1. Mechanics of Solids ZHCET ME 213
Strain
Mechanics of Solids
ZHCET ME 213

2. Linear & Shear Strains

3. Contd…

4. Contd…
From these equations the strain tensor in matrix representation can be assembled,

5. Strain Tensor

6. Engineering Shear Strain

7. Strain transformation equation

8. Strain Rosettes
Mechanics of Solids
ME 213

9. Principle
A electrical resistance strain gauge is a device for measuring normal strain (ε) on the surface of a stressed object.

10. Principle of Operation

11. GAGE FACTOR
When a metallic conductor is strained, it undergoes a change in electrical resistance, and it is this change that makes the strain gage a useful device.
The measure of this resistance change with strain is GUAGE FACTOR, GF.
Gage factor is defined as the ratio of the fractional change in resistance to the fractional change in length (strain) along the axis of the gage. Gage factor is a dimensionless quantity, and the larger the value, the more sensitive the strain gage

12. Strain Gauge
A typical strain gage attachment consists of three major parts:
The wire,
The backing, and
The adhesive.

13. Installation

14. Wheat stone Brodge

15. Gauge Pattern

16. Strain Rosette
To generate the strain tensor on a surface, a group of several gauges are arranged in a pattern called as Rosette.
We can use the transformation equations for the plane strain to calculate the strains in various directions.

18. Installed Rosette

19. Installed Rosette on a Machine element

20. Analysis

21. Using the strain transformation equations (for ) for each gauge:
Eqn (1)

22. (2ε b − (ε − ε ) (ε ) ε ε = ε = ε γ ε 1 = + 2ε 3 + ε ) = 2ε γ 2 = − εx a x a 1
(2ε b
− ε ) ε =
+ 2ε y c a 3 y c
+ ε ) 2 γ
= 2ε (ε ) γ =
− ε xy b a c xy b c 3

23. Problem

24. Prob

25. Prob

26. Principal Strains

27. Maximum Shear Strain

28. Applications examples
Structural Integrity
Bridge Construction
Failure Prevention
Bicycle Frame Design
Engine Component Design

29. Applications