# Smallest cross-sectional area of rod-end?

• samtrix
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.
samtrix
i was doing some reading on structural mechanics and i stumbled across this example:

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

:)

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 $4P/\pi d^2$ (diameter d). At the end of the rod, the cross section is flattened into a rectangle, so the stress is $P/wt$ (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, $P/(w-d)t$. Does this make sense?

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.

## 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.

• Classical Physics
Replies
8
Views
971
• Classical Physics
Replies
15
Views
724
• Engineering and Comp Sci Homework Help
Replies
4
Views
466
• General Engineering
Replies
11
Views
1K
• Classical Physics
Replies
48
Views
2K
• Classical Physics
Replies
35
Views
2K
• Classical Physics
Replies
1
Views
2K
• Engineering and Comp Sci Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
25
Views
1K
• Mechanical Engineering
Replies
5
Views
460