# Deriving an equivalent system of forces and moments

• bugatti79
In summary, accurately representing a force system on a complex geometry can be challenging, but there are ways to overcome this. This could involve breaking down the geometry into simpler shapes or using specialized FEA software. With some effort and analysis, it is possible to find a solution.
bugatti79
Folks,

Consider a 2d disk with 2 forces ( ie a bolt pattern) acting axially ie into the page. One can easily get the equivalent force and its point of application to represent the given force system.

One can do the same with an annulus, get an equivalent force and its point of application etc.

However, I have a calculation where the resultant point of application is at a radius smaller than than the inside radius of annulus.

This is no good to me because I need to apply the load physically on the FEA model.

So it appears it is not possible to do this since the calculations are independent of the geometry...

Opinions?

I understand your frustration with trying to accurately represent a force system on a complex geometry. However, I believe that it is possible to find a solution to your problem.

Firstly, it is important to understand that the equivalent force and its point of application are calculated based on the assumption that the geometry is a simple 2d disk or annulus. This means that the results may not be accurate for a more complex geometry.

To accurately represent the force system on your FEA model, you may need to consider the specific geometry and how the forces are distributed throughout it. This could involve breaking down the complex geometry into smaller, simpler shapes and analyzing the forces on each individual shape. From there, you can determine the equivalent force and its point of application for each shape and then combine them to represent the overall force system on the entire geometry.

Another approach could be to use finite element analysis software that allows for more complex geometry and can accurately represent the forces on it. This would eliminate the need for simplifying the geometry and potentially provide more accurate results.

In conclusion, while it may not be possible to directly apply the calculated equivalent force and its point of application on a complex geometry, there are methods and tools available that can help you accurately represent the force system on your FEA model. It may require some additional effort and analysis, but it is certainly possible to find a solution. I hope this helps and good luck with your calculations.

## 1. What is an equivalent system of forces and moments?

An equivalent system of forces and moments refers to a set of forces and moments that produce the same external effects on a body as the original set of forces and moments. This means that the overall translation and rotation of the body will remain the same, but the individual forces and moments may be different.

## 2. Why is it important to derive an equivalent system of forces and moments?

Deriving an equivalent system of forces and moments is important because it allows us to simplify complex systems of forces and moments into a single resultant force and moment. This makes it easier to analyze and understand the overall effects of the forces and moments on a body.

## 3. How do you derive an equivalent system of forces and moments?

To derive an equivalent system of forces and moments, you must first identify all of the external forces and moments acting on the body. Then, you can use the principles of statics, such as the law of action and reaction and the principle of transmissibility, to determine the equivalent system. This may involve resolving forces and moments, finding the resultant force and moment, and balancing equations.

## 4. What are the benefits of using an equivalent system of forces and moments?

Using an equivalent system of forces and moments can simplify complex systems, making them easier to analyze and understand. It can also help in designing structures or machines, as the equivalent system can be used to determine the necessary dimensions and materials to withstand the forces and moments. Additionally, it allows for easier comparison of different systems and their effects on a body.

## 5. Are there any limitations to using an equivalent system of forces and moments?

While deriving an equivalent system of forces and moments can be useful, it is important to note that it is only applicable in static situations. If the body is in motion or undergoing acceleration, then the equivalent system may not accurately represent the actual effects of the forces and moments. Additionally, the assumptions and simplifications made in deriving the equivalent system may not hold true in all cases, so it is important to carefully consider the accuracy and limitations of the results.

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