# Finding stress in three rods

• stinlin
In summary, the conversation discusses a problem involving calculating the load and stress on columns supporting a structure. Two different approaches are suggested, one involving equal distribution of load among the columns and the other considering the displacement of the top cap. The latter approach is found to be successful.

## Homework Statement

See attached - not the yellow engineering paper.

## Homework Equations

PL/AE = deformation

## The Attempt at a Solution

See attached

I can't figure out what the heck I'm doing wrong - my work is a little scattered because I was kind of thinking while doing it...

#### Attachments

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Looks like the outside columns equally support the portion of the load up to the point where their deflections equal 0.3 mm. Calculate what that load is for that deflection, and the stress in the outside columns (no stress or deflection in the interior column) under that load. Then the remainder of the load will be divided equally amongst the 3 columns.

Another way of doing it is to let the displacement of the top cap be x downwards.

Then assuming all the columns take some load, the strain in the end posts is x/125 and the strain in the middle post is (x-0.3)/125. Find the force in each column corresponding to the strain, and get an equation for x by saying the forces in the 3 columns sum to the total load.

If x comes out as less than 0.3, then the middle column did not take any load, in which case finding the load in the two end columns is easy!

I did it the way PhantomJay said and it worked like a charm! Thanks you guys!

## 1. How do three rods contribute to stress?

Three rods can contribute to stress in a system by transferring forces and moments between each other. This can result in increased stress on the rods and potential failure if not properly accounted for in the design.

## 2. What factors affect stress in three rods?

The amount of force applied, the material and geometry of the rods, and the connection points where the rods meet can all affect the stress in a system with three rods. Additionally, external factors such as temperature and environmental conditions can also impact stress levels.

## 3. How do you calculate stress in three rods?

To calculate stress in three rods, you can use the formula: stress = force/area. This can be applied to each individual rod and then combined to determine the overall stress in the system. It is also important to consider the distribution of forces and moments between the rods.

## 4. What is the importance of finding stress in three rods?

Finding stress in three rods is important for ensuring the safety and structural integrity of a system. By identifying areas of high stress, engineers and designers can make necessary adjustments to prevent failure and ensure the longevity of the rods.

## 5. How can stress in three rods be minimized?

To minimize stress in three rods, you can adjust the geometry and material of the rods to better distribute forces and moments. Additionally, adding support structures or redistributing the load can help decrease stress levels. It is also important to regularly monitor and maintain the rods to prevent wear and tear that could lead to higher stress levels.