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Old Dec 27th 2018, 08:02 AM   #1
Aro
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Rigidity

Hi,
I have a general question about the rigidity of a simply supported beam.
Say the beam is loaded with a single force P acting downard at it's center, the defection of the beam at the center is given by :
PL≥/(48EI) - Eq. 1
Now say the same beam is loaded with a longitudinal weight (kN/m) of intensity w, the defection at the center is:
5wL^4/(384EI) - Eq. 2
(L = length of beam).
Now, say L = 1 m, and inverse the Eq. 1 to obtain the rigidity (Hooke --> F=K*u, where u is displacement, K rigidity and F the applied force) we get
K = 48EI
Do the same for Eq. 2 we get (I did leave a w*L term to make it equal to P as w*L = P since L = 1):
K = 384EI/5
Now, the rigidity of the beam aren't the same due to the loading condition??? I thought rigidity was a fundamental property of the geometric section and material considered? Guess I make a mistake, but if any1 can enlighten me here, thanks!
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Old Dec 27th 2018, 01:32 PM   #2
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The deflection at the center of the beam is indeed a function of how the load is applied, and consequently the calculation of 'k' varies between the two cases. To demonstrate this even more clearly, consider the beam with a point loads applied directly over one of the supports - in this case the beam doesn't deflect at all, so it's "rigidity" as you've defined would be infinite. Regarding the fundamental property of the material that defines its stiffness, that would be Young's modulus: 'E'.
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