Question

Design a cantilever beam with a circular cross-section in a way that is cheap and also has the maximum first natural frequency. Choose the best aluminum alloys from below.

Answer 1

Design of a Cantilever Beam

A Cantilever beam is one in which it is supported at one end and free at other end. the cantilever beam can be made from either steel or concrete whose one end is anchored to vertical support.  It is a horizontal beam structure whose free end is exposed to vertical loads.

This is how the cantilever beam looks like and load can be applied at the end.

Due to loading effect the cantilever beam looks like this

A cantilever beam under the action of laod will apply moment and shear stresses. The objective of any design process is to transfer stresses safely to the support.

The bending moment of the cantilever varies from one at one end to maximum at the free end. hence while designing the cantilever beam the main reinforcement is provided to the upper fiber of the concrete beam to withstand the tensile stress safely.

The maximum span of the cantilever beam depends on following factors.

1. The depth of the cantilever

2. The magnitude, type, and location of the load

3. The quality and type of material used

Usually for the small cantilever beam the span is restricted to 2 to 3 meters But we can increase the  span either by increasing the depth or using a steel or pre-stressed structural unit.The span can be constructed long, given that the structure can counteract the moments generated by the cantilever and safely transfer it to the ground.

To get maximum natural frequency by providing intermediate elastic support

If we provide intermediate elastic support to the beam we can increase the natural frequency and it is proved in many research work. But the task to find which the exact loaction where the support should be placed so that we get optimum natural frequency. Consider the diagram which shows about elastic support

Now this is the trend to increase the natural frequency

According the Courant’s maximum–minimum principle an additional support can increase the structural frequency, to between the ith and the (i+1)th natural frequencies of the original system.

Once the optimum position of an additional support is prescribed properly, a natural frequency of a beam can be raised to its upper limit with a minimum requirement on the support stiffness.

If we use this condition the cost of the poject will be reduced as we use carbon steels the cost of the compoent will be reduced and it will make weight also less.

Properties of variuous Aluminium alloys

1. properties of 2024-T3

2. properties of 6061-T6

3. properties of 7075-T6

4. properties of 5083-H111

Conclusion :

By comparing all the above tables the tensile strength, Young modulus and other properties are high for 2024-T3 aluminium alloy. Hence as a design engineer i will prefer to use 2024-T3 alloy. Even we can go with other as 7075-T6 which as good tensile properties when compared to all but it lags at other properties

Hence 2024-T3 is overall the best aluminum alloy that we can use to get best results.