How to get stress tensor from force

[wahaj]

Homework Statement

I'm analyzing the landing gear of a plane for an extracurricular project. I know that the landing gear will undergo impact loading during touch down. Using what we've been taught, I converted the impact load to a static load, P that will act on the landing gear. Now I need to know how much stress the gear will be under so I can select the best material to make it out of. There is no specific problem statement, see picture for a diagram of what I'm trying to do. I got the normal stress, but how would I get the bending stress at the root ($\sigma_n$)? I don't know if the beam bending formula is the right one to use here. I need to get the stress tensor so I can use the failure theories to select the best material.

Homework Equations

$$\sigma = \frac{N}{A}$$
$$\sigma = \frac{Mc}{I}$$

The Attempt at a Solution

See attached image

 

[KataKoniK]

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I would first like to commend you on your thorough approach to analyzing the landing gear for this project. It is important to consider all factors, such as impact loading and stress, when designing a critical component like the landing gear of a plane.

To determine the bending stress at the root, you are correct in using the beam bending formula. However, you will need to take into account the geometry and loading conditions of the landing gear. This includes the length and cross-sectional shape of the gear, as well as the location and magnitude of the applied load.

Additionally, you mentioned using failure theories to select the best material for the landing gear. It is important to consider not only the stress levels, but also the specific material properties such as strength, ductility, and fatigue resistance. This will ensure that the chosen material can withstand the expected loading conditions and have a long lifespan.

In order to fully determine the stress tensor, you may also need to consider other factors such as shear stress and thermal stress. It is important to thoroughly analyze all aspects of the landing gear to ensure its safety and effectiveness.

I wish you the best of luck with your project and I hope this information helps you in your analysis. Keep up the good work!