Is it well analyzed? Doubt about a bar: tension/compresion

AI Thread Summary
The discussion revolves around calculating the force P at which a bar yields under tension and compression, specifically for three bars with a diameter of 25 mm and a yield stress of 250 MPa. Initial calculations using Hooke's Law yield forces for each bar, indicating that the CF bar yields first. When two bars, BE and CF, yield, equilibrium equations are applied to find the new force P, resulting in a value of 243,605.30 N, with the AD bar unexpectedly transitioning from tension to compression. Participants seek clarification on the equations used, particularly the geometric compatibility of deformations represented by Δ, and request visual aids for better understanding. The conversation emphasizes the need for accurate interpretations of mechanical behavior in structural analysis.
Queren Suriano
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Homework Statement


upload_2015-4-23_0-6-37.png


Calcular the force P when a bar starts yield, when 2 bars start yield, and when the 3 bars start yield
Diameter = 25 mm (for every bar), Yield Stress of Steel = 250 MPa.

Homework Equations

The Attempt at a Solution


[/B]
[F][/AD] + [F][/BE] + [F][/CF] = P

2[Δ[/AD] - 3[Δ][/BE] + [Δ][/AC]= 0

I calculate first what happened when the 3 bars were in elastic zone, with the Hooke law I obtain:

[F][/AD]= 0.14P
[F][/BE]= 0.29 P
[F][/CF] = 0.57P

So the firs bar in reach yield stress is CF.

0.57P = [σ][/y] * A => P=215, 295.54 NWhen the 2 bars (BE and CF) are with the yield stress, [F][/BE]=[F][/CF]

From equations of equilibrium, sumatory of moments in C:

0.4P = 1.2 [F][/AD] + 0.8 [F][/BE]

and I know from the eq (1) [F][/AB] + [F][/BE] + [F][/CF] = P, so 2[F][/BE] + [F][/AD]= P. Solving this 2 eq. I obtain P=243, 605.30 N and [F][/AD]= -1831.62 N ...So I don't know if this answer is correct, because it says that the bar AD now is in compresion, when before it was in tension
 
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Can you explain how you got this equation?
2[Δ[/AD] - 3[Δ][/BE] + [Δ][/AC]= 0
 
From semejant triangles, ( delta AD - delta BE) / 0.4 = (delta AD- delta CF) /1.2. Is the C.G.D compatibility geometry of deformation
 
What is Δ? Maybe a picture would help.
 
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paisiello2 said:
What is Δ? Maybe a picture would help.
paisiello2 said:
What is Δ? Maybe a picture would help.
upload_2015-4-23_7-37-51.png
 
OK, I see now. The ΔAC was a typo then.

Can you show how you used Hooke's Law to get the forces?
 

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