• Toronto Metropolitan University

• MEC 430

Abstract

This report details the use of various strain gauges for different applications. Firstly, a single

strain gauge is used to measure strain on a cantilever beam at five different loads. Deflection at

these loads was also measured. This data was used to find the modulus of elasticity and

compared with theoretical values for error. In the pure bending experiment, two strain gauges

were used to measure strain at two points on a beam, and deflection was measured at these points

as well. These values again were compared to theoretical values using graphs. The deflection

was found to be greatest at the middle of the beam. For the strain on a structural section

experiment, load was applied at the midpoint of a T-section. Deflection and strain at the gauge

were measured. Due to broken equipment, the strain on a casted component was unable to be

performed experimentally. Values for the strain and deflection were provided. The graph

comparing stress and strain shows a linear relationship. To measure strain of a pressure vessel, a

rosette strain gauge was used. A rosette strain gauge uses 3 gauges arranged at 120o apart from

each other. The reading of each gauge was recorded. The applied load and measured strain were

used to determine Poisson’s ratio, hoop and axial stress, and the directions of principal stresses

and strains.

Table of Contents

1. Introduction 4

2. Cantilever Beam 5

3. Beam in Pure Bending 10

4. Strain Distribution on a Structural Section 14

5. Strain Distribution on a Casted Component 22

6. Pressure Vessel 27

7. Discussion and Sources of Discrepancies 33

8. References 35

1

List of Tables

Table 2.1: Experimental Strain and Deflection of Cantilever Beam

Table 2.2: Calculated Stress and Strain of Cantilever Beam

Table 2.3: Modulus of Elasticity for each Gauge of Cantilever Beam

Table 2.4: Calculated Deflection of Cantilever Beam

Table 3.1: Measured Deflection and Strain of Beam in Pure Bending

Table 3.2: Measured and Theoretical values of 1/R and M/EI

Table 4.1: Applied Stress and Measured Strain and Deflection of the T-Section

Table 4.2: Strain Gauge Location of T-section

Table 4.3: Theoretical Mid-Point Deflection and Strain of T-section

Table 4.4: Theoretical Stress at Each Strain Gauge Location of T-section (psi)

Table 5.1: Strain Gauge Results for Increasing Applied Loads on the C-Clamp

Table 5.2: Strain Gauge Locations (from Neutral Axis in inches)

Table 5.3: Theoretical Strain Values

Table 5.4: Theoretical Stress Values at Each Strain Gauge, S.G (psi)

Table 6.1: Strain Gauge Results for Increasing Pressure Readings on the Vessel

Table 6.2: Poisson Ratios for Each Load on Vessel

Table 6.3: Hoop and Axial Stress For Each 30 Psi Increment on Vessel

Table 6.4: Direction of Principal Stresses and Strains at Each Load on Vessel

List of Figures

Figure 2.1: Measured and Calculated Deflection vs. Load of Cantilever Beam

Figure 2.2: Stress vs. Measured and Calculated Strain of Cantilever Beam (Gauge 1)

Figure 2.3: Stress vs. Measured and Calculated Strain of Cantilever Beam (Gauge 2)

Figure 2.4: Stress vs. Measured and Calculated Strain of Cantilever Beam (Gauge 3)

Figure 3.1: Graph of Stress vs. Applied Load of Beam in Pure Bending

Figure 3.2: Measured and Theoretical Deflection vs. Applied Load of Beam in Pure Bending

Figure 3.3: Measured and Theoretical Strain vs. Applied Stress of Beam in Pure Bending

Figure 3.4: Measured and Theoretical 1/R vs. M/EI of Beam in Pure Bending

Figure 4.1: Graph of Deflection v.s Applied Load of T-section

Figure 4.2: Graph of Stress v.s Theoretical (calculated) Strain of T-section

Figure 4.3: Graph of Stress v.s Measured Strain of T-section

Figure 4.4: Strain Distribution of the T-Beam

Figure 4.5: Free Body Diagram of T-section

Figure 4.6: Shear Force Diagram of T-section

Figure 4.7: Bending Moment Diagram of T-section

Figure 5.1: Cross Section of Casted Clamp

Figure 5.2: Graph of Stress v.s Applied Load of C-Clamp

Figure 5.3: Graph of Stress v.s Measured Strain of C-Clamp

2

Figure 5.4: Graph of Stress v.s Theoretical Strain of C-Clamp

Figure 5.5: Stress v.s Strain Gauge Location (from Neutral Axis)

Figure 6.1: Experimental and Theoretical Hoop Stress v.s Pressure of Vessel

Figure 6.2: Experimental and Theoretical Axial Stress v.s Pressure of Vessel

Figure 6.3: Experimental and Theoretical Shear Stress v.s Pressure of Vessel