# Longitudinal stiffness EA

• whammy123
In summary, the conversation discusses the concept of longitudinal stiffness (EA) in a structure, where EA represents the product of the Young's modulus and the cross-sectional area. The conversation explores the implications of EA being equal to infinity for some members of a structure and a finite number for others. The conversation also mentions the use of longitudinal stiffness in calculating displacement and the significance of having an infinite or precise value for it. The conversation concludes by discussing the meaning of a member having infinite stiffness and the calculation of displacement in different scenarios.
whammy123

## Homework Statement

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?

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!

## What is longitudinal stiffness EA?

Longitudinal stiffness EA refers to the resistance of a material or structure to longitudinal deformation under an applied load. It is a measure of the material's ability to maintain its shape and resist bending or stretching along its length.

## What is the significance of longitudinal stiffness EA?

Longitudinal stiffness EA is an important property in structural engineering and material science. It determines the strength and stability of a structure or material, and its ability to withstand external forces without breaking or deforming. It is also crucial in designing and constructing buildings, bridges, and other structures.

## How is longitudinal stiffness EA calculated?

The longitudinal stiffness EA is calculated by multiplying the modulus of elasticity (E) by the cross-sectional area (A) of the material or structure. The resulting value represents the force required to cause a unit of deformation (length or strain) in the material or structure along its length.

## What factors affect longitudinal stiffness EA?

Several factors can affect longitudinal stiffness EA, including the material's composition, structure, and shape. The type of load applied, temperature, and environmental conditions can also impact the stiffness. Additionally, the method of measurement and testing can also influence the calculated value of longitudinal stiffness EA.

## How is longitudinal stiffness EA measured?

The longitudinal stiffness EA is typically measured using specialized equipment such as a tensile or compression testing machine. The material is subjected to a known load, and the resulting deformation is measured and used to calculate the stiffness. The accuracy of the measurement also depends on the precision of the equipment and the testing procedure.

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