Re: What is the relationship between the length of a beam and the am't it bends

Hello 
Beam problems can be very complex.  
The type of beam you are describing is called a cantiliever beam, fixed at 
one end, load at the other.  I believe the reason that you are seeing 
different equations to describe the deflection of your beam is the elastic 
curvature in the beam.  When a beam is loaded, especially with a point 
load, the amount of deflection gradually increases as you move along the 
beam towards the load.  I suspect that you may not be taking enough 
readings for this curvature to show up.

The general formula for deflection of a cantilever beam at any point is:

        Wx^2              Where: W=the load  x=distance along the beam
     y=------(3l-x)              E=the modulus of elasticity of the 
        6EI                        of the material
                                 l=the total length of the beam
                                 I=the moment of inertia of the cross      
                              section of the beam

The formula for maximum deflection for this type of beam is:

           Wl^3
     ymax=------
           3EI

I would bet that your constant,k, is the moment of inertia for your 
yardstick.  The moment of inertia is a function of the shape of the cross 
section of the beam.  I hope this helps. 
Greg