Polymorf - Knowhere - Cantilever bending moment

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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