Quiz on Stress, Strain, and Strain Gages

Question 1: Here is a schematic diagram of a simple Wheatstone bridge circuit:

True or False: A standard Wheatstone bridge is balanced when R₁R₃ = R₂R₄.
True
False

Question 2: True or False: Wire resistance increases with axial strain.
 True
 False

Question 3: For typical commercial strain gages, the strain gage factor is approximately_______

Question 4: Most commercial strain gages have a nominal resistance of what (in ohms)?
_______

Question 5: A strain gage has a resistance of 350 ohms when no strain is applied. Its strain gage factor is 2.00. When an axial strain of 0.0002 is applied, calculate the change in resistance, dR, in ohms.
_______

Question 6: Consider the Wheatstone bridge circuit shown in the first problem above. Resistors R₁ and R₃ are strain gages, while the other two resistors are fixed resistors. What kind of Wheatstone bridge circuit is this?
a quarter bridge circuit
a half bridge circuit
a full bridge circuit
none of the above

Question 7: Consider the Wheatstone bridge circuit shown in the first problem above. Resistors R₁ and R₃ are strain gages, while the other two resistors are fixed resistors. This circuit is used to measure the axial strain on a cantilevered beam. Which of the following statements is most correct?
The two strain gages should be mounted on the same surface (top or bottom) of the cantilevered beam.
The strain gages should be mounted on opposite surfaces (top and bottom) of the cantilevered beam.
It is irrelevant whether the strain gages are mounted on the same surface of the beam or on opposite surfaces of the beam.

Question 8: In a full bridge circuit, the sensitivity improves by a factor of ________ compared to a quarter bridge circuit.

Question 9: In which region of the stress-strain diagram are strain gages designed to work?
the plastic deformation region
just beyond the elastic limit
the region where stress is nearly constant
the region where stress decreases with strain
none of the above

Question 10: What are the S.I. units of strain gage factor S?
m
ohms
m/s
s
ohms/V
N/m²
m²/N
none of the above

Scroll Down for Answers

1) True.  

The equation for output voltage of a Wheatstone bridge has the following in the numerator: R3R1 - R4R2. Thus, whenever these two terms are equal, the output voltage is zero, and the bridge is considered balanced. This can also be seen easily in the schematic diagram, since R1 and R3 are on diagonally opposite sides of the bridge. 

2) True

Explanation: As axial strain increases, the wire is stretched. The increase in wire length, as well as the decrease in cross-sectional area contributes to an increase in wire resistance.

3) 2

Explanation: Credit is given for any answer in the range 1.8 to 2.2, since most commercial strain gages have a strain gage factor right around 2.0.

4) 120

Explanation: There are actually two 'standard' strain gage resistances, 120 ohms and 350 ohms., but the most widely used strain gages are those with a resistance of 120 ohms. 

5) 0.14

6) a half bridge circuit

Explanation: When two of the resistors (two out of four) are strain gages, this is called a half bridge circuit.

7) The two strain gages should be mounted on the same surface (top or bottom) of the cantilevered beam.

Explanation: Since the two resistors being used for strain gages are on diagonally opposite sides of the Wheatstone bridge, they have the same sign in the equation for output voltage. Therefore, each strain gage contributes equally to the output. Thus, the two strain gages should be mounted on the same surface. (Note: If they were mounted on opposite surfaces of the beam, the resistance changes would cancel each other out!)

8) 4

Explanation: Since four resistors are active in a full bridge circuit, while only one is active in a quarter bridge circuit, the full bridge circuit sensitivity is increased by a factor of four. 

9) none of the above

Explanation: The correct answer is the elastic stress region. Since none of the choices agree with this answer, the answer to the question is none of the above.

10) none of the above

Explanation: Actually, S has no dimensions, i.e. the strain gage factor is dimensionless.