# Bending moment by discovery: measuring strains on an aluminum beam

OVERVIEW

This inquiry-based learning activity (IBLA) is completed by students in class before elastic bending theory is presented.

PRINCIPLES

By completing this scripted exercise, students are exposed to the varying strain profile through the depth of a beam. From this strain profile, students apply Hooke’s law to develop the stress profile, then calculate equivalent tension and compression forces, and conclude with the discovery of an internal moment!

WHAT YOU NEED

• 0.25-in x 1-in rectangular aluminum stock (we cut our 6061-T6 stock to 17-in lengths so we could get a certain number of beams out of the stock we had available)
• Aluminum supports (we cut ours from 0.25-in thick aluminum plate, creating a notch in which the beam rests, and welded to another piece of 0.25-in thick aluminum plate)
• Strain gages mounted on the top and bottom and at mid-depth of the beam
• Strain indicator box (we used a Vishay P-3500)
• Switch and balance box (unless your strain data reading or acquisition system allows connection of multiple strain gages)
• Hanger and weights (we used three 2-kg weights)
• Enough copies of the IBLA handout for all students (see attached file below)

HOW IT’S DONE

1. Ensure the system is reading strains correctly before class.
2. Have the students follow the steps on the IBLA (see attached file above). This exercise is intended for students to make guesses prior to measurements in order to expose potential errors in intuition (one of the objectives of inquiry-based learning)
3. The instructor leads the class through step 4 from the IBLA handout – plotting the strain values through the depth of the cross-section, calculating the associated stresses and discovering that the top portion of the beam is in compression while the bottom is in tension. See Figure 2.
4. Realizing that the resulting internal forces represent a force couple, the class can continue to discover how a transverse load generates an internal moment. See Figure 3.
5. The lesson concludes with introduction of the elastic flexure formula by integrating the stress profile. See Figure 4.

REFERENCES

This exercise was inspired by a 2015 ASEE talk by Brian Self, Jim Widman and one of their students about using IBLAs to repair misconceptions. That interesting paper is found here. A search in ASEE’s PEER for other papers Brian and Jim have authored yields even more inspiration for developing IBLAs.