## Bending Deflection of Beams

**Lab Section** (e.g. A, B, C, etc…)

Term: (e.g. Spring 2015)

Your Name: (e.g. John Smith, Jane Smith)

Abstract (5 pt.)

The objective of this experiment is to determine how the flexural deflection of a beam is influenced by the load, modulus of elasticity, cross-sectional dimensions, boundary conditions, and span length. This was accomplished by … … The findings were … … Based on the findings, the author concluded that …**Results **(70 pt.)

Figure 1 illustrates the influence that Flexural Stiffness has on the bending deflection of a beam.

Insert Figure 1 here

Figure 1. W versus δ data for a simply supported aluminum beam (9.5 x 3 mm) with varying load (slope=k).

Table 1 presents a comparison between expected and measured slope values for Figure 1.

Table 1. Summary of Figure 1 Results

Beam Experiment 4A Slope (W/δ), K (units) % diff*

measured expected

- % diff = (measured – expected)/expected

Figure 2 illustrates the influence that Young’s Modulus has on the bending deflection of a beam.

Figure 2. W versus 48δI/L3 data for beams with varying moduli of elasticity (slope=E).

Table 2 presents a comparison between expected and measured slope values for Figure 2.

Table 2. Summary of Figure 2 Results

Beam Experiment 4B Slope (WL3/48δI), E (units) % diff*

measured expected

Aluminum

Steel

Brass

† cite source

- % diff = [(measured – expected)/expected]*100

Figure 3 illustrates the influence that cross-section has on the bending deflection of a beam.

Insert Figure 3 here

Figure 3. W versus 48δE/L3 data for beams with varying cross-sections (slope=I).

Table 3 presents a comparison between expected and measured slope values for Figure 3.

Table 3. Summary of Figure 3 Results

Beam Experiment 4C Beam Dimensions (units) Slope (WL3/48δE), I (units) % diff*

b d measured expected

Area #1

Area #2

Area #3

Area #4

- % diff = (measured – expected)/expected

Figure 4 illustrates the influence that Boundary Conditions have on the bending deflection of a beam.

Insert Figure 4 here

Figure 4. W versus δEI/L3 data for beams with varying boundary conditions (slope=1/C).

Table 4 presents a comparison between expected and measured slope values for Figure 4.

Table 4. Summary of Figure 4 Results

Beam Experiment 4D Slope (WL3/δEI), 1/C % diff*

measured expected

Simply – Supported

Propped Cantilever

Fixed – Supported

- % diff = (measured – expected)/expected

Table 5 presents the influence that Span Length has on the bending deflection of a beam.

Table 5. Summary of Figure 5 Results

Beam Experiment 4E Distance (units) Slope (W/δ), 1/L^3 (units) % diff*

measured expected

Distance #1

Distance #2

Distance #3

Distance #4

Distance #5

Distance #6

- % diff = (measured – expected)/expected

**Lab Questions** (15 pt.)

What is the significance of the values chosen for the x- and y-axis on the graphs above? Explain.

```
Of the experimentally variables that you measured, which has the greatest influence on flexural deflection? How would that influence the decision of an engineer designing a beam?
Define “flexural stiffness” in terms of a member’s geometric and material properties.
```

**Conclusions** (10 pt.)

The original objective of this experiment was to determine how the flexural deflection of a beam is influenced by the load, modulus of elasticity, cross-sectional dimensions, boundary conditions, and span length. Based on the above results, the author determined that …

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