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

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21 Oct 2020

School

Department

Course

Professor

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