The phenomenon is called buckling, and it occurs when construction collapses and loses its load-bearing capacity. We were curious and did some virtual testing around the topic to see what really happens.
The skiing season is here again, and people in the Nordic countries are especially good on that. For example, this is one thing that Norwegians are particularly good at.
In this sport you need a pair of skis (which you attach to your feet) and one pair of ski poles (which you attach to your hands), and these ski poles is what we will have a closer look at in this study.
We saw it in the 30 km cross country skiing in the Pyeongchang Winter Olympics 2018 when Simen Hegstad Krüger from Norway broke his ski pole. Another Norwegian skier for whom this phenomenon is not completely unknown is Oddvar Brå who broke a ski pole in the men’s relay at the 1982 World Cup.
Buckling
If you imply a load on a long and thin pole with a compressive force as you do in cross-country skiing, the pole can suddenly become unstable and bend. This happens when the pole loses its strength and we get large elastic deformations.
A good comparison to this is if you take a plastic ruler and press it down onto a table with an axially directed force. The ruler will then bend out about the weakest axis and eventually break if the load is large/ big enough. What actually happens here is that the construction (in this case the ruler) collapses and loses its load-bearing capacity.
This phenomenon is called buckling and is rarely desired in constructions, especially not in a ski pole that is designed to help our Norwegian heroes win the gold medals.
Buckling is a bit scary since it can occur at stresses far below the yield strength of the material, and therefor is not considered when calculating the traditional safety factor (with regards to the maximum Von Mises stresses) safety factor as we do in static analysis.
It is important to note that any load affects the structural stiffness.
- Tensile loads give a stiffer model since the elastic stiffness increases.
- Compressive loads give a softer model since the elastic stiffness decreases.
- Buckling occurs when the structural stiffness due to compressive loads becomes =0.
SOLIDWORKS Simulation Buckling Study
We have the capability to analyse this phenomenon in SOLIDWORKS Simulation Professional with a study type called Buckling.
The theory used for linear buckling studies in SOLIDWORKS Simulation Professional is based on Euler’s buckling formula:
Where:
F = Maximum or critical load
E = Modulus of elasticity
I = Moment of inertia (Second moment of area)
L = Length of column (Unsupported length of profile)
K = Factor describing the profiles effective length. (depends on the supports at the end of the beams)
To do this type of analysis in SOLIDWORKS Simulation Professional we first need some geometry, such as this ski-pole, and to start a new Buckling study:
Then we specify the material (in this case aluminum).
When this is done, we add boundary conditions in the form of fixtures and loads to best simulate the real-life conditions.
After the study has been run, we retrieve the results in the form of BLF (Buckling Load Factor).
This is a factor of safety against buckling. To find the maximum load that the ski pole in question can can withstand before buckling we multiply the applied load with the retrieved factor.
Such as in this case with the ski pole: We added an axial load of 100kg, as we can see the lowest BLF= 0,64364 (BLF 2, 3, 4, etc. is only included for academical purposes, as buckling will occur at BLF 1). Note that we also get a display of how the buckling will occur.
If we multiply the applied load with BLF we get: 100kg x 0,64364 = 64,36kg – Meaning that 64.36kg is the maximum load that the ski pole will be able to withstand before it fails due to buckling.
Buckling, as previously mentioned, can occur at stresses far below yield strength, so this phenomenon is important to consider when designing long slender structures.
To clarify this, we have created a traditional static study of this ski pole by copying the boundary conditions from the buckling study.
If we look at the results here, we can see that the maximum Von Mises stresses reported are 4Mpa. If we compare this to the yield strength of the aluminum, which is 27,57 MPa we get a factor of safety of: 27,57/4 = 6,89. One can therefore be deceived to believe that the rod holds the given load of 100kg.
So let’s hope that our national skiing team will take buckling into account when the next competition starts. Until then, enjoy the skiing season!
