Your team of technologists has been hired by C. R. Azy and Associates, Civil Engineers, to design a beam to be used in a highway overpass. The goal of this beam is to hold the most weight with a fixed amount of material. Beam designs will be tested by loading a prototype to failure while it spans an eight inch gap. You must provide an informational report of your results showing all of the cross-sections that you tested and specifying which cross-section resulted in the strongest beam.

To meet the requirements of your contract, your team will:

- Design and construct a beam to span an eight inch gap while supporting a force downward at the center
- Demonstrate the performance of each beam by loading it to failure. For each test you should
- sketch the cross-section of the beam.
- determine the cross-sectional area (A) of the beam.
- record the amount of force (F) required to break the beam.
- calculate the bending moment (M) applied to the beam when it failed.
- calculate the second moment of area (I) and section modulus (Z).
- use the elastic flexure formula to estimate the stress at failure (σ
_{yield}). - Design and construct different beams with the goal of making a stronger beam.
- Test each new beam as before.
- Do the assigned problems to learn more about material properties.
- Plot the many beam properties you have learned against force at failure to see what factors make one beam stronger than another.
- Provide your results in an informational report in the required format.

- Students will design, build and test their beams in teams of 1 or 2.
- The gap that must be spanned is eight inches wide.
- Beams will be made from 1/8" x 1/8" balsa wood.
- The maximum cross-sectional area at any point on the beam cannot be more than one eighth of one square inch.
- Any readily available glue (except hot glue) may be used. Glue should be used to join pieces and not as a coating.
- The wood must be dry when the beam is tested.

The evaluation of the task will be based on the following

The performance of your beam will be based on the amount of force your beam carried as compared to the maximum in the lab

30 points – Maximum in lab

27 points – 90% of maximum

24 points – 50% of maximum

21 points – 25% of maximum

18 points – any beam tested

Each problem should be solved in pencil on its own sheet of plain white or engineering paper

1 point for Given, Find, Relationships

- Given information translated into symbols. Each symbol given a numerical value and units assigned.
- Correct items to be found identified, symbols used to identify them
- Sketch provided if needed
- Relationships include all required formulas and conversion factors

3 points for solution correctly laid out

- Follows logical sequence.
- Relationships (formulas) shown then variables replaced with numbers and units.
- Units are carried throughout.
- Answers on "Find" list underlined.

1 point for correct answers including units (may include errors carried forward)

- Answers match "Find" list.
- Final answers boxed together at the end.

Provide an informational report in the required format. It will be evaluated for content (10 points), organization (5 points), style (5 points), and presentation (10 points) using the standard rubric.

Make sure the report

- Contains the required information.
- Shows calculations in enough detail to determine if results are correct.
- Demonstrates an understanding of the various factors that determine the strength of a beam.
- Contains your beam sketches and tables of results that are introduced, integrated, and discussed in the text of the report.
- Contains a sample calculation that is explained in the text of the report.
- Contains enough information in the
**Details**section to support the conclusions.

In addition to the general requirements, use this guidance.

Write this section last. The summary (or abstract) should be a clear and concise 3 or 4 sentence version of the report. Be sure and include your best result and most important conclusions. Here is a prompt for the summary:

Summarize the task for a student who was absent. Be sure and include all rules and limits.

Then explain the math and science involved, including the theory behind your calculations. Define all terms and explain how they are determined.

Tell the whole story from the beginning in several well-organized paragraphs. Tell what you expected each beam to do and how this compares to the results that you got.

Include a sketch of each beam and a table of results.

Make sure that you include enough information to support each of your conclusions.

What were your best results?

Which of these statements is most true? Why?

- The beam with the most
**area**is the strongest. - The beam with the most
**height**is the strongest. - The beam with the most
**Y**is the strongest._{max} - The beam with the most
**Second Moment of Area (I)**is the strongest. - The beam with the most
**Section Modulus (Z)**is the strongest.

If you could start over again today, what would you do differently?

Make sure you are being specific. Go back to the **Details** section and make sure that all of your conclusions are supported.

Engineers Edge Explanation

A lesson on Beams

A lesson using slightly different symbols

Problems | Blank Data Table | Evaluation |

Teacher Resources | Daily Lesson Power Point |