Prelab

Print this document, and bring it to the lab.

Procedure

1. Support the strain gauge apparatus and measure the distance between the supports, and all 5 gauges.

2. Weigh the load using the balance, and note it on your data sheet.

3. Measure the dimensions required from the apparatus.

4. Acquire the strain readings from the pDaq software, and note the results on you datasheet.

5. Add the additional load and remeasure the strains.

Results

For the beam measurements find:

• The stress at the 5 points σ_meas = E * ϵ .

  • E is the Modulus of Elasticty of Aluminum (68.9 GPa)

  • ϵ is strain (measured in microStrain, 10^-6 )

• The bending moments M_max = ( P * A * B ) / L where:

  • A and B are the distance from an end to the Load (m)

  • P is the total Load (N)

  • L is the total length (m)

  • you may use the method of sections or ratios to find the moments (Nm)

• The stresses can be calculated from the moments as follows:

  • σ_calc = ( M * y ) / I

    • y is the distance from the central axis to the exterior of the beam (m)

    • I is the moment of Inertia, about the central axis (m⁴)

• You can then compare the measured and calculated moments, and find the average absolute error:

  • Σ [ (σ_meas - σ_calc) / σ_calc ] / 5, that is, you should sum the error found as: (σ_meas - σ_calc) / σ_calc from all 5 points, and divide by 5.

• Plot a Stress vs Distance curve for both measured and calculated stresses.

• From the above data, find the mass of the unknown load.

Questions

1. How would the appearance of the curve change if we used an Iron beam instead of Aluminum with the same load applied?

2. How would the appearance of the curve change if we doubled the load applied to the same beam?