Concept of strain : if a bar is subjected to a direct load, and hence a stress the bar will change in length. If the bar has an original length L and changes by an amount dL, the strain produce is defined as follows:

**Deformation of simple bars under axial load
Deformation of bodies**

**Concept of strain : **if a bar
is subjected to a direct load, and hence a stress the bar will change in** **length.
If the bar has an original length L and changes by an amount dL, the strain
produce is defined as follows:

Strain is thus, a measure of the deformation of the material
and is a nondimensional Quantity i.e. it has no units. It is simply a ratio of
two quantities with the same unit.

**Shear strain: **As we know that the shear
stresses acts along the surface. The action of the** **stresses is to
produce or being about the deformation in the body consider the distortion
produced b shear sheer stress on an element or rectangular block This shear
strain or slide is f and can be defined as the change in right angle. or The
angle of deformation g is then termed as the shear strain. Shear strain is
measured in radians & hence is non -
dimensional i.e. it has no unit.So we have two types of strain i.e. normal stress
& shear stresses.

**Hook's
Law :**

A material is said to be elastic if it returns to its
original, unloaded dimensions when load is removed.

Hook's
law therefore states that Stress ( s ) a strain( Î )

**Modulus
of elasticity : **Within the elastic limits of materials i.e. within
the limits in which Hook's law applies, it has been shown that

Stress /
strain = constant

This constant is given by the symbol E and is termed as the
modulus of elasticity or Young's modulus of elasticity Thus ,The value of
Young's modulus E is generally assumed to be the same in tension or compression
and for most engineering material has high, numerical value of the order of 200
GPa

**Poisson's ratio: **If a bar
is subjected to a longitudinal stress there will be a strain in this direction**
**equal to s / E . There will also be a strain in all directions at right
angles to s . The final shape being shown by the dotted lines.

It has been observed that for an elastic materials, the
lateral strain is proportional to the longitudinal strain. The ratio of the
lateral strain to longitudinal strain is known as the poison's ratio .

Poison's
ratio ( m ) = - lateral strain / longitudinal strain

For most engineering
materials the value of m his between 0.25 and 0.33.

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Civil : Mechanics Of Solids : Stress, Strain And Deformation Of Solids : Deformation of simple bars under axial load Deformation of bodies |

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