Reference no: EM132071787

This case study is submitted no later than the end of Module 8. It is to be written in a report style.

Water has a specific weight, 1 liter (10cm³) equals 1 kg. This equates to 9.81 N force. We have covered the bending of a beam extensively in the first few modules. Here the focus is to use the Beam Theory to estimate material properties. We will use a simply supported beam, see Figure 1.

The bending moment at each end will be equal but opposite if symmetrically loaded. The maximum stress, σ, will be in the center of the beam for this design, not as at the root on a cantilever. The maximum liner deflection downwards is determined by the following equation:

δ max = Pl³/48EI

If you measure the deflection under a load then this can be substituted into the above equation to estimate Young's Modulus. With this you can then substitute in the Engineer's Beam Equation to estimate σ max and the theoretical radius, which can be verified by your measurement.

Material:
You need to find, or buy a piece of wood that is longer than 0.6 m (over two feet). This can be placed between two chairs or tables see Figure 2. Do not have something too large or the deflections will be small and difficult to measure.

Process:

When set up, hook a bucket below and pour in enough water to record a reasonable deflection. Measure and record the deflection. Add more water to increase the deflection and record this value.

Use both of these values to estimate the Young's modulus.

What difference is there between using each?

Use the average of the two to substitute in the Engineer's Beam Equation and then calculate the maximum stress. You can calculate the 'I' value from the dimensions. In addition, use the deflection to estimate the radius of curvature and compare to what the equation predicts.

With this data predict the load that would cause the beam to break.

In your report explain your stages, support with photos and present the measurements in a table.

In the summary comment on errors and inaccuracies. Also if the beam was made from steel with an E=210GPa, show how that would compare with your results.

Refer to the Discussions and Report Criteria page for report format and other information.

MUST INCLUDE:
- Front cover with name and detail of work
- Introduction
- Subsections
- A summary
- Appendices (if needed)
- References must be in current APA format
- Times New Roman - 12 point font and double lined space
- Minimum of 2,000 words (for the final report including calculations)