Okay. I have been at this for two nights now. I want to derive, step by step, the equivalent spring constant of a Beam cantilevered at both ends with a loading at its center.(adsbygoogle = window.adsbygoogle || []).push({});

Here is a schematic with A=B=L/2

Now I would like to use superposition to find the deflection at L/2 due to the loading. I know there are tables out there, but I want to "derive" this. (I know that I am not really deriving it since I am using superposition and tables...but bear with me).

Here are the equations I have at my disposal. Calling them from top to bottom 1-6,

I think that 1, 2, and 4 will prove the most useful, but I could be wrong.

Now, if I replace the fixed end at the right with its reaction force and moment I have:

=

1

+

2

+

3

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Derivation of an Equivalent Spring Constant

**Physics Forums | Science Articles, Homework Help, Discussion**