Measuring the bending moment of a hinged
cantilever beam |
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Empirical method - Simply place an object at different distances from
the root (or in this |
case the pivot point) of a model of a hinged cantilever beam. Note
how moving the load |
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out away from root (pivot) increases the tensile stress |
induced in the counterbalancing rubber band located |
in
the rear of the model. This causes the rubber to |
stretch and the beam to be lowered. Since the load |
remained constant, the stretching of the rubber band |
indicates that the bending moment increased as the |
load moved farther away from the root. |
click the image to see details of how the model is made |
. |
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Quantifiable method - Place the model on a scale. Press down
on the beam at different |
distances from the root (pivot) so that the beam is lowered to a level
position. Record the |
reading on the scale and measure the distance from the root that the load
was applied. |
Graph your results to confirm that there is an indirect relationship
between the load ( P ) |
measured by the scale and the distance from the root ( L ) the load is
applied. That is, the |
farther away from the root the load is applied, the less load is required
to lower (bend) the |
beam. The amount of tensile stress induced in the |
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counterbalancing rubber band remains the same since it |
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stretches the same amount in each case. This means that |
the bending moment remains constant in each case also, |
since it is the bending moment that induces the stress. |
This can be confirmed mathematically by calculating the |
bending moments to see that they are more or less equal. |
Load
(oz./lb.) |
Distance (in./ft.) |
M (ft. lb.) |
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4.4 / .28 X
2 / .17 =
.048 |
1.8 / .11 X
4.8 / .4
= .044 |
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