Statically indeterminate axially loaded problem

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Discussion Overview

The discussion revolves around a statically indeterminate problem involving axial loads on a structural member. Participants explore how to calculate the total stretch in the member under load, considering the effects of ground contact and material properties.

Discussion Character

  • Homework-related, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant presents a homework statement and initial equations related to axial loads.
  • Another participant inquires about calculating the total stretch in the member, assuming it can stretch without contacting the ground.
  • A subsequent reply confirms the use of the formula ΔL = FL/AE for calculating stretch.
  • Further contributions detail a complex equation for total deflection, incorporating multiple forces and material properties.
  • One participant emphasizes the importance of considering the gap between the member and the ground, suggesting that a reaction force develops once contact is made.
  • Another participant proposes using a deflection of zero in their calculations, but this is challenged, indicating that the member will stretch under load.
  • There is a discussion about determining the amount of stretch if the ground were not present and how to find the reactions that allow for a specific deflection when equilibrium is reached.
  • Young's Modulus is mentioned as a necessary parameter for solving the problem, with steel's value being suggested.

Areas of Agreement / Disagreement

Participants express differing views on how to approach the problem, particularly regarding the treatment of deflection and the implications of ground contact. No consensus is reached on the correct method to solve the problem.

Contextual Notes

Participants highlight the need for careful reading of the problem statement and the importance of free body diagrams in understanding the forces at play. The discussion reflects uncertainty about the correct approach to the calculations involved.

Matthew Heywood
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Homework Statement


stat indet.jpg

Homework Equations


FAB = FBC etc...

The Attempt at a Solution


FAB = FBC + 300kN = FCD = FDE + 600kN

Sorry for another post. I'm really not sure where to go with this one...
 

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You've got a situation involving axial loads.

How would you calculate the total stretch in the member, assuming the member could stretch under load without coming into contact with the ground?
 
Using ΔL = FL/AE ?
 
Yes.
 
So ∂ = 4.5mm = FAB(150mm)/125mm2EAB + (FBC + 300)(150mm)/125mm2EBC + FCD(150mm)/200mm2ECD + (FDE + 600)(150mm)/200mm2EDE ?
 
Matthew Heywood said:
So ∂ = 4.5mm = FAB(150mm)/125mm2EAB + (FBC + 300)(150mm)/125mm2EBC + FCD(150mm)/200mm2ECD + (FDE + 600)(150mm)/200mm2EDE ?
Not necessarily.

Read the problem statement carefully. There is a gap of 4.5 mm between the bottom of the member and the ground, when the member is unloaded. Once the loads are applied to the member, it stretches until contact with the ground prevents further extension, which suggests that a reaction force with the ground develops.

You need to write equations of statics here along with calculating the extensions in the member under load, because the member becomes statically indeterminate once contact is made with the ground and the reaction develops. It also means you're probably going to need to use a value for Young's Modulus for the material in the member in order to solve this problem.
 
Ah okay. So you'd use ∂ = 0, FAB = FBC + 300kN = FCD = FDE + 600kN and E = 200GPa as it is steel?
 
Matthew Heywood said:
Ah okay. So you'd use ∂ = 0, FAB = FBC + 300kN = FCD = FDE + 600kN

No, the deflection δ ≠ 0, since the member is loaded and is going to stretch.

What you need to do first is find out by how much the member would stretch if the ground wasn't in the way, and then determine what reactions would develop so that the member only stretches 4.5 mm when it reaches equilibrium with the ground. (Hint: a free body diagram would be helpful here.)

and E = 200GPa as it is steel?

This is OK.
 

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