Machine elements - deflection and stress problem

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SUMMARY

The discussion focuses on calculating deflection and stress in a composite assembly of steel and aluminum under a tensile load of 200 kN. The incorrect approach of treating the materials as being in series led to erroneous deformation calculations, specifically δ = 0.481 mm. The correct method involves analyzing the assembly as two springs in parallel, which requires understanding the individual contributions of each material's properties to the overall deformation and stress. Key equations used include δ = Pl/AE for deflection and σ = P/A for stress.

PREREQUISITES
  • Understanding of material properties, specifically Young's modulus for steel and aluminum.
  • Familiarity with the concepts of deflection and stress in structural mechanics.
  • Knowledge of the equations δ = Pl/AE and σ = P/A.
  • Basic principles of parallel and series spring systems.
NEXT STEPS
  • Study the concept of composite materials and their mechanical behavior under load.
  • Learn about calculating equivalent spring constants for springs in parallel.
  • Explore the application of Young's modulus in real-world engineering problems.
  • Review examples of deflection and stress calculations in multi-material assemblies.
USEFUL FOR

Mechanical engineers, students studying structural mechanics, and professionals involved in materials science and composite material design will benefit from this discussion.

Triathlete
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Homework Statement



upload_2016-2-3_20-44-39.png

Homework Equations



δ = Pl/AE
σ = P/A

The Attempt at a Solution



I had calculated the deformation for both the steel and aluminum, and added them together to give me δ = 0.481 mm, which is incorrect. I also thought I could simply plug in the force P = 200kN and the respective cross sectional areas for each material into the stress formula, which also gave me incorrect answers. Not sure where to go from here.
upload_2016-2-3_20-44-39.png
 
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Triathlete said:

Homework Statement



View attachment 95263

Homework Equations



δ = Pl/AE
σ = P/A

The Attempt at a Solution



I had calculated the deformation for both the steel and aluminum, and added them together to give me δ = 0.481 mm, which is incorrect.
Not sure why you would do that. The steel and the aluminum pieces are not in series. Each of the pieces must stretch the same amount, since there is a flange welded to one end and a tensile force is then applied to the assembly.

I also thought I could simply plug in the force P = 200kN and the respective cross sectional areas for each material into the stress formula, which also gave me incorrect answers. Not sure where to go from here.View attachment 95263
Instead of two stiff springs in series, why don't you think of this assembly as two stiff springs in parallel? What's the spring constant for two springs of different spring constants in parallel?
 

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