MATH 223 Lecture Notes - Lecture 2: Elastic Modulus, Strain Gauge, Wheatstone Bridge

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EMCH 361 Mechanical Engineering Laboratory I, Spring 2020
Mechanical Engineering, USC
Laboratory I
STRAIN MEASUREMENTS
Jacob Hinchman
Department of Mechanical Engineering
University of South Carolina
Columbia, SC 29208
Abstract
In an engineers career, knowing
how to measure the strain of material and
making use of that data is critical. In this
lab, students measured the stain of a
cantilever beam while force was being
applied to the unfixed end of the beam.
This provided students a hands-on learning
experiencing using the proper tools and
measurement devices to collect the data
correctly and accurately. Through this lab,
students will be able to use the experience
to translate it into their careers. In this lab,
force was measured in Newtons (N) and
strain was measured in millivolts (mV). As
force applied increased, so did the quantity
of millivolts.
This stress value was utilized in
determining the elastic modulus of the
material of the beam, which was found
using two different methods. The first was
through calculation using the young’s
modulus equation, with the result being
that the beam had an elastic modulus value
of 6827869901.8333 ±20494382.358(80%
confidence interval). The second making a
scatter plot of the stress vs strain to
determine that the beam had an elastic
modulus value of 68,164,459,328.70.
Introduction
To measure strain on a beam one
can, use a strain gage on the surface of the
beam. The strain gages will follow the
relation:
      (1), where:
 - change in resistance
 Gage factor for the strain gage
strain applied
base strain gage resistance
To convert this change in resistance to
voltage output a Wheatstone bridge will be
used. Hooke’s Law is used in the laboratory
because of the isotropic material in the
linear-elastic region. When one has uniaxial
stress in the x-direction, Hooke’s Law will
become:
 
(2), where:
 strain
stress
Young’s modulus
Shown below is the setup of the laboratory:
Youngs Modulus:    (3),
(stress/strain). Stress can be found using
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