# Ski pole three point bending-calculation of load at yield

• pd2905
In summary, the conversation discusses the bending of a ski pole through three-point bending and the calculation of the minimum load needed for it to fail due to plastic deformation. The formula for calculating this load is given, taking into account the material properties of the ski pole and the use of the von Mises yield criterion for ductile materials. The final calculation results in a necessary load of 2751N.
pd2905

## Homework Statement

A ski pole is bent(plastic deformation) in three point bending by applying a load 2F perpendicularly to the ski pole. The forces at the end points are of magnitude F. If the pole yields due to plastic deformation at the mid point longitudinal span of the ski pole which is 90 cm long and which is a hollow tube with inner radius Ri and outer radius Ro give the formula to calculate the minimum load for which the pole will fail, given that the pole is made of an isotropic 5086 Al alloy with E=71GPa modulus of elasticity and that the yield stress of the alloy is Y=230 MPa. We assume a static load.

## Homework Equations

Stress at tip=Yield stress=Moment of cross-sectional area*Distance from the centroid/Second moment

I calculate moment of cross-section by M=F*length/2

I would like to know if any other more suitable yield criterion can be used
such as Von mises or Tresca. I think Al alloys are considered ductile materials.

So I get M=Yield stress/Distance from the centroid*Second moment
2F=4M/length=4.

## The Attempt at a Solution

Yield stress=230Mpa
Distance from centroid=9mm
Ri=16.5mm
Ro=18mm
length=900mm
2F==4*230/(900)/9*(3.14/4)*(18^4-16.5^4)=2751N is the load to necessary bend the pole.
It seems kind of ridiculous although I have never bent a ski pole.

Nice work, pd2905. Your answer is correct. Al 5086 is a ductile material. For ductile materials, von Mises theory is preferred over Tresca, and is more accurate. For ductile materials, you generally use von Mises stress, but in your particular case, von Mises would reduce to give you the same answer you already obtained.

I would first verify the calculations and equations used in the attempt at a solution. It is important to ensure that the equations and values used are appropriate for the given scenario. Additionally, it would be helpful to provide a diagram or illustration of the ski pole and the forces applied to better understand the setup.

In terms of the yield criterion, both Von Mises and Tresca criteria can be used for ductile materials such as Al alloys. However, it is important to note that the yield stress values obtained using these criteria may differ. It would be beneficial to compare the results obtained using both criteria to determine which one is more suitable for this specific scenario.

Furthermore, the assumption of a static load may not accurately represent the real-life scenario of skiing. It would be more realistic to consider dynamic loading, as the forces applied to the ski pole may vary while skiing. This could affect the yield stress and ultimately the minimum load for failure.

In conclusion, while the calculations and equations used may be correct, it is important to consider the limitations and assumptions made in this scenario. It would be beneficial to verify the results using different yield criteria and to consider dynamic loading for a more accurate analysis.

## 1. What is ski pole three point bending?

Ski pole three point bending refers to a method of testing the strength and durability of ski poles by applying a load at three specific points along the pole. This helps determine the amount of weight or force the pole can withstand before breaking or permanently bending.

## 2. How is the load at yield calculated in ski pole three point bending?

The load at yield in ski pole three point bending is calculated by measuring the deflection of the pole at the point of yield, where it begins to permanently deform. This deflection is then used to determine the corresponding load or force applied to the pole.

## 3. What factors can affect the load at yield in ski pole three point bending?

Several factors can affect the load at yield in ski pole three point bending, including the material and design of the pole, the temperature and environmental conditions, and any previous damage or wear on the pole.

## 4. Why is it important to calculate the load at yield in ski pole three point bending?

Calculating the load at yield in ski pole three point bending is important because it helps determine the maximum amount of weight or force that the pole can withstand before breaking or permanently bending. This information is crucial for ensuring the safety and durability of ski poles for use in winter sports.

## 5. Are there any standards or regulations for ski pole three point bending?

Yes, there are several standards and regulations in place for ski pole three point bending, including those set by the International Ski Federation (FIS) and the American Society for Testing and Materials (ASTM). These standards outline specific testing methods and requirements for ski poles to ensure their strength and durability.

• Engineering and Comp Sci Homework Help
Replies
5
Views
1K
• Classical Physics
Replies
3
Views
751
• Engineering and Comp Sci Homework Help
Replies
4
Views
6K
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K
• Engineering and Comp Sci Homework Help
Replies
11
Views
139K
• Mechanical Engineering
Replies
1
Views
3K
• Mechanical Engineering
Replies
5
Views
4K
• Engineering and Comp Sci Homework Help
Replies
3
Views
6K
• Engineering and Comp Sci Homework Help
Replies
4
Views
13K
• General Engineering
Replies
7
Views
2K