Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Increasing Cantilever Beam Stiffness

  1. Sep 24, 2015 #1
    Is it possible to create a cantilever beam with constant or increasing stiffness. I've been experimenting with several different shapes and profiles, and have not had any luck.

    I know that there are shapes with constant stress throughout, but I'm hoping to find a shape with constant or increasing stiffness, or the shape of a cantilever beam that has maximum stiffness throughout.
  2. jcsd
  3. Sep 24, 2015 #2


    User Avatar
    Science Advisor
    Gold Member

    There are many ways of making cantilever beams stiffer but any practical solution depends very much on what you are actually trying to do .

    What is basic requirement ?

    Leading dimensions and applied loads ?

    Class of job - basic plate and girder type construction or something more sophisticated ?

    Deflection limits ?

    Clear diagram would very useful .
  4. Sep 28, 2015 #3
    Hi, thanks for you reply. This is for applications in the prosthetics field, so geometry and construction is dependent upon what can be contained within a biological form factor.

    Basic dimensions:
    Cross Section: 6 x 25 mm
    Length: 100 mm

    Carbon Fiber with E = 3.8E10 Pa

    Maximum applied load is around 1200 N

    Attached is a picture of the general setup, please let me know if you have any other questions.


    Attached Files:

  5. Sep 28, 2015 #4


    User Avatar
    Science Advisor
    Gold Member

  6. Sep 28, 2015 #5
    Somewhat, but that is designing for constant stress. I am hoping to find the optimum shape for stiffness. What I have been trying to do is using the equations for angular deflection, vertical displacement in order to find a shape that maximizes stiffness (F/displacement). These are the equations I have been using.

    $$\theta (x) = \frac{1}{E} \int \frac{M(x)}{I(x)} dx$$
    $$\delta (x) = \int \theta(x) dx$$

    I have varied the equation for I(x) based on different profiles, but am wondering what the optimal shape for k(x) would be.
  7. Sep 28, 2015 #6


    User Avatar
    Science Advisor
    Gold Member

    Maximum stiffness as such is open ended - for a simple parallel or tapering down cantilever beam the deeper the sections used the stiffer it gets .

    Need some constraints for a meaningful analysis .

    Would it be useful for your purpose if we try to find shape of a cantilever beam with best stiffness compared to stiffness of your existing parallel one and using same amount of material ?
    Last edited: Sep 28, 2015
  8. Sep 28, 2015 #7
    Yes, that would be helpful. Finding the max stiffness of a cantilever beam at its tip with the same amount of material, and both being the same length would be of use to me.

    Thank you
  9. Oct 12, 2015 #8


    User Avatar
    Science Advisor
    Gold Member

    Jeffrey Lee - please contact me .
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook