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 :
PL³/(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!
