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11.20 A bathroom scale uses four internal strain gauges to measure the displacement of its diaphragm as a
means for determining load. Four active gauges are used in a bridge circuit. The gauge factor is 2,
and gauge resistance is 120 V for each gauge. If an applied load to the diaphragm causes a
compression strain on R 1 and R 4 of 20 me, while gauges R 2 and R 3 experience a tensile strain of 20
me, estimate the bridge deflection voltage. The supply voltage is 9 V. Refer to Figure 11.24 for gauge
position.
11.21 Suppose in Problem 11.20 that the lead wires of two gauges (R 2 and R 4 ) are accidently interchanged
on the assembly line such that a compression strain is now sensed on R 1 and R 2 of 20 me, while
gauges R 4 and R 3 experience a tensile strain of 20 me. Should this really matter? Explain. Estimate
the bridge deflection voltage. Refer to Figure 11.24 for gauge position.
Problems 11.22 through 11.24 address measuring strains associated with a thin-walled pressure
vessel. The pressure vessel is constructed of steel and has a circular cross-section. The tangential and
longitudinal stresses in the wall of the pressure vessel are:
s t ¼ pD=2t
s l ¼ pD=4t
where
s t ¼ tangential stress
s l ¼ longitudinal stress
p ¼ pressure
t ¼ wall thickness
11.22 A single-strain gauge is mounted on the surface of a thin-walled pressure vessel that has a diameter
of 1 m. For a strain gauge oriented along the tangential stress direction, determine the percentage
error in tangential strain measurement caused by lateral sensitivity as a function of pressure and
vessel wall thickness. The lateral sensitivity is 0.03.
11.23 Consider a Wheatstone bridge circuit that has all fixed resistances equal to 100 V and with a strain
gauge located at the R 1 position, which has a value of 100 V under conditions of zero strain. The
strain gauge is mounted so as to sense longitudinal strain for a thin-walled pressure vessel made of
steel that has a wall thickness of 2 cm and a diameter of 2 m. The strain gauge has a gauge factor of 2
and cannot sustain a power dissipation of more than 0.25 W. What is the maximum static sensitivity
that can be achieved with this proposed measurement system? Is this static sensitivity constant with
input pressure? If not, under what conditions would it be reasonable to assume a constant static
sensitivity? The static sensitivity should be expressed in units of V/kPa.
11.24 Design a Wheatstone bridge measurement system to measure the tangential strain in the wall of the
pressure vessel described above, and develop a reasonable estimate of the resulting uncertainty.
You may assume that the strain does not vary with time, and that the bridge is operated in a balanced
mode. Your selection of specified values for the input voltage, the fixed resistances in the bridge
and the galvanometer sensitivity, and their associated uncertainties will allow completion of
this design.
11.25 A steel cantilever beam is fixed at one end and free to move at the other. A load F of 980 N is applied
to the free end. Four axially aligned strain gauges (GF ¼ 2) are mounted to the beam a distance L
from the applied load, two on the upper surface, R 1 and R 4 , and two on the lower surface, R 2 and R 3 .
The bridge deflection output is passed through an amplifier (gain, G A ¼ 1000) and measured. For a
502 Chapter 11 Strain Measurement
13:14:7 Page 502
11.20 A bathroom scale uses four internal strain gauges to measure the displacement of its diaphragm as a
means for determining load. Four active gauges are used in a bridge circuit. The gauge factor is 2,
and gauge resistance is 120 V for each gauge. If an applied load to the diaphragm causes a
compression strain on R 1 and R 4 of 20 me, while gauges R 2 and R 3 experience a tensile strain of 20
me, estimate the bridge deflection voltage. The supply voltage is 9 V. Refer to Figure 11.24 for gauge
position.
11.21 Suppose in Problem 11.20 that the lead wires of two gauges (R 2 and R 4 ) are accidently interchanged
on the assembly line such that a compression strain is now sensed on R 1 and R 2 of 20 me, while
gauges R 4 and R 3 experience a tensile strain of 20 me. Should this really matter? Explain. Estimate
the bridge deflection voltage. Refer to Figure 11.24 for gauge position.
Problems 11.22 through 11.24 address measuring strains associated with a thin-walled pressure
vessel. The pressure vessel is constructed of steel and has a circular cross-section. The tangential and
longitudinal stresses in the wall of the pressure vessel are:
s t ¼ pD=2t
s l ¼ pD=4t
where
s t ¼ tangential stress
s l ¼ longitudinal stress
p ¼ pressure
t ¼ wall thickness
11.22 A single-strain gauge is mounted on the surface of a thin-walled pressure vessel that has a diameter
of 1 m. For a strain gauge oriented along the tangential stress direction, determine the percentage
error in tangential strain measurement caused by lateral sensitivity as a function of pressure and
vessel wall thickness. The lateral sensitivity is 0.03.
11.23 Consider a Wheatstone bridge circuit that has all fixed resistances equal to 100 V and with a strain
gauge located at the R 1 position, which has a value of 100 V under conditions of zero strain. The
strain gauge is mounted so as to sense longitudinal strain for a thin-walled pressure vessel made of
steel that has a wall thickness of 2 cm and a diameter of 2 m. The strain gauge has a gauge factor of 2
and cannot sustain a power dissipation of more than 0.25 W. What is the maximum static sensitivity
that can be achieved with this proposed measurement system? Is this static sensitivity constant with
input pressure? If not, under what conditions would it be reasonable to assume a constant static
sensitivity? The static sensitivity should be expressed in units of V/kPa.
11.24 Design a Wheatstone bridge measurement system to measure the tangential strain in the wall of the
pressure vessel described above, and develop a reasonable estimate of the resulting uncertainty.
You may assume that the strain does not vary with time, and that the bridge is operated in a balanced
mode. Your selection of specified values for the input voltage, the fixed resistances in the bridge
and the galvanometer sensitivity, and their associated uncertainties will allow completion of
this design.
11.25 A steel cantilever beam is fixed at one end and free to move at the other. A load F of 980 N is applied
to the free end. Four axially aligned strain gauges (GF ¼ 2) are mounted to the beam a distance L
from the applied load, two on the upper surface, R 1 and R 4 , and two on the lower surface, R 2 and R 3 .
The bridge deflection output is passed through an amplifier (gain, G A ¼ 1000) and measured. For a
502 Chapter 11 Strain Measurement