What Does It Mean When Longitudinal Stiffness (EA) Equals Infinity?

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Discussion Overview

The discussion revolves around the concept of longitudinal stiffness (EA) in structural analysis, particularly what it implies when EA is considered to be infinite compared to when it has a finite value. Participants explore the implications of these stiffness values on displacement calculations and structural behavior.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant seeks clarification on the meaning of longitudinal stiffness being equal to infinity and its implications for structural members with varying stiffness values.
  • Another participant explains that longitudinal axial stiffness is defined as AE/L, noting that as L approaches 0 or AE becomes infinite, the stiffness approaches infinity, but emphasizes that true infinite stiffness cannot exist in reality.
  • A different participant mentions that infinite stiffness can be used in structural analysis software to test functionality or to understand behavior when transitioning to a finite stiffness value, indicating that infinite stiffness means no relative movement between member ends.
  • It is noted that with infinite longitudinal stiffness, displacement due to normal forces does not need to be calculated, whereas with finite stiffness, such displacements can be computed using the Maxwell-Mohr formula.

Areas of Agreement / Disagreement

Participants express varying interpretations of the implications of infinite versus finite longitudinal stiffness, indicating that multiple competing views remain regarding the practical application and theoretical understanding of these concepts.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the existence of infinite stiffness and its practical implications in real-world scenarios, as well as the dependence on definitions of stiffness in different contexts.

whammy123
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Homework Statement


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".

Homework 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?
 
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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.
 
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.
 
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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