FUNDAMENTAL CONSIDERATIONS AND DEFINITIONS

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

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

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

Stress is measured in pounds (or other unit of weight or force).  A unit stress is the stress on a unit of the sectional
      { P }
area. { Unit stress = —–­ } For instance, if a load (P) of one
      { A }
hundred pounds is uniformly supported by a vertical post with a cross-sectional area (A) of ten square inches, the unit compressive stress is ten pounds per square inch.

Strain is measured in inches (or other linear unit).  A unit strain is the strain per unit of length.  Thus if a post 10 inches long before compression is 9.9 inches long under the compressive stress, the total strain is 0.1 inch, and the unit
l 0.1
strain is --- = ----- = 0.01 inch per inch of length. 
L 10

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