THEORY OF STRAIN GAUGES STRAIN GAUGE: A gauge which measures the change in length of a structure from where strain, stress and force is calculated indirectly is known as strain gauge. The sequence is given as;
Gauge → ∆L → ε → σ → F WORKING PRINCIPLE: The working principle of a strain gauge gau ge is that “ resistance is directly proportional to the change in length” as given below: R = (ρ*L)/A Where R = Resistance of the strain gauge ρ = Resistivity of the material L = Length A = Area of strain gauge Now Since the area is very small so from the abo ve equation, we have: R = constant*L Or ∆R = constant * ∆L Or ∆R α ∆L The figure is shown below:
The slope of this graph is known as sensitivity of the gauge.
Mathematically: Sg = (∆ (∆R/R)/ (∆L/L) (∆L/L) Where Sg = sensitivity of the gauge. From this graph, it is cleared that different gauges have different sensitivities means that each gauge has its own value of ‘Sg’. High sensitivity means, it can sense a very small change in length. The figure shows gauge sensitivities of different gauges as follows:
Generally the normal resistance of the strain gauge is 120Ω 120Ω and after loading it becomes 120.002 Ω i.e. 2milli ohm change in resistance is so small that it cannot be detected by the ordinary multimeter or ohm meter. So for this purpose, we use wheat stone bridge (W.S.B). The figure is shown below:
The wheat stone bridge gives the output in terms of change in voltage and that change in voltage is then amplified using an amplifier, which is then detected by an oscilloscope. The graph for the wheat stone bridge is shown below.
The sensitivity of this graph is known as wheat stone bridge sensitivity. Mathematically Sw = (∆V/V)/ (∆V/V)/ (∆R/R) The two graphs for wheat stone bridge and strain gauge are given below.
Now for the whole circuit the combined graph becomes:
And the sensitivity of this graph is known as sensitivity of the circuit. Mathematically, we have: Sc = (∆V/V) (∆V/V)// (∆ (∆L/L) Or Sc = (∆V/V)/ε From this equation we can find the strain as follows: Strain =ε =ε = (∆V/V)/ (∆V/V)/ Sc
