# General Cantilever Equations for Bending Aluminum

I am trying to determine some general cantilever equations.

I have an aluminum beam extending out 235 mm (L) from an aluminum
block. The beam is 25 mm wide (W) and 3 mm thick (H). A force is
applied at a point approx. 200 mm from the block and I am interested
at a point 25 mm away from the block. I know the exact measurement of
vertical deflection at a point 100 mm from the block.

I am assuming the modulus of elasticity E is 10*10^6 psi.

In general, I have the following diagram:
http://www.brentless.com/Images/station2.jpg
In the diagram

A: a driving rod that moves up and down from a loudspeaker setup not
shown, this guides the cantilever on this end
B: a measuring caliper to measure the vertical displacement at point
alpha measured from the aluminum block
C: a mounted strain gauge, the point of interest, centered at delta
from the aluminum block
D: an aluminum block mounted the cantilever on one end

Z1: a known, measurable displacement at alpha distance
Z2: a displacement not known, at the end of the beam

alpha: the measurement from the block to the measuring caliper
beta: the measurement from the caliper to the end of the beam
gamma: the measurement from the caliper to the driving rod
delta: the measurement from the block to the strain gauge

My problems to this point, most formulas I have found assume that the
measurement of deflection is actually taken at the end of the beam.
So how can I use the measurement at the 100 mm point above. I don't
specifically know the value of the force being applied (my cantilever
is being driven up and down by a loudspeaker, so if possible I would
like to leave out the force value and determine an equation based on
the measurement of deflection. Thoughts?

I am trying to determine a general equation of which I can relate to
stress and strain the values and measurements I have stated above for
a testing model. I am not a mechanical engineer, so I don't really
understand this stuff, so I appreciate any advice or help anyone can
give me.

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