Statically Indeterminate Problem

In summary, the conversation discusses a problem involving a circular bar made of 3in diameter aluminum alloy and 4in diameter steel separated by a rigid piece. The bar is fixed between two end supports and is unstressed at 0°F. The question is whether the pressure on both walls is equal and if the normal stress of the aluminum and steel bars is also equal. The solution involves calculating the normal stress in both bars and the change in diameter. It is mentioned that the stresses are inversely proportional to area and Young's modulus, indicating that the two members will not have the same stresses.
  • #1
wisper
12
0
Before you start going through equations and trying to solve this I just need a simple question answered about this problem.

1) Is it correct for me to assume that the pressure on both walls is equal?

If so, I think the normal stress of the aluminum and steel bars are equal.

Problem:

A circular bar consist of 3in diameter aluminum alloy with Young’s modulus, E = 10,600 ksi, poisson ratio, ν = 0.33, and temperature coefficient, α = 12.5 * 10-6 /°F and 4in diameter steel with Young’s modulus, E = 30,000 ksi, poisson ratio, ν = 0.3, and temperature coefficient, α = 6.6 * 10-6 /°F separated by a rigid piece as shown. The bar is fixed between two rigid end supports and is considered unstressed at 0°F. Determine (a) the normal stress in both the aluminum bar and the steel bar, and (b) the change in diameter of the aluminum and steel bar.

http://members.cox.net/gfs4/1.bmp
 
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  • #2
Since the stresses are inversely proportional to area and Young's, the two members will not have the same stresses.
 
  • #3
Thank you.
 
  • #4
The force is the same through the entire section, but not the pressure.
 

1. What is a statically indeterminate problem?

A statically indeterminate problem is a structural engineering problem where the number of unknown forces or reactions is greater than the number of available equations to solve for them. This means that the problem cannot be solved using traditional methods and requires more advanced techniques.

2. What causes a problem to be statically indeterminate?

A problem can become statically indeterminate due to various factors, such as the complexity of the structure, the presence of redundant members, or the use of incomplete or insufficient information in the analysis.

3. How is a statically indeterminate problem solved?

Solving a statically indeterminate problem requires the use of advanced structural analysis methods, such as the flexibility method or the stiffness method. These methods involve considering the deformations and forces in the structure as a whole, rather than analyzing individual members.

4. What are the advantages of solving a statically indeterminate problem?

Solving a statically indeterminate problem allows for a more accurate and realistic analysis of a structure. It also allows for a more efficient use of materials, as redundant members can be eliminated or optimized.

5. Are there any real-world examples of statically indeterminate problems?

Yes, there are many real-world examples of statically indeterminate problems, such as bridges, buildings, and other large structures. These structures often have redundant members or complex geometries that make them statically indeterminate and require advanced analysis techniques for their design and construction.

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