Normal Stress

3 Key excerpts on "Normal Stress"

• 

  eBook - ePub

  Strength of Materials and Structures

  • Carl T. F. Ross, The late John Case, A. Chilver(Authors)
  • 1999(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  A ) as δA becomes infinitesimally small. Thus

  Figure 1.4 Normal load on an element of area of the cross-section.

  (1.2)

  This defmition of stress is used in studying problems of non-uniform stress distribution in materials.

  When the forces P in Figure 1.3 are reversed in direction at each end of the bar they tend to compress the bar; the loads then give rise to compressive stresses. Tensile and compressive stresses are together referred to as direct (or normal) stresses , because they act perpendicularly to the surface.

  Problem 1.1: A steel bar of rectangular cross-section, 3 cm by 2 cm, carries an axial load of 30 kN. Estimate the average tensile stress over a normal cross-section of the bar.

  Solution: The area of a normal cross-section of the bar is

  The average tensile stress over this cross-section is then

  Problem 1.2: A steel bolt, 2.50 cm in diameter, carries a tensile load of 40 kN. Estimate the average tensile stress at the section a and at the screwed section b , where the diameter at the root of the thread is 2.10 cm.

  Solution: The cross-sectional area of the bolt at the section a is

  The average tensile stress at A is then

  The cross-sectional area at the root of the thread, section b , is

  The average tensile stress over this section is

  1.4 Tensile and compressive strains

  In the steel wire experiment of Figure 1.1 we discussed the extension of the whole wire. If we measure the extension of, say, the lowest quarter-length of the wire we find that for a given load it is equal to a quarter of the extension of the whole wire. In general we find that, at a given load, the ratio of the extension of any length to that length is constant for all parts of the wire; this ratio is known as the tensile strain.

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  eBook - ePub

  Mechanical Engineers' Handbook, Volume 1

  Materials and Engineering Mechanics

  • Myer Kutz, Myer Kutz(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  .
• SHEAR STRESS is the internal total stress 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 . If the internal total stress is uniformly distributed over the area, the unit shear stress .
• 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 gauge length , the unit strain . 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