Question

As shown below (Fig.1), A strain gage with gage factor of 2.02 is mounted on the bottom of a beam to measure the strain on the surface of the beam. The beam's Young's Modulus is 193 GPa. A wheatstone bridge circuit was constructed as sketched in Fig. 2. Al resistors including the gage itself is 1202. Supply voltage is 5.0 V DC. The bridge is initially balanced when there is no load (a). when a downward load is added, will stress and output voltage Vo be positive o negative? (b). calculate the strain (in unit of microstrain) for a loading in which Vo is 1.25mV (c). calculate the axial stress in the beam under the same loading as in (b) (d). calculate the voltage output Vo after we glue another strain gage on top of the beam, and replace R2 for the second strain gage. (hint: half bridge circuit). Compare the sensitivity for the quarter bridge and the half bridge circuit in (b) and (d) Strain gage Fig .1 Ri R: bc Ri Strain gauge Fig.2

Answer 1

1) When Downward load is added, will stress and output voltage Vo be positive or negative ?

	PA F B e4 3

• The total strain, or output voltage of the circuit (Vo) is equivalent to the difference between the voltage drop across R4 and R3. This can also be written as:
  • Vo= V_AD –V_AB , where A,B,C,D is as shown in above figure
• However, when a downward force is applied, it will bend downward and compression occurs.
• Compression causes resistance decrease of R4, so voltage across V_AD also decrease.
• Which results Negative Output Voltage and stress.

2) calculate Strain(in microstrain) for a loading in which Vo is 1.25mV:

Strain (ε_a ) = 4 (Vo / Vs) /S ,Where S is gauge factor

Here, Given Vo = 1.25 mV

            Vs=5 VDC

            S=2.02

            Strain = 4(1.25mV / 5) /2.02  

            Strain (ε_a) = 495 Microstrain

3) Calculate axial stress in the beam under the same loading as in (b):

As per Hooke’s law,

Axial Stress σ_a = E ε_a , where E = Young’s modulus, also called the modulus of elasticity

  = 193 * 495

Axial Stress σ_a = 95535 N/m²

4) Calculate Vo after replace R2 as a second strain gauge:

After adding second strain gauge circuit which is Half bridge circuit as shown below,

     

Vo = - Vs (S * ε_a)/2 , Where S is gauge factor

= - (5 * 2.02 * 495) /2

    Vo   = -2499.75 V

By comparing Sensitivity,

Half-bridge strain gauges are two times more sensitive than quarter-bridge strain gauges.