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Types of Stress and Strain

In the mechanics of solids, the stress and strain analysis provide an important insight on the behavior of solids. In this article we shall deal with types of stress and strain and try and understand them a bit better.

The restoring force per unit area, set up inside a body is called stress. It is measured by the magnitude of the deforming force acting on unit area of the body.  

 Stress  =  Restoring force / area =  `(F)/(A)`  , where F is the deforming force acting on an area A of the body.

 Its unit :  N m-2  in SI system and dyne cm-2  in CGS system. Dimensional formula is  [`(MLT^-2)/(L^2)`   =   ML-1 T-2 .


Types of Stress and Strain : Stress


Different types of stress : Stress is of two different types mainly  (i) Normal Stress  (ii) Shearing  or Tangential Stress .

Normal Stress : If the stress is normal to the surface, it is called normal stress. Stress is always normal in the case of a change in length or a wire or in the case of change in volume of a body

Longitudinal Stress : When a normal stress change the length of a body then it is called longitudinal stress which is given by

Longitudinal Stress = Deforming Force / Area of cross section   =  `(F)/(A)`

The longitudinal stress can be further divided into two types. When a wire or a rod is stretched at the two ends by equal and opposite forces, the stress is called tensile stress. When a rod is pushed at the two ends by equal and opposite forces, it will be under compression. The stress in such a case is called compressive stress. The pillars of a building experience compressive stress.

Volume Stress  (or ) Bulk Stress : When a normal stress changes the volume of a body then it is called volume stress. When a solid body is immersed in a fluid, the force at any point is normal to the surface of the body and the magnitude of the force on any small area is proportional to the area i.e., the body is under the action of a pressure P.

                          Bulk Stress =  `(Force)/(Area)`  = Pressure

Shearing Stress : When the Stress is tangential to the surface due to the application of forces parallel to the surface, then the stress is called tangential or shearing stress. It changes the shape of the body.

                         Shearing Stress = Force / Surface Area  =  F  /  A


  Stress Types


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Types of Stress and Strain : Strain


Normal stress on a body causes change in length or volume and tangential stress produces change in shape of the body. The ratio of change produced in the dimensions of a body by  a system of forces or couples, in equilibrium, to its original dimensions is called strain.

Strain is of three types depending upon the change produced in a body and the stress applied. The three types of strain are (i)Longitudinal strain (ii) Volume strain and (iii) Shearing strain

Longitudinal Strain : It is the ratio of the change in length of a body to the original length of the body. If  L is the original length of a wire or a rod and the final length of the wire or the rod is L + e under the action of a normal stress, the change in length is e.

Longitudinal Strain = Change in length / Original length =  e / L


  Longitudinal Strain


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If the length increases due to tensile stress, the corresponding strain is called tensile strain. If the length decreases due to compressive stress, the strain is called compressive strain.

Volume Strain : It is the ratio of the change in volume of a body to its original volume.

If V is the original volume of a body and   v + `Delta` v  is the volume of the body under the action of a normal stress, the change in volume is `Delta`v .

Volume Strain  =  Change in volume  / Original volume  =  `(DeltaV)/(V)` .


  Volume Strain


Shearing Strain : If is the angle through which a face originally perpendicular to the fixed face is turned. (or)  It is the ratio of the displacement of a layer to its distance from the fixed layer.  


  Shearing Strain


As strain is a ratio , it has no units and dimensions.


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