Thickness of components for equal strength

In summary, the problem states that there are two cylindrical posts, each 0.5 inches thick, made of galvanized steel, and permanently fixed to unbreakable surfaces that move in opposite directions with infinite strength. The question is asking for the thickness of the chain links so that they start to break at the same time as the posts when pulled apart. The equations needed to solve this problem are not specified, but it can be assumed that the material is incompressible and the tension per unit area will be the same throughout the chains. However, the tension per unit area on the posts will not be uniform and it is important to determine where it will be greatest.
  • #1
Noel Clause
1
0

Homework Statement


Givens:
- Each of the 2 cylindrical posts are 0.5 inches thick.
- The posts and chain links are made of galvanized steel of identical material composition.
- The posts and chain links are solid.
- Each post is permanently fixed to unbreakable surfaces. The surfaces will move in exactly opposite directions with infinite (unstoppable) strength.
Problem:
How thick must each chain link be, when the posts are pulled apart, so that the posts and chain links start to bend/break at the same time?

Homework Equations


What is/are the equation(s) to solve this problem?

The Attempt at a Solution


No idea what the equation(s) are.
 

Attachments

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  • #2
I'm not too sure about this either, but "bend/break" is problematic. The posts will start to bend, and the chains stretch, straight away, so to make sense of the question I would delete "bend".
Next, there's the question of compressibility. If the material is highly compressible then the posts can bend a long way without breaking, so maybe assume incompressible.
Now it comes down to comparing tensions. The material will break at some tension per unit area.
The chains are easy since the tension per unit area will be the same throughout. But in the posts the tension per unit area is not uniform across them or along their lengths.
Where will it be greatest on the posts?
 

1. What is the importance of considering thickness for equal strength in components?

The thickness of components is crucial in ensuring equal strength because it determines the ability of the component to withstand stress and load without breaking or deforming. Without equal strength, the component may fail prematurely, leading to safety hazards and costly replacements.

2. How does the thickness of a component affect its strength?

The thickness of a component directly affects its strength. Generally, thicker components have higher strength because they can distribute stress and load over a larger area, reducing the risk of failure. However, thickness can also add weight to a component, which may not always be desirable.

3. What factors should be considered when determining the appropriate thickness for equal strength in components?

There are several factors to consider when determining the appropriate thickness for equal strength, such as the type of material, the expected stress and load, and the intended use of the component. Other factors may include cost, weight, and manufacturing limitations.

4. How can I calculate the optimal thickness for equal strength in components?

Calculating the optimal thickness for equal strength requires knowledge of the material properties, stress and load calculations, and engineering principles. It is best to consult with a materials expert or use specialized software for accurate calculations.

5. Are there any standard guidelines or regulations for determining the thickness of components for equal strength?

There are many industry standards and regulations that provide guidelines for determining the appropriate thickness of components for equal strength. These include the International Organization for Standardization (ISO), American Society for Testing and Materials (ASTM), and various government regulations, depending on the type of component and its intended use.

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