# Making free bodies of a static structure

• Kyelek
In summary, the problem is to create freebody diagrams for all members of a structure and determine internal stresses. The platform is being lowered by strings with 150 lbs of force applied. One leg was analyzed and the force was divided by three to get 50 lbs on the lowered platform. By using the properties of similar triangles, it was found that 96.18 lbs of force is acting in tension on the string. This force is transferred to the tower at a 90 degree angle, with 35.43 lbs of force exerted perpendicular to the top of the tower and 60.74 lbs exerted at the bottom. However, these are just components of larger forces in other directions. In order to accurately draw a freebody
Kyelek

## Homework Statement

The problem is this. We have a structure (see the attached image) and need to make freebodies of all of the members. 150 lbs are applied to the platform being lowered by the strings. We also need to figure internal stresses, but I think I can get those if I can understand this first.

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## The Attempt at a Solution

I picked one of the legs, and I idealized it into an elevation. Since each of the legs is equal in all ways, I divided the force applied by three, so 50lbs on the lowered platform.

Using the properties of similar triangles, and knowing that the string has to resist 50lbs of downward force, I found that 96.18lbs of force is acting in tension on the string.

This force is transferred to the tower at a 90 degree angle. I placed a pin at the bottom and a pin at the top. Using the sum of the moments, I found that 35.43 lbs of force were being exherted perpendicular to the top of the tower, and 60.74 to the bottom of the tower.

I started with the beam at the top of the tower. Again using similar triangles, I found that the forces acting on the end were 30.26lbs going into the beam in the x direction, and 18.42lbs going down. So the forces being applied where the three beams meet (from this beam) is the same, but opposite directions.

I think I'm wrong there, but I'm not sure how.

I also tried to figure it going to the base. Using the figures that I had from the tower, it's exherting 31.57lbs of pressure onto the base. That has to be wrong, as each tower needs to support 50 lbs.

So...I'm really not sure where I'm going wrong. I tried to figure everything more holistically, but I still don't see how the forces are moving, and how the 50lbs are getting to the points of connection. Thanks in advance for your help!

#### Attachments

• Axonometric.jpg
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• homework.pdf
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Look at your fbd for the tower where you have wrongly assumed that the end forces are at rightangles to the tower. The 35.43 and 60.74 are not wrong but are just components of bigger forces in other directions.. It was good for you to realize that the answer must be wrong.

Additional comment: When you draw a freebodydiagram, you must state ALL the forces on it before making an equilibrium statement.

## 1. What is the purpose of creating free bodies in a static structure?

The purpose of creating free bodies in a static structure is to simplify the analysis of the structure by isolating individual components and studying the forces acting on them. This allows for a more accurate understanding of the structure's stability and potential points of failure.

## 2. How do you determine the forces acting on a free body in a static structure?

The forces acting on a free body can be determined by using the principles of equilibrium, which state that the sum of all forces acting on a body must equal zero. This can be achieved by analyzing the external and internal forces acting on the body and setting up equations of equilibrium.

## 3. What are the key assumptions made when creating free bodies in a static structure?

The key assumptions made when creating free bodies in a static structure include the assumption of rigid body behavior, neglecting the effects of friction and air resistance, and assuming that the structure is in a state of static equilibrium where all forces are balanced.

## 4. Can free bodies be used to analyze non-static structures?

No, free bodies are only applicable to static structures where there is no motion or acceleration. For non-static structures, dynamic analysis methods must be used to account for the effects of motion and changing forces.

## 5. How can free body diagrams be used to improve the design of a static structure?

Free body diagrams can be used to identify areas of high stress or potential failure in a structure, which can then inform design changes to improve its strength and stability. They can also be used to optimize the placement and orientation of structural components to distribute forces more evenly.

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