Experimental Modulus of Cantilevered Aluminum Beam Using
Engauge Digitizer
Objective:
Experimentally determine the modulus of elasticity of an aluminum 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. An aluminum beam with 1.001in x .126in 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 bag of lead shot was hung by running wire through the bag
and through the beam. A steel dowel pin through the wire allowed the beam to be easily loaded or
unloaded. The load measured 205.6 grams or 0.45327 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:
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The equation v 
PL3
was used with the previously measured parameters to calculate a modulus of
3EI
9.37*106 psi. The values used in the calculation are displayed below. With only 6.3% difference
between this modulus and published values, this experiment has relatively good agreement between
beam theory and measured values.
P (lbs)
L (in)
b (in)
h (in)
I (in^4)
0.453270411 24.25 1.001 0.126 0.000166865
Unloaded Y
Value
-0.108978
Loaded Y
Value
-1.48666
v (in)
1.377682 9372553
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. These concerns could be addressed by creating an experiment similar to the model shown in
Fig. 5.
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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E (psi)