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 .
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
Try this formula for strain keep checking my blogs for more help on related topics.
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
Check this topic Center of Mass of a Semicircle it may help you keep checking my blogs for more.
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)` .
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.
As strain is a ratio , it has no units and dimensions.
I want to help you with Strain Equation for more keep reading my blogs and express your views.