# Engineering - Stress and Buckling Load problems

• MHB
• Plasma2
In summary: N while the buckling load for sample 1 is only 10kN when the wire is stretched from 10.6 cm to 10.9 cm.
Plasma2
Hello,
I am in an engineering summer camp, but since this is a condensed course and it seems the professors assumed the class already had some background in the subject, I am slowly getting lost. They gave us practice tests from previous years, and I was wondering if someone could show me how to complete a few problems. Though I know you wonderful people will explain your answers, could you also tell what conversions you use as well since that is likely what we will have to apply ourselves? Thanks in advance!

1)

You have two samples of the same material. These samples have different lengths and diameters.
• Sample 1: 10 cm long and 1.0 mm diameter -- Buckling load at failure: 10kN
• Sample 2: 20 cm long and 1.0 mm diameter
What is the buckling load that would cause Sample 2 to fail? (report answer in kN)

2)

A circular rod with a diameter of 10 mm experiences a tensile force of 100 kN. What is the stress in the rod in MPa?

3)

A wire that is 1.0 mm in diameter is stretched from 10.6 cm to 10.9 cm by a force of 150 N. Assuming the elastic limit is not exceeded, what is the force required to stretch the wire from 10.6 cm to 11.1 cm?

Plasma said:
Hello,
I am in an engineering summer camp, but since this is a condensed course and it seems the professors assumed the class already had some background in the subject, I am slowly getting lost. They gave us practice tests from previous years, and I was wondering if someone could show me how to complete a few problems. Though I know you wonderful people will explain your answers, could you also tell what conversions you use as well since that is likely what we will have to apply ourselves? Thanks in advance!

Hi again Plasma! ;)

To be honest, I'd rather not just give fully worked answers.
I believe that's ultimately not very useful to you, and no fun for me either.
Anyway, let's see what we can do.

Plasma said:
1)

You have two samples of the same material. These samples have different lengths and diameters.
• Sample 1: 10 cm long and 1.0 mm diameter -- Buckling load at failure: 10kN
• Sample 2: 20 cm long and 1.0 mm diameter
What is the buckling load that would cause Sample 2 to fail? (report answer in kN)

Do you have a formula for the stress in a material of a certain length and diameter?
We should be able to tell what the answer is from that formula.

On a different note, do you have a sense of what's going on?
We have a sample that is twice as long. What do you think about its buckling strength when the same load is applied?

Plasma said:
2)

A circular rod with a diameter of 10 mm experiences a tensile force of 100 kN. What is the stress in the rod in MPa?

Again we're looking for a formula. Do you have one?

The definition of stress $\sigma$ is:
$$\sigma = \frac F A$$
where $F$ is the tensile force, and $A$ is the area of a cross section.

Does it look familiar? Can you find the stress from that?

Plasma said:
3)

A wire that is 1.0 mm in diameter is stretched from 10.6 cm to 10.9 cm by a force of 150 N. Assuming the elastic limit is not exceeded, what is the force required to stretch the wire from 10.6 cm to 11.1 cm?

This is where Hooke's Law comes into play. Did you see it in your notes?
Do you have a formula for the force when stretching a wire by a certain amount?

Hooke's Law says that the force is linear with the distance it is stretched - if there is no permanent elastic deformation.
So stretching it twice as far means the force is twice as big.
Can we find the force from that?

I like Serena said:
To be honest, I'd rather not just give fully worked answers.
Seems fair.

I like Serena said:
Do you have a formula for the stress in a material of a certain length and diameter?
Found it, 1/4 the strength.
I like Serena said:
The definition of stress $\sigma$ is:
$$\sigma = \frac F A$$
where $F$ is the tensile force, and $A$ is the area of a cross section.
Does it look familiar? Can you find the stress from that?
I knew that part, I didn't know how to convert between Newtons and Pascals

I like Serena said:
This is where Hooke's Law comes into play. Did you see it in your notes?

Not in my notes, but online yes. Thanks for the pointer.

Sorry for the long delay, but thanks for encouraging me to get it. After all said and done, these were not the parts of the quiz I lost points on. If you want I can show you the final result that will come of all these and other calculations once my group and I build our spaghetti bridge. Anyway, off topic. Thanks for the help.

## 1. What is stress in engineering?

Stress in engineering is a measure of the internal forces within a material that arise from external forces or loads. It is typically measured in units of force per unit area, such as pounds per square inch or newtons per square meter. Stress can cause a material to deform or break, so it is an important consideration in the design and analysis of structures and components.

## 2. How is stress calculated in engineering?

Stress can be calculated by dividing the applied force by the cross-sectional area of the material. This results in a value known as the stress intensity, which can be further analyzed using various equations and formulas to determine the maximum stress and potential failure points in a structure or component.

## 3. What is a buckling load in engineering?

A buckling load is the maximum load that a structure can withstand before it becomes unstable and collapses due to compressive stress. It is an important consideration in the design of tall or slender structures, such as columns and beams, as they are more susceptible to buckling under heavy loads.

## 4. How is buckling load calculated in engineering?

The calculation of buckling load involves considering the geometry, material properties, and boundary conditions of a structure. It can be determined using various analytical methods, such as the Euler buckling formula or the Johnson buckling formula. Finite element analysis is also commonly used to accurately predict buckling behavior in complex structures.

## 5. What are some common ways to prevent stress and buckling in engineering?

There are several ways to prevent stress and buckling in engineering, including selecting appropriate materials with high strength and stiffness, designing structures with sufficient cross-sectional area to resist applied loads, and incorporating bracing or support systems to increase stability. Additionally, conducting thorough stress and buckling analyses during the design phase can help identify potential issues and allow for adjustments to be made before construction.

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