AbstractThis experiment used strain gauges along a cantilever beam to explore properties such as stress, strain and tip deflection as different loads are supplied to the tip. Comparing the results of this experiment reveals that the experimental values were marginally higher than the theoretical values calculated. This experiment was able to show its usefulness in exploring properties of how loads affect beams, as well as how to apply strain gauges in the industry.PurposeThis lab will be used to familiarize students with the use of strain gauges. In doing so, students will study and compare the theoretical and experimental results of stresses on the cantilever beam.Apparatus Cantilever beam Strain indicator Precision dead loadFigure 1: Cantilever Beam Experiment Setup

Procedure1. Measure the distances of the strain gauges through the cantilever beam, as well as the length of the cross-sectional geometry of the beam 2. The maximum allowable load was calculated using the maximum allowable stress.3. The strain indicator was turned on an each strain channel was balanced.4. Starting at 2 lb load, the strain displayed by each gauge as well as the tip deflections was recorded. Increasing the increments of the load by 2 lb was continued until 10 lb was reached.

ObservationsTable 1: Beam Geometry and PropertiesBeam Length10 in

Beam Width1 in

Beam Height0.25 in

Distance from wall to Gauge 11 in

Distance from wall to Gauge 24 in

Distance from wall to Gauge 37 in

Poissons Ratio0.32

Modulus of Elasticity10.4 Msi

Maximum allowable Stress10 ksi

Table 2: Strain Gauge RecordingsLoad Experiment [lb]Strain Gauge 1 []Strain Gauge 2 []Strain Gauge 3 []Top Deflection[in]

2177113500.067

43492141090.126

65173411600.184

86934492090.224

108655602740.301

Calculations*Note, all sample calculations are done for Load = 2 lb , results are tabulated in tables 3 and 4Table 3: Theoretical Stress and DeflectionLoad [lb]Theoretical Stress Gauge 1 [ksi]Theoretical Stress Gauge 2 [ksi]Theoretical Stress Gauge 3 [ksi]Theoretical Tip Deflection [in]

21.7281.1521.5760.0492

43.4562.3041.1520.0985

65.1843.4561.7280.1477

86.9124.6082.3040.1969

108.645.762.880.2462

Table 4: Theoretical StrainLoad [lb]Theoretical Strain Gauge 1 [in/in]Theoretical Strain Gauge 2 [in/in]Theoretical Strain Gauge 3 [in/in]

20.0001660.0001110.000055

40.0003320.0002220.000111

60.0004980.0003320.000166

80.0006640.0004430.000221

100.0008310.0005540.000277

For moment of Inertia

Maximum Allowable Load

Theoretical deflection

Theoretical Stress at Gauge 1

Theoretical Stress at Gauge 2

Theoretical Stress at Gauge 3

Theoretical Strain at Gauge 1

Theoretical Strain at Gauge 2

Theoretical Strain at Gauge 3

Graph 1: Tip Deflection vs. Load

Graph 2: Stress vs. Strain for Gauge 1

Graph 3: Stress vs. Strain for Gauge 2

Graph 4: Stress vs. Strain for Gauge 3

DiscussionAfter comparing the results of stress and strain to both the theoretical and experimental values, it is evident that the data are very similar and the experiment was done accurately. Graph 1, exhibited the most variance, which showed that the tip deflection of the experimental values were higher than the theoretical values calculated. On the other hand, the theoretical and experimental values for the stress vs. strain graphs had nearly identical values for slope. This slope is the modulus of elasticity, and because the values for stress and strain were so similar, it shows the data obtained and calculated were correct. The discrepancies that occurred in this experiment came from the balancing of the channels. Some channels were not completely zeroed. Therefore, since we are dealing with micro strain, the order of magnitude is so minute that the deviations are higher. Furthermore, the values indicated by the strain indicator always fluctuated between values. Next time, taking more readings and averaging the values would probably give a more accurate experiment, but this is probably not needed since the experiment was already very accurate to begin with.ConclusionThis lab helped students understand how stress and strain acts at various points along a cantilever beam using strain gauges, by comparing values calculated to values obtained through calculation. Comparing the values showed that showed that there was very little error in this experiment because the values were so similar. The point where the tip deflection was the greatest was the location of the higher strain. When a different force was applied to the beam, it changed the distribution along the beam varying the value in the strain gauges. This was an effective method to help students understand the concept of strain gauges.