# Trying to make a cantilever with the highest efficiency

1. Jul 6, 2007

### koujidaisuki76

Right now I'm trying to make a cantilever with the highest efficiency. I'm trying to design several models but I have questions:

How can one make one without having to find the best design through numerous times of trail and error? Is there an equation for cantilevers which dictate the efficiency of the design?

How do professional engineers come up with ideas to complete this sort of task?

2. Jul 7, 2007

### FredGarvin

How are you defining efficiency? "Efficiency" by itself is an ambiguous word. You need to be specific.

Yes. There are standard well defined equations for all types of beams with varying loading and boundary conditions. In pure bending, they all stem from the solutions derived from the differential equation relating moment to shear:

$$EI\left[\frac{d^4v}{dx^4}\right]=-W_{(x)}$$

Theory:
http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm
http://en.wikipedia.org/wiki/Euler-Bernoulli_beam_equation

Solved Equations:
https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=me&chap_sec=&page=&appendix=beams

3. Jul 7, 2007

### koujidaisuki76

efficiency: Total load that the structure held in grams/ mass of structure.

For the Euler Buckling Formula, I do not understand how to get the compressive load P or I. In example problems, the question gives the value of E and the L. Is the P just the load in N? or do you have to calculuate something inorder to get it? and for I.

The load I'm using is 15 kg or 33 pounds. The L is 43 cm and the structure which touches the wall is a sqaure, 5 by 5 cm. How would you apply this to the equation?

4. Jul 7, 2007

5. Jul 7, 2007

### FredGarvin

If that is how you define efficiency, then the only options you have are to change the cross section of the beam or the material choice.

The cross sectional moment of inertia is a calculated parameter. You're looking for Ix.

http://www.efunda.com/math/areas/rectangle.cfm

6. Jul 10, 2007

### koujidaisuki76

Also, i have another quesiton. I need to write a research report on cantilevers for another class. I need to somehow explain the importance and advantages of cantilevers for the common world. Does anyone have ideas?

7. Jul 11, 2007

### Mech_Engineer

I suspect a very "efficient" design for a cantilever beam would use an I-beam cross-section, or something like an hourglass shape.

8. Jul 27, 2007

### haynewp

A triangle shaped truss should give the least material for a required strength. But I normally can't use these in practice because of the depth required for them.

The most common case you will find is floor beams that are cantilevered out to create a balcony, or roof beams that are cantilevered to create an overhang. An advantage of cantilevers is that they do not require supporting columns at the free end (hence the term "cantilever") so there is un-interrupted open space below the free end which is normally desirable to the public and when column placement at the free end would be impossible for other reasons (balcony at a beach condo on the 40th floor).