Stress can be defined as the force acting on a given area. This is mathematically represented as

Robert hook investigated the behavior of material under tensile force and found out that the extension on materials was proportional to the applied load. This is called the hooks law. Hooks law apply up to the elastic limit. Continued application of load beyond the elastic limit results to the material becoming plastic, That is, its elongation is not proportional to the applied load and does not regain its original shape once the force is removed.

The concept of stress was introduced by Cauchy in 1822; Cauchy found out that a body was subjected to surface and internal forces. These caused the deformation on the body. When stress is uniformly distributed over the cross-sectional area of a body, it can be calculated using the formula (1), however, the stress is not uniformly distributed. Cauchy calculated the state of stress at a given point and found it to be given by the second order tensor given below.

Another version of the Mohr stress circle is using the polar approach method. The Mohr stress circle can also be used for the determination of stress in the three dimensional plane. A special Mohr circle is drawn to calculate the nominal and shear stress in the three dimensional plane. ...

Are the normal stresses. Where:

Are the shear stresses

Stress can also be calculated using the Mohr stress circle; this is the graphical representation of the stress. The diagrammatic representation of the Mohr stress circle is as shown below

Fig 1 showing the Mohr stress circle

Another version of the Mohr stress circle is using the polar approach method. The Mohr stress circle can also be used for the determination of stress in the three dimensional plane. A special Mohr circle is drawn to calculate the nominal and shear stress in the three dimensional plane. Other methods used in the determination of stress include the Biot stress tensor and the Kirchhoff stress tensor (Dieter, 1989).

In general the determination of stress using the graphical methods was laborious and complex, one required a lot of skills to draw these circles and determine the normal and shear stress. The method had many mathematical errors. These methods have largely been replaced by computerized material strength analysis (Marsden & Hughes1994).

Current methods for the evaluation of stress include the use of software's. Software's such as AutoCAD and solid works enable engineers to have a detailed analysis of the behavior of the designed product under loading. This helps in developing products that don't fail easily. Another program that is widely used is the Finite element analysis program. It enables the graphical representation of a designed engineering component under load.

References

Dieter, G. (1989). Mechanical Metallurgy. New York: McGraw-Hill.

Ferdinand, P. (1992). Mechanics of Materials. New York: McGraw-Hill Professional

Marsden, J. & Hughes, T. (1994). Mathematical Foundations of Elasticity. New York: Dover
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