STRAIN In engineering the deformation of a body is specified using the concept of normal strain and shear strain whenever a force is applied to a body, it will tend to change the body s shape and size. These changes are referred as Deformation. Deformation is the term used to signify the entire geometric change by which points in a body in the initial state with all loads absent go to another con as a result of the action of loads. The initial state is called un-deformed state, the subsequent state occurring in the presence of loads is called deformed state. The deformation so de include the following contributions f or each element of the body 1. Rigid body translation 2. Dilation contribution from changes in geometry associated with volume changes 3. Distortion contribution resulting from the change in angularity between the line seg-ments. Normal Strain: The elongation or contractions of a line segment per unit length is referred to as normal strain denoted by Greek symbol. Referring to Cartesian coordinate axes, the material experiences three normal strains corresponding to three normal stresses. x, y, and z. Normal strain x at a point P is the change in length in the x direction per unit original length of vanishingly small line segment originally in the x direction. Similar interpretations can be given to y and z. Generally, in most engineering applications normal strain e will be very small and so the measurements of strains are in micrometers/meter and expressed as (μm/m), where 1μm = 10-6 m.
Shear Strain The change in angle that occur between two line segments that were originally perpendicular to one another is referred to as shear strain, denoted by Greek symbol and is measured in radians. The engineering shear strain is the decrease in right angle of a pair of infinitesimal line segments in two directions at a point P. For three dimensional stress state, corresponding to three normal and three shear stresses, we will have corresponding three normal strains ( x, y, and z ) and three shear strains ( xy, yz and zx )
If we consider an infinitesimal rectangular parallel piped in the un-deformed geometry, with zero shear strain, the sides must remain orthogonal to one another on deformation, (the length of the sides may change). If the shear strain imposed, the effect of shear strain is imposed in uncoupled manner. The result is the orientation of the sides may loose their perpendicularity with one another. In conclusion we say that size of rectangular parallel piped is changed by normal strain and the basic shape is changed by shear strains. Poisson s Ratio When a deformable body is subjected to an axial force, not only it elongates but also contracts laterally. When a load P is applied to a uniform circular rod, the length of the rod increases by an amount and radius of the rod decreases by an amount say, Then longitudinal strain is given by long = /l and lateral strain is given by lat = /r. Both long and lat are normal strains. The ratio of lateral strain to longitudinal strain is called poisson s ratio (after French Scientist S.D. Poisson) and is denoted by = - lat / long Even though, according to the above definition is negative, normally poisson s ratio is given by a positive constant that varies from 0 to 0.5. Note: Tensile normal stress produces negative lateral (contraction) strain and compressive normal stress produces positive (elongation) lateral strain.
Strain Transformation Strain is actually measured by experiments at a point using strain gauges and is related to the stress acting within the body using material property relations called constitution relationships, that relates stress and strain with material properties. For both analysis and design, we must sometimes transform strain data in order to obtain the strain in other directions. Sign Conventions