Fundamental Definitions
Static Stresses
TOTAL STRESS on a section mn through a loaded body is the resultant force S exerted by one part of the body on the other part in order to maintain in equilibrium the external loads acting on the part. Thus, in Figs. 1, 2, and 3 the total stress on section mn due to the external load P is S. The units in which it is expressed are those of load, that is, pounds, tons, etc.
UNIT STRESS, more commonly called stress , is the total stress per unit of area at section mn. In general it varies from point to point over the section. Its value at any point of a section is the total stress on an elementary part of the area, including the point divided by the elementary total stress on an elementary part of the area, including the point divided by the elementary area. If in Figs. 1, 2, and 3 the loaded bodies are one unit thick and four units wide, then when the total stress S is uniformly distributed over the area, P/A P/4. Unit stresses are expressed in pounds per square inch, tons per square foot, etc.
TENSILE STRESS OR TENSION is the internal total stress S exerted by the material fibers to resist the action of an external force P (Fig. 1), tending to separate the material into two parts along the line mn. For equilibrium conditions to exist, the tensile stress at any cross section will be equal and opposite in direction to the external force P. If the internal total stress S is distributed uniformly over the area, the stress can be considered as unit tensile stress S/A.
COMPRESSIVE STRESS OR COMPRESSION is the internal total stress S exerted by the fibers to resist the action of an external force P (Fig. 2) tending to decrease the length of the material. For equilibrium conditions to exist, the compressive stress at any cross section will be equal and opposite in direction to the external force P. If the internal total stress S is distributed uniformly over the area, the unit compressive stress S/A.
SHEAR STRESS is the internal total stress S exerted by the material fibers along the plane mn (Fig. 3) to resist the action of the external forces, tending to slide the adjacent parts in opposite directions. For equilibrium conditions to exist, the shear stress at any cross section will be equal and opposite in direction to the external force P. If the internal total stress S is uniformly distributed over the area, the unit shear stress S/A.
NORMAL STRESS is the component of the resultant stress that acts normal to the area considered
(Fig. 4).
AXIAL STRESS is a special case of normal stress and may be either tensile or compressive.
It is the stress existing in a straight homogeneous bar when the resultant of the applied
loads coincides with the axis of the bar.
SIMPLE STRESS exists when tension, compression, or shear is considered to operate singly
on a body.
TOTAL STRAIN on a loaded body is the total elongation produced by the influence of an
external load. Thus, in Fig. 4, the total strain is equal to . It is expressed in units of
length, that is, inches, feet, etc.
UNIT STRAIN, or deformation per unit length, is the total amount of deformation divided by
the original length of the body before the load causing the strain was applied. Thus, if
the total elongation is in an original gage length l, the unit strain e / l. Unit strains
are expressed in inches per inch and feet per foot.
TENSILE STRAIN is the strain produced in a specimen by tensile stresses, which in turn are
caused by external forces.
COMPRESSIVE STRAIN is the strain produced in a bar by compressive stresses, which in turn
are caused by external forces.
SHEAR STRAIN is a strain produced in a bar by the external shearing forces.
POISSON’S RATIO is the ratio of lateral unit strain to longitudinal unit strain under the
conditions of uniform and uniaxial longitudinal stress within the proportional limit. It
serves as a measure of lateral stiffness. Average values of Poisson’s ratio for the usual
materials of construction are:
Material Steel Wrought iron Cast iron Brass Concrete
Poisson’s ratio 0.300 0.280 0.270 0.340 0.100
ELASTICITY is that property of a material that enables it to deform or undergo strain and
return to its original shape upon the removal of the load.
HOOKE’S LAW states that within certain limits (not to exceed the proportional limit) the
elongation of a bar produced by an external force is proportional to the tensile stress
developed. Hooke’s law gives the simplest relation between stress and strain.
Franklin E. Fisher
Professor Emeritus
Mechanical Engineering Department
Loyola Marymount University
Los Angeles, California
and
Raytheon Company
El Segundo, California
