| Topic: |
Science > Physics |
| User: |
"Whatever I Fear" |
| Date: |
14 Feb 2007 07:48:46 AM |
| Object: |
General Cantilever Equations |
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
deflection at a point 100 mm from the block.
I am assuming the modulus of elasticity E is 10*10^6 psi. Moment of
inertia, or measure of how cross sectional area is distributed around
ts center is I = (1/12)*W*H^2. Poisson's ratio for aluminum I believe
is 0.33.
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 or physics guy, so I
don't really understand this stuff, so I appreciate any advice or help
anyone can give me.
.
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| User: "Whatever I Fear" |
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| Title: Re: General Cantilever Equations |
14 Feb 2007 10:24:55 AM |
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To further help, I would like to show a diagram of what I have:
Link: 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
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| User: "Andy Resnick" |
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| Title: Re: General Cantilever Equations |
15 Feb 2007 08:57:32 AM |
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Whatever I Fear wrote:
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
deflection at a point 100 mm from the block.
I am assuming the modulus of elasticity E is 10*10^6 psi. Moment of
inertia, or measure of how cross sectional area is distributed around
ts center is I = (1/12)*W*H^2. Poisson's ratio for aluminum I believe
is 0.33.
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?
Try looking at Chapter 9 of the class notes:
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 or physics guy, so I
don't really understand this stuff, so I appreciate any advice or help
anyone can give me.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
.
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| User: "Andy Resnick" |
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| Title: Re: General Cantilever Equations |
15 Feb 2007 08:58:52 AM |
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Whatever I Fear wrote:
I am trying to determine some general cantilever equations.
<snip>
Message was sent before the URL was included.
Again, try looking at chapter 9:
http://www.clarkson.edu/class/es22201/
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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