Padeepz E-Learning Materials PH8151 Engineering Physics
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Modulus of elasticity
Types of moduli of elasticity:
Based on the 3 types of strain, elastic modulli of solids are.
(i) young’s Modulus:
Within elastic limit, ratio of longitudinal stress to longitudinal strain
consider a wire, length – L
Area of cross section – a
One end is fixed at top and load is applied at the bottom. Force acting along the length of wire is `F’. Let – elongation in length of the wire due to force applied.
Longitudinal stress = F/A
(II) Bulk Modulus:
Within elastic limit, ratio of bulk stress to bulk stress.
Bulk Modulus (k) = Bulk stress / Bulk Strain
Consider a body of volume ‘v’ and area of cross section A let ‘F’ the force applied to the whole surface of the body. This results in the change in volume but no change in shape of the body. Let v he the change in volume.
Bulk modules is sometimes called in compressibility its reciprocal is compressibility =1/k
(iii)Rigidity Modulus
Within elastic limit, ratio of sharing stress to shearing strain
Consider cube ABCDEFGH . lower ABCD is fixed and force is applied 11l to surface EFGH. So the body is sheared by angle o . Let ‘L’ he the length of the cube and sL be the change in length of the upper surface
Shearing stress = F/A
Poisson’s Ratio:
When a body is subjected to a force, the deformation is not only in one direction but all along.
Ex: If a wire is stretched, besides undergo extension along the direction of force, it also undergoes contraction in perpendicular direction strain produced along the direction of force longitudinal strain
Similarly, strain produced in perpendicular direction is lateral strain
Within elastic limit, ratio, of lateral strain to the longitudinal strain is called poisson’s ratio ‘’
Let us consider a body which is subjected to an uniformly increasing stress Due to the application of stress, strain is developed If we plot a graph b/w stress & strain we get a curve and is called stress. Strain diagram
- Itis found that the bodyobey’s Hooke’s law up to the region OA called elastic lang
- As soon as the yieldpt‘B’ is crossed, the strain & rapidly than the stress
- Atthis stage the body remains partly elastic and partly plastic which is represented by BC
- Noweven if a small external face is applied, the body will take a new path CD and remains plastic called plastic law where D is the ultimate strength.
- Afterthis, the body will not some to its Original state and the body acquires a permanent residual strain I and it breaks down at aptl/ called a breaking stress indicated by EF.