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Homework Help: Longitudinal stiffness EA

  1. Dec 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Can somebody please explain me:

    What does it mean that Longitudinal Stiffness (EA) is equal to infinity? What does it change if for some members of a structure "EA = infinity", and for other members "EA = finite number".


    2. Relevant equations

    I know that we use longitudinal stiffnes to calculate displacement, by Maxwell - Mohr Formula: fi = sum of integrals [N*Ń/EA dS], but what meaning has the infinity or precise value of Longitudinal Stiffness?
     
  2. jcsd
  3. Dec 12, 2009 #2

    PhanthomJay

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    I don't know if we're talking the same thing, but longitudinal axial stiffness of a member is AE/L, wher L is the length, so as L approaches 0, the stiffness approaches infinity, or if AE is infinite (Rigid body), the stiffness is also infinite. In reality, however, there is no such thiing as an infinite stiffness, because this would imply a completely totally rigid body, which can never exist.
     
  4. Dec 12, 2009 #3
    We sometimes feed in an infinite value of stiffness in a structural analysis program in order to check that the program is working properly, or because it helps us understand the real behaviour when, on a second run, we 'release' the member by giving it a trial finite value. The meaning is that if a member has infinite stiffness, then its ends cannot move relative to each other. If there is a finite value, then the relative movement of the ends (however small) can be calculated. When asking about the meaning of something, consider its units.
     
  5. Dec 13, 2009 #4
    So when the longitudianal stiffness is equal to infinity, we don't have to calculate the displacement due to the normal forces, but when longitudinal stiffness has some finite value, than the normal forces cause displacement and we can calculate, f. ex. by Maxwell Mohr formula.

    Thank you both so much for help!
     
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