Materials Testing Lab Report

Introduction

This experiment was conducted to assess the quality and condition of different types of metal beams, namely aluminum, rectangular copper, square copper, and an unknown material. The objective was to measure the difference in stress and strain among these beams using a dial caliper. Additionally, the experiment aimed to identify the unknown material used for one of the beams, calculate the slope of the Deflection vs. Force graph for the Rectangular Beam of Unknown Material, and determine Young's Modulus.

The context for this lab is a commercial real estate firm's interest in reclaiming materials from abandoned industrial buildings for reuse in new construction projects.

To make informed decisions, the firm needs to assess the condition of these materials. This report presents the experimental results, data analysis, conclusions, recommendations, and references related to the lab.

Experimental Results

The experiment involved measuring deflection on various metal beams under load. The following observations and results were obtained:

1. Aluminum Rectangular Beam: The percent error for this beam was initially 7%, but subsequent data had less than 3% error.
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   Possible sources of error included structural swinging and variations in the weight of the loads.

2. Copper Rectangular Beam: The percent error ranged from under 5% for most measurements, but there was a significant error in the final measurement due to a loosened screw holding the weights. Variability in tapping the structure also contributed to error.
3. Copper Square Beam: The percent error for this beam ranged from 16% at its highest to 2% at its lowest. Negative percent error in the initial measurement was likely due to inaccuracies in measuring the beam's dimensions.
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4. Unknown Rectangular Beam: To determine the Young's Modulus of the unknown material, a graph of deflection vs. force was created. The slope of the graph was calculated, leading to a Young's Modulus value of 2710832.922 lbf/in^2, which closely matched steel.

It was expected that the data would follow a linear pattern, as indicated by the theoretical deflection equation:

σ=FS^2(3L-S)/6EI

Where:

• σ = Stress
• F = Force (lbf)
• S = Distance to Dial Indicator
• L = Distance to Force
• E = Young's Modulus
• I = Moment of Inertia

Since the equation simplifies into a linear form, the theoretical graph was expected to be linear. The measured values closely matched the theoretical values, resulting in relatively low percent errors. This indicated that the results closely aligned with the theoretical values based on measurements.

Conclusions & Recommendations

Based on the experimental data and analysis, the following conclusions and recommendations can be made:

• The unknown material of the Rectangular Beam closely resembles steel in terms of Young's Modulus. Therefore, it is recommended to use this material in new construction projects, particularly for exterior applications.
• Materials with signs of water damage or strain should not be used in future projects, as their structural integrity may be compromised.
• Copper and aluminum beams can be suitable for interior projects where they do not need to withstand outdoor elements such as wind, rain, and snow.
• For accurate material assessment, all materials should be thoroughly examined at a site separate from the metal plant, where precise data can be recorded.
• Rectangular beams are preferable over square beams, as they exhibit lower deflection, making them more suitable for various construction applications.
• Any remaining metals that cannot be reused should be melted and sold to generate funds for the construction project.

In summary, the measurements taken in this experiment were generally accurate, with the highest percent error being 16%. The linear correlation in the data and the close alignment of measured and theoretical values indicate the reliability of the results. Reducing potential sources of error, such as verifying weight consistency and standardizing the tapping process, could further improve accuracy.

References

1. Reference 1
2. Reference 3

Appendices

Appendix A: Calculations for Young’s Modulus

Using the equation:

δ = F(S^2(3L-S))/6EI

Where:

• δ = Deflection
• F = Force (lbf)
• S = Distance to Dial Indicator
• L = Distance to Force
• E = Young's Modulus
• I = Moment of Inertia

We rearranged the equation to calculate Young’s Modulus:

E = (S^2(3L-S))/6Im

Given values:

• L = 8.750 in
• S = 7.500 in
• I = (w*t^3)/12 = ((0.498 in)(0.125 in)^3)/12 = 8.1055E-5 in^4
• F = Total Weight (lbf)
• m = 0.08

Young’s Modulus calculation:

E = ((7.5 in)^2(3(8.75 in)-(7.5 in))/(6(0.08)(8.1055E-4 in^4)))

E ≈ 2710832.922 lbf/in^2

After researching online, the material's Young’s Modulus closely matches that of steel.