Measuring the bending moment of a hinged
cantilever beam 

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 

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 
. 

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 

counterbalancing rubber band remains the same since it 

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.) 

4.4 / .28 X
2 / .17 =
.048 
1.8 / .11 X
4.8 / .4
= .044 



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