Constitution anatomique du
bois," pp. 140-141): "The sides of the medullary rays sometimes
produce planes of least resistance varying in size with the
height of the rays. The medullary rays assume a direction more
or less parallel to the lumen of the cells on which they border;
the latter curve to the right or left to make room for the ray
and then close again beyond it. If the force acts parallel to
the axis of growth, the tracheids are more likely to be
displaced if the marginal cells of the medullary rays are
provided with weak walls that are readily compressed. This
explains why on the radial surface of the test blocks the plane
of rupture passes in a direction nearly following a medullary
ray, whereas on the tangential surface the direction of the
plane of rupture is oblique--but with an obliquity varying with
the species and determined by the pitch of the spirals along
which the medullary rays are distributed in the stem." See
Jaccard, _op. cit._, pp. 57 _et seq._]
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.
[Footnote 8: Shear should not be confused with ordinary cutting
or incision.]
[Illustration: FIG. 10.--Example of shear along the grain.]
[Illustration: FIG. 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) |
|---------------------------------------------|
| | When | When |
| COMMON NAME | surface of | surface of |
| OF SPECIES | failure is | failure is |
| | radial | tangential |
|-------------------+------------+------------|
| | Lbs. per | Lbs. per |
| | sq. inch | 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.
[Illustration: FIG. 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
P
with the axis of the specimen. In this case, shear = -----. When
2 A
the value of the angle [Greek: theta] is less than 45 degrees,
P
the shear along the plane = --- sin [Greek: theta] cos [Greek:
A
theta]. (See Fig. 13.) The effect of oblique shear is often
visible in the failures of short columns. (See Fig. 14.)
[Illustration: FIG. 13.--Oblique shear in a short column.]
[Illustration: FIG. 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 | KIND OF WOOD | Lbs. per |
| | sq. inch | | 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.
[Footnote 9: While in reality this relationship does not exactly
hold, the formulæ for beams are based on its assumption.]
[Illustration: FIG. 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.)
[Illustration: FIG. 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]
[Footnote 10: Only this form of beam is considered since it is
the simplest. For cantilever and continuous beams, and beams
rigidly fixed at one or both ends, as well as for different
methods of loading, different forms of cross section, etc.,
other formulæ are required. See any book on mechanics.]
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) |
|-------------------------------------------------------------------------------------|
| | Fibre | | | Work in Bending |
| COMMON NAME | stress at | Modulus | Modulus |-------------------------------|
| OF SPECIES | elastic | of | of | To | To | |
| | limit | rupture | elasticity | elastic | maximum | Total |
| | | | | limit | load | |
|-----------------+-----------+----------+------------+----------+----------+---------|
| | | | | In.-lbs. | In.-lbs. | In.-lb. |
| | Lbs. per | Lbs. per | Lbs. per | per cu. | per cu. | per |
| | sq. in. | sq. in. | sq. in. | inch | inch | 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]
[Footnote 11: See Tiemann, Harry D.: Some results of dead load
bending tests of timber by means of a recording deflectometer.
Proc. Am. Soc. for Testing Materials. Phila. Vol. IX, 1909, pp.
534-548.]
~Maximum load~ is the greatest load a material will support and
is usually greater than the load at rupture.
~Safe load~ is the load considered safe for a material to
support in actual practice. It is always less than the load at
elastic limit and is usually taken as a certain proportion of
the ultimate or breaking load.
The ratio of the breaking to the safe load is called the factor
of safety. (Factor of safety = ultimate strength / 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:
[Footnote 12: A fourth might be added, namely, ~vibratory~, or
~harmonic repetition~, which is frequently serious in the case
of bridges.]
(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]
[Footnote 13: Johnson, J.B.: The materials of construction, pp.
81-82.]
(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.
[Footnote 14: See Tiemann, Harry D.: The theory of impact and
its application to testing materials. Jour. Franklin Inst.,
Oct., Nov., 1909, pp. 235-259, 336-364.]
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) |
|-------------------------------------------------------|
| | Fibre | | Work in |
| COMMON NAME | stress at | Modulus of | bending |
| OF SPECIES | elastic | elasticity | to |
| | limit | | elastic |
| | | | limit |
|-------------------+-----------+------------+----------|
| | | | In.-lbs. |
| | Lbs. per | Lbs. per | per cu. |
| | sq. in. | sq. in. | 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]
[Footnote 15: See Proc. Int. Assn. for Testing Materials, 1912,
XXIII_{2}, pp. 12-13.]
Within the elastic limit the elongations and shortenings are
equal, and the neutral plane lies in the middle of the beam.
(See TRANSVERSE OR BENDING STRENGTH: BEAMS, above.) 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.
[Illustration: FIG. 17.--Characteristic failures of simple
beams.]
(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.
~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.
[Illustration: FIG. 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) |
|-----------------------------------------------------------|
| | Total | Per cent of total failing by |
| COMMON NAME | number |---------+-------------+-------|
| OF SPECIES | of | Tension | Compression | Shear |
| | tests | | | |
|------------------+--------+---------+-------------+-------|
| 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" x 10" to 8" x 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.
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.
[Illustration: FIG. 19.--Torsion of a shaft.]
[Illustration: FIG. 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 | Radial | Tangential |
| | | surface | surface | 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.
[Footnote 16: See articles by Gabriel Janka listed in
bibliography, pages 151-152.]
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.
[Illustration: FIG. 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) |
|---------------------------------------------|
| | When | When |
| COMMON NAME | surface of | surface of |
| OF SPECIES | failure is | failure is |
| | radial | tangential |
|-------------------+------------+------------|
| | Lbs. per | Lbs. per |
| | sq. inch | 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 |
| Hackberry | 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 |
|---------------------------------------------|