Take a long cylindrical balloon and, with a thin
felt-tip pen, mark a small square on it. What
will be the shape of this square after you blow
up the balloon: (1) a larger square, (2) a rectangle, with its long axis in the circumferential directions, (3) a rectangle, with its long axis in the
longitudinal direction, or (4) an ellipse? Perform this experiment and, based on your observations, explain the results, using appropriate
equations. Assume that the material the balloon is made of is perfectly elastic and isotropic,
and that this situation represents a thin-walled
closed-end cylinder under internal pressure.
This is a simple graphic way of illustrating the
generalized Hooke’s law equations. A balloon
is a readily available and economical method of
demonstrating these stress states. It is also encouraged to assign the students the task of predicting the shape numerically; an example of a
valuable experiment involves partially inflating
the balloon, drawing the square, then expanding it further and having the students predict
the dimensions of the square.
Although not as readily available, a rubber tube
can be used to demonstrate the effects of torsion in a similar manner.