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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