Discussion Overview
The discussion revolves around a homework problem involving the analysis of stresses in a compound cylinder subjected to internal pressure and the effects of shrink fitting. Participants explore the application of Lame's equations to determine maximum stresses and the relationship between the dimensions of the tubes before shrinkage.
Discussion Character
- Homework-related
- Mathematical reasoning
- Technical explanation
Main Points Raised
- One participant presents a calculation resulting in a negative maximum stress, questioning its validity in the context of cylindrical structures.
- Another participant suggests that a negative stress could indicate compression, but this raises further questions about its applicability to cylinders.
- A subsequent reply provides revised calculations for hoop stress, yielding values of 83.3 MPa for the inner cylinder and 33.3 MPa for the outer cylinder, suggesting a more realistic outcome.
- Concerns are raised about the assumption that both tubes are made of the same material, based on the single value of Young's modulus provided.
- One participant mentions recalculating the stress due to the interference fit before considering the internal pressure, indicating a change in approach to the problem.
Areas of Agreement / Disagreement
Participants express uncertainty regarding the interpretation of negative stress values and whether the assumption of uniform material properties is valid. There is no consensus on the correctness of the initial calculations or the implications of the results.
Contextual Notes
Participants note the need to consider both the interference fit and internal pressure in their calculations, highlighting potential dependencies on assumptions about material properties and the conditions of the problem.
