Background reading for Lab 5 (Calibration of a Cantilever Beam / Wheatstone
1.1 Motivation for resistance bridges – measuring small changes in resistance
A large number of sensors that are used in engineering applications convert the desired
measurement signal into a variable resistance.
This was done for temperature in recent labs
using thermistors, but it can also be done for other physical parameters such as strain, pressure,
However, most often we need the sensor signal to be in the form of a voltage
that can be easily measured and processed using an analog to digital signal converter and a data
We have used simple resistive voltage divider circuits in the past to
accomplish this, but these have some inherent drawbacks.
A resistance bridge configuration can
get around many of these issues by allowing for automatic compensation for resistance
tolerances, variations with temperature (if we don’t want to measure such variations), and
resistance in the wires leading to the sensor.
Also, resistance bridges can remove the offset (DC
component) of a signal and allow closer examination of small changes relative to this offset.
1.2 Intro to strain gages, sensors commonly connected to resistance bridges
Strain gages operate on one of four different principles: changes in semiconductor
characteristics, capacitance, wire vibration, or electrical resistance when the test piece to which
they are mounted undergoes a strain. Use of the resistance strain gage surpasses the others in
engineering practice and is therefore the focus in this course. The relationship between the
electrical resistance of a wire and the corresponding strain was first observed by Lord Kelvin in
1856. Although the effect would become a great contribution to the engineering field, Kelvin
regarded it as an experimental nuisance. During the early 1930's, the first resistance strain gage
was developed for industry, consisting of a carbon strip surrounded by an insulating pad. Its first
use was to measure vibrating strains on aircraft propellers. The rapidly growing aircraft industry
during WWII had the largest influence on strain gage development, and in 1952 the first modern
foil resistance strain gage was produced.
2.0 Strain Gages
2.1 Gage Construction
The components of a resistive strain gage are shown in Figure 1. The manufacture of the foil
element requires great precision. An alloy (usually constantan - 55% Cu, 45% Ni ) is rolled to a
constant thickness (typically 0.003 mm to 0.005 mm) and the pattern is stamped out. Foil
elements commonly have unstrained resistance values of 60, 120, 350, 500 and 1000 Ω. In our
experiment, the unstrained resistance is approximately 350 Ω. By adjusting the characteristics of
the strain gage (e.g., the alloy or geometry), it is possible to obtain a gage that is customized for
unique applications (e.g., an engineer measuring the thermal expansion of a combustor would be
concerned with the temperature-dependence of the gage's resistance).