Uses and Testing of Cantilevers A cantilever is a beam that is supported at only one end and carries a load at the other end. Engineers use cantilevers in many different contexts. For instance many cranes depend on the idea of a cantilever.

Other examples of the use of a cantilever include balconies in buildings, or springboards in swimming pools.

When a load is applied to the free end it causes a moment to be applied about the fixed end of the cantilever. As a result of this moment, the free end deflects and the cantilever bends. The greater the applied moment (given by force x distance from the fixed end) the greater the deflection.

Material on top gets stretched (tension)

Material underneath gets compressed

When the cantilever bends, the solid material has to change its shape. The material on the top of the board gets stretched ie it is under tension while at the same time the material on the underneath side gets squashed together ie it is in compression. Provided that the amount of tension or compression is not too high, when the load is removed the cantilever will spring back to its original position. In fact, the beam will obey Hookes Law, since this applies to both tension and compression in a solid. Thus the deflection of the beam will be directly proportional to the size of the bending moment applied to it. When a manufacturer is designing a cantilever â&#x20AC;&#x201C; for instance a divingboard maker â&#x20AC;&#x201C; they should test their design to make sure that the loads applied by the divers do not over-stretch or over compress the springboard material. They can do this by applying a series of increasing bending moments to the board and plotting a graph of its deflection. If the moment applied causes tension and compression forces that are within the elastic limits of the material they should see a straight line plot through the origin. Factors which affect the bending moment are the force (weight) applied and the distance from the fixed end at which the force is applied (since moment = force x distance). Since a given diving board is a fixed length, but the swimmers using it vary a lot in weight, it is normal when testing the board material to choose a fixed distance and vary the weight applied. In this way the manufacturer can establish safe limits for the weight of swimmer allowed to use the board, and can determine just how far it will deflect when in use so that any swimmer in the water under it will not be affected if someone uses the board.

Rather than test a full sized springboard, it can sometimes be useful to test a model in the laboratory. A typical setup is shown below. Different values of weight are suspended from a strip of material to be tested, and the deflection can be measured. The performance of a full-sized springboard can then be estimated from these results.

Deflection

When carrying out such tests, however, care must be taken to prevent accidents. A typical risk assessment would include factors such as the strip under test snapping, which could send splinters into the testerâ&#x20AC;&#x2122;s eyes, damaging their eyesight. It would also allow the weights to fall suddenly which might hit someone and cause bruising. Another, less obvious, hazard is that the setup means that gangways next to lab benches are obstructed by the cantilever beam and the sharp pointer at its end. Anyone moving round the lab carelessly might collide with the beam or pointer and be injured. These hazards can be controlled using the normal measures â&#x20AC;&#x201C; eye protection, being careful how you move round the lab, and keeping clear of hanging weights.

Introduction to Cantilevers

General description of cantilevers