Analysis of simple strain of solid

1. ANALYSIS OF SIMPLE STRAIN OF
SOLID

2. STRAIN
 When a body is subjected to load, it will deform and can be detected through
the changes in length and the changes of angles between them.
 The deformation is measured through experiment and it is called as strain.
 The important of strain: it will be related to stress in the later chapter

3. STRAIN
 Strain: Strain is the deformation of a material from stressStrain:Strain is the deformation of a material
from stress. It is simply a ratio of the change in length to the original length. Deformations that are
applied perpendicular to the cross section are normal strains.
 Linear Strain: Linear strain of a deformed body is defined as the ratio of the change in length of the
body due to the deformation to its original length in the direction of the force. If L is the original
length and dL the change in length occurred due to the deformation, the linear strain e induced is
given by ε=dL/L.
 Linear strain may be a tensile strain, εt or a compressive strain εc according as dl refers to an
increase in length or a decrease in length of the body. If we consider one of these as +ve then the
other shouldbe consideredas –ve, as these are opposite in nature.
 Lateral Strain: Lateral strain of a deformed body is defined as the ratio of the change in length
(breadth of a rectangular bar or diameter of a circular bar) of the body due to the deformation to
its original length (breadth of a rectangular bar or diameter of a circular bar) in the direction
perpendicular to the force.

4. Normal Strain
 Normal strain is detected by the changes in length.
e (epsilon)
l’: length after deformed
I': original length.
Note e:
 Dimensionless
 small (normally is mm (=10-6 m))
 480(10)-6 m/m = 480 mm/m = 480 “micros” = %

5. EXAMPLE 1
When load P is applied, the RIGID lever arm rotates by 0.05o. Calculate the normal strain of wire BD
Foundationtion: DL/L
Knowledge required: geometrical equation
Rigid: no deformation on the lever

6. Geometry: The mathematics
 Sine and Cosine Rule

7. Example 1
When force P is applied to the rigid lever arm
LBD after deformed is DB’Cosine rule can be applied here
Strain:

8. SOLUTION

9. Conventional Stress–Strain Diagram
 Nominal or engineering strain is obtained by dividing the
change in the specimen’s gauge length by the specimen’s
original gauge length.

10. Conventional Stress-Strain Diagram