E1C11 09/14/2010
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cantilever, the relationship between applied load and strain is
F ¼
2E m Ie
Lt
where I is the beam moment of inertia (¼ bt
3
=12), t is the beam thickness, and b is the beam width.
Estimate the measured output for the applied load if L = 0.l m, b = 0.03 m, t = 0.01 m, and the bridge
excitation voltage is 5 V. E m ¼ 200 GPa.
11.26 A cantilever beam is to be used as a scale. The beam, made of 2024-T4 aluminum, is 21 cm long,
0.4 cm thick, and 2 cm wide. The scale load of between 0 and 200 g is to be concentrated at a point
along the beam centerline 20 cm from its fixed end. Strain gauges are to be used to measure beam
deflection and mounted to a Wheatstone bridge to provide an electrical signal that is proportional to
load. Either 1/4-, 1/2-, or full-bridge gauge arrangements can be used. Design the sensor arrangement and its location on the beam. Specify appropriate signal conditioning to excite the bridge and
to measure its output on a data acquisition system using a Æ5 V, 12-bit A/D converter. Can the
system achieve a 4% uncertainty at the design-stage? The following specifications and system
choices are stated at the 95% confidence level:
Sensors: one, two, or four axial gauges at 120 V Æ 0.2% (selectable)
Gauge factor of 2.0 Æ 1%
Bridge excitation: 1, 3, 5 V Æ 0.5% (selectable)
Bridge null: within 5 mV
Signal conditioning:
Amplifier gain: 1X, 10X, 100X, 1000X Æ 1% (selectable)
Low-pass filter: f c at 0.5, 5, 50, 500 Hz @ À12dB/octave (selectable)
Data acquisition system:
Conversion errors: < 0.1% reading
Sample rate: 1, 10, 100, 1000 Hz (selectable)
11.27 A rectangular strain gauge rosette is composed of strain gauges oriented at relative angles of 0, 45,
and 90 degrees, as shown in Figure 11.17b. The rosette is used to measure strain on a steel structural
member having E m ¼ 200 GPa and n p ¼ 0:3. The measured values of strain are
e 1 ¼ 10000 me
e 2 ¼ 5000 me
e 3 ¼ 50000 me
Determine the principal stresses and the angle that the maximum principal stress makes with the 0degree gauge.
11.28 Research the equivalent of Equation 11.39 for a 60-60-60 degree strain rosette.
Problems 503
13:14:7 Page 503
cantilever, the relationship between applied load and strain is
F ¼
2E m Ie
Lt
where I is the beam moment of inertia (¼ bt
3
=12), t is the beam thickness, and b is the beam width.
Estimate the measured output for the applied load if L = 0.l m, b = 0.03 m, t = 0.01 m, and the bridge
excitation voltage is 5 V. E m ¼ 200 GPa.
11.26 A cantilever beam is to be used as a scale. The beam, made of 2024-T4 aluminum, is 21 cm long,
0.4 cm thick, and 2 cm wide. The scale load of between 0 and 200 g is to be concentrated at a point
along the beam centerline 20 cm from its fixed end. Strain gauges are to be used to measure beam
deflection and mounted to a Wheatstone bridge to provide an electrical signal that is proportional to
load. Either 1/4-, 1/2-, or full-bridge gauge arrangements can be used. Design the sensor arrangement and its location on the beam. Specify appropriate signal conditioning to excite the bridge and
to measure its output on a data acquisition system using a Æ5 V, 12-bit A/D converter. Can the
system achieve a 4% uncertainty at the design-stage? The following specifications and system
choices are stated at the 95% confidence level:
Sensors: one, two, or four axial gauges at 120 V Æ 0.2% (selectable)
Gauge factor of 2.0 Æ 1%
Bridge excitation: 1, 3, 5 V Æ 0.5% (selectable)
Bridge null: within 5 mV
Signal conditioning:
Amplifier gain: 1X, 10X, 100X, 1000X Æ 1% (selectable)
Low-pass filter: f c at 0.5, 5, 50, 500 Hz @ À12dB/octave (selectable)
Data acquisition system:
Conversion errors: < 0.1% reading
Sample rate: 1, 10, 100, 1000 Hz (selectable)
11.27 A rectangular strain gauge rosette is composed of strain gauges oriented at relative angles of 0, 45,
and 90 degrees, as shown in Figure 11.17b. The rosette is used to measure strain on a steel structural
member having E m ¼ 200 GPa and n p ¼ 0:3. The measured values of strain are
e 1 ¼ 10000 me
e 2 ¼ 5000 me
e 3 ¼ 50000 me
Determine the principal stresses and the angle that the maximum principal stress makes with the 0degree gauge.
11.28 Research the equivalent of Equation 11.39 for a 60-60-60 degree strain rosette.
Problems 503