Prelab

Printouts are available in the lab for this session.

Procedure

1. Select a wooden beam and measure it's cross-sectional dimensions, both height and width.

2. Select two points at which you will attach the supports that are about 70cm to 100cm apart and mark them on the wood.

3. Mark the two spots using thumbtacks, try to have the height of each centered in the beam.

4. Using the ruler, draw a line along the centroidal axis between the two tacks.

5. Select a third point for the loading point between the two supports and mark it on the wooden beam.

6. Record the distances A and B from the load to each end.

7. Simulate a load between 6-8 kN with the Instron test machine. Record the load.

8. Draw a new line between the two tacks showing the degree of deflection.

9. Continue the loading until the beam fails. Record the break load.

10. Measure the deflection at 1/10^th L divisions along the beam between the thumbtacks. Record these values.

Results

1. Calculate the Max Bending Moment given the load and its location

   • 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)

2. Calculate the Ultimate Normal Stress

   • σ_calc = ( M_max * 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)

3. Calculate the Modulus of Elasticity of the Spruce Beam using the deflection and the relations from the image below.

4. Calculate the Ultimate Shear Stress along the neutral axis using τ = V * Q / I * t where:

   • V is the shear force

   • Q is the first moment of area or Centroid

   • I is the moment of inertia

   • t is the beam thickness

5. Graph the Experimental Deflection vs Distance of the 10 points along the beam.

6. Using the Lab 4 Workbook, input your data and view the calculated results of the Singularity Functions. Only fill in yellow cells.

   • Save a copy, don't ask for permission to edit.

7. Compare the graph to your Deflection graph.

The following relationships and diagrams might help you in your preparation.

It is suggested that you you one of the three lower cases using values at the point of loading, or just before or after as appropriate.