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Hello!

Attached is the HW file. It is due on Friday night (Eastern US time).

Thank you!

Homework 3 – 2021
1. What is the strain in a single strain gauge (GF=2.2) in position 1 for an output voltage of 2.5 mV
with an excitation voltage of 6V?
2. If the gauge in problem 1 has a resistance of 1000Ω, what is the change of resistance for the
same output and excitation voltage?
3. A pair of strain gauges with GF=2.11 and an unstrained resistance of 120Ω are placed in the 1
and 4 location in the bridge below and are placed on opposite sides of an aluminum beam that
is 2.5 mm thick and 15 mm wide. The excitation voltage to the bridge is 8 V and the elastic
modulus is 70 GPa. (Ignore the balancing resistor on position 3.)
a. What is the output voltage if the beam is subjected to a tensile load of 13.5 kN?
b. What is the output voltage if the beam is subjected to a bending moment of 20 Nm?
4. A pair of strain gauges with GF=2.17 and a resistance of 120Ω are placed in the 1 and 2 location
in the bridge below and are placed on opposite sides of a steel beam that is 5 mm thick and 25
mm wide. The excitation voltage to the bridge is 3 V and the elastic modulus is 207 GPa.
(Ignore the balancing resistor on position 3.)
a. What is the output voltage if the beam is subjected to a tensile load of 25 kN?
b. What is the output voltage if the beam is subjected to a bending moment of 20 Nm?
5. A 100 kN load cell has a sensitivity of 3.43 mV/V. What must the excitation voltage be if we
amplify the bridge output by 100 and want a 10V output for full scale load?
6. If the gauge factor of the strain gauges is GF =2.1, what is the strain at maximum load if the load
cell sensitivity is 3.4 mV/V?
7. A 10 N load cell with a sensitivity of 2.9 mV/V is subjected to 6 N load. If the gain on the
amplifier is 50 and the excitation voltage is 8 V, what is the output voltage?
8. Assume you have a full bridge of 120 strain gauges with a 5 V excitation voltage and gauge
factors of GF = 2.07.
a. What shunt resistor should you choose if you want to simulate  = 10-3 for one of the
gauges?
b. What would the output voltage be?
c. If the shunt resistor has a 1% tolerance, what is the potential strain variation?
9. Plot the strain on the surface of a 1 m long, 10 mm thick, 100 mm wide cantilever steel beam as
a function of distance from the clamping point if a force of 5 kN is applied to the end of the
beam.
10. A rectangular bar is loaded in tension along the long axis with an axial load of 1500 lbs. The bar
is 12 inches long and is 0.5 inches thick and 4 inches wide. An axial strain gauge records a strain
of 1500 µ and a gauge mounted to measure the transverse strain records a strain of -465 µ.
a. What is the modulus of elasticity for this material?
b. What is the Poisson’s ratio?
c. What would be the bridge output in volts if the axial gauge were in position 1 and the
transverse gauge was in position 2, the excitation voltage was 9 V, the gauge factor of
both gauges was 2.17?
11. A thin-walled steel pressure vessel with a radius of 0.05 m and a 5 mm wall thickness is
subjected to an internal pressure of 20 MPa.
a. What would the bridge output be for a quarter bridge configuration where the active
gauge is oriented to measure the hoop stress. Assume GF = 2.05 and the bridge
excitation voltage is 5 V.
b. What would the bridge output be if the active gauge was oriented to measure the
longitudinal stress?
c. What strains would be observed for both gauges.

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