kidzsearch.com > wiki Explore:web images videos games
Stress is a measure of the internal forces in a body between its particles. These internal forces are a reaction to the external forces applied on the body that cause it to separate, compress or slide. External forces are either surface forces or body forces. Stress is the average force per unit area that a particle of a body exerts on an adjacent particle, across an imaginary surface that separates them.
The formula for uniaxial normal stress is:
where σ is the stress, F is the force and A is the surface area.
In SI units, force is measured in newtons and area in square metres. This means stress is newtons per square meter, or N/m2. However, stress has its own SI unit, called the pascal. 1 pascal (symbol Pa) is equal to 1 N/m2. In Imperial units, stress is measured in pound-force per square inch, which is often shortened to "psi". The dimension of stress is the same as that of pressure.
In continuum mechanics, the loaded deformable body behaves as a continuum. So, these internal forces are distributed continually within the volume of the material body. (This means that the stress distribution in the body is expressed as a piecewise continuous function of space and time.) The forces cause deformation of the body's shape. The deformation can lead to a permanent shape change or structural failure if the material is not strong enough.
Some models of continuum mechanics treat force as something that can change. Other models look at the deformation of matter and solid bodies, because the characteristics of matter and solids are three dimensional. Each approach can give different results. Classical models of continuum mechanics assume an average force and do not properly include "geometrical factors". (The geometry of the body can be important to how stress is shared out and how energy builds up during the application of the external force.)
In some situations, the stress within an object can be described by a single number, or by a single vector (a number and a direction). Three such simple stress situations are the uniaxial normal stress, the simple shear stress, and the isotropic normal stress.
Uniaxial normal stress
Tensile stress (or tension) is the stress state leading to expansion; that is, the length of a material tends to increase in the tensile direction. The volume of the material stays constant. When equal and opposite forces are applied on a body, then the stress due to this force is called tensile stress.
Therefore in a uniaxial material the length increases in the tensile stress direction and the other two directions will decrease in size. In the uniaxial manner of tension, tensile stress is induced by pulling forces. Tensile stress is the opposite of compressive stress.
Tensile stress may be increased until the reach of tensile strength, namely the limit state of stress.
Stress in one-dimensional bodies
All real objects occupy three-dimensional space. However, if two dimensions are very large or very small compared to the others, the object may be modelled as one-dimensional. This simplifies the mathematical modelling of the object. One-dimensional objects include a piece of wire loaded at the ends and viewed from the side, and a metal sheet loaded on the face and viewed up close and through the cross section.
- Walter D. Pilkey, Orrin H. Pilkey (1974). Mechanics of solids. p. 292. https://books.google.com/books?id=d7I8AAAAIAAJ&q=average+shear+stress+approximation&dq=average+shear+stress+approximation&ei=FdBkS837NJPyNMLQzNgB&cd=2.
- Daintith, John, ed. (2005). A Dictionary of Physics (Fifth ed.). Oxford University Press. p. 509. .
- Ronald L. Huston and Harold Josephs (2009), "Practical Stress Analysis in Engineering Design". 3rd edition, CRC Press, 634 pages. ISBN 9781574447132
- Ameen, Mohammed (2005). Computational elasticity: theory of elasticity and finite and boundary element methods. Alpha Science Int'l Ltd.. pp. 33–66.
- Atanackovic, Teodor M.; Guran, Ardéshir (2000). Theory of elasticity for scientists and engineers. Springer. pp. 1–46.
- Chadwick, Peter (1999). Continuum mechanics: concise theory and problems. Dover books on physics (2 ed.). Dover Publications. pp. 90–106.
- Chakrabarty, J. (2006). Theory of plasticity (3 ed.). Butterworth-Heinemann. pp. 17–32.
- Chatterjee, Rabindranath (1999). Mathematical Theory of Continuum Mechanics. Alpha Science Int'l Ltd.. pp. 111–157.
- Chen, Wai-Fah; Han, Da-Jian (2007). Plasticity for structural engineers. J. Ross Publishing. pp. 46–71.
- Fung, Yuan-cheng; Tong, Pin (2001). Classical and computational solid mechanics. Volume 1 of Advanced series in engineering science. World Scientific. pp. 66–96.
- Hamrock, Bernard (2005). Fundamentals of Machine Elements. McGraw-Hill. pp. 58–59.
- Hjelmstad, Keith D. (2005). Fundamentals of structural mechanics. Prentice-Hall international series in civil engineering and engineering mechanics (2 ed.). Springer. pp. 103–130.
- Irgens, Fridtjov (2008). Continuum mechanics. Springer. pp. 42–81.
- Jaeger, John Conrad; Cook, N.G.W, & Zimmerman, R.W. (2007). Fundamentals of rock mechanics (Fourth ed.). Wiley-Blackwell. pp. 9–41.
- Lubliner, Jacob (2008). Plasticity Theory (Revised Edition). Dover Publications.
- Mase, George E. (1970). Continuum Mechanics. McGraw-Hill. pp. 44–76.
- Mase, G. Thomas; George E. Mase (1999). Continuum Mechanics for Engineers (Second ed.). CRC Press. pp. 47–102.
- Prager, William (2004). Introduction to mechanics of continua. Dover Publications. pp. 43–61.
- Smith, Donald Ray; Truesdell, Clifford (1993). An introduction to continuum mechanics -after Truesdell and Noll. Springer.
- Wu, Han-Chin (2005). Continuum mechanics and plasticity. CRC Press. pp. 45–78.