Column buckling under axial+transverse combined load

In summary, the conversation is about determining the buckling load of a column with one end clamped and one end free, under axial compressive and transverse lateral forces applied at the top free end. The question is whether the lateral load reduces the critical load or just reduces the stiffness of the column. The person asking for help has tried to use Timoshenko's energy method but has failed. They also mention that the problem seems related to the eccentrically loaded column buckling problem. A diagram is included for reference.
  • #1
Vigardo
88
7
Dear experts,

Do you know the buckling load of a column (one end clamped one end free) under axial compressive and transverse lateral forces (applied combined at top free end)?

Does the lateral load reduce the critical load or just reduces the stiffness of the column?

Would you help me?
-Thanks!
 
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  • #2
What do you think ?

Try drawing some diagrams and see if you can see intuitively what is likely to happen .
 
  • #3
Thanks for the quick reply!

Intuitively, this problem seems related to the eccentrically loaded column buckling problem. Am I right? I tried to follow Timoshenko´s energy method to determine the buckling load but I failed.
[itex]
{U_{(\delta )}} = {V_{(\delta )}} \\
\frac{{4{P^2}{\delta ^2}L}}{{15EI}} = F\delta + \frac{{2{\delta ^2}P}}{{3L}}
[/itex]
Where U is the internal bending energy and V the work done by the axial (P) and transverse (F) forces. I´m not sure about the "F" contribution to energy...

Please, find below the diagram of my problem:
Buckling_column_axial_transverse_combined_loading.jpg
 

1. What is column buckling under axial+transverse combined load?

Column buckling under axial+transverse combined load is a phenomenon in structural engineering where a column experiences failure or deformation due to the combined effects of axial and transverse loads. This can occur in various structures such as buildings, bridges, and other load-bearing structures.

2. What causes column buckling under axial+transverse combined load?

The main cause of column buckling under axial+transverse combined load is the applied loads exceeding the column's capacity to resist them. This can be due to a variety of factors such as improper design, material defects, or excessive loading. Additionally, the column's length, cross-sectional shape, and support conditions can also contribute to its susceptibility to buckling.

3. What are the effects of column buckling under axial+transverse combined load?

The effects of column buckling under axial+transverse combined load can range from minor deformations to catastrophic failure. In addition to compromising the structural integrity of the column, it can also lead to damage to surrounding structures and potential safety hazards.

4. How can column buckling under axial+transverse combined load be prevented?

To prevent column buckling under axial+transverse combined load, proper design and construction practices must be followed. This includes accurately calculating the loads and ensuring the column's dimensions and support conditions are appropriate for the applied loads. Using high-quality materials and regularly inspecting and maintaining the column can also help prevent buckling.

5. What are some techniques for analyzing column buckling under axial+transverse combined load?

There are various analytical and numerical methods for analyzing column buckling under axial+transverse combined load. These include Euler's buckling formula, which considers the column's length and material properties, and finite element analysis, which uses a computer model to simulate the column's behavior under different loads. It is important to use a combination of these techniques to accurately predict and prevent column buckling.

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