Smallest cross-sectional area of rod-end?

In summary, the conversation discusses an example in structural mechanics where a pin exerts a force on a rod with a circular cross section in the middle and a flattened rectangle cross section at the end. The stress calculations for these two sections are different due to a reduction in width where material is cut out to fit the pin. The question asks for clarification on this concept.
  • #1
samtrix
2
0
i was doing some reading on structural mechanics and i stumbled across this example:

01.gif


i don't really get the highlighted part. anyone care to explain?

02.gif


:)
 
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  • #2
The pin at C exerts a force of 50kN on rod BC. In the middle of the rod, the cross section is circular, and we calculate the stress as [itex]4P/\pi d^2[/itex] (diameter d). At the end of the rod, the cross section is flattened into a rectangle, so the stress is [itex]P/wt[/itex] (width w, thickness t). BUT the width is reduced where material is cut out to fit the pin. At this cross section the stress is higher, [itex]P/(w-d)t[/itex]. Does this make sense?
 
  • #3


The smallest cross-sectional area of a rod-end refers to the narrowest part of the rod where it meets the end. This is important in structural mechanics because it affects the strength and stability of the rod. A smaller cross-sectional area means there is less material to resist forces and therefore the rod may be weaker and more prone to failure. Engineers must carefully consider the smallest cross-sectional area of a rod-end when designing structures to ensure they can withstand the necessary forces.
 

Related to Smallest cross-sectional area of rod-end?

1. What is the smallest cross-sectional area of a rod-end?

The smallest cross-sectional area of a rod-end refers to the narrowest point of a rod-end where it connects to the rod. It is typically measured in square inches or millimeters.

2. Why is the smallest cross-sectional area important in a rod-end?

The smallest cross-sectional area is important because it determines the strength and stability of the rod-end. A smaller cross-sectional area means the rod-end is weaker and more prone to bending or breaking under pressure.

3. How is the smallest cross-sectional area of a rod-end calculated?

The smallest cross-sectional area of a rod-end is calculated by measuring the diameter of the rod-end at its narrowest point and using the formula A = πr^2, where r is the radius of the rod-end.

4. Can the smallest cross-sectional area of a rod-end be modified?

Yes, the smallest cross-sectional area of a rod-end can be modified by altering the design or shape of the rod-end. However, this could potentially compromise the strength and stability of the rod-end.

5. How does the smallest cross-sectional area of a rod-end affect its load-bearing capacity?

The smallest cross-sectional area of a rod-end directly affects its load-bearing capacity. A smaller cross-sectional area means a lower load-bearing capacity, while a larger cross-sectional area can support a heavier load without bending or breaking.

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