Mechanics of Solids ZHCET ME 213 Strain Mechanics of Solids ZHCET ME 213

Linear & Shear Strains

Contd…

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

Strain Tensor

Engineering Shear Strain

Strain transformation equation

Strain Rosettes Mechanics of Solids ME 213

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

Principle of Operation

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

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

Installation

Wheat stone Brodge

Gauge Pattern

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.

Installed Rosette

Installed Rosette on a Machine element

Analysis

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

(2ε b − (ε − ε ) (ε ) ε ε = ε = ε γ ε 1 = + 2ε 3 + ε ) = 2ε γ 2 = − ε x 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

Problem

Prob

Prob

Principal Strains

Maximum Shear Strain

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

Applications