Study of the mechanical properties of a material is concerned mostly with its behavior in relation to stresses and strains, and the factors affecting this behavior. A stress is a distributed force and may be defined as the mutual action (1) of one body upon another, or (2) of one part of a body upon another part. In the first case the stress is external; in the other internal. The same stress may be internal from one point of view and external from another. An external force is always balanced by the internal stresses when the body is in equilibrium.

If no external forces act upon a body its particles assume certain relative positions, and it has what is called its natural shape and size. If sufficient external force is applied the natural shape and size will be changed. This distortion or deformation of the material is known as the strain. Every stress produces a corresponding strain, and within a certain limit (see elastic limit, page 5) the strain is directly proportional to the stress producing it.1 The same intensity of stress, however, does not produce the same strain in different materials or in different qualities of the same material. No strain would be produced in a perfectly rigid body, but such is not known to exist.

[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 area.

For instance, if a load (P) of one hundred pounds is uniformly supported by a vertical post with a cross-sectional area (A) of ten square inches, the unit compressive stress is ten pounds per square inch.

Strain is measured in inches (or other linear unit). A unit strain is the strain per unit of length. Thus if a post 10 inches long before compression is 9.9 inches long under the compressive stress, the total strain is 0.1 inch, and the unit strain is

As the stress increases there is a corresponding increase in the strain. This ratio may be graphically shown by means of a diagram or curve plotted with the increments of load or stress as ordinates and the increments of strain as abscissæ. This is known as the stress-strain diagram. Within the limit mentioned above the diagram is a straight line. (See Fig. 1.) If the results of similar experiments on different specimens are plotted to the same scales, the diagrams furnish a ready means for comparison. The greater the resistance a material offers to deformation the steeper or nearer the vertical axis will be the line.

Figure 1

Stress-strain diagrams of two longleaf pine beams. E.L. = elastic limit. The areas of the triangles 0(EL)A and 0(EL)B represent the elastic resilience of the dry and green beams, respectively.

There are three kinds of internal stresses, namely, (1) tensile, (2) compressive, and (3) shearing. When external forces act upon a bar in a direction away from its ends or a direct pull, the stress is a tensile stress; when toward the ends or a direct push, compressive stress. In the first instance the strain is an elongation; in the second a shortening. Whenever the forces tend to cause one portion of the material to slide upon another adjacent to it the action is called a shear. The action is that of an ordinary pair of shears. When riveted plates slide on each other the rivets are sheared off.

These three simple stresses may act together, producing compound stresses, as in flexure. When a bow is bent there is a compression of the fibres on the inner or concave side and an elongation of the fibres on the outer or convex side. There is also a tendency of the various fibres to slide past one another in a longitudinal direction. If the bow were made of two or more separate pieces of equal length it would be noted on bending that slipping occurred along the surfaces of contact, and that the ends would no longer be even. If these pieces were securely glued together they would no longer slip, but the tendency to do so would exist just the same. Moreover, it would be found in the latter case that the bow would be much harder to bend than where the pieces were not glued together - in other words, the stiffness of the bow would be materially increased.

Stiffness is the property by means of which a body acted upon by external forces tends to retain its natural size and shape, or resists deformation. Thus a material that is difficult to bend or otherwise deform is stiff; one that is easily bent or otherwise deformed is flexible. Flexibility is not the exact counterpart of stiffness, as it also involves toughness and pliability.

If successively larger loads are applied to a body and then removed it will be found that at first the body completely regains its original form upon release from the stress - in other words, the body is elastic. No substance known is perfectly elastic, though many are practically so under small loads. Eventually a point will be reached where the recovery of the specimen is incomplete. This point is known as the elastic limit, which may be defined as the limit beyond which it is impossible to carry the distortion of a body without producing a permanent alteration in shape. After this limit has been exceeded, the size and shape of the specimen after removal of the load will not be the same as before, and the difference or amount of change is known as the permanent set.

Elastic limit as measured in tests and used in design may be defined as that unit stress at which the deformation begins to increase in a faster ratio than the applied load. In practice the elastic limit of a material under test is determined from the stress-strain diagram. It is that point in the line where the diagram begins perceptibly to curve.2 (See Fig. 1.)

[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 length.

It is a number indicative of stiffness, not of strength, and only applies to conditions within the elastic limit. It is nearly the same whether derived from compression tests or from tension tests.

A large modulus indicates a stiff material. Thus in green wood tested in static bending it varies from 643,000 pounds per square inch for arborvitæ to 1,662,000 pounds for longleaf pine, and 1,769,000 pounds for pignut hickory. (See Table IX.) The values derived from tests of small beams of dry material are much greater, approaching 3,000,000 for some of our woods. These values are small when compared with steel which has a modulus of elasticity of about 30,000,000 pounds per square inch. (See Table I.)