Experimental Modulus of Cantilevered Basswood Beam Using Engauge Digitizer

Objective:

Experimentally determine the modulus of elasticity of a basswood beam.

Description of Model:

A gridded mat was bolted onto a sheet of plywood which was then bolted to a pre-threaded steel base. A level was used to ensure that the horizontal gridlines were parallel to the floor and that the mat itself would be perpendicular to the floor. The grid assembly was attached to a cart to ease positioning of the grid. A basswood beam with 0.269.in x 0.268.in cross section was set into a wooden block as shown in Fig. 1 and clamped to a cart to allow mobility of the experiment.

Fig. 1: Close-up of Support

The beam was positioned in front of the grid assembly as shown in Fig. 2.

Fig. 2: Unloaded Experiment Set-up

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The load was applied as shown in Fig. 3. A small screw was set into the tip of the beam. A bag of lead shot was hung on the beam using a twist tie. This method of loading allowed the beam to be easily loaded or unloaded. The load measured 38.3 grams or 0.084437 lbs on a triple beam balance.

Fig. 3: Loading Close-up

Below is the loaded beam in front of the grid assembly.

Fig. 4: Loaded Experiment Set-up

The unloaded and loaded images were imported into Engauge Digitizer to obtain the deflection at the load point.

Results:

The equation was used with measured parameters to calculate a modulus of 1.56*106 psi. The values used in the calculation are displayed below. The modulus published in The Encyclopedia of Wood is 1.46*106 psi. With only 6.85% difference between this modulus and published values, this experiment has relatively good agreement between beam theory and measured values.

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P (lbs) L (in) b (in) h (in) I (in^4) Unloaded Y Value

Loaded Y Value

v (in) E (psi)

0.084437 36 0.2690.26

8 0.000431 -0.69233 -2.64113 1.948799 1561625

Recommendations:

If independent measurements were desired for comparison, modification would be required for supporting the measurement instruments. For example, one or more dial indicators could be used but the current model does not easily support indicators. If the beam were mounted in a proper frame, the frame could allow the instruments to be positioned as desired and the frame itself could be designed for portability. The experiment could be recreated in a similar set-up as below.

Fig. 5: Inspiration for Improvement or Recreation of Model

Relevant Files and Documents:

Results and Reports, End of Summer\Cantilevered Aluminum Beam\Engauge Digitizer Files

Results and Reports, End of Summer\Cantilevered Aluminum Beam\Photos

Results and Reports, End of Summer\Cantilevered Aluminum Beam\Cantilevered Aluminum Beam.xlsx

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