Axial Deformation on Statically indeterminate beam

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Discussion Overview

The discussion revolves around solving a problem related to axial deformation in a statically indeterminate beam, specifically focusing on the forces acting at different sections of the beam and the application of relevant equations for deformation. The scope includes homework-related mathematical reasoning and technical explanation.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a problem involving a beam with different cross-sectional areas and material properties, specifying forces acting at points B and C.
  • The participant expresses confusion about whether to make a cut at point B or C to analyze the forces and moments effectively.
  • There is mention of the need to ensure that the sum of forces in the X direction equals the applied forces, leading to a total of 80 kN.
  • Another participant attempts to clarify the approach by discussing the compatibility equation involving forces in sections AB and CD, suggesting a relationship between the forces and the lengths of the sections.
  • The participant updates their approach by stating the forces in sections AB and CD, indicating a need for a compatibility equation that sums the forces.

Areas of Agreement / Disagreement

The discussion does not present a consensus, as participants are still exploring different approaches to the problem and expressing uncertainty about the correct method to apply.

Contextual Notes

Participants have not fully resolved the assumptions regarding the cuts to be made in the beam or the application of the compatibility equation, indicating potential limitations in their current understanding.

SteliosVas
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Homework Statement



I am trying to find a solution to the below attached image.
The area for AB=CD = 0.8m^2
Area of BC = 0.3m^2

Force at B = 140 kN (left)
Force at C = 60 kN (right)

AB=CD = Concrete with a E of 25,000N/mm^2
CD = Steel with an E = 200,000N/mm^2

Homework Equations



PL/AE

The Attempt at a Solution

This is where I get confused because there is a force acting at B and a force acting at C I am not sure if I need to make a cut at say B or make a cut at C.

I understand the the sum of the forces in X direction have to equal Ax + Dx = 80 kN (As a result of 140 - 60 kN)

Now taking BC as the redundant section

PL/AE for section AB should that of section CD?

I am not sure if I am going about it the right way?

If it was one continuous section with forces only in one direction or even two I understand but because of that section BC it has thrown me out .
 
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  • Screen Shot 2014-11-02 at 2.24.25 pm.png
    Screen Shot 2014-11-02 at 2.24.25 pm.png
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Second Attempt at solution

Taking Section AB

δA/D = Fab*L(ab)/AE = Fcd*L(cd)/AE

Now F in AB = 140 kN
and F in CD = -60 kN

*** Edit ***

My compatibility equation of Fab + Fcd = 80 kN?
 
Last edited:

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