Modulus of Elasticity/Beam Deflection?
I'm attempting to find the modulus of elasticity for E for a piece of aluminium.
When given a load of 500 grams, it had a displacement of .024 inches.
The equation we were given was delta y = (Px^2)/(6EI) * 3L-X.
L = 12.125, X = 11.75, I = (bh^3)/12, b = 1.104 in, h = .2522 in.
I = .001475785.
What I don't know is what are the units of P? we were told "force due to the mass" but I couldn't tell if that was PSI or Newtons or what. Supposedly we should be getting E to equal 10 x 10^6psi but I'm not getting anywhere near that in calculations.
I'm probably doing something really simply wrong like missing a conversion, but I really need help.
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Please repost following equation with proper parentheses. (L-X) is a suspect.
Also, things to be multiplied to the fraction could be put in front to avoid confusion.
Recall that fractions require parentheses on the numerator and denominator.
(Px^2)/(6EI) * 3L-X.
Once that is clear, you can find the unit of P by dimensional analysis.
deflection = m
x,(L-x) = m
EI = N-m^2
so equate units on both sides and solve for the unit of P which is usually just in force units.
Also, it would help verify the formula if you mentioned how the "beam" was supported, simply, fixed, or cantilever.
Assuming the beam is rectangular in cross section, the value of I is correct.
Do not forget to convert 500g to kg then to pounds.
From the formula given, it turns out that you are doing an experiment on a cantilever beam.|dw:1443807417294:dw|
P is a concentrated force in pounds, since all data are given in inches and pounds (Except for load, which is given in grams.)
To convert from grams to pounds, divide number of grams by 453.6.
Wish I'd been able to reply sooner. I did convert everything to USCS units but nothing seemed to answer correctly. I can take the hit though. Thanks for the help.
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From the data given, I get 17.6*10^6 psi when Al has an E=10*10^6.
Check if there is any typo in the data.
Did you measure the deflection under the load or the tip of the beam?
The equation assumes you measure the deflection at the tip (free end) of the cantilever.