E1C11 09/14/2010
13:14:7 Page 499
G
shear modulus (m t
À2 )
G A
amplifier gain
GF
gauge factor
K
strain optical coefficient
K B
bridge sensitivity (V)
K I
strain gauge lateral sensitivity
L
length (l)
dE o voltage change (V)
dL
change in length (l)
dR
resistance change (V)
M
bending moment (m l
2
t
À2 )
R
electrical resistance (V)
T
temperature (
)
T 0
reference temperature (
)
a
moir e grating width to spacing
parameter
g xy
shear strain in the xy plane (m l
À1
t
À2 )
d
relative retardation between two light beams
in a photoelastic material
e a
axial strain
e b
bending strain
e r
strain in the i coordinate direction (i.e., x
direction)
e l
lateral or transverse strain
e t
apparent strain due to temperature
k
bridge constant
n p
Poisson ratio
n po
Poisson ratio for gauge factor calibration test
p 1
piezoresistance coefficient (t
2 l m
À1 )
r e
electrical resistivity (V l)
s
stress (m l
À1
t
À2 )
s a
axial stress (m l
À1
t
À2 )
t xy
shear stress in the xy plane (m l
À1
t
À2 )
PROBLEMS
11.1 Calculate the change in length of a steel rod (E m ¼ 30 Â 10
6 psi) that has a circular cross section, a
length of 10 in., and a diameter of 1/4 in. The rod supports a mass of 50 lbm in such a way that a state
of uniaxial tension is created in the rod.
11.2 Calculate the change in length of a steel rod (E m ¼ 20 Â 10
10 Pa) that has a length of 0.3 m and a
diameter of 5 mm. The rod supports a mass of 60 kg in a standard gravitation field in such a way that
a state of uniaxial tension is created in the rod. Make the same calculation for a rod made of
aluminum E m ¼ 70 GPa
ð
Þ .
11.3 An electrical coil is made by winding copper wire around a core. What is the resistance of 20,000
turns of 16-gauge wire (0.051 in. diameter) at an average radius of 2.0 in.?
11.4 Compare the resistance of a volume of p  10
À5 m
3 of aluminum wire having a diameter of 2 mm,
with the same volume of aluminum formed into 1-mm-diameter wire. (The resistivity of aluminum
is 2:66 Â 10
À8
V m.)
11.5 A conductor made of nickel (r e ¼ 6:8 Â 10
À8
V m) has a rectangular cross section 5 Â 2 mm and is
5 m long. Determine the total resistance of this conductor. Calculate the diameter of a 5-m-long
copper wire that has a circular cross section that yields the same total resistance.
11.6 Consider a Wheatstone bridge circuit that has all resistances equal to 100 V. The resistance R 1 is a
strain gauge that cannot sustain a power dissipation of more than 0.25 W. What is the maximum
applied voltage that can be used for this bridge circuit? At this level of bridge excitation, what is the
bridge sensitivity?
11.7 A resistance strain gauge with R = 120 V and a gauge factor of 2 is placed in an equal-arm
Wheatstone bridge in which all the resistances are equal to 120 V. If the maximum gauge current is
to be 0.05 A, what is the maximum allowable bridge excitation voltage?
11.8 A strain gauge that has a nominal resistance of 350 V and a gauge factor of 1.8 is mounted in
an equal-arm bridge, which is balanced at a zero applied strain condition. The gauge is mounted on a
Problems 499
13:14:7 Page 499
G
shear modulus (m t
À2 )
G A
amplifier gain
GF
gauge factor
K
strain optical coefficient
K B
bridge sensitivity (V)
K I
strain gauge lateral sensitivity
L
length (l)
dE o voltage change (V)
dL
change in length (l)
dR
resistance change (V)
M
bending moment (m l
2
t
À2 )
R
electrical resistance (V)
T
temperature (
)
T 0
reference temperature (
)
a
moir e grating width to spacing
parameter
g xy
shear strain in the xy plane (m l
À1
t
À2 )
d
relative retardation between two light beams
in a photoelastic material
e a
axial strain
e b
bending strain
e r
strain in the i coordinate direction (i.e., x
direction)
e l
lateral or transverse strain
e t
apparent strain due to temperature
k
bridge constant
n p
Poisson ratio
n po
Poisson ratio for gauge factor calibration test
p 1
piezoresistance coefficient (t
2 l m
À1 )
r e
electrical resistivity (V l)
s
stress (m l
À1
t
À2 )
s a
axial stress (m l
À1
t
À2 )
t xy
shear stress in the xy plane (m l
À1
t
À2 )
PROBLEMS
11.1 Calculate the change in length of a steel rod (E m ¼ 30 Â 10
6 psi) that has a circular cross section, a
length of 10 in., and a diameter of 1/4 in. The rod supports a mass of 50 lbm in such a way that a state
of uniaxial tension is created in the rod.
11.2 Calculate the change in length of a steel rod (E m ¼ 20 Â 10
10 Pa) that has a length of 0.3 m and a
diameter of 5 mm. The rod supports a mass of 60 kg in a standard gravitation field in such a way that
a state of uniaxial tension is created in the rod. Make the same calculation for a rod made of
aluminum E m ¼ 70 GPa
ð
Þ .
11.3 An electrical coil is made by winding copper wire around a core. What is the resistance of 20,000
turns of 16-gauge wire (0.051 in. diameter) at an average radius of 2.0 in.?
11.4 Compare the resistance of a volume of p  10
À5 m
3 of aluminum wire having a diameter of 2 mm,
with the same volume of aluminum formed into 1-mm-diameter wire. (The resistivity of aluminum
is 2:66 Â 10
À8
V m.)
11.5 A conductor made of nickel (r e ¼ 6:8 Â 10
À8
V m) has a rectangular cross section 5 Â 2 mm and is
5 m long. Determine the total resistance of this conductor. Calculate the diameter of a 5-m-long
copper wire that has a circular cross section that yields the same total resistance.
11.6 Consider a Wheatstone bridge circuit that has all resistances equal to 100 V. The resistance R 1 is a
strain gauge that cannot sustain a power dissipation of more than 0.25 W. What is the maximum
applied voltage that can be used for this bridge circuit? At this level of bridge excitation, what is the
bridge sensitivity?
11.7 A resistance strain gauge with R = 120 V and a gauge factor of 2 is placed in an equal-arm
Wheatstone bridge in which all the resistances are equal to 120 V. If the maximum gauge current is
to be 0.05 A, what is the maximum allowable bridge excitation voltage?
11.8 A strain gauge that has a nominal resistance of 350 V and a gauge factor of 1.8 is mounted in
an equal-arm bridge, which is balanced at a zero applied strain condition. The gauge is mounted on a
Problems 499