# strain gauge lab, young's modulus....

• posted

i have a bit of a retarded question which im quite frankly embarrassed to ask, but given that im in the middle of exams, i havent done any strengths for about a year, and im too stressed (no pun intended) to care about a token lab report for a token module.

so, i have a plot of strain against load for a cantilever beam, and i have to use it to find E for the beam.

i have the equation [sigma] = (y * W / EI )*(x-L)

where, x = distance of gauge along beam from the built in end y = distance through the beam's thickness from the centreline of the beam to the gauge. W = load E = youngs modulus. (aluminum beam so should be about 70Gpa) I = 2nd moment of area = bd^3/12 L = length of the beam.

im trying to find E, so i figured on my graph, [sigma] = gradient * W

comparing that to the equation above, i guessed that gradient = (x-L) * y / (EI)

rearranging to give

E = (x-L)*y/MI ......

..... except it doesnt. i know im going wrong somewhere..... obviously. can someone give me a kick up the ass in the right direction.

ta.

• posted

At first glance everything you do seems correct. Except for the fact that over here sigma is normally the *stress* and epsilon is the *strain*. [epsilon=strain] = (y * W / EI )*(x-L) and [sigma=stress] = (y * W / I )*(x-L) Are you sure that you are not looking at a load/stress diagram?

• posted

sorry, yes, that's a typo. my sigma should be epsilon, and its definitely the strain i was measuring. my brain's just a bit scrambled.

so yeah, im using [epsilon=strain] = (y * W / EI )*(x-L)

taking from my graph [epsilon] = gradient * W

comparing to get, gradient = (x-L) * y / (EI) rearranging for E = (x-L)*y/MI.

so if you reckon that looks right, then i guess there's either something wrong with my 2nd moment value or my gradient is rubbish.

• posted

Strain switched for stress to correct formula.

L should be the length of beam from support to load point. The load point may not be at the end of the beam.

So y = d/2 so E = 6*(x-L)/(m*b*d^2)

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