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

In summary, the conversation discusses calculating the force P when a bar starts to yield, when 2 bars start to yield, and when 3 bars start to yield. The given information includes the diameter of the bars (25 mm) and the yield stress of steel (250 MPa). The equations used in the solution include the sum of forces in equilibrium and the compatibility geometry of deformation. Using Hooke's Law, the forces at points AD, BE, and CF are calculated to be 0.14P, 0.29P, and 0.57P respectively. The final answer for P is 243,605.30 N, with bar AD now in compression.
  • #1
Queren Suriano
50
0

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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  • #2
Can you explain how you got this equation?
2[Δ[/AD] - 3[Δ][/BE] + [Δ][/AC]= 0
 
  • #3
From semejant triangles, ( delta AD - delta BE) / 0.4 = (delta AD- delta CF) /1.2. Is the C.G.D compatibility geometry of deformation
 
  • #4
What is Δ? Maybe a picture would help.
 
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  • #5
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
 
  • #6
OK, I see now. The ΔAC was a typo then.

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

1. Is it necessary to analyze the tension and compression forces in a bar?

Yes, it is important to analyze the tension and compression forces in a bar as they can affect the structural integrity and stability of the bar. Tension forces can cause the bar to elongate and potentially fail, while compression forces can cause the bar to buckle.

2. How do tension and compression forces affect the design of a bar?

Tension and compression forces must be considered in the design of a bar to ensure that the bar can withstand the expected loads and remain stable. This may involve selecting appropriate materials and dimensions for the bar, as well as incorporating reinforcement or bracing to counteract the forces.

3. What methods are used to analyze tension and compression forces in a bar?

There are several methods that can be used to analyze tension and compression forces in a bar, including static analysis, finite element analysis, and experimental testing. The choice of method will depend on the complexity of the bar and the level of accuracy required.

4. Can tension and compression forces change over time in a bar?

Yes, tension and compression forces can change over time in a bar due to factors such as creep, fatigue, and external loads. It is important to consider potential changes in forces when designing and analyzing a bar to ensure its long-term stability.

5. How can I determine if a bar is experiencing tension or compression?

The direction of the force acting on the bar will determine if it is experiencing tension or compression. If the force is pulling or stretching the bar, it is experiencing tension. If the force is pushing or compressing the bar, it is experiencing compression. Additionally, the direction of the force can be determined through mathematical analysis or experimental testing.

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